Questions related to mathematical physics which include application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories

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1answer
1k views

What does the little d and d^2 mean in equations?

I'm reading a text on ray tracing. There is this section about radiometric quantities where radiance is defined as $L = \frac{d^2\Phi}{dA cos\Theta d\omega}$ $\Phi$ is the radiant flux $\Theta$ is ...
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3answers
551 views

Scale Operator $Uf(x)=f(kx)$

I am looking for an operator $U$, that can do this to a function: $$Uf(x)=f(2x).$$ In particular I am happy if there is an $U$ for the general case: $Uf(x)=f(kx)$. Does such an operator exist for ...
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vote
1answer
125 views

Continuum limit of (DE) equation

I have a system described an equation, and I want to find an (DE) equation for z(x,t), in the limit as l->0. First some definitions to simplify it some: $Z1=z(x,t)-z(x+l,t)$ $Z2=z(x,t)-z(x-l,t)$ ...
0
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1answer
427 views

Is it possible to calculate an angle of movement from the horizontal from accelerometer and magnetometer data?

I have a home made device (think baseball) with an accelerometer and a magnetometer embedded within it and would like to capture some details of an attempted 'throw' of the device. All I need is the ...
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7answers
3k views

Books to learn physics, being a math major

What books would you recommend to learn physics, being a a Math major, from classical mechanics, electricity, etc. to modern physics?
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2answers
183 views

sum of N light sources

[sorry for the bad English] I am fond of astronomy and environment. I want to try to make a "light pollution map" but I haven't my satellites... so I use as approximation of light pollution the ...
3
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1answer
655 views

Why does acceleration = $v\frac{dv}{dx}$

If we define $x$ = displacement, $v$ = velocity and $a$ = acceleration then I am used to the ideas that $a= \frac{dv}{dt} = \frac{d^2x}{dt^2}$ However I also understand $a=v \frac{dv}{dx}$. Can ...
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2answers
725 views

Newtonian Physics: ball A is dropped, ball B is thrown - where do they coincide?

I'm doing a physics course in my spare time and the problem set is: Ball A is dropped from rest from a building of height H exactly as ball B is thrown up vertically from the ground. When they ...
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2answers
196 views

Vector Force Fields and Their Physical Interpretations

The vector force field F=(yi,-xj) has a curl of -2. The acceleration of a particle in space is given by: ax=y/m ay=-x/m This vector field has a divergence of 0. Will particles in this vector FORCE ...
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9answers
16k views

What is the meaning of the third derivative of a function at a point

(Originally asked on MO by AJAY.) What is the geometric, physical, or other meaning of the third derivative of a function at a point? If you have interesting things to say about the meaning of the ...
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1answer
402 views

Complexifying representations

Let me try to split the question in a few parts, I would like to understand the claim that all non-degenerate bilinear symmetric forms are equivalent over the complex while for the reals they can be ...
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2answers
498 views

sl(2,C) and the harmonic oscillator

I've been studying the finite-dimensional representations of the lie algebra sl(2,C). I've read that these representations are related to the harmonic oscillator and the associated raising and ...
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3answers
525 views

Fourier analysis for waves

I'm studying physics, so I'm sorry if I'll write some inexact things in this post. I wish you can understand me. If we have 1D wave equation: $$\frac{\partial^2 \psi}{\partial ...
15
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4answers
2k views

Why does dust gather in corners?

I've noticed when sweeping the floor that dust gathers particularly in the corners. I assume there is a fluid mechanics reason for this. Does anyone know what it is? Edit: No, really, this is a ...
14
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2answers
3k views

What is the resistance between two points a knights move away on a infinite grid of 1-ohm resistors

On an infinite grid of ideal one-ohm resistors, what's the equivalant resistance between two nodes a knights move away? (please fix the tags, I didn't really know where to put it)
2
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1answer
264 views

Temporal aberration. Shape of telescope mirror large enough that light transit time is significant

Suppose a parabolic mirror of a telescope is large enough (or equivalently that the camera exposure time is short enough) that you need to take into account the transit time of the light signal from ...
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4answers
3k views

Given a radius and velocity calculate position of an aircraft banking to make a turn

