Ajit R. Jadhav's blog
https://www.imechanica.org/blog/1150
enPart 2 of my document on STR, incomplete, but gives outline of my solution
https://www.imechanica.org/node/27405
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Part 2 of my document on STR, incomplete, but gives outline of my solution. iMechanica was not available about 15 minutes ago, so I posted it first at my blog. The copy here is for public and third-party "storage."</p>
<p>--Ajit</p>
<p>Pune, India</p>
<p>2024.09.17 11:55 IST</p>
</div></div></div><div class="field field-name-upload field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><table class="sticky-enabled">
<thead><tr><th>Attachment</th><th>Size</th> </tr></thead>
<tbody>
<tr class="odd"><td><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://www.imechanica.org/files/ARJ_Research_Note_STR_Problem_and_the_New_Solution_02_Posted.pdf" type="application/pdf; length=417890">ARJ_Research_Note_STR_Problem_and_the_New_Solution_02_Posted.pdf</a></span></td><td>408.1 KB</td> </tr>
</tbody>
</table>
</div></div></div>Tue, 17 Sep 2024 06:26:28 +0000Ajit R. Jadhav27405 at https://www.imechanica.orghttps://www.imechanica.org/node/27405#commentshttps://www.imechanica.org/crss/node/27405My doc on STR, incomplete, myself leaked, version 1
https://www.imechanica.org/node/27362
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>FWIW,</p>
<p>So that no Indian-born, especially BJMC graduate / JPBTI / UDCT graduate, esp. the rich, esp. the ब्राम्हण-born variety, esp in the United States of America (or the United Kingdom, or similar), can at all have an advantage over me in making public this info.</p>
<p>I will myself ``leak'' it. Periodicallt / aperiodically.</p>
<p>...</p>
<p>Don't ask me any questions on it, for now... I am busy... Will be.</p>
<p>And, if you have any sense left (and BTW, ``sense'' doesn't always ``NLP'' Objectivism etc.-translate into ``sensory-perceptual level of cognition,'' you Americans / Westerners / Indians of the above kind / etc., OK?</p>
<p>Best,</p>
<p>--Ajit</p>
<p> </p>
<p>Update starting at 23:39 2024.09.03 IST:</p>
<p>Link No. 1: [<a title="IIT Bombay Placements 2024 Average Package" href="https://www.google.com/search?q=iit+bombay+placements+2024+average+package" target="_blank" rel="noopener noreferrer">^</a>]. These JPBTI's produced in INDIA i.e. भारत have it at Rs. (sorry IITB IDC graduate, I have no desire to insert your symbol for the Indian Rupee): 23.5 Lakhs/annum, if Google Search is not hallucinating (the way ब्राम्हण from पुणे have a tendency to think I do).</p>
<p>Link No. 2: [<a href="https://www.google.com/search?client=ubuntu-sn&channel=fs&q=iim+ahmedabad+placements+2024" target="_blank" rel="noopener noreferrer">^</a>]: These MBAs produced in INDIA i.e. भारत have it at Rs. (etc.): [<a href="https://www.google.com/search?q=iim+ahmedabad+placements+2024+average+package" target="_blank" rel="noopener noreferrer">^</a>]: 34.36 Lakhs/annum, if Google Search ... (you fill in the rest)</p>
<p>I suppose their parents were <em>active</em>, (perhaps also using ActiveX controls using OLE 2.0 nothing like OLE 1.0 and CORBA etc. if I remember those times right of their <em>activity</em>) also when I was for myself, <em><strong>with all my talents,</strong></em> going jobless. After all, jobless-ness is just a tag at my personal blog at [<a title="Joblessness" href="https://ajitjadhav.wordpress.com/tag/joblessness/" target="_blank" rel="noopener noreferrer">^</a>][<a href="https://ajitjadhav.wordpress.com/tag/years-of-joblessness/" target="_blank" rel="noopener noreferrer">^</a>}, you know?</p>
<p>And what amount of money I <em><strong>now</strong></em> make?</p>
<p>B's & B's all! [Get in touch with me to know the finer shades of difference between the first B and the second B, will you? [On second thoughts: <span><em><strong>Don't!]</strong></em></span>]</p>
<p>Rely on them (and their parents, grandparents, offspring, et alia) to sing this one [<a href="https://www.google.com/search?q=ajinkya+bharat+ajinkya+janata" target="_blank" rel="noopener noreferrer">^</a>] but if Marathi. [There, I give the reason to Bong females sometime in Pune graduated by Harvard and now RICH in SF Bay Area to reject this entire thing because I said only one language whereas गोळवलकर गुरुजी had said many. Also हेगडेवार गुरुजी, Etc,(</p>
<p>Ditto for many others. [I am not objectively obliged to list all of them --- all their sub-cultures. Esp. if from the ब्राम्हण etc. communities.]</p>
<p>Update over at 00:03 2024.09.04 IST</p>
<p> </p>
<p> </p>
</div></div></div><div class="field field-name-upload field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><table class="sticky-enabled">
<thead><tr><th>Attachment</th><th>Size</th> </tr></thead>
<tbody>
<tr class="odd"><td><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://www.imechanica.org/files/ARJ_Research_Note_STR_Problem_and_the_New_Solution_01_Posted.pdf" type="application/pdf; length=197607" title="ARJ_Research_Note_STR_Problem_and_the_New_Solution_01_Posted.pdf">ARJ_Research_Note_STR_Problem_and_the_New_Solution_01_Posted.pdf</a></span></td><td>192.98 KB</td> </tr>
</tbody>
</table>
</div></div></div>Thu, 29 Aug 2024 18:10:03 +0000Ajit R. Jadhav27362 at https://www.imechanica.orghttps://www.imechanica.org/node/27362#commentshttps://www.imechanica.org/crss/node/27362A question: The entropy of the universe taken as a whole, modelled as a molecular dynamics system
https://www.imechanica.org/node/27168
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/1055">entropy</a></div><div class="field-item odd"><a href="/taxonomy/term/93">molecular dynamics</a></div><div class="field-item even"><a href="/taxonomy/term/14005">universe</a></div><div class="field-item odd"><a href="/taxonomy/term/180">thermodynamics</a></div><div class="field-item even"><a href="/taxonomy/term/800">mechanical engineering</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>``Everyone knows'' that the entropy of the universe, taken as a whole, increases.</p>
<p>Suppose that we model the entire universe (i.e. the entirety of the known physical universe) as a huge isolated system, using molecular dynamics (MD for short).</p>
<p>The question is: How would you show that the entropy of such a system does in fact always increase? that it neither decreases nor stays the same? Is it even possible to show it, using MD?</p>
<p>Notes:</p>
<p>Assume infinite space (or at least a sufficiently large space that never falls short in simulation, may be with some technique for on-the-fly extension of space).</p>
<p>Treatments such as <a href="https://doi.org/10.1063/1.1636153">https://doi.org/10.1063/1.1636153</a> do not address the above question. Neither does the answer in this Physics StackExchange thread: <a href="https://physics.stackexchange.com/questions/360487/computing-entropy-properly-during-molecular-dynamics-simulation">https://physics.stackexchange.com/questions/360487/computing-entropy-pro...</a> Both deal with a finite portion of the universe, and not with the universe taken as a whole. </p>
<p>Notice that in MD simulations, heat exists only in the form of the motion of the molecules (particles).</p>
<p>I thought of raising this question because I thought of a certain ontological-physical principle which I thought was necessary, and so, should be mentioned in such discussions, but didn't find it mentioned. However, before giving my thoughts, I would like to see whether this principle is really necessary, or is it a false indicator (i.e., a wrong way of thinking about this issue). BTW, what I had in mind here was a very simple observation, not a big principle as such. It doesn't change the existing theory or maths; I was only trying to figure out how the theory might be applied. The interest is only limited to conceptual clarity.</p>
<p>See if it interests any one.</p>
<p>Best,</p>
<p>--Ajit</p>
<p> Updated a bit after posting at 2024.03.20 18:25 IST.</p>
</div></div></div>Wed, 20 Mar 2024 10:20:09 +0000Ajit R. Jadhav27168 at https://www.imechanica.orghttps://www.imechanica.org/node/27168#commentshttps://www.imechanica.org/crss/node/27168Thankless Satya NaDella, Hyderabad, India and others
https://www.imechanica.org/node/27167
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>The arranged for Drupal bug removed the content here, but not in the title.</p>
<p>I had mentioned the Principal Secretary of the Prime Minister of India, the Donation Based Graduation of Satya NaDella, and the California-based origins of LinkedIn, as also my Poverty.</p>
<p>And, Tearing Hurry.</p>
<p>And the lesser PhD graduate of IISc Bangalore, a poor soul called Dr. Anil D. Sahasrabudhe, and his favourites, especially the IIT BOMBAY graduated ``Dr.'' Deepak Waman Pande.</p>
<p>And the morality of the infamous Microsoft vs. Department of Justice case.</p>
<p>Was trying to attach a screen shot.</p>
<p>Here: [<a href="https://ajitjadhav.files.wordpress.com/2024/03/screenshot-at-2024-03-20-01-22-07.2.jpg">^</a>]</p>
<p>I do think that Steve Balmer and Bill Gates are already deranged. I was just thinking that Drupal and Harvard, in general, were not. I was proved wrong.</p>
<p>Hi Harvard IT Department? May I help you?</p>
<p> </p>
<p> </p>
</div></div></div>Tue, 19 Mar 2024 20:15:44 +0000Ajit R. Jadhav27167 at https://www.imechanica.orghttps://www.imechanica.org/node/27167#commentshttps://www.imechanica.org/crss/node/27167Just talking to another mechanician...
https://www.imechanica.org/node/27151
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Dear Zhigang,</p>
<p>As of this writing, none of the Twitter (now called `X' or `x', you know best) accounts I follow have gone against me. Or, the Chinese either, for that matter.</p>
<p>Just noting, for the time being,</p>
<p>Just the way, you know, I could've left a PhD program (that one because I already had had an MTech from IIT Madras), and joined American Industry,</p>
<p>or,</p>
<p>just the way, you know, I could've completed my PhD at UAB, and come to join you all guys at Hutchinson's group, or some other suitable. Harvard had a big heart, back then. Also, other places. Evans was big at UCSB ``Materials'' department.</p>
<p>Nothing of the sort happened.</p>
<p>But you kept your promise.</p>
<p>This note, just to remind you of that one.</p>
<p>I will keep mine.</p>
<p>Just in case you have doubts, be willing to not only experience but also suffer through a huge deluge. Purely from my own personal side. [Don't ask for it., Zhigang. Even, say, I mean, even Confucious said so. Or, must've had.]</p>
<p>So, anyway, thank you.</p>
<p>Best,</p>
<p>--Ajit</p>
<p> </p>
</div></div></div>Sun, 17 Mar 2024 17:45:57 +0000Ajit R. Jadhav27151 at https://www.imechanica.orghttps://www.imechanica.org/node/27151#commentshttps://www.imechanica.org/crss/node/27151A poor but independent researcher from Pune, India, is in the middle of an embarrassment of the riches, of sorts --- [aka: what to do with my conference paper on my new approach to QM?]
