# All Questions

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### How to discover the $F = m\cdot a$ equation from scratch? [duplicate]

Is there a paper or a book that conceptually 'discover' the Newton's famous formula? I've been thinking about this equation, and I really don't know it for sure. Did Newton empirically noticed that ...
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### Association of financial phenomena/indications with the conservation laws of Black Scholes equation

For a while I've been doing research on methods of obtaining conservation laws via the symmetries of differential equations (DEs). I'm presently doing research on identifying financial ...
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### Why must a singularity form inside a black hole? [duplicate]

What is the exact reason that normal matter can not exist within an event horizon? I can understand how a super-dense object like a neutron star could accrete mass until its physical radius is less ...
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### Dipole charge attractions while one of them is turning around other [closed]

There is a electric dipole which is fixed. So angular momentum isn't conserved. And there is charge $Q$ which has initial velocity $u$. My question is: What is the tangential velocity of the charge ...
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### What's the critical temperature of the XY model on a triangular lattice

I've been looking deeply into many bibliographic references without finding the answer. I would be interested in knowing the numerical value of the critical 2d XY spin model on triangular lattice. ...
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### Proof of the conservation of the energy functional for the Gross-Pitaevskii equation?

From the Gross-Pitaevskii equation $$i\hbar\frac{\partial\psi}{\partial t}=\left(-\frac{\hbar^2}{2m}\nabla^2+V+g|\psi|^2\right)\psi$$ using the variational relation ...
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### Will a blanket warm you if you are underwater?

Suppose a man falls into very cold water and gets their foot stuck under a heavy rock. Fortunately, his head is above water and someone is able to call for help. The paramedics want to keep him warm ...
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I was taught today that the Electromagnetic wave Theory is unable to explain black body radiation. The example that was given to me: When a metal is heated, it emits different frequencies of light as ...
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### What is different in representation?

I'm sorry if this is somewhat a dumb question. First: "Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear ...
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### Existence and uniqueness of solutions to $\nabla^a T_{ab}$ in general (or special) relativity

The equation in the title of this question can be a relativistic analogue of the Navier-Stokes equation (in the sense that, in the low-velocity limit, it reduces to Euler's equation when $T_{ab}$ is ...
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### Gravitational collapse of a photon cloud

The Schwarzschild solution shows that a spherically symmetric, static fluid will undergo gravitational collapse if too much mass-energy is concentrated together (i.e. if the fluid's radius is less ...
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### Why does a mirror reverse polarization of circularly polarised light?

A glass mirror (with metal backing layer) will reverse the polarisation of circularly polarised light upon reflection. A polished piece of metal will also reverse the polarisation of circularly ...
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### Specific Internal Energy Decreases with Increasing Pressure?

I was looking at "Properties of Compressed Liquid Water" (Table A-5) in Fundamentals of Engineering Thermodynamics by Moran. Table A-5 shows that the specific internal energy $u$ of compressed liquid ...
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### Leg Press & Actual Lifted Weight [duplicate]

I was doing leg press at the gym today and was curious how much weight I actually lift when I do the exercise as compared to when I do a squat. Suppose I load $w_L$ onto the machine, which has an ...