I have a radius, R, for an aircraft traveling at velocity, V. If we start at point, (X,Y), ...
0
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1answer
368 views

Calculation of G force

I have a formula which is G-force = velocity*omega/9.8. Omega is the angular velocity. I've seen on the internet that G force is actually acceleration/9.8. I'm confused as to which formula is correct. ...
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3answers
384 views

Summing divergent series based on physics

Solving a heat equation with central symmetry i got the following result: The problem is to find a sphere center temperature vs. time given that the surface of the sphere is kept constant at $$T_1$$ ...
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2answers
886 views

two-body problem circular orbits

I've been trying to google the answer to this question, but have had no luck, so I'm asking this question here. Let's say the origin is at (0, 0), body 1 with mass m1 is at (-r1, 0), and body 2 with ...
2
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3answers
3k views

Probability concerning unfair dice with N sides

Fair warning: I am not a math expert (that's why I'm here). I would like to be able to calculate the probability of rolling a certain side on a die with n sides where any number of those sides has an ...
0
votes
1answer
191 views

slipping rod on moving truck

we have a truck in our game we have a rod against the wall of that truck, and we know the acceleration of truck when the rod start slipping... we just want to know what is acceleration of rod when it ...
2
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1answer
1k views

Dirac's identity

Do somebody knows anything about the Dirac's identity? \begin{equation} \label{Dirac} \frac{\partial^2}{\partial x_{\mu}\partial x^{\mu}} \delta(xb_{\mu}xb^{\mu}) = -4\pi ...
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2answers
709 views

What is the optimal angle when throwing a stone on a slope?

The question what-is-the-optimum-angle-of-projection-when-throwing-a-stone-off-a-cliff was asked and answered a while back. This one has a much cleaner answer. Now you are on a uniform slope, a line ...
8
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0answers
237 views

What are D-branes (in a topological field theory)?

In the past couple years, I've read many words pertaining to D-branes without feeling I have really comprehended them. In broad terms, I think I get what they're about: They're supposed to serve as ...
0
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1answer
598 views

If a bead is suspended by 2 strings, one vertical, the other diagonally, why are the tensions equal?

I have a text book which gives two diagrams of beads suspended from strings with different angles, and worked examples to calculate the tension in the strings. The first bead is suspended by 2 ...
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2answers
580 views

Feynman's vector potential

I'd like to understand the physical meaning of the Feynman's vector potential definition: $$ A_{m}^{(b)}(x) = e_b \int \delta (xb_{\mu}xb^{\mu})db_m(b), \qquad m=0,1,2,3 $$ (component m of the ...
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2answers
342 views

Equation of a mirror

So let's say you have a curved mirror, $y=y(x)$ with this property: Whenever a ray of light emanates from the origin, it reflects parallel to the x axis. Find the equation of the mirror.
3
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1answer
177 views

Characterising a function involving the max and min of other functions

Given $n$ smooth real functions $f_1, f_2, \dots, f_n$, define a composite function like this: $$f(x) = \max(f_1(x), f_2(x), \dots, f_n(x)) - \min(f_1(x), f_2(x), \dots, f_n(x))$$ Is it possible to ...
7
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2answers
1k views

Do Vector Calculus Cartesian coordinates identities with Div, Grad, Curl hold in cylindrical and spherical coordinates?

These operators are written in different forms in Cartesian, cylindrical and spherical coordinates. For instance, in spherical coordinate system, one has $$\nabla \cdot ...
2
votes
1answer
134 views

about homological mirror symmetry

why in homological mirror symmetry, we restrict us to a projective variety (calabi-yau)? Because in physics we don't need this condition. What's the general picture for general calabi-yau?
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0answers
154 views

How do physicists compute path integrals in Chern-Simons theory?

The space of connection has no measure right?
3
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1answer
195 views

What does “Gromov Witten potential” the “potential” mean

"Gromov Witten potential", when does "potential" mean here? What does the whole thing mean in physics? Thanks!
0
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1answer
264 views

Why $ \int{\rho}dV = \frac{1}{c} \int{j^0}dV = \frac{1}{c} \int{j^i}dS_i $?