https://www.imechanica.org/node/26123
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/838">quantum mechanics</a></div><div class="field-item odd"><a href="/taxonomy/term/13529">foundations of physics</a></div><div class="field-item even"><a href="/taxonomy/term/13530">foundations of QM</a></div><div class="field-item odd"><a href="/taxonomy/term/13531">Measurement Problem</a></div><div class="field-item even"><a href="/taxonomy/term/13532">Conference Papers and Journal Papers</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><strong>Special note: </strong></p>
<p>This is a long post; it covers a dilemma I'm facing right now; but there is no real ``masaalaa'' to it; so, if you aren't a researcher yourself, leave it alone. </p>
<p><strong>Background:</strong></p>
<p>I submitted a conference paper --- the first ever paper on my new theory of QM --- to the International Conference ICCTPP-2022 [<a href="https://icctpp.mitwpu.edu.in/" target="_blank" rel="noopener noreferrer">^</a>] which was held in collaboration with the Institute of Physics (IoP, UK). My paper was accepted (the acceptance rate was about 50%), and then, I made an oral presentation too, which was on 10th June 2022. The presentation slides are attached [].</p>
<p>Subsequent to this oral presentation, and following the IoP procedure, full-length papers had to be resubmitted at the IoP's online processing platform/portal. I re-submitted a pretty well revised manuscript. </p>
<p>Now, following peer-review, a few, relatively minor, modifications have been suggested. In particular, the feeeback asks me to improve the manuscript as per the IOP journal format, consisting of: Title, Introduction, Theoretical Aspects, Results and Discussion, Conclusion, References, Any Funding Details, etc. The peer-review feedback also says that after improving the present manuscript it can be accepted.</p>
<p>This was a happy piece of news for me, though also expected. I always have carried a deep sense of gratitude for all the work put in by reviewers, and this time round, it was especially pronounced. After all, I am an engineer, not a physicist, but the paper is in physics, in fact, on QM --- its foundations.</p>
<p>The revision is due before the next week-end.</p>
<p>As to me: In the light of the nature of this particular paper, I am not planning to revise it as extensively as the reviewers' suggestion says it should be. I might perhaps add just a small Conclusion section to the paper, and be done with it. </p>
<p>Please note, this paper of mine is not like a typical, short, conference paper reporting on some specific set of experimentation or a single set of simulation trials, or so. This paper aims to present a whole new theoretical approach, and that too, to QM. It can't be fit into that usual neat ``format'' (actually, the boilerplate) which has been suggested. Further, note, my ``conclusions'' are actually interspersed throughout the paper. (That's what happens when you write in a completely ab initio manner, when you propose a completely new theoretical approach.) Given the quality of working epistemology evident in today's physics, I am not willing to take the risk of supplying a fodder of misconceptions to the improper-reductionists in physics, by handing out to them what they want: a neat and long conclusions section on which they could latch with all their might and / or mindless-ness, and try to keep on engaging me in some never-ending ``discussions'' if not ``debates''.</p>
<p>To understand the preceding paragraph, you would need to have a look at my paper. For publishing this particular, personal, version on the 'net, I have added a copyright notice, and also made a few formatting changes (from that for the IoP), but the content otherwise remains exactly the same (including any minor lapses) as that in the version which was submitted to the IoP. Please find it here [^].</p>
<p>However, please understand, the revision (which is yet to be effected) is not so much of my problem. My problem is altogether different.</p>
<p><strong>Context for my problem:</strong></p>
<p>To understand my problem, please note the following:</p>
<p>Usually, at least in the core engineering fields, publishing a conference paper on some research findings, does not prevent you from publishing a proper journal paper covering the same findings (with some other findings), later on. Typically, there is a length restriction to conference papers, and so, conference papers are just 5--8 pages long. Further, conference papers (at least in fields like mechanics / simulations) are almost never indexed even in the Scopus database, let alone in the ISI Web of Science (previously owned by Thomson Reuters, now by Clarivate Anlytics). A rule of thumb in the engineering field, therefore, is this: You go ahead and publish some 2--4 conference papers, and then add some further material to hold them together, and publish it all in one, proper, journal paper. </p>
<p>However, the idea of the ``IoP Journal of Physics: Conference Series'' (``JPCS'' for short) is different. </p>
<p>JPCS is not ``just'' a conference publications avenue. The papers published in JPCS are indexed in Scopus, though not in ISI/Thomson Reuters/Clarivate Analytics. They also have no length limit, technicall speaking --- even if most JPCS papers are pretty short; they look like any other conference papers.</p>
<p>But my paper is 18 pages long, even in the IoP format. (In the default LaTeX article class format, it becomes about 22 pages long.) Even going by the contents, you can see that although it was presented at a conference, and if published in JPCS, it will be, technically, a conference paper, it already has all the characteristics of a journal paper. In fact, it has more material content than for just a single journal paper.</p>
<p><strong>My problem:</strong></p>
<p>If, right now, I go ahead with the publication of my attached paper into JPCS, and later on, if I wish to convert the same material (plus some more extra material though not much more) into a journal paper proper, then, the question is: Would I run into those ``prior publication'' issues?</p>
<p>In particular, suppose that later this year or early next year, I submit a paper on this same theory to Nature (or Nature Communications), or Science, or PRL, would they say ``Sorry, JPCS has already published most (75+ percent) of your material, and so, it has already lost the novelty value. So, we can't recommend acceptance in our journal''? Would they say that? That is at the heart of my problem.</p>
<p><strong>Other relevant aspects:</strong></p>
<p>The way the science publication industry works, I can always post papers at my blog, even at arXiv (or at any other avenue which does not take away my copyright), without bothering about the ``prior publication'' issues. The whole idea is this: At the time of submitting a paper to a journal (say to Nature or Science), I should have all the rights with me --- in particular, the rights to publish / distribute my paper. However, if I right away publish the attached paper in IoP's JPCS, then what happens is this: I do keep the copyright, but I also relinquish the distribution rights to IoP. This consideration is apart from the ``no prior publication'' or ``novelty'' clauses that the other journals proper might come up with. If such issues do come up, where would that leave me?</p>
<p>I don't have any institutional affiliation. No one is going to even stand up for me, let alone fight for me, in a systematic/institutionalized manner. As far as this research is concerned, I have been, and am, entirely on my own --- funding-wise, legal-help-wise, as also in every other respect. ... Unfortunately, my PhD guide too has passed away (too early, at his age of 52, back in 2012). Since then, I haven't had any mentor either, let alone collaborations. All my research since then has been, purely, a one-man show. </p>
<p>As to my experiences with researchers/physicists community: Last year, not even Indian physicists bothered to reply my email requests for an informal feedback on my ideas (most of which now appear in the attached paper), let alone professors/researchers from abroad (e.g., those from USA, Germany, etc.). </p>
<p>In short: As things stand, right now, I have to rely purely on my own self --- even in deciding this matter.</p>
<p>In a way, I do have some standing in the engineering field --- I have a PhD in engg., and work experience in industries and academia. But all of that has been only in engineering. I don't have any formal training, experience, or any standing in physics as such --- not even friends (i.e. those who reply in situations like requests for feed-backs, or the current one).</p>
<p>It is possible that Professor Ian Stewart, for example, might have published some Scopus-indexed conference paper, and then, he might have published an ``improved'' version of the same in an ISI-indexed journal too. Fair enough; he has had a standing reputation in the field in which he was publishing. But can such examples be of any relevance to my present case? Who the hell, in comparison, is going to care for this unknown *engineer* from a third-world country who says he has solved the Measurement Problem --- namely me?</p>
<p>One last point. While I do care for priority (actually, for proper credit), and also for proper publications, I am not employed in any research institution / academia. So, citation metrics don't matter to me. Not too much, anyway. To be specific: My progression in my career doesn't depend on citations to my paper(s).</p>
<p><strong>My request to you:</strong></p>
<p>If you are still with me, and should you still care: Please consider my problem, and let me know which course of action you advise:</p>
<p><em><strong>(A) Publish!:</strong></em> Go ahead, and submit a revision to JPCS, and have it published there ASAP, because a later publication in a reputed journal won't get adversely affected because of it. That's the norm in science, especially in physics, and so, all this is a non-problem, really speaking. </p>
<p><em><strong>OR</strong></em></p>
<p><em><strong>(B) Withdraw!:</strong></em> Withdraw the paper while there still is time. With the ``publication'' of the paper at my blog (supported by the third-party evidence of the talk which I did deliver at the ICCTPP conference), the priority issue has well been taken care of. So, now, I should withdraw from the JPCS process right away, take my own time, write a proper journal paper and submit it to the journal at that time. If at all I want, I can always submit the attached paper to arXiv.</p>
<p><em><strong>You need to come back soon, preferably within 2--3 days.</strong></em> Thanks in advance, if you do.</p>
<p>Best,<br />--Ajit</p>
</div></div></div><div class="field field-name-upload field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><table class="sticky-enabled">
<thead><tr><th>Attachment</th><th>Size</th> </tr></thead>
<tbody>
<tr class="odd"><td><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://www.imechanica.org/files/AjitRJadhav_ICCTPP_253_main_paper_upload_to_Blog.pdf" type="application/pdf; length=230263" title="AjitRJadhav_ICCTPP_253_main_paper_upload_to_Blog.pdf">Ajit R. Jadhav -- Paper -- ICCTPP -- Personal Version</a></span></td><td>224.87 KB</td> </tr>
<tr class="even"><td><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://www.imechanica.org/files/AjitRJadhav-ICCTPP-253-Slides.pdf" type="application/pdf; length=179318" title="AjitRJadhav-ICCTPP-253-Slides.pdf">Ajit R. Jadhav -- Slides presented at ICCTPP</a></span></td><td>175.12 KB</td> </tr>
</tbody>
</table>
</div></div></div>Sat, 23 Jul 2022 11:37:56 +0000Ajit R. Jadhav26123 at https://www.imechanica.orghttps://www.imechanica.org/node/26123#commentshttps://www.imechanica.org/crss/node/26123I presented my new theory of QM yesterday
https://www.imechanica.org/node/26034
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>I presented my new theory of QM yesterday.</p>
<p>Just that.</p>
<p>Best,</p>
<p>--Ajit</p>
<p> </p>
</div></div></div>Fri, 10 Jun 2022 20:18:31 +0000Ajit R. Jadhav26034 at https://www.imechanica.orghttps://www.imechanica.org/node/26034#commentshttps://www.imechanica.org/crss/node/26034Request to physicists: Would you be willing to provide some informal feedback on my new approach to QM?
