Interesting Definition and 790 Threads

Hi all, I've come across an interesting matrix identity in my work. I'll define the NxN matrix as S_{ij} = 2^{-(2N - i - j + 1)} \frac{(2N - i - j)!}{(N-i)!(N-j)!}. I find numerically that \sum_{i,j=1}^N S^{-1}_{ij} = 2N, (the sum is over the elements of the matrix inverse). In fact, I...

You can see the effect around minute 1:20 in this video. It seems to me that the un-twist of the elastic band and the rotation of the ball about the line that joins them is what keep the constant the initial zero angular momentum, though I can't tell for sure. The inversion of in the...

132g/ml 870g/mol 2-propanol acetate

I've lately been interested in series and how they converge to interesting values. It's always interesting to see how they end up adding up to something involving pi or e or some other unexpected solution. I learned about the Leibniz formula back in college : pi/4 = 1/1-1/3+1/5-1/7+1/9-... and...

For all you solar astronomers out there An interesting new article from Emily Mason at the NASA’s Goddard Space Flight Centre in Greenbelt, Maryland continue reading at ... https://www.nasa.gov/feature/goddard/2019/unexpected-rain-on-sun-links-two-solar-mysteriesDave

I found these timelines on the Computer History Museum which are quite interesting to checkout: https://www.computerhistory.org/timeline/ai-robotics/ For me, it brought back memories of machines long past. They even mentioned the construction of my robot persona for the Forbidden Planet...

I'm an undergraduate student and thinking of doing a research in plasma physics. Any suggestion? I prefer to do it computationally. Most research topic in plasma physics I googled are about fusion, but do you think it's too advanced for my education level?

Hello all, I have recently moved house, and it's something of a downsize. as a result, we are struggling to fit everything in that we have been accustomed to having. I am embracing this downsize as a chance to throw some ideas around for space-saving furniture etc., as a bit of practice as I...

Homework Statement Suppose we have an isolated, long, narrow straight wire with low electrical resistivity. A constant current ##I## is sent through this wire. We know that if an electron is sent on a path which is perpendicular to the wire, towards it, with an initial speed ##v_0##, and the...

Hello, I'm a Ph.D. student of Astrophysics and I would like to expand my horizons in this field. The best is probably to read papers around. I don't mean just new ones. But how to effectively find papers from my field when there are so many papers for example at https://arxiv.org/ or...

Thought you all might be interested in this article. It could just be hype, but there also might be something deeper to it. You hear of so many schemes of tying together quantum mechanics with a relativistic understanding of gravity, that it's easy to respond to yet another announcement like...

2019 is the smallest number that can be expressed as sum of 3 squares of prime number in 6 different ways 2019 = $7^2+11^2+43^2$ = $7^2 + 17^2 + 41^2$ = $13^2+13^2 + 41^2$ = $11^2+23^2+37^2$ = $17^2 + 19^2 + 37^2$ =$ 23^2+23^2+31^2$

Homework Statement Three ants A, B and C are crawling on a large horizontal tabletop always occupying vertices of an equilateral triangle, size of which may vary with time. If at an instant, speeds of A and B are vA and vB, prove that vC>= vA+vB. Homework Equations Well, that's what I don't...

I've recently viewed a bunch of YouTube videos by mustie1. Here's one, in which he repairs an old generator that hasn't run for years -- In other videos that I've seen, he takes mopeds, motorcycles, and a variety of things with small engines, and gets them running, even some with frozen...

What are some interesting topics in the field of material fracture and deformation? Maybe a newer area of research?

https://arxiv.org/abs/1808.00659 Popular version: https://techxplore.com/news/2018-08-defensive-technique-software-buggier.html The basic idea here is to create a large number of non-exploitable bugs, then add them to existing code. Do not worry as much about remediating existing bugs. The...

While I was was numerically integrating the magnetic field caused by an infinite array of magnetic moments, I observed the interesting limit ( limit (1) in the image). It may seem difficult to prove it mathematically but from the physics point of view, I think it can be proved relatively...

Hi, maybe as you know ##\nabla. J = -\frac {\partial p} {\partial t}## where J is current density p is charge density. But also we know current density flux outward the circuit is 0 because current density does not flow out of circuit an this actually volume integral of ##\nabla. J## is zero (...

Prove that, $$\int_{0}^{\pi/2}\ln^2\left(\ln^2 (\sin x)\over \pi^2+\ln^2 (\sin x)\right){\mathrm dx\over \tan x}=\color{blue}{(2\pi)^2\ln 2}$$

Pi day is tomorrow! 3.14! What is your most interesting fact or insight about the number Pi?

I really love seeing derivations of the EFE's, Maxwell's equations, Schrodinger equation etc. I have seen a number of derivations of Maxwell's Equations but this is the shortest, most illuminating and best I have come across - it basically just uses covarience - and as it says - a little bit...

I want to do tricky physics and maths questions that require only A-level knowledge of maths and physics to solve. Questions that don't have a straightforward answer and will help me to develop my logic and problem-solving skills. I'm looking books, online resources and etc.

Hi, I'm doing my third year project on diffraction gratings and patterns and analysaing them via computer software and Fourier transforms. I'm going to design my diffraction gratings this week and then create them via taking a picture with a disposable camera and using the negative film. What...

