Yes I know about the [essentials of] QM!
Check out here [at my personal blog] [^] and the post before that.
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Have a happy holiday season!
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Sincerely,
--Ajit
Ajit R. Jadhav's blog
A ``small'' but interesting riddle from the theory of vibrations
A ``small'' but interesting riddle from the basic theory of vibrations. Haven't run into it in any physics/classical mechanics text/reference.
Explicit vs. implicit FDM: Could you please suggest a reference?
The context is the finite difference modeling (FDM) of the transient diffusion equation (the linear one: $\dfrac{\partial T}{\partial t} = \alpha \dfrac{\partial^2 T}{\partial x^2}$).
Two approaches are available for modeling the evolution of $T$ in time: (i) explicit and (ii) implicit (e.g., the Crank-Nicolson method).
It was obvious to me that the explicit approach has a local (or compact) support whereas the implicit approach has a global support.
Expansion of a function into a basis set
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 am [still] confused about gradients, vectors, deformation gradient, etc.
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 [^]. In particular, I realized my confusions after writing this comment [^] there.
MWR for the first- and third-order differential equations
Hi all,
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.
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?
Those were not waves: A bit historical re. Huygens' principle
A few points that might be of general interest:
1. The dates: 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.
Journals in Physics and Engineering, and Preprint Servers Like arXiv
Hi all,
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.
What would you choose as the Top 5 Equations? Top 10?
Equations are of central importance in all of science and engineering, but especially so in mechanics.
An interesting arXiv paper: "Precession optomechanics"
Hi all,
Just thought that the following paper archived at the arXiv yesterday could be of general interest to any mechanician:
Xingyu Zhang, Matthew Tomes, Tal Carmon (2011) "Precession optomechanics," arXiv:1104.4839 [^]
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.
--Ajit
[E&OE]