https://www.imechanica.org/node/25432
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/3403">quantum</a></div><div class="field-item odd"><a href="/taxonomy/term/8294">Quantum Chemistry</a></div><div class="field-item even"><a href="/taxonomy/term/838">quantum mechanics</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>I have a request to make to physicists: <em>Would they be willing to provide some informal feedback on my new approach to QM?</em></p>
<p><em><strong>Update (2021.09.21 15:57 IST): </strong></em>There were unusually many blog hits for the document. ... I do like the work getting noticed, but still, I guess, a clarification is in order:</p>
<p>What the attached document deals with is the <em>question in the title of this post</em>. But it does <em><strong>not</strong></em> contain any new QM theory. The document only raises the title question, and states some salient ("outward") features of my new theory, and the results I've obtained so far. But, to repeat, the attached document does <em><strong>not</strong></em> give the theory itself!</p>
<p>With that knowledge, if you still wish to check it out, then please proceed!</p>
<p>Also, now that the corrections / updates to the document are over, I don't have to supply a link to my personal blog (where the earlier versions of the PDF document were originally posted). Now, the PDF document has been attached right to this post.</p>
<p>Please circulate it to <strong><em>physicists</em></strong> you know, especially those from <em><strong>academia</strong></em>.</p>
<p>Thanks in advance.</p>
<p>Best,</p>
<p>--Ajit</p>
<p> </p>
</div></div></div><div class="field field-name-upload field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><table class="sticky-enabled">
<thead><tr><th>Attachment</th><th>Size</th> </tr></thead>
<tbody>
<tr class="odd"><td><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://www.imechanica.org/files/FeedbackRequestToPhysicists.3.pdf" type="application/pdf; length=51653" title="FeedbackRequestToPhysicists.3.pdf">This document probes whether physicists would be interested in a new theory of QM, but itdoes not give the details of the theory</a></span></td><td>50.44 KB</td> </tr>
</tbody>
</table>
</div></div></div>Sun, 19 Sep 2021 06:27:18 +0000Ajit R. Jadhav25432 at https://www.imechanica.orghttps://www.imechanica.org/node/25432#commentshttps://www.imechanica.org/crss/node/25432Looking for Head -Marketing and Communication for MNC in Pune
https://www.imechanica.org/node/24305
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/12865">Intended Indirect Insults</a></div><div class="field-item odd"><a href="/taxonomy/term/12866">Ridiculous</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Today, I received this email from some one at <span class=""><span class="N_dRA D_X q_52qC mq_AQ"><span class="u_b">Neptune consultants </span><span class="C_Z1VRpVF" dir="auto">in Pune [<a href="http://www.neptuneconsultants.com/" target="_blank" rel="noopener noreferrer">^</a>], through Naukri.com [<a href="https://www.naukri.com/" target="_blank" rel="noopener noreferrer">^</a>]. </span></span></span></p>
<p><span class=""><span class="N_dRA D_X q_52qC mq_AQ"><span class="C_Z1VRpVF" dir="auto">My CV, posted at Naukri.com, is here [<a href="https://jadhavresearch.files.wordpress.com/2020/05/ajit-r.-jadhav-short-cv-may-2020.pdf" target="_blank" rel="noopener noreferrer">^</a>]. It includes summary as well as an Objective section. See if the Neptune Consultants should have got in touch with me for this post, given my CV. <br /></span></span></span></p>
<p>Also, feel free to contact them directly, if any one of you is interested in this job.</p>
<p>I quote the email below the horizontal line.</p>
<p> </p>
<p><strong>Experience required for the Job:</strong> 15 - 30 years
</p><p> </p>
<p><strong>Annual Salary of the Job:</strong> 40.00 - 100.00 Lacs - Best in Industry
</p><p> </p>
<p>
</p><p> </p>
<p><strong>Job Location:</strong> Pune
</p><p> </p>
<p> </p>
<p> </p>
<p><strong>Dear Ajit R. Jadhav,</strong></p>
<p> </p>
<p>Hello We are looking for Head -Marketing and Communication for MNC in Pune About CompanyWe are looking to hire a Marketing Director who will be in charge of leading our company's marketing efforts. As a successful hire, you will be responsible for providing guidance to our marketing department by evaluating and developing marketing strategies, planning and coordinating marketing efforts, communicating the marketing plans to those involved, and building awareness and positioning for our company's brands. You will also be working closely with our sales department to develop a pricing strategy that will help us maximize profits and market share. Finally, you will be in charge of organizing company conferences, trade shows, and major events.To be considered for this position, you will need a bachelor's degree in business, marketing or communications. You will also need to have proven experience in running a marketing team and marketing campaigns. High competency in project and stakeholder management is a huge advantage.Marketing Director Responsibilities:Overseeing marketing department.Evaluating and developing our marketing strategy and marketing plan.Planning, directing, and coordinating marketing efforts.Communicating the marketing plan.Researching demand for our products and services.Competitor research.Working with sales department to develop pricing strategies to maximize profits and market share while balancing customer satisfaction.Identifying potential customers.Developing promotions with advertising managers.Understanding and developing budgets and finance, including expenditures, research and development appropriations, return-on-investment and profit-loss projections.Compiling lists describing our offerings.Developing and managing advertising campaigns.Building brand awareness and positioning.Supporting sales and lead generation efforts.Coordinating marketing projects from start to finish.Organizing company conferences, trade shows, and major events.Overseeing social media marketing strategy and content marketing.Marketing Director Requirements:Bachelors degree in business, marketing, communications, or related field.Experience in marketing and running a marketing team.Proven marketing campaign experience.Effective time management skills and the ability to multitask.Strong copywriting skills.Attention to detail.Proven ability to manage budgets.Professional and proactive work ethic.High competence in project and stakeholder management.Excellent interpersonal, written and oral communication skills.Experience with digital marketing forms such as social media marketing and content marketing.Competency in Microsoft applications including Word, Excel, and Outlook. If interested, Please reply back with below detailsTotal ExpExp in Product marketing and communicationExp in Software and IT servicesCurrent CTCexpected CTCNotice PeriodReason for Job ChangeCurrent LocationReady to relocate to PuneReason for relocation
</p><p> </p>
<p>Thanks [snip (name)] </p>
</div></div></div>Fri, 19 Jun 2020 12:41:02 +0000Ajit R. Jadhav24305 at https://www.imechanica.orghttps://www.imechanica.org/node/24305#commentshttps://www.imechanica.org/crss/node/24305The Machine Learning as an Expert System
https://www.imechanica.org/node/23261
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/10902">machine learning</a></div><div class="field-item odd"><a href="/taxonomy/term/12491">expert systems</a></div><div class="field-item even"><a href="/taxonomy/term/11581">data science</a></div><div class="field-item odd"><a href="/taxonomy/term/11938">artificial intelligence</a></div><div class="field-item even"><a href="/taxonomy/term/12101">deep learning</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><strong>1.</strong></p>
<p>To cut a somewhat long story short, I think that I can ``see'' that Machine Learning (including Deep Learning) can actually be regarded as a rules-based expert system, albeit of a special kind.</p>
<p>I am sure that people must have written articles expressing this view. However, simple googling didn’t get me to any useful material.</p>
<p>I would deeply appreciate it if someone could please point out references in this direction. Thanks in advance.</p>
<p><strong>2.</strong></p>
<p>BTW, here is a very neat infographic on AI: [<a href="https://techjury.net/stats-about/ai/" rel="noopener" target="_blank">^</a>]; h/t [<a href="https://www.visualcapitalist.com/ai-revolution-infographic/" rel="noopener" target="_blank">^</a>]. ... Once you finish reading it, re-read this post, please! Exactly once again, and only the first part---i.e., without recursion!. ...</p>
<p>[Originally published today at my personal blog, here [<a href="https://ajitjadhav.wordpress.com/2019/04/16/the-machine-learning-as-an-expert-system/" target="_blank">^</a>].)</p>
<p>Best,</p>
<p>--Ajit</p>
<p> </p>
</div></div></div>Tue, 16 Apr 2019 18:34:56 +0000Ajit R. Jadhav23261 at https://www.imechanica.orghttps://www.imechanica.org/node/23261#commentshttps://www.imechanica.org/crss/node/23261A preliminary document on my fresh new approach to QM
https://www.imechanica.org/node/23078
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/838">quantum mechanics</a></div><div class="field-item odd"><a href="/taxonomy/term/411">Mechanics in the quantum regime</a></div><div class="field-item even"><a href="/taxonomy/term/3403">quantum</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Hello, World</p>
<p>Here is a document that jots down, in a brief, point-wise manner, the elements of my new approach to understanding quantum mechanics.</p>
<p>Please note that the writing is very much at a preliminary stage. It is very much a work in progress. However, it does jot down many essential ideas.</p>
<p>I am uploading the document at iMechanica just to have an externally verifiable time-stamp to it. Further versions will also be posted at this thread.</p>
<p>Comments are welcome. However, I may not be able to respond all of them immediately, because (i) I wish to immediately switch over to my studies of Data Science (ii) discussions on QM, especially on its foundations, tend to get meandering very fast.</p>
<p>Best,</p>
<p>--Ajit</p>
<p> </p>
</div></div></div><div class="field field-name-upload field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><table class="sticky-enabled">
<thead><tr><th>Attachment</th><th>Size</th> </tr></thead>
<tbody>
<tr class="odd"><td><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://www.imechanica.org/files/0.7.NewShorterOutlineElementsNewApproachQP.pdf" type="application/pdf; length=93845" title="0.7.NewShorterOutlineElementsNewApproachQP.pdf">Version 0.7: An Outline of the Elements of a New Approach to Understanding Quantum Physics.</a></span></td><td>91.65 KB</td> </tr>
</tbody>
</table>
</div></div></div>Mon, 11 Feb 2019 15:50:15 +0000Ajit R. Jadhav23078 at https://www.imechanica.orghttps://www.imechanica.org/node/23078#commentshttps://www.imechanica.org/crss/node/23078Stress is defined as the quantity equal to ... what?
https://www.imechanica.org/node/22146
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/128">education</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/822">Stress Tensor</a></div><div class="field-item odd"><a href="/taxonomy/term/11964">definition of stress</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>In this post, I am going to note a bit from my <em>personal</em> learning history. I am going to note what had happened when a clueless young engineering student that was me, was trying hard to understand the idea of tensors during my UG years, and then for quite some time even <em>after</em> my UG days. May be for a decade or even more....</p>
<p>There certainly were, and are likely to be even today, many students like [the past] me. So, in the further description, I will use the term ``we.'' Obviously, the ``we'' here is the collegial ``we,'' perhaps even the pedagogical ``we,'' but certainly neither the pedestrian nor the royal ``we.''</p>
<p>========================</p>
<p>What we would like to understand is the idea of tensors; the question of what these beasts are really, really like.</p>
<p>As with developing an understanding of any new concept, we first go over some usage examples involving that idea, some instances of that concept.</p>
<p>Here, there is not much of a problem; our mind easily picks up the stress as a ``simple'' and familiar example of a tensor. So, we try to understand the idea of tensors via the example of the stress tensor. [Turns out that it becomes far more difficult this way... But read on, anyway!]</p>
<p>Not a bad decision, we think.</p>
<p>After all, even if the tensor algebra (and tensor calculus) was an achievement wrought only in the closing decade(s) of the 19th century, Cauchy was already up and running with the essential idea of the stress tensor right by 1822---i.e., more than half a century <em>earlier</em>. We come to know of this fact, say via James Rice's article on the history of solid mechanics [(.PDF) <a href="http://esag.harvard.edu/rice/163_Ri_Mech_Solids_EB93.pdf" target="_blank">^</a>].</p>
<p>Given this bit of history, we become confident that we are on the right track. After all, if the stress tensor could not only be conceived of, but even a divergence theorem for it could be spelt out, and the theorem could even be used in applications of engineering importance, all for decades before any other tensors were even abstractly conceived of, then, of course, developing a good understanding of the stress tensor ought to provide for a sound pathway to understanding tensors in general.</p>
<p>So, we begin with the stress tensor, and try [very hard] to understand it.</p>
<p>========================</p>
<p>We recall what we have already been taught: stress is defined as force per unit area. In symbolic terms, read for the very first time in our XI standard physics texts, the equation reads:</p>
<p><img src="http://physweb.bgu.ac.il/cgi-bin/mimetex.cgi?\sigma \equiv\frac{F}{A}" alt="" align="middle" border="0" /> ... Eq. (1)</p>
<p>Admittedly, we had been made aware, that Eq. (1) holds only for the 1D case.</p>
<p>But given this way of putting things as the starting point, the only direction which we could at all possibly be pursuing, would be nothing but the following:</p>
<p>The 3D representation ought to be just a simple generalization of Eq. (1), i.e., it must look something like this:</p>
<p><img src="http://physweb.bgu.ac.il/cgi-bin/mimetex.cgi?\overline{\overline{\sigma}}= \frac{\vec{F}}{\vec{A}}" alt="" align="middle" border="0" /> ... Eq. (2)</p>
<p>where the two overlines over <img src="http://physweb.bgu.ac.il/cgi-bin/mimetex.cgi?\sigma" alt="" align="middle" border="0" /> represents the idea that it is to be taken as a tensor quantity.</p>
<p>But obviously, there is some trouble with the Eq. (2). This way of putting things can only be wrong, we suspect.</p>
<p>The reason behind our suspicion, well-founded in our knowledge, is this:</p>
<p>The operation of a division <em>by</em> a vector is not well-defined, at least, it is not at all noted in the UG vector-algebra texts. [And, our UG maths teachers would happily fail us if we were to try an expression of that sort in our exams!]</p>
<p>For that matter, from what we already know, even the idea of ``multiplication'' of two vectors is not uniquely defined: We have at least two ``product''s: the dot product [or the inner product], and the cross product [a case of the outer or the tensor product]. The absence of divisions and unique multiplications is what distinguishes vectors from complex numbers (including phasors, which are often noted as ``vectors'' in the EE texts).</p>
<p>Now, even if you attempt to ``generalize'' the idea of divisions, just the way you have ``generalized'' the idea of multiplications, it still doesn't help a lot.</p>
<p>[To speak of a tensor object as representing the result of a division is nothing but to make an indirect reference to the very operation [viz. that of taking a tensor product], and the very mathematical structure [viz. the tensor structure] which itself is what we are trying to understand. ... ``Circles in the sand, round and round... .'' In any case, at this stage, the student is just as clueless about divisions by vectors, as he is about tensor products.]</p>
<p>But, still being under the spell of what had been taught to us during our XI-XII physics courses, and later on, also in the UG engineering courses--- their line and method of developing these concepts---we then make the following valiant attempt. We courageously rearrange the same equation, obtain the following, and try to base our ``thinking'' in reference to the rearrangement it represents:</p>
<p><img src="http://physweb.bgu.ac.il/cgi-bin/mimetex.cgi?\overline{\overline{\sigma}} \vec{A} = \vec{F}" alt="" align="middle" border="0" /> ... Eq (3)</p>
<p>It takes a bit of time and energy, but then, very soon, we come to suspect that this too could be a wrong way of understanding the stress tensor. How can a mere rearrangement lead from an invalid equation to a valid equation? That's for the starters.</p>
<p>But a more important consideration is this one: Any quantity must be definable directly, i.e., via an equation that follows the following format:</p>
<p><em>the quantiy being defined, and nothing else but only that quantity, appearing on the left hand-side </em><br /><em>= </em><br /><em>some expression involving some other quantities, appearing on the right hand-side.</em></p>
<p>Let's call this format Eq. (4).</p>
<p>Clearly, Eq. (3) does not follow the format of Eq. (4).</p>
<p>So, despite the rearrangement from Eq. (2) to Eq. (3), the question remains:</p>
<p><em>How can we define the stress tensor (or for that matter, any tensors of similar kind, say the second-order tensors of strain, conductivity, etc.) such that its defining expression follows the format given in Eq. (4)?</em></p>
<p></p>
<p>========================</p>
<p>A few more words:</p>
<p>It would be easy enough to abstractly do just a bit of algebraic manipulation and arrive at the solution. The point isn't that. The point is to understand the physical implications of that manipulation.</p>
<p>And, further, the point is this: If it were that obvious or simple, why is it that not even a <em>single</em> text-book/class-notes ever anticipates the above-mentioned possible line of thought on the part of a beginning student, and therefore, proceeds to provide him with the required definition in direct terms?</p>
<p>And then, as I might note later on, there are a few other conceptual advantages with a direct defintion, too. But more on it, later, if there is enough interest in this topic.</p>
<p>--Ajit</p>
</div></div></div>Mon, 19 Feb 2018 13:15:13 +0000Ajit R. Jadhav22146 at https://www.imechanica.orghttps://www.imechanica.org/node/22146#commentshttps://www.imechanica.org/crss/node/22146Also remember Alcoa
https://www.imechanica.org/node/22127
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Also remember Alcoa.</p>
</div></div></div>Thu, 08 Feb 2018 21:30:37 +0000Ajit R. Jadhav22127 at https://www.imechanica.orghttps://www.imechanica.org/node/22127#commentshttps://www.imechanica.org/crss/node/22127Yes I know about the [essentials of] QM!
