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Ajit R. Jadhav's blog

Just talking to another mechanician...

Dear Zhigang,

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.

Just noting, for the time being,

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,

or,

I presented my new theory of QM yesterday

I presented my new theory of QM yesterday.

Just that.

Best,

--Ajit

 

Request to physicists: Would you be willing to provide some informal feedback on my new approach to QM?

I have a request to make to physicists: Would they be willing to provide some informal feedback on my new approach to QM?

Update (2021.09.21 15:57 IST): 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:

Looking for Head -Marketing and Communication for MNC in Pune

Today, I received this email from some one at Neptune consultants in Pune [^], through Naukri.com [^].

The Machine Learning as an Expert System

1.

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.

I am sure that people must have written articles expressing this view. However, simple googling didn’t get me to any useful material.

I would deeply appreciate it if someone could please point out references in this direction. Thanks in advance.

2.

A preliminary document on my fresh new approach to QM

Hello, World

Here is a document that jots down, in a brief, point-wise manner, the elements of my new approach to understanding quantum mechanics.

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.

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.

Stress is defined as the quantity equal to ... what?

In introducing the very concept of the stress tensor to the beginning student, text-books always present only indirect relations involving the concept. Thus, you have the relations like "traction = (stress-transposed)(unit normal)" (i.e. Cauchy's formula, for uniform stress), or the relations for the coordinate transformations of the stress tensor, or the divergence theorem (for non-uniform stress). These are immediately followed or interspersed with alternative notations, and the rules for using them.

But what you never ever get to see, in text-books or references, is this: a *direct* definition of the stress tensor, i.e. an equation in which there is only the stress tensor on the left hand-side, and some expression involving some *other* quantities on right hand-side. Why? What possibly could be the conceptual and pedagogical advantages of giving a direct definition of this kind, and its physical meaning? I would like to ponder on these matters here, giving my answers to these and similar questions in the process.

Also remember Alcoa

Also remember Alcoa.

Yes I know about the [essentials of] QM!

Check out here [at my personal blog] [^] and the post before that.

---

Have a happy holiday season!

---

Sincerely,

--Ajit

 

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.

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.

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]

Any tips/comments regarding the latest version of the C++ library: Eigen (v. 3.0)?

Hi all,

1. A new version of Eigen (v 3.0 now) is out (on March 23, 2011), and it seems promising. First, a few links:

The main page for the project is here: [^]. The page for v.3.0 is here: [^]. It seems to be very fast: [^].

Open House: Can you define FEM in one line?

Can you define FEM in one line?

If yes, what would it be? And, in that case, permit me a second question: How?

 

...Really interested in knowing what the members of this community think (of this matter), if they do...

 

--Ajit

[E&OE]

 

What would you like for an undergraduate book on QM to explain to you?

 

1. Background:

A couple of things concerning books happened recently, in the last week or two.

(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.

How about having a special Mechanics Gallery here?

Here is an idea I submit for consideration by all iMechanicians, but esp. so by the admins and moderators. Discussion is welcome.

 

Idea: Why not have a Mechanics Gallery section here?

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.

How to supply a visualization for the displacement gradient tensor

Hi all, 

[Warning: The writing is long, as is usually the case with my posts :)]

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.

Mohr's Circle---When Was the Last Time You Used It in Your Professional Engineering Work?

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.)

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:

Question 1:

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