I'd like to understand why $ \int{\rho}dV = \frac{1}{c} \int{j^0}dV = \frac{1}{c} \int{j^i}dS_i $ (the second equality), where $j^i = \rho \frac{dx^i}{dt} $ is the current density 4-vector ...
6
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1answer
764 views

Fitting a parameter dependent matrix to its eigenvalues

The essence of my question is, if I have a Hermitian matrix that is linearly dependent on a set of parameters and I have an estimate of its eigenvalues, is there a "simple" way to determine the values ...
2
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1answer
325 views

Dimensional Analysis

Can anyone explain how to do these types of questions for me? I am having trouble wrapping my head around it. Thanks. A spherical soap bubble is seen to undergo oscillations when slightly deformed. ...
2
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1answer
445 views

Why do we need to study mathematical aspects of quantum field theory, especially axiomatic picture

What is the usefulness in mathematics, I know it can provide topological invariants, any other things?
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1answer
603 views

Physics: Calculating the Forces Needed from an Angle and a Force

This is probably a very simple question to all of you, but I have never taken a physics class, so I am lost for what I need to do for a programming problem. I will need to specify a force by inputting ...
11
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4answers
307 views

Distributions of point charges

Problem $N$ point charges are distributed in the unit ball in $\mathbb{R}^k$, $k=2,3$. Given locations of the particles $x_1,\ldots,x_N$ the potential energy is $E=\sum_{j=1}^{N-1}\sum_{k=j+1}^N ...
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0answers
214 views

What categorical mathematical structure(s) best describe the space of “localized events” in “relational quantum mechanics”?

In a recent (and to me, very beautiful) paper, entitled "Relational EPR", Smerlak and Rovelli present a way of thinking about EPR which relies upon Rovelli's previously published work on relational ...
6
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1answer
821 views

How can angular velocity or angular momentum be a vector?

Rotations in 3 dimensions are not commutative; however they are in the plane. In classical mechanics, are we allowed to say that angular momentum is a vector because particles only rotate along a ...
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3answers
996 views

Pendulum with moving pivot

I'm making a game which you can see here, if you are on Windows or Linux: http://insertnamehere.org/birdsofprey/ If you click and hold your mouse on a bird, you can see I'm just swinging the bird ...
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2answers
385 views

How is moduli of curves relevant in physics?

From: http://en.wikipedia.org/wiki/Moduli_space we see that moduli of curves is a very algebro-geometric topic. It is easy to understand its relevance and importance in algebraic geometry. But the ...
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4answers
3k views

Can this gravitational field differential equation be solved, or does it not show what I intended?

This is the equation I'm having trouble with: $G \frac{M m}{r^2} = m \frac{d^2 r}{dt^2}$ That's the non-vector form of the universal law of gravitation on the left and Newton's second law of motion ...
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1answer
642 views

Center of mass of an $n$-hemisphere

Related to this question. Note that I'm using the geometer definition of an $n$-sphere of radius $r$, i.e.$ \{ x \in \mathbb{R}^n : \|x\|_2 = r \} $ Suppose I have an $n$-sphere centered at $\bf 0$ ...
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0answers
119 views

Analysing an optics model in discrete and continuous forms

A discrete one-dimensional model of optical imaging looks like this: $$I(r) = \sum_i e_i P(r - r_i)$$ Here, the $e_i$ are point light sources at locations $r_i$ in the object and $P$ is a point ...
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1answer
613 views

Using differential equations to graph velocity over time of a falling object subject to wind resistance

Wind resistance -- upwards acceleration, typically varies either linearly or quadratically by the current velocity. There is a constant downward acceleration due to gravity. How can we model the ...
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2answers
2k views

Finding Moment of Inertia (rotional inertia?) $I$ using integration?

I just came back from my Introduction to Rotational Kinematics class, and one of the important concepts they described was Rotational Inertia, or Moment of Inertia. It's basically the equivalent of ...
92
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8answers
6k views

Importance of Representation Theory

Representation theory is a subject I want to like (it can be fun finding the representations of a group), but it's hard for me to see it as a subject that arises naturally or why it is important. I ...
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2answers
4k views

What is the optimum angle of projection when throwing a stone off a cliff?

You are standing on a cliff at a height $h$ above the sea. You are capable of throwing a stone with velocity $v$ at any angle $a$ between horizontal and vertical. What is the value of $a$ when the ...