https://www.imechanica.org/node/21967
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/838">quantum mechanics</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Check out here [at my personal blog] [<a href="https://ajitjadhav.wordpress.com/2017/12/12/yes-i-know-it-part-2/" target="_blank">^</a>] and the post before that.</p>
<p>---</p>
<p>Have a happy holiday season!</p>
<p>---</p>
<p>Sincerely,</p>
<p>--Ajit</p>
<p> </p>
</div></div></div>Sat, 23 Dec 2017 18:35:44 +0000Ajit R. Jadhav21967 at https://www.imechanica.orghttps://www.imechanica.org/node/21967#commentshttps://www.imechanica.org/crss/node/21967A ``small'' but interesting riddle from the theory of vibrations
https://www.imechanica.org/node/21295
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/612">vibrations</a></div><div class="field-item odd"><a href="/taxonomy/term/180">thermodynamics</a></div><div class="field-item even"><a href="/taxonomy/term/6006">classical physics</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Here is a ``small'' riddle from classical physics which I recently happened to think of, in connection with my studies of QM. See if it interests you.</p>
<p>See the figure below.</p>
<p><img src="http://imechanica.org/files/vib_string_with_middle_support_touching_it.png" alt=" An ideal vibrating string with a removable support at the mid-point" width="600" height="120" /></p>
<p>There is an idealized string tautly held between two fixed end-supports that are a distance L apart. The string can be put into a state of vibrations by plucking it. There is a third support exactly at the mid-point; it can be removed at will. When touching the string, the middle support does not permit vibrations to pass through it.</p>
<p>Initially, the middle support is touching the string. </p>
<p>At time t_0, the left-half carries a standing wave pattern in the fundamental normal mode (i.e. it is the fundamental mode for the <em>half</em> part on the left hand-side, i.e., its half-wavelength is L/2). Denote its frequency as \nu_1. At this time, the right-half is perfectly quiscent. Thus, energy is present only in the left-half of the system.</p>
<p>At time t_1, the middle support is suddenly removed. Now, disturbances from any of the two halves can freely propagate into the other half.</p>
<p>Assume that at a time t_F >> t_1, the system reaches a steady-state pattern of standing waves.</p>
<p>The issue of interest is:</p>
<p><em>What is/are the frequency/frequencies of the standing waves now present over the entire length L?</em></p>
<p>Mathematically, the fundamental mode for the entire length L as well as <em>any</em> and <em>all</em> of its overtones are possible, provided that their individual amplitudes are such that the law of energy conservation would not get violated.</p>
<p>Practically speaking, however, <em>only</em> the fundamental mode for the total length (L) is observed. </p>
<p>In short:</p>
<p>Thermodynamically, an infinity of tones are perfectly possible. Yet, in reality, only one tone of them gets selected, and that too is always only the fundamental mode (for the new length). What gives?</p>
<p><em>What precisely is the reason that the system gets settled into one and only one option—indeed an extreme option—out of an infinity of them, all of which are, energetically speaking, equally possible?</em></p>
<p>Comments are welcome!</p>
<p>A very verbose version of this problem was posted yesterday at my personal blog, here: [<a href="https://ajitjadhav.wordpress.com/2017/06/07/an-interesting-problem-from-the-classical-mechanics-of-vibrations/" target="_blank">^</a>] </p>
<p>PS: If there is a useful reference where this problem already appears, please do drop a line; thanks in advance.</p>
<p>Best,</p>
<p>--Ajit</p>
<p> </p>
<p> </p>
</div></div></div><div class="field field-name-upload field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><table class="sticky-enabled">
<thead><tr><th>Attachment</th><th>Size</th> </tr></thead>
<tbody>
<tr class="odd"><td><span class="file"><img class="file-icon" alt="Image icon" title="image/png" src="/modules/file/icons/image-x-generic.png" /> <a href="https://www.imechanica.org/files/vib_string_with_middle_support_touching_it.png" type="image/png; length=1131" title="vib_string_with_middle_support_touching_it.png">An ideal vibrating string with a removable support at the mid-point</a></span></td><td>1.1 KB</td> </tr>
</tbody>
</table>
</div></div></div>Thu, 08 Jun 2017 09:50:12 +0000Ajit R. Jadhav21295 at https://www.imechanica.orghttps://www.imechanica.org/node/21295#commentshttps://www.imechanica.org/crss/node/21295Explicit vs. implicit FDM: Could you please suggest a reference?
https://www.imechanica.org/node/19490
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/4847">Explicit algorithm</a></div><div class="field-item odd"><a href="/taxonomy/term/10988">explicit vs implicit</a></div><div class="field-item even"><a href="/taxonomy/term/1010">FDM</a></div><div class="field-item odd"><a href="/taxonomy/term/10989">local vs. global support of solution</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>The context is the finite difference modeling (FDM) of the transient diffusion equation (the <em>linear</em> one: $\dfrac{\partial T}{\partial t} = \alpha \dfrac{\partial^2 T}{\partial x^2}$).</p>
<p>Two approaches are available for modeling the evolution of $T$ in time: (i) explicit and (ii) implicit (e.g., the Crank-Nicolson method).</p>
<p>It was obvious to me that the explicit approach has a local (or compact) support whereas the implicit approach has a global support.</p>
<p>However, with some simple Google searches (and browsing through some 10+ books I could lay my hands on), I could not find any prior paper/text to cite by way of a reference.</p>
<p>I feel sure that it must have appeared in some or the paper (or perhaps even in a text-book); it's just that I can't locate it.</p>
<p>So, here is a request: please suggest me a reference where this observation (about the local vs. global support of the solution) is noted explicitly. Thanks in advance.</p>
<p>Best,</p>
<p>--Ajit</p>
<p>[E&OE]</p>
</div></div></div>Thu, 18 Feb 2016 07:42:55 +0000Ajit R. Jadhav19490 at https://www.imechanica.orghttps://www.imechanica.org/node/19490#commentshttps://www.imechanica.org/crss/node/19490Expansion of a function into a basis set
https://www.imechanica.org/node/18322
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/10489">basis sets</a></div><div class="field-item odd"><a href="/taxonomy/term/8709">Fourier series</a></div><div class="field-item even"><a href="/taxonomy/term/10490">polynomial expansion</a></div><div class="field-item odd"><a href="/taxonomy/term/10491">function expansion</a></div><div class="field-item even"><a href="/taxonomy/term/10492">expansion of a function</a></div><div class="field-item odd"><a href="/taxonomy/term/10055">computational mechanics; finite elements</a></div><div class="field-item even"><a href="/taxonomy/term/1612">CFD</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Consider a ``neat'' function such as what an engineer is most likely to use in his typical theory/work. Such a function would typically be: (i) defined over a single finite interval, (ii) continuous throughout, and (iii) smooth enough. In other words, the sort of a function they used when they introduced the very idea of a graph of a function to you, back in high-school. ... Feel free to add any other qualifications you like, but note them explicitly, e.g., (iv) bounded throughout, and (v) periodic. [I don't mind any additional qualifications; basically, as of now, reaching even just the low-hanging fruit would be gratifying.]</p>
<p>Suppose we want to represent this function, may be only in a limiting sense, as a sum of some linearly independent functions. (The basis set itself may be infinite.)</p>
<p>From whatever I know of numerical analysis and computational science and engineering, speaking off-hand, I can think of (only) two methods:</p>
<p>Expansion into <br /><strong>(A)</strong> a polynomial basis set<br /><strong>(B)</strong> the Fourier-theoretical basis set</p>
<p>These respectively cover the cases of $latex \sum a_n x^n$ and $latex \sum a_n e^{inx}$. </p>
<p>I now have two questions:</p>
<p><strong>Q1.</strong> Why don't we use <strong>(C)</strong> $latex \sum a_n e^{nx}$ in our routine numerical analysis/computational modeling work (e.g. FEM)? Can you think of some application/reference where someone has used it?</p>
<p><strong>Q2.</strong> Theoretically, a much more interesting (and demanding) question: </p>
<p>Do these three categories exhaust all the possibilities? Can we logically say so? Is there a mathematical theorem that allows us to say so? <br />If the answer is a no: What is the obvious objection if I were to formulate this conjecture as a lemma?<br />If the answer is a yes: Can such a theorem be proved? </p>
<p><em>What are your thoughts on Q1 and Q2? Care to share? Thanks in advance.</em></p>
<p>As to me, here I swiftly go:</p>
<p>Q1: Never seen one in a real application; don't know the reason; can't even guess why.</p>
<p>Q2: As one who mathematically has always been much more starry- and dewy-eyed than rigorous, when compared to an average engineer, I am inclined towards immediately jumping to the second conclusion, viz. ``yes.'' The ``reason'' which appeals to me here is that theorem proved by Gauss in 1800, viz., that complex numbers form an algebraically closed field. ... But, rigorously speaking, is this theorem even relevant here? To me, it does seem so; but rigorously speaking, I have no clue.</p>
<p>Anyway, over to you; am listening.</p>
<p>Best,</p>
<p>--Ajit<br />[E&OE]</p>
</div></div></div>Tue, 19 May 2015 02:47:33 +0000Ajit R. Jadhav18322 at https://www.imechanica.orghttps://www.imechanica.org/node/18322#commentshttps://www.imechanica.org/crss/node/18322I am [still] confused about gradients, vectors, deformation gradient, etc.
https://www.imechanica.org/node/17619
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>I am creating this blog entry to have my confusions about gradients, vectors, and deformation gradient, etc., straightened out once (and hopefully for all time!) ... My confusions got exposed (even to me) while commenting on a thread started by Prof. Suo here [<a href="http://imechanica.org/node/17565" target="_blank">^</a>]. In particular, I realized my confusions after writing this comment [<a href="http://imechanica.org/comment/26661#comment-26661" target="_blank">^</a>] there.</p>
<p>So, let me note down my confusions in the form of a few questions; the order may not be exactly from the simplest/basic to the complex:</p>
<ol>
<li>What is a vector space?</li>
<li>What is a vector field?</li>
<li>(Perhaps a repetition) What is the difference between (a) a function that is defined on a scalar field and outputs a vector-valued "field," and (b) a vector space?</li>
<li>Is the set of traction vectors directed along a given (local) direction, a field? Does it span a vector space? which one?</li>
<li>What exactly is a gradient of a scalar field? is it a vector field?</li>
<li>Is there a gradient of a vector field? What is the nature of its output?</li>
<li>Is the nabla operator always a vector? why or why not? examples?</li>
<li>Is there any technical difference between the terms: displacement gradient and deformation gradient?</li>
<li>Is the deformation gradient a gradient?</li>
<li>Is the deformation gradient a vector?</li>
</ol>
<p>May be, I will add more questions as they strike me, but this should be enough to get going.</p>
<p>Thanks in advance for clarifying these matters.</p>
<p>Best,</p>
<p>--Ajit</p>
<p>[E&OE]</p>
<p> </p>
</div></div></div>Mon, 08 Dec 2014 13:25:55 +0000Ajit R. Jadhav17619 at https://www.imechanica.orghttps://www.imechanica.org/node/17619#commentshttps://www.imechanica.org/crss/node/17619MWR for the first- and third-order differential equations
https://www.imechanica.org/node/16093
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/128">education</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/248">finite element analysis</a></div><div class="field-item odd"><a href="/taxonomy/term/3394">Weighted Residual</a></div><div class="field-item even"><a href="/taxonomy/term/7465">Variational Methods</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Hi all,
</p>
<p>
In engineering sciences, we usually end up using either the second- or the fourth-order differential equations, and the MWR (the method of weighted residuals) works pretty well for them.