I came across this article about using Pandas in Python to read in a multi-tab spreadsheet to Python, and work with the data then write back to an Excel spreadsheet...

Hi there, I'm looking for some interesting activities regarding nuclear physics in high school. I already have: - building a cloud chamber with dry ice or peltier modules - simulating radioactive decay with dice - simulating Rutherford's experiment hitting with glass marbles a hidden target...

Hi, I found this rather interesting article on gravity and the zero point energy. Here is the link and abstract Abstract When Planck introduced the 1/2 hv term to his 1911 black body equation he showed that there is a residual energy remaining at zero degree K after all thermal energy ceased...

I've seen many people who is studying it.. but why ? is there any contributions to physics at a foundamentalist level ? I mean, the properties of matter inside nêutron stars is the interesting part to theoretical physics and not the whole object right ?

This video came up in a Private Conversation I was having with @Grands recently. The level of sophistication and precision of this production line is amazing to me. Thinking about all of the design work and experimentation and fabrication work and optimization that went into it... :smile:

and it is free (legal) Quantum Mechanics for Engineers by Dommelen

Homework Statement Can anyone please give me hard and interesting problems regarding fluid mechanics problems such as hydrostatic and air prssure bouyance force and Bernoullis equation(Bernoullis equation problems only for liquids)? I tried looking for them but the ones I found were quite...

Hi, This looked interesting. Determinant and Linear-Algebraic aspects of Sudoku puzzles: http://www.student.montefiore.ulg.ac.be/~merciadri/docs/papers/sudoku.pdf

http://www.tandfonline.com/doi/full/10.1080/00295450.2017.1384269 According to this paper, two nuclear explosions and one steam explosion took place.

The mirror that I'm talking of, is situated in Hazarduari Palace in Murshidabad, West Bengal, India. This place was once the capital of Bengal under the Nawab before the British defeated the Nawab in the historic battle of Plassey, 1757. The history is not that important here, but the mirror...

https://www.theguardian.com/science/2017/aug/24/mathematical-secrets-of-ancient-tablet-unlocked-after-nearly-a-century-of-study <Moderator's note: link corrected, Article intro added>

A^p - B^p - C^p = A - B - C With p > 1 this appears to occur only when p = 5: A = 17: B = 16 : C = 13 A^p - B^p - C^p = D^p - E^p - F^p = G^p - H^p - I^p = Y A,B,C = 3,2,1...

https://www.amazon.com/dp/0521592100/?tag=pfamazon01-20 Yes, this is the same Shankar who wrote the QM book. It is not a pure QFT introduction like his QM book but seems more like QFT's application too Condensed matter.

I rather like Terry Tao, not only because he is Australian, a great mathematician, maybe even the greatest currently living, whose contributions range across a wide gamut of areas including QM (which interestingly he actually failed at university - but that is a story of bad study habits for...

http://www.sciencemag.org/careers/2017/06/gres-dont-predict-grad-school-success-what-does To me these results are in no way surprising; although I do wonder if you would see a difference if you compared theory vs experimental PhDs; I''ve come across some students that were clearly very clever...

Hey Everyone, My name is James, and I am a 2nd year University student. I'm switching my major to Engineering, and I am beginning to study physics (as a pre-requisite), and I love it! I think I would like to study materials engineering ... my mind may change as I keep studying). however, right...

Hey, is this patent legit? Does anyone know anything more about this? The information I can found about the 'TR-3B' are from non reliable / verifiable sources << Unreliable Source Deleted by Mentors >>

Homework Statement HI! I'm in need of some help to come with an interesting physics-related topic for a short, five-minute presentation. We'll be graded by our ability to speak well rather than our physics knowledge, so I want to talk about something simple, straight-to-the-point and not too...

Som news outlets are reporting a potential solution to the cosmological constant problem: https://arxiv.org/pdf/1703.00543.pdf opinions on this paper are much appreciated.

I'm opening this thread for discussion on the latest debate over inflationary cosmology as outlined over at scientific american the original article on inflation was Scientific American published an article by Ijjas, Steinhardt and Loeb https://www.cfa.harvard.edu/~loeb/sciam3.pdf then a...

I'm looking for some non-big project related to physics or/and abstract math. It firstly should be a good programming task(since its my programming credit) Bachelor student in theoretical physics. Not bad at C and Python, a bit of C++ and Haskell. Interested in field theory, quantum stuff, diff...

Hi all, I was doing some math and I stumbled upon a very interesting thing. When I do ln(-1), I get πi, and when I turn that into polar coordinates on the calculator, it gives me πeiπ/2 . Why is that? I'm very curious to know, because they are so intertwined! Thank you

This suggests to me that the early universe did not contain as much dark matter. Is this correct? If so it might give a clue what D.M actually is? http://www.space.com/36083-dark-matter-minor-ingredient-of-early-galaxies.html

Which Scientific Discovery (that you've experienced during your life) has been the most interesting or surprising to you, based on your prior knowledge? And why?

While cleaning out an old house I found this book. I have later (much) copies of this book that I often refer to. A little mouse chewed but nonetheless a nifty find. Was amused there is a chapter on knob and tube wiring. - -

I'm currently a junior in high school, and I'm really interested in physics, especially particle physics and quantum mechanics. At my school, everybody needs to do a big senior project to graduate, involving multiple papers and about 30 hours of work, usually to build something or organize a...