</p>
<p>
The question is: how about the first- and the third-order differential equations? Why don't we see any applications of MWR for these odd-ordered differential equations? What gives?
</p>
<p>
If not equations of real application importance, then at least some hypothetical situations or toy applications involving the first- and third-order (and possibly fifth-order as well!) could have been taken up, just to illustrate the method itself. However, that is never found done, not at least in the introductory text-books/course notes. They only mention the issue, if they at all do, but they mostly remain silent about the mathematical reasons behind it.
</p>
<p>
So, here is a request: If you know of any nice introductory passages in a book (or course-notes, or articles) dealing with this issue in sufficient detail, and, preferably, at the final-year undergraduate level, then please leave comments giving references to them. (Treatments at more advanced level too are welcome.)
</p>
<p>
Ditto, if you don't know any references but could work it out and explain the issue to me. (I really don't know the reason. I have tried to think through the issue, but have ended up deriving nothing but some guesses. These guesses could not only be plain naive, they could also easily turn out to be completely besides the point if not outright wrong. And, so, this request. (If you wish, I could easily share my guesses right here; just let me know.))
</p>
<p>
Thanks in advance for your replies.
</p>
<p>
</p>
<p>
--Ajit <br />
PS: Since these days I check blogs etc. at most only once a day or so, I might be a bit late in coming back posting replies, and if so, please bear with me a bit. Thanks!
</p>
<p>
[E&OE]
</p>
</div></div></div>Sat, 15 Feb 2014 14:03:44 +0000Ajit R. Jadhav16093 at https://www.imechanica.orghttps://www.imechanica.org/node/16093#commentshttps://www.imechanica.org/crss/node/16093Those were not waves: A bit historical re. Huygens' principle
https://www.imechanica.org/node/11825
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/153">waves</a></div><div class="field-item odd"><a href="/taxonomy/term/656">education</a></div><div class="field-item even"><a href="/taxonomy/term/1553">philosophy</a></div><div class="field-item odd"><a href="/taxonomy/term/3117">electromagnetism</a></div><div class="field-item even"><a href="/taxonomy/term/3196">light</a></div><div class="field-item odd"><a href="/taxonomy/term/7053">scientific method</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
A few points that might be of general interest:
</p>
<p>
<strong>1. The dates</strong>: The date of Huygens' first written down material, which was orally presented to the French Academy of Sciences, is 1678---in contrast to the oft-quoted date of 1690. 1690 was the year of the first, French, publication of these notes (plus other material) in the form of a book.
</p>
<p>
Surprisingly, Huygens' book was not translated into English until 1912. Reason: The English mechanicians' dogma favored the Newtonian corpuscular theory of light, warts and all, and, being a dogma---not an exercise in Reason---they either attacked, or at least didn't allow for, the wave theory to be taken any serious notice of. (Such practices are not entirely unnoticeable in our times, either!)
</p>
<p>
Thus, the translation in English of the very beginnings of the first modern wave theory of light occurred some 50 years after the last grand theoretical synthesis involving the wave nature of light by Maxwell (1861 through 1865).
</p>
<p>
Also note, the translation/publication occurred in the USA, not in UK. USA was, back then, an "also ran" country when it came to top few frontline research countries. Germany and UK were the top two superpowers in research back then. Clearly, men like Stokes (a Lucasian Professor at Cambridge) were happy to make do with the original French (or possibly a German translation thereof!)
</p>
<p>
<strong>2. Pulses, not Wave(lets):</strong> When Huygens said waves, he meant pulses. His theoretical arguments never did address a *periodic* or *regularly* repeatative phenomenon. He sure had successive rings in his diagrams, but these were not crests/troughs of waves in his imagination---even if he did allude to waves, actual waves, those on the surface of a pond, right in the same writeups. Instead, per his theory, those successive rings simply were the loci, at successive time instances, of what essentially was a pulse (something like the Dirac delta.)
</p>
<p>
Huygens was concerned with the transmission of momentum from a star to the all-pervading aether surrounding it, in the process of emission of light. Terminology was still evolving back then, and so, the word he used was "movement," not "momentum." He first considered a 1D row of balls, and the propagation of an initially imparted "movement" through that array of balls (rather like in Newton's cradle), in a *finite* amount of time. The Rationalistic philosophic tradition held instantaneous propagation for light. As far as I know, Huygens' argument is the first mechanically based (and hence respectable) departure in asserting finitude to the speed of light.
</p>
<p>
(The premise of instantaneous action at a distance has not completely died yet; indeed it is thriving well: read up any mathematical proof affirming weirdities of quantum entanglement, esp., the proofs involving variational principles/energetics arguments, e.g., von Neumann's proof, or almost any thing after that.)
</p>
<p>
Huygens then extended this logic of movement transfers, via intervening balls, from the 1D situation to 2D and 3D. He continued imagining particles of aethers arranged as systematically arranged spheres (as in an FCC lattice). He thought of an expanding circular locus as if in the process of taking a limit for the decreasing radius for the balls (which, he took to be uniform in size). Throughout this development, however, it was the transmission of a single sharp impulse that he was concerned about, not the propagation of waves. (Indeed, this was the reason why eliminating those backwards propagating "waves" came naturally to him.)
</p>
<p>
<strong>3. Phases:</strong> It was Fresnel who independently rediscovered the Huygens principle on his own, and introduced phases in the theory.
</p>
<p>
Fresnel, in fact, also independently formulated the idea of Young's interference experiment. At first, Fresnel was too isolated to even know about Huygens' or Young's work. During the day, he worked as an on-site engineer building roads (or railroads? I am not sure). He worked on optics and mathematics only in the evenings, as a part-time hobby. (Go through the idea of Fresnel integrals, and try to imagine how a young on-site engineer might have built this theory after coming back tired from the field work in the day, living in tents, with only a handful of mathematics books gathered at radom serving as references, writing with the quilt pen, and of course without electric light.)
</p>
<p>
It was Fresnel's 1815 paper that, for the first time, treated the Huygens waveslets as waves in the modern sense of the term---as something that can interfere/diffract, as something that can have a *phase*.
</p>
<p>
BTW, as far as dates go, note that de Alembert had already formulated and solved the wave PDE by then (around 1757); it was not available in Huygens' time.
</p>
<p>
<strong>4. A quirk in the development of mathematics:</strong> Huygens was brilliant enough to solve the problem of finding the curvature for the guide-walls of a short pendulum of uniform oscillations. It therefore is especially intriguing that he still didn't think of including anything like a phase in his account of this principle discovered by he himself.
</p>
<p>
This curious omission is sort of like Einstein publishing original arguments on both Brownian movement (leading in part to Perin's Nobel) and the photoelectric effect (his own Nobel), both in the same year (1905), but without connecting the two, in putting forth an explanation regarding the nature of light.
</p>
<p>
<strong>5. The Correspondence with the Action/Variational principles:</strong> Yet, it is interesting to note that Huygens had, right back then, explicitly noted the correspondence between his principle and Fermat's principle. A local, transient, propagating process had thus already been shown to produce the same results as those by a "static," global---and, IMO, very dull sort of---principles, viz., variational principles, in particular, the action principle.
</p>
<p>
Do note that this argument was put forth way before even Maupertius' times, let alone those of Euler, Lagrange, or Hamilton.
</p>
<p>
If you read modern (20th century) accounts, you are likely to come out with the impression (i) that there has been this fantastically fundamental development of the action and variational principles, beginning with Hero's or Fermat's and culminating with Hamilton's (or someone else's still later on), (ii) that the fundamental way to justify Huygens' principle to derive it within the PDE formalism, which itself is to be derived within a topological and variational formalism (with fond allusions to be made to either non-viability or outright triviality of Huygens' principle in comparing 1D vs 2D vs 3D vs nD situations, and (iii) that a rigorous proof of Huygens' principle has been established only in the second half of the 20th century---together with its enormous "limitations" or triviality, of course.
</p>
<p>
Nothing is farther from the truth. Variational principles (and their hodge-podge equivalent of the weighted residuals etc.) are among the high favorites of modern mathematicians (esp. the mathematically inclined Indians, Russians, Frenchmen, and Americans) perhaps only because it's so hard (at least for them) to associate a neat physical mechanism with these principles. (It's the same story as with the Fourier/spectral analysis. They love anything for which a physical system (or "picture") is hard or impossible to conceive of.) However, the outright failures of such mathematicians to supply physical systematic explanation does not make variational/action/topological formalism any more fundamental than Huygens'.
</p>
<p>
It might be best to end this post with a sentence shamelessly lifted from Encyclopaedia Britannica's biographic entry on Fresnel:<cite></cite>
</p>
<p>
<cite>"Although his work in optics received scant public recognition during his lifetime, Fresnel maintained that <strong>not even acclaim from distinguished colleagues could compare with the pleasure of discovering a theoretical truth or confirming a calculation experimentally.</strong>"</cite> [<strong>emphasis</strong> mine]
</p>
<p>
BTW, have a happy Randsday!
</p>
<p>
--Ajit
</p>
<p>
[E&OE]
</p>
</div></div></div>Thu, 02 Feb 2012 06:55:01 +0000Ajit R. Jadhav11825 at https://www.imechanica.orghttps://www.imechanica.org/node/11825#commentshttps://www.imechanica.org/crss/node/11825Journals in Physics and Engineering, and Preprint Servers Like arXiv
https://www.imechanica.org/node/10895
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/162">computational mechanics</a></div><div class="field-item odd"><a href="/taxonomy/term/238">journals</a></div><div class="field-item even"><a href="/taxonomy/term/584">mechanics</a></div><div class="field-item odd"><a href="/taxonomy/term/920">physics</a></div><div class="field-item even"><a href="/taxonomy/term/948">Computational Science</a></div><div class="field-item odd"><a href="/taxonomy/term/973">software</a></div><div class="field-item even"><a href="/taxonomy/term/1044">engineering</a></div><div class="field-item odd"><a href="/taxonomy/term/4617">arXiv</a></div><div class="field-item even"><a href="/taxonomy/term/6513">preprints</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Hi all,
</p>
<p>
</p>
<p>
1. In the past, we have had quite some discussion regarding both open-access and open-access journals. However the slant in this blog post is different. I am not concerned here much about open-access journals per say.
</p>
<p>
Here, I am concerned about the policies that the prominent commercial journals keep regarding posting preprints on the Internet before these articles are submitted to them. I would like to know about policies kept in this regard by the commercial journals in the fields of physics, mechanics, and engineering (including software engineering, computational science and engineering, etc.).
</p>
<p>
</p>
<p>
2. The place of "Nature" among journals is pre-eminent. People, even those at highest ranked universities, with pride state acceptance of their work at "Nature." It also happens, I guess, to be the oldest continuously published scientific journal (older than its closest competitors, e.g., Science).
</p>
<p>
"Nature Physics," these days, does allow putting your pre-prints on arXiv. Since 2010, Nature Physics has a policy that says that:
</p>
<p>
"...any submission to <em>Nature Physics</em> or its sister journals may be posted, in that original submitted form, on the preprint server (although we do ask that the final, revised and accepted version is not posted until six months after publication in the journal; the published version, in the <em>Nature Physics</em> layout, may not be posted)." [<a href="http://blogs.nature.com/nautilus/2010/03/nature_physics_calls_for_suppo_1.html" target="_blank">^</a>]
</p>
<p>
Also that:
</p>
<p>
"You are welcome to post pre-submission versions or the original submitted version of the manuscript on a personal blog, a collaborative wiki or a preprint server at any time (but not subsequent pre-accept versions that evolve due to the editorial process)." [<a href="http://www.nature.com/authors/policies/confidentiality.html" target="_blank">^</a>].
</p>
<p>
Reasonable enough! (BTW, no, I am not a socialist. In fact, I consider myself a capitalist, in Ayn Rand's sense of the term.)
</p>
<p>
</p>
<p>
3. Now I know that many other journals of a similar standing---most notably, "Science"---do not have a clear general policy that allows for doing so:
</p>
<p>
"Posting of a paper on the Internet may be considered prior publication that could compromise the originality of the <em>Science</em> submission, although we do allow posting on not-for-profit preprint servers in many cases. Please contact the editors for advice about specific cases." [<a href="http://www.sciencemag.org/site/feature/contribinfo/faq/#prioronline_faq" target="_blank">^</a>]
</p>
<p>
</p>
<p>
4. I tried to locate for myself if other journals had any policy statement on this matter. These journals most notably included: "PRL," "Foundations of Physics," "PNAS," etc. I could not succeed doing so. (The information may be there, but it is hard to find. Even on "Science" mag Web site, it's a few links deeper and not at all obvious, whereas at "Nature," it's more or less very easily accessible starting from the home page.)
</p>
<p>
</p>
<p>
<strong>5. So, here is my request:</strong>
</p>
<p>
Are you aware of policies in this regard maintained by the journals which you help edit or to which you often submit your articles---esp. the journals from the mechanics and engineering fields? What are these policies like? Care to share (about those policies)? BTW, here, also the journals on computational mechanics and those dealing with software in engineering, are to be included.
</p>
<p>
Does posting a preprint of a paper at iMechanica disqualify submitting it to the journals that iMechanicians often use? How about posting it at arXiv?
</p>
<p>
What if I discuss the basic germ of an idea itself here at iMechanica, even though it's not written in the format of a paper? How strict or lenient are the views regarding such pre-submission publication that the journals in Mechanics field take? How do you know---in the sense, to what extent could I be reassured?
</p>
<p>And, finally, how does the iMechanica Creative Commons License work out for this situation? I guess that at iMechanica it's the CC BY-NC-SA license [<a href="http://creativecommons.org/licenses/by-nc-sa/3.0/" target="_blank">^</a>] that we follow/require, and not the CC BY-NC-ND one [<a href="http://creativecommons.org/licenses/by-nc-nd/3.0/" target="_blank">^</a>]. What if I wish to publish at iMechanica, but only with the latter (more restrictive) license? (However, please note, it's not just the policy of iMechanica that is important to me; I actually am more concerned with the preceding questions.) </p>
<p>
</p>
<p>
Thanks in advance for any information and clarifications.
</p>
<p>
--Ajit
</p>
<p>
[E&OE]
</p>
<p>
</p>
</div></div></div>Mon, 08 Aug 2011 09:21:52 +0000Ajit R. Jadhav10895 at https://www.imechanica.orghttps://www.imechanica.org/node/10895#commentshttps://www.imechanica.org/crss/node/10895What would you choose as the Top 5 Equations? Top 10?
https://www.imechanica.org/node/10188
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/584">mechanics</a></div><div class="field-item odd"><a href="/taxonomy/term/920">physics</a></div><div class="field-item even"><a href="/taxonomy/term/1577">equation</a></div><div class="field-item odd"><a href="/taxonomy/term/1867">mathematical modeling</a></div><div class="field-item even"><a href="/taxonomy/term/6221">top 5 equations</a></div><div class="field-item odd"><a href="/taxonomy/term/6222">top 10 equations</a></div><div class="field-item even"><a href="/taxonomy/term/6223">fundamental equations</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Equations are of central importance in all of science and engineering, but especially so in mechanics.</p>
<p>Even leaving aside algebraic equations, handbooks on PDEs alone list hundreds of equations. However, a few of these do stand out, either because they encapsulate some fundamental aspect of physics/science/engg., or because they serve as simpler prototypes for more complex situtations, or simply because they are so complex as to be fascinating by themselves. There might be other considerations too... But the fact is, some equations really do stand out as compared to others.</p>
<p>If so, what equations would you single out as being most important or interesting? To make the matters more interesting, first, please think of making a short list of only 5 equations. Then, if necessary, make it one of 10 equations---but no more, please! :)</p>
<p>As to me, here is my list, put together in a completely off-hand manner:</p>
<p>Top five:<br />
(1-3) The linear wave-, diffusion- and potential-equations.<br />
(4) The Schrodinger equation<br />
(5) The Navier-Stokes equation</p>
<p>Additionally, perhaps, these equations:<br />
(6) The Maxwell Equations<br />
(7) The equation defining the Fourier transform<br />
(8) Newton's second law (dp/dt = F)<br />
(9) The Lame equation (of elasticity)</p>
<p>Am I already nearing the limit or what... Hmm... But, nope, I am not sure whether I want to include E = mc^2. ... I will give this entire matter a second thought some time later on.</p>
<p>But, how about you? What would be your choices for the top 5/10 equations? Why?
</p>
<p>
</p>
<p>
--Ajit<br />
PS: Also posted today in the Computational Scientists & Engineers group at LinkedIn, and also will post soon at my personal blog. </p>
<p>[E&OE]
</p>
<p>
</p>
</div></div></div>Sat, 30 Apr 2011 12:03:13 +0000Ajit R. Jadhav10188 at https://www.imechanica.orghttps://www.imechanica.org/node/10188#commentshttps://www.imechanica.org/crss/node/10188An interesting arXiv paper: "Precession optomechanics"
https://www.imechanica.org/node/10166
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/283">Mechanics of Photonic Devices</a></div><div class="field-item odd"><a href="/taxonomy/term/838">quantum mechanics</a></div><div class="field-item even"><a href="/taxonomy/term/3403">quantum</a></div><div class="field-item odd"><a href="/taxonomy/term/6207">photon</a></div><div class="field-item even"><a href="/taxonomy/term/6208">photon mechanics</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Hi all,
</p>
<p>Just thought that the following paper archived at the arXiv yesterday could be of general interest to any mechanician:</p>
<p>
Xingyu Zhang, Matthew Tomes, Tal Carmon (2011) "Precession optomechanics," arXiv:1104.4839 [<a href="http://arxiv.org/abs/1104.4839" target="_blank">^</a>]
</p>
<p>
The fig. 1 in it makes the matter conceptually so simple that the paper can be recommended to any mechanician for his general reading, and not only to a specialist in the field.
</p>
<p>
<br />
--Ajit
</p>
<p>
[E&OE]
</p>
</div></div></div>Wed, 27 Apr 2011 07:26:09 +0000Ajit R. Jadhav10166 at https://www.imechanica.orghttps://www.imechanica.org/node/10166#commentshttps://www.imechanica.org/crss/node/10166Any tips/comments regarding the latest version of the C++ library: Eigen (v. 3.0)?
https://www.imechanica.org/node/9987
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/2864">solvers</a></div><div class="field-item odd"><a href="/taxonomy/term/3255">linear solvers</a></div><div class="field-item even"><a href="/taxonomy/term/6112">Eigen 3.0</a></div><div class="field-item odd"><a href="/taxonomy/term/6113">eigenvalues computations</a></div><div class="field-item even"><a href="/taxonomy/term/6114">CPP</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Hi all,
</p>
<p>
<strong>1. A new version of Eigen (v 3.0 now) is out</strong> (on March 23, 2011), and it seems promising. First, a few links:
</p>
<p>
The main page for the project is here: [<a href="http://eigen.tuxfamily.org/index.php?title=Main_Page" target="_blank">^</a>]. The page for v.3.0 is here: [<a href="http://eigen.tuxfamily.org/index.php?title=3.0" target="_blank">^</a>]. It seems to be <em>very</em> fast: [<a href="http://eigen.tuxfamily.org/index.php?title=Benchmark" target="_blank">^</a>].
</p>
<p>
<br />
<strong>2. No compilation issues on the Win32 platform:</strong> I just downloaded it today, and found that it compiles OK with VC++ 10.0 on Win32 (the BUILD_ALL project). I haven't had the time to try anything further, though.
</p>
<p>
<br />
<strong>3. Please share your experience:</strong> For whatever reasons, if anyone here eventually decides to use it, or not to use it, or has any comments or tips to offer, I would like to hear from him/them, esp. in respect of the following points:
</p>
<p>
<strong>3.1</strong> <strong>For eigenvalue computations</strong>, comparative advantages/disadvantages, including speed comparisons, with the existing libraries like ARPACK, Trilinios, etc.
</p>
<p>
Assume that the system to solve has origins in a typical structural/solid mechanics FEM. If possible, please share your experience for global [A] matrix orders of 3k, 10k, 100k, and bigger, the matrices being the typical FEM ones: sparse, symmetric, etc.
</p>
<p>
[This note is not really necessary, but just in the interest of clarity: If a matrix has 10 rows and 10 columns, then its order is taken to be 10, not 100.]
</p>
<p>
<strong>3.2 For solving a linear FEM-generated system</strong> using a direct solver, speed comparisons with the existing FORTRAN/C++ code as implemented in GOTO (latest version), Taucs, etc. Again, matrix orders go from 3k to 100k and bigger, and the matrices, of course, are sparse, symmetric, etc.
</p>
<p>
<strong>4.</strong> Any <strong>other tips</strong> you care to share would also be appreciated.
</p>
<p>
</p>
<p>
Thanks in advance.
</p>
<p>
--Ajit
</p>
<p>
[E&OE]
</p>
</div></div></div>Thu, 24 Mar 2011 13:51:35 +0000Ajit R. Jadhav9987 at https://www.imechanica.orghttps://www.imechanica.org/node/9987#commentshttps://www.imechanica.org/crss/node/9987Open House: Can you define FEM in one line?
https://www.imechanica.org/node/9919
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/248">finite element analysis</a></div><div class="field-item odd"><a href="/taxonomy/term/370">finite element methods</a></div><div class="field-item even"><a href="/taxonomy/term/447">Finite Element Method</a></div><div class="field-item odd"><a href="/taxonomy/term/846">FEM</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Can you define FEM in one line?
</p>
<p>
If yes, what would it be? And, in that case, permit me a second question: How?
</p>
<p>
</p>
<p>
...Really interested in knowing what the members of this community think (of this matter), if they do...
</p>
<p>
</p>
<p>
--Ajit
</p>
<p>
[E&OE]
</p>
<p>
</p>
</div></div></div>Thu, 10 Mar 2011 06:40:59 +0000Ajit R. Jadhav9919 at https://www.imechanica.orghttps://www.imechanica.org/node/9919#commentshttps://www.imechanica.org/crss/node/9919What would you like for an undergraduate book on QM to explain to you?
https://www.imechanica.org/node/9791
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/838">quantum mechanics</a></div><div class="field-item odd"><a href="/taxonomy/term/976">undergraduate education</a></div><div class="field-item even"><a href="/taxonomy/term/1036">books</a></div><div class="field-item odd"><a href="/taxonomy/term/6006">classical physics</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
</p>
<p><strong>1. Background:</strong></p>
<p>A couple of things concerning books happened recently, in the last week or two.</p>
<p>(i) Dr. Biswajit Banerjee announced last week that a new book on metamaterials and waves in composites authored by him is coming out in print within a few months.</p>
<p>(ii) In one of my regular visits to bookshops, I noticed a hardcover copy of Prof. Allan Bower's book on mechanics of solids. Someone (or more likely, some institution) in Pune had ordered it, and the copy happened to be lying near the top of the stack. The book had been online for some time and I had browsed through it already. So, now, when I opened the printed version out of curiosity, I directly went to the Preface part. This is how Prof. Bower opens his Preface:</p>
<p>
</p>
<p> Ronald Rivlin, a pioneer in the field of nonlinear elasticity, was asked once whether he intended to write a treatise on his field. "Why should I write a book?" he replied. "<strong>People write books to learn a subject.</strong> I already know it."</p>
<p>[Emphasis in <strong>bold</strong> is mine.]</p>
<p>
</p>
<p>
<strong>2. "People write books to learn a subject:"</strong></p>
<p>That line really hit me---in two different ways.</p>
<p>Firstly, it has always been a part of the folklore among engineering college teachers that the best way to learn a subject is to teach it. I first heard it in 1984 in the teachers' room in Bharati Vidyapeeth's College of Engineering. I had then realized, first-hand, how true the saying was. And, I had wondered right back then: if it is not possible to teach a course, how about writing a book on it---mainly for learning the subject.</p>
<p>Secondly, it occurred to me now that if I were to pick out just one subject that I wish to understand better, it would undoubtedly have to be Quantum Mechanics. And, so the thought became: why not write a book on QM---in order to learn it. The idea is not so objectionable after all. Especially if you consider that most physicists (and all mainstream physicists) assure all the rest of us (and very probably also to themselves) that nobody understands quantum mechanics.</p>
<p>Actually, I was planning to write 2--3 journal papers that would extend and better explain some of the fundamental features of quantum physics as using my new approach. I had been gathering my thoughts and background material together. Yet, the more I thought about it, the better it began looking to me that perhaps it makes sense to first write a book on QM before writing those articles.</p>
<p>
</p>
<p>
<strong>3. A question for you:</strong></p>
<p>So, with those thoughts in mind, I would like to raise the title question to you:</p>
<p><strong>What would you like an undergraduate book on QM to explain to you?</strong> Or, better still (because it makes it more personal): <strong>What do you want me to explain to you, concerning the introductory topics of QM?</strong></p>
<p>By introductory topics, I mean the topics covered in (roughly in the order of increasing depth or complexity): Eisberg and Resnick, Hameka, Phillips, Scherrer, Liboff, Gasiorowicz, etc. Also, many other books falling within this same range, e.g.: Griffiths, Zettilli, etc.</p>
<p>If you have any points to raise in this regard, feel free to do so. I will keep this particular post open for comments until I finish writing the book (whenever I come to do that).</p>
<p>Any one may write me. However, a word about the intended audience and the nature of treatment is in order.</p>
<p>
</p>
<p>
<strong>4. The intended audience and the intended treatment of the book:</strong></p>
<p>The primary intended audience is: 3rd/4th year undergraduate students in engineering and applied sciences. Especially, those who did not have a course on electromagnetic fields beforehand (such as those majoring in mechanical, materials, chemical, aeronautical, etc. areas).</p>
<p>The treatment will follow the historical order of developments. I will begin with a summary of the pre-requisites, including very rapid (and perhaps rather conceptual) surveys (done from my own viewpoint, sort of "an engineer's viewpoint") of such topics as: Newton's laws; partial differential equations; The beginning of the energy- and fields-based reformulation of Newton's mechanics by Leibniz; complex numbers and Euler's identity; Lagrangian reformulation of Newtonian mechanics; relevant matrix theory; Fourier theory; relevant probability theory; Hamilotonian reformulation of Newtonian mechanics; electromagnetic field theory from say Coulomb to Maxwell and Hertz; the eigenvalue problem in classical physics; cavity radiation; special relativity (taken as highlighting certain features of the classical electrodynamics).</p>
<p>The QM proper will begin with Planck, of course, and will closely follow the historical sequence, though the notation might be modern---however, I wish to emphasize that I will not introduce Dirac's notation until he introduces it, so to say. Similarly, I will introduce Heisenberg's matrix mechanics before Schrodinger's wave mechanics. I intend to leave the reader at about 1935, though an appendix or two on entanglement is possible.</p>
<p>I will try to keep the length at about 300 pages at the most. I would love to see if it can be done within 250 pages, but doing so seems not easily possible. I will leave out many conceptual explanations, esp. of the prior theories, primarily because that burden has already been relieved for me in the form of Manjit Kumar's book. In a way, I do see my intended book as being complementary to Kumar's book.</p>
<p>I will cover neither Feynman's reformulation nor Bohm's ideas.</p>
<p>The book will also not be a vehicle to introduce my own approach. However, it is impossible for any author to keep aside his viewpoint, while thinking or writing. In this case, I will try to restrict myself to highlighting the wonderful series of ridiculous conclusions to which the earlier theories lead (often isolated and put forth by the formulators of those theories themselves), and providing some explicit hints for getting out of them. However, in the planned book, I will not go beyond providing hints alone. ... Yes, I will be willing to give out some of the material or thoughts that, properly, should have come in the research articles first. However, as far as journal articles go, frankly, I do not care!</p>
<p>The book <strong>will </strong>carry mathematics. (It won't be addressed to the layman.) It will carry derivations too, but only in simple and essential terms. (By simple, I do not mean: devoting inordinate time to one-dimensional and time-independent cases. Adopting this policy may mean that the book ends up being suitable only to the beginning graduate students of engineering. If so, that would be OK by me.)</p>
<p>Further, I would often provide the derivations in an order other than what is found in the usual treatments. For instance, the prerequisites part itself will cover spherical harmonics---right in the context of classical physics. Also, the angular momentum of the EM field. (Yes, the prerequisites part will be a major part in this book, perhaps 40% of the total material.) The prerequisites part will also point out the issue of the instantaneous action-at-a-distance, right in the PDE section.</p>
<p>In short, it will almost be a university text-book. Except that I don't expect any university to adopt it for their classroom usage! Therefore, there won't be any routine kind of chapter-end exercises, nor a section at the beginning of the chapter motivating the student. However, some pointers for further thought might be provided via notes at the end of the book.</p>
<p>Most readers here at iMechanica (and many of the readers of my personal blog) come from engineering and applied sciences background. They are likely to have run into QM as a part of their courses on modern physics, solid physics, nanomaterials, etc. They might have had run into issues concerning the real QM. I would love it if I can provide answers to their questions. And, it goes without saying that students of "pure" sciences---physics, chemistry, etc.---would be as welcome as those of engineering sciences. This book would be directed at them, not at the layman---or at the philosophers.</p>
<p>Of course, as far as raising the questions go, any one may feel free to submit his query via a comment. (I may not reply every comment at iMechanica; I do not moderate anything here.)</p>
<p>All in all, it would be a book written by an engineer, and primarily for engineering/applied science undergraduates/beginning postgraduate students. There already is an excellent book in this space: Prof. Leon van Dommelen's online book. I really like it, but thought that I would have approached many things differently, and so, thought of writing my book. Most important difference, to my mind, is that I would stick to the historical approach throughout. But, yes, as far as undertaking this huge an effort goes, Prof. van Dommelen's book would remain a kind of an inspiration for me.</p>
<p>
</p>
<p>
<strong>5. One final point: Sample questions:</strong></p>
<p>Some time ago, I had written a list of questions that I thought UG students should ask their professors. However, there were also other topics in that post. For ease of direct referencing, here I am copy-pasting those questions below (with a bit of editing). Go through them and see if you have any other questions you wish to raise:</p>
<p>
</p>
<ol>
<li>
Why are quantum-mechanical forces conservative?</li>
<li>Does the usual time-dependent Schrodinger’s equation (TDSE) apply to propagation of photons? If yes, why does no textbook ever illustrate TDSE involving photons? If not, what principle goes against applicability of TDSE to photons?</li>
<li>What kind of physics would result if the QM wavefunction were not to be complex-valued but real (scalar)-valued? What if the wavefunction were to be deterministic rather than probabilistic? What contradictions would result in each case?</li>
<li>Does QM at all need an interpretation? If yes, why? Why is it that no other theory of physics seems to need special efforts at interpreting it but only QM does, esp. so if all physics theories ultimately describe the same reality? If QM does not need an interpretation, why do people talk about the phrase: “interpretation of QM”? What do they mean by that phrase?</li>
<li>What, precisely, is the physical meaning of an operator? Please don’t simply repeat for us its definition. Instead, please give us the physical meaning of the concept. Or is it the case that no physical meaning is possible for this concept and that it is doomed to remain an exclusively mathematical concept? If yes, why use it in the postulates of a physical theory—without ever taking the care to define its physical correspondents?</li>
<li>Are all quantum-theoretical operators Hermitian? If yes, why? What physical fact does this property indicate/highlight/underscore? What if they are not Hermitian?</li>
<li>Give one example of an important eigenvalue problem from classical mechanics in which the differential equation formalism is very clearly shown to be equivalent to the matrix formalism.</li>
<li>Does the QM theory necessarily require the concept of a wavepacket when it comes to detailing what a QM particle is? If yes, why? What would happen if it were not a packet of waves but instead just a monochromatic wave? If the theory does not necessarily require packets of waves, then can you suggest us any alternative treatment—if there is one?</li>
<li>In every differential equation we have studied thus far, the primary unknown always carried some or the other physical units/dimensions. For example, for mechanical waves, the primary variable would be the displacement from the equilibrium position. But the QM wavefunction seems to be a dimensionless quantity; at least, textbooks don’t seem to note down any units for it. Is it a dimensionless quantity? Why? What important things does this tell us about the nature of theorization followed in QM?</li>
<li>Is QM an action-at-a-distance theory?</li>
<li>How, precisely, does QM relate to the classical EM? Is the term V(x,y,z,t) in Schrodinger’s equation to be understood in the classical sense? If yes, why do people say that between the two, QM is more basic to EM?</li>
<li>Explain precisely how the Newtonian mechanics is implied by QM.</li>
<li>And, one question I raised yesterday, via a tweet: In the mainstream interpretation---taught to all undergraduates world-wide---it is not meaningful to speak of emission of particles. Particles are never emitted, only absorbed---because only absorption can be "observed." The whole world is a series of absorptions, so to speak. True or false? (Hint: In Keynesian economics, there are only consumers, no producers!)
</li>
</ol>
<p>
<br />
Those were the questions I thought of, some time ago. ... I am sure you can do better.
</p>
<p>
I now look forward to hearing from you.
</p>
<p>
</p>
<p>
--Ajit
</p>
<p>
Also posted at my personal blog [<a href="http://ajitjadhav.wordpress.com/2011/02/12/what-would-you-like-an-undergraduate-book-on-qm-to-explain-to-you/" target="_blank">^</a>].
</p>
<p>
[E&OE]
</p>
<p>
</p>
</div></div></div>Sat, 12 Feb 2011 09:54:34 +0000Ajit R. Jadhav9791 at https://www.imechanica.orghttps://www.imechanica.org/node/9791#commentshttps://www.imechanica.org/crss/node/9791How about having a special Mechanics Gallery here?
https://www.imechanica.org/node/9752
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/643">iMechanica</a></div><div class="field-item odd"><a href="/taxonomy/term/5986">Mechanics Gallery</a></div><div class="field-item even"><a href="/taxonomy/term/5987">What is mechanics</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Here is an idea I submit for consideration by all iMechanicians, but esp. so by the admins and moderators. Discussion is welcome.
</p>
<p>
</p>
<p>
<strong>Idea: Why not have a Mechanics Gallery section here? </strong>
</p>
<p>
Origin: Recently, I was browsing for some OpenGL-encapsulating C++ class libraries, e.g. OpenSceneGraph, VTK, the game development libraries, etc. The Web sites of all such libraries always carry a "Gallery" page which is designed to attract the potential users. The Gallery page shows the capabilities and advantages of that library/framework.
</p>
<p>
A similar idea is possible for our field too.
</p>
<p>Many iMechanicians do excellent work in mechanics. Their own Web sites often carry attractive illustrations and explanations of their research and education programs. Thus, many of us could very easily contribute exhibits for the iMechanica Gallery.</p>
<p>
We can perhaps have a <strong>main Gallery Section page</strong> which will carry a list of the resources being exhibited. The main page may also carry brief (say 100 words) description for each exhibit, preferably with an<br />
attractive graphic, with hyperlinks provided for further information (Web URLs, PDF files, graphics, software, etc.).
</p>
<p>
<strong>Each </strong><strong>exhibit item</strong> should identify the broad area of mechanics via our usual tags. Further, the item should also explicitly identify <strong>the</strong> <strong>assumed level of the target audience, </strong>e.g.: layman, undergraduate, graduate students, advanced researchers, etc.
</p>
<p>
The resource items should be rather <strong>general-purpose</strong> in nature; they should avoid the tunnel-vision syndrome. The brief description should avoid equations as far as possible, though I do agree that in certain cases using equations would be unavoidable. The idea is to keep the focus more on the main concepts being illustrated.
</p>
<p>
The exhibits may come from professionals working in <strong>industry</strong> as well as from <strong>lab. researchers</strong> and <strong>academics (professors as well as students).</strong>
</p>
<p>
I sugget that at least in the beginning, there could be a limit on the number of exhibit items that an individual might submit, say, <strong>at most 2 exhibits per person</strong>. The limit is expected to help the member think hard as to what item of <strong>general </strong>interest he might submit.
</p>
<p>
The visual format of the gallery may be finalized after further discussion.
</p>
<p>
<strong>Over a period of time, the Gallery could easily become a good initial place of contact between the layman and professionals from other fields on the one hand, and we iMechanicians on the other.<br />
</strong>
</p>
<p><strong>Feel free to add further ideas, suggestions and discussions in this regard.<br />
</strong></p>
<p>
</p>
<p>
- - - - -
</p>
<p>
History: This idea was initially posted as a comment at Bisjwajit's blog a few days ago. I wanted to edit the text before posting it to a separate thread, but find no time, and so I have just copy-pasted it here.
</p>
<p>
Biswajit noted that Drupal may not be the ideal platform for a gallery. At the Drupal site, they say: "Convert <strong>any</strong> website layout or template into a Drupal theme - easily!" [<a href="http://drupal.org/node/313510" target="_blank">^</a>] (<strong>bold</strong> emphasis added.) I have no idea how easy it would be to create a special Gallery page, but at Drupal they say that it is possible to customize only a section of the overall Web site. Admins/IT Support people may be able to tell us better.
</p>
<p>
<strong>Over to you all.<br />
</strong>
</p>
<p>
--Ajit
</p>
</div></div></div>Mon, 07 Feb 2011 09:40:50 +0000Ajit R. Jadhav9752 at https://www.imechanica.orghttps://www.imechanica.org/node/9752#commentshttps://www.imechanica.org/crss/node/9752How to supply a visualization for the displacement gradient tensor
https://www.imechanica.org/node/9159
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/131">stress</a></div><div class="field-item odd"><a href="/taxonomy/term/132">strain</a></div><div class="field-item even"><a href="/taxonomy/term/973">software</a></div><div class="field-item odd"><a href="/taxonomy/term/5262">Tensor Visualization</a></div><div class="field-item even"><a href="/taxonomy/term/5263">Visualization</a></div><div class="field-item odd"><a href="/taxonomy/term/5550">displacement</a></div><div class="field-item even"><a href="/taxonomy/term/5689">toy</a></div><div class="field-item odd"><a href="/taxonomy/term/5690">displacement gradient</a></div><div class="field-item even"><a href="/taxonomy/term/5691">rotation</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Hi all,
</p>
<p>
[Warning: The writing is long, as is usually the case with my posts :)]
</p>
<p>
It all began with a paper that I proposed for an upcoming conference in India. The extended abstract got accepted, of course, but my work is still in progress, and today I am not sure if I can meet the deadline. So, I may perhaps withdraw it, and then submit a longer version of it to a journal, later.
</p>
<p>
Anyway, here is a gist of the idea behind the paper. I am building a very small pedagogical software called "toyDNS." DNS stands for <strong>D</strong>isplacement, strai<strong>N</strong>, and stre<strong>S</strong>s, and the order of the letters in the acronymn emphasizes what I (now) believe is the correct hierarchical order for the three concepts. Anyway, let's keep the hierarchical order aside and look into what the software does---which I guess could be more interesting.
</p>
<p>
The sofware is very very small and simple. It begins by showing the user a regular 2D grid (i.e. squares). The user distorts the grid using the mouse (somewhat similar to the action of an image-warping software). The software then, immediately (in real time, without using menus etc.) computes and shows the following fields in the adjacent windows: (i) the displacement vector field, (ii) the displacement gradient tensor field, (iii) the rotation field, (iv) the strain field, (v) and the stress field. The software assumes plane-stress, linear elasticity, and uses static configuration data for material properties like nu and E. The software also shows the boundary tractions (forces) that would be required to maintain the displacement field that the user has specified.
</p>
<p>
Basically, the idea is that the beginning undergraduate student encountering the mechanics of materials for the first time, gets to see the importance of the rotation field (which is usually not emphasized in textbooks or courses), and thereby is able to directly appreciate the reason why an arbitrary displacement field does uniquely determines the corresponding stress fields but why the converse is not true---why an arbitrary stress/strain field cannot uniquely determine a corresponding displacement field. To illustrate this point (call it the compatibility issue if you wish) is the whole rationale behind this toy software.
</p>
<p>
Now, when it comes to visualizing the fields, I can always use arrows for showing the vector fields of displacements and forces. For strains and stresses, I can use Lame's ellipse (in 2D). In fact, since the strain and stress fields are symmetric, in <em>2D</em>, they each have only 3 components, which means that the symmetric tensor object as a whole can directly map onto an RGB (or HLS) color-space, and so, I can also show a single, full-color field plot for the strain (or stress) field.
</p>
<p>
Ok. So far, so good.
</p>
<p>
The problem is with the displacement gradient tensor (DG for short here). Since the displacement field is arbitrary, there is no symmetry to the DG tensor. Hence, even in 2D, there are 4 independent components to it---i.e. one component too many than what can be accomodated in the three-component color-space. So, a direct depiction of the tensor object taken as a whole is not possible, and something else has to be done. So, I thought of the following idea.
</p>
<p>
First, the notation. Assume that the DG tensor is being described thus:
</p>
<p>
DG11 DG12<br />
DG21 DG22
</p>
<p>
=
</p>
<p>
du/dx du/dy<br />
dv/dx dv/dy
</p>
<p>
where DGij are the components of the DG tensor, u and v are the x- and y-components of the displacement field, and the d's represent the <em>partial</em> differentation. (Also imagine as if the square brackets of the matrix notation are placed around the components listing above.)
</p>
<p>
Consider that DGij can be taken to represent a component of a vector that refers to the i-th face and j-th direction. Understanding this scheme is easier to do for the stress tensor. For the stress tensor, Sij is the component of the traction vector acting across the i-the face and pointing in the j-th direction. For instance, in fig. 2.3 here: <a href="http://en.wikipedia.org/wiki/Stress_(mechanics">http://en.wikipedia.org/wiki/Stress_(mechanics</a>), T^{e_1} is the vector acting across the face normal to the 1-axis.
</p>
<p>
Even if the DG tensor is not symmetric, the basic idea would still apply, wouldn't it?
</p>
<p>
Thus, each row in the DG tensor represents a vector: the first row is a vector acting on the face normal to the x-axis, and the second is another vector (which, for DG, is completely indpendent of the first) acting on the face normal to the y-axis. For 2D, subsitute "line" in place of "face."
</p>
<p>
If I now show these two vectors, they would completely describe the DG tensor. This representation would be somewhat similar to the "cross-bars" visualization commonly used in engineering software for the stress tensor, wherein the tensor field is shown using periodically cross-bars---very convenient if the grid is regular and uniform and has square elements.
</p>
<p>
Notice a salient difference, however. Since the DG tensor is <em>asymmetric</em>, the two vectors will not in general lie at right-angles to each other. The latter is the case only with the symmetric tensors such as the strain and stress tensors.
</p>
<p>
My question is this: Do you see any issues with this kind of visualization for the DG tensor? Is there any loss of generality by following this scheme of visualization? I mean, I read some literature on visualization of asymmetric tensors, and noticed that they sometimes worry about the eigenvalues being complex, not real. I think that complex eigenvalues would not be a consideration for the above kind of depiction of the DG tensor---the rotation part will be separately shown in a separate window anyway. But, still, I wanted to have the generality aspect cross-checked. Hence this post. Am I missing something? assuming too much? What are the other things, if any, that I need to consider? Also: Would you be "intuitively" comfortable with this scheme? Can you think of or suggest any alternatives?
</p>
<p>
Comments are welcome.
</p>
<p>
--Ajit
</p>
<p>
[E&OE]
</p>
</div></div></div>Mon, 25 Oct 2010 08:06:29 +0000Ajit R. Jadhav9159 at https://www.imechanica.orghttps://www.imechanica.org/node/9159#commentshttps://www.imechanica.org/crss/node/9159Mohr's Circle---When Was the Last Time You Used It in Your Professional Engineering Work?
https://www.imechanica.org/node/8341
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/131">stress</a></div><div class="field-item odd"><a href="/taxonomy/term/132">strain</a></div><div class="field-item even"><a href="/taxonomy/term/846">FEM</a></div><div class="field-item odd"><a href="/taxonomy/term/5261">Mohr's Circle</a></div><div class="field-item even"><a href="/taxonomy/term/5262">Tensor Visualization</a></div><div class="field-item odd"><a href="/taxonomy/term/5263">Visualization</a></div><div class="field-item even"><a href="/taxonomy/term/5264">Post-Processor</a></div><div class="field-item odd"><a href="/taxonomy/term/5265">Professional Engineering</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
As a consultant in computational mechanics, I currently help write some FEM-related code, and while doing this job, an episode from a recent past came to my mind. Let me go right on to the technical issue, keeping aside the (not so good) particulars of that episode. (In case you are curious: it happened outside of my current job, during a job interview.)</p>
<p>If you are a design engineer, FE analyst, researcher, or any professional dealing with stress analysis in your work, I seek answers to a couple of questions from you:</p>
<p>
<strong>Question 1:<br />
</strong>
</p>
<p>
When was the last time you used Mohr's circle of strain/stress in your professional work? Was it a week ago? a month? a year? five years? ten years? longer? In what kind of an application or research context?</p>
<p>Please note, I do not mean to ask whether you directly or indirectly used the coordinate transformation equations---the basis for constructing Mohr's circle---to find the principal quantities. The question is: whether you spoke of Mohr's circle itself---and not of the transformation equations---in a direct manner, in a professional activity of yours (apart from teaching Mohr's circles). In other words, whether, in the late 20th and early 21st century, there was any occasion to plot the circle (by hand or using a software) in the practice of engineering, did it directly illuminate something/anything in your work.</p>
<p>In case you are curious, my own answer to this question is: No, never. I would like to know yours.
</p>
<p>
<br />
<strong>Question 2:<br />
</strong>
</p>
<p>
The second question just pursues one of the lines indicated in the first.</p>
<p>In a modern FEM postprocessor, visualizations of stress/strain patterns are provided, usually via field plots and contour lines.</p>
<p>For instance, they show field plots of individual stress tensor components, one at a time.</p>
<p>Recently, there also have been some attempts to try to directly show tensor quantities in full directly, via systematically arranged ellipsoids of appropriate sizes and orientations. The view you get is in a way analogous to the arrow plots for visualizing vector fields in those CFD and EM software packages. Other techniques for tensor visualization are not, IMHO, as successful as the ellipsoids. Mostly, all such techniques still are at the research stage and have not yet made to the commercial offerings.</p>
<p>Some convenience can be had by showing some scalar measures of the tensors such as the von Mises measure, in the usual field/contour plots.</p>
<p>The questions here are:</p>
<p><strong>(2.a)</strong> Would you like to see an ellipsoids kind of visualization in your engineering FEM software? If yes, would this feature be a "killer" one? Would you consider it to be a decisive kind of advantage?
</p>
<p>
<strong>(2.b)</strong> Would a simpler, colored cross-bars kind of visualization do? That is, two arrows aligned with the principal directions. The colors and the lengths of the arrows help ascertain the strength of the principal quantities.
</p>
<p>
<strong>(2.c)</strong> Would you like to see Mohr's circles being drawn for visualization or any other purposes in such a context? If yes, please indicate the specific way in which it would help you.</p>
<p>My own answers to question 2 are: (a) Ellipsoids would be "nice to have" but not "killer." I wouldn't be very insistent on them. Having them is not a decisive adavantage. (b) For 2D, this feature should be provided. (c) Not at all.</p>
<p>Please note, the questions are directed rather at experienced professionals, even engineering managers, but not so much at students as such. The reason is that the ability to buy is an important consideration here, apart from the willingness. Of course, experienced or advanced PhD students and post-docs may also feel free to share their experiences, thoughts and expectations.</p>
<p>Thanks in advance for your comments.</p>
<p>PS: Also posted in my other, personal blog here [<a href="http://ajitjadhav.wordpress.com/2010/06/03/mohrs-circle-when-was-the-last-time-you-used-it-in-your-professional-engineering-work/" target="_blank">^</a>]
</p>
<p>
[E&OE]
</p>
</div></div></div>Thu, 03 Jun 2010 17:01:13 +0000Ajit R. Jadhav8341 at https://www.imechanica.orghttps://www.imechanica.org/node/8341#commentshttps://www.imechanica.org/crss/node/8341