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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2
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0answers
4 views

Dipole-Coupling Tensor: Electrostatic Dipole Moments

I've been struggling with this problem today. Here's an image of the question I'm attempting to answer. I'm relatively new to tensor algebra (I've been studying it for about a week or two), and I've ...
-2
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0answers
24 views

How is Mathematics and Space related?

I've seen scientists come up with equations and proofs in mathematics of some incident happened or happening in space. How do they relate mathematics with that? For Example How do you start ...
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0answers
32 views

Relationship between Möbius transformations and flows/vector fields

I've noticed that the pictures illustrating the effect of Möbius transformations on the Riemann sphere (after stereographic projection to the plane) resemble the phase portrait of a vector field. For ...
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0answers
33 views

Basic physics question about calculating resistance [on hold]

Why is the total resistance calculated differently when resistors are in parallel, compared to when they are in a series? For example, $$ \dfrac{1}{R_t} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \ldots + ...
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0answers
14 views

divergence theorem with singularity at r = 0

I am trying to evaluate the volume integral given by \begin{align} \int_V [\nabla(\vec{x} \cdot \vec{u}) - \nabla \cdot (\vec{x}\vec{a})] dV \end{align} where $\vec{x}$ is the position vector and ...
8
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4answers
695 views

Derivation of the Boltzmann factor in statistical mechanics

I have seen similar derivation of the Boltzmann factor many times before, (http://micro.stanford.edu/~caiwei/me334/Chap8_Canonical_Ensemble_v04.pdf , just for example), which I think is incomplete. ...
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2answers
12 views

Calculating quantities with regards to a pendulum

The set up is a pendulum of length 2m with a mass on the end at 0.5kg. The mass is released at a small initial angle of 6 degrees moving into harmonic motion. I need to calculate the angular ...
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0answers
31 views
+50

Davenport's Q-method (Finding an orientation matching a set of point samples)

I have an initial set of 3D positions that form a shape. After letting them move independently, my goal is to find the best rotation of the original configuration to try to match the current state. ...
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0answers
31 views

Uniform current in cylinder and straight wire causing same magnetic field?

The tridimensional version of the Biot-Savart law says that the magnetic field generated at the point $\boldsymbol{r}\in\mathbb{R}^3$ by a tridimensional distribution of current defined by the current ...
5
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1answer
2k views

Riemann, Ricci curvature tensor and Ricci scalar of the n dimensional sphere

I am calculating the Riemann curvature tensor, Ricci curvature tensor, and Ricci scalar of the n sphere $x_0^2 + x_1^2 + ....+x_n^2=R^2$, whose metric is $$ds^2=R^2(d\phi_1^2 + \sin{\phi_1}^2 ...
4
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1answer
311 views

Solving laplace's equation for an inviscid and incompresible fluid

Background I'm working on a 2D inviscid, incompressible fluid sim using vortex methods (that is, treating vortex as discrete particles), and I'm trying to (numerically) solve the no-through boundary ...
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1answer
21 views

two dimensional heat equation

Please I really need some help for this exercise, I can't solve it for any ways... I need to prove the maximum principle for the two dimensional heat equation with zero boundary data. Really I need ...
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0answers
31 views

Math / Physics - Curcular motion [closed]

What is the maximum speed a car can turn a 50m radius corner if the corner is banked at 15 degrees and has a coefficient of friction of 0.3?
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0answers
9 views

Relationship Between two trays with different weights on an analog scale

If I have an analog scale sitting on a table, how would I determine the distance that one tray will drop if it is heavier than the other. Alternatively, how would I determine the weight based on the ...
0
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0answers
8 views

Error propagation in complex formula

I'm currently trying to use error propagation formulae to calculate an estimate for the error in the following molecular dynamics formula: $C_v^* = \frac{3}{2}\bigg[1-\frac{2}{3NT^{*2}}\big\langle ...
2
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1answer
149 views

Tough second order differential equation

I can't figure out this diff equation (in cylindrical coordinate). How can I solve it ? Any comments appreciated $$ \frac{1}{r}\frac{d}{dr}(r\frac{dE}{dr})+\frac{d^2E}{dz^2}+(\epsilon_0 ...
1
vote
1answer
24 views

finding curvature radius

given a projectory equation of the form $ y=y(x) $find the curvature radius as a function of $x.$ a projectory equation , hence $ x=x(t)$, input that in y and we get $y=y(x(t))$, which is what one ...
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1answer
17 views

calculate the speed of a ball, with a laser

I'm doing a project where I have to calculate the speed of a ball, passing a certain point. I want to do this with a laser, by taking the time the laser is broken in comparison of the ball it's size. ...
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0answers
21 views

Approaching a Trajectory Problem

I am trying to design a railgun simulation. The idea is that the user can supply a starting point and velocity vector for a launcher and for a target, and the launcher will find the angle to launch ...
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0answers
29 views

Heat problem with an internal source of heat for which the maximum principle doesn't hold.

Heat problem with an internal source of heat for which the maximum principle doesn't hold. The problem is the following and honestly I don't know how to solve it... $$u_{t}=u_{tt}+2(t+1)+x(1-x) , ...
2
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0answers
35 views

$\frac{\omega}{2\pi}\int_0^{\frac{2\pi}{\omega}}\frac{\sin^2\theta \cos^2\omega t}{(1+\beta\cos\theta \sin\omega t)^5} dt$

I'm going to write out the whole problem as it is given to me (bad grammar and all) even though some of the info may be irrelevant to finding a solution. A charge $e$ moving along a straight line ...
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1answer
30 views

Instantaneously at Rest. What does it mean?

What is instantaneously at rest? Does it mean that velocity and acceleration must be both 0? So for question, $v(t) = 3 - t/2$, $t>4$, why is $t=6$ instantaneously at rest?
3
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0answers
26 views

The Virasoro-Bott group and the KdV equations

The Euler Arnold equation expresses equations (usually from mathematical physics) as geodesic equations on a Lie group. For the famous $KdV$ equations these equations are given on the Virasoro-Bott ...
2
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1answer
29 views

Projectile motion: Proving:$ x^2 + 4 \left(y-\frac{v^2}{4g} \right)^2 = \frac{v^2}{4g^2} $

Question: Projectiles are fired with initial speed $v$ and variable launch angle $0< \alpha < \pi$. Choose a coordinate system with the firing position at the origin. For each ...
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0answers
78 views

how to solve this integral ? It seems bounded and well defined integral but I don't know how to solve this

how to solve the following integral ? It seems well defined i.e. bound but I could not solve it. I tried by expanding series expansion of tanh[x] but after that I got a series as an answer, which I ...
8
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3answers
427 views

What is the difference between |(d/dt)velocity| and (d/dt)|velocity| [Physical Interpretation] [closed]

According to me the modulus of $\frac {\text{d}v}{\text{d}t}$ gives the magnitude of acceleration without accounting for direction but I am stumbled on how to interpret ...
3
votes
0answers
18 views

Finding the work done, given a function.

A heavy metal 2 pound bucket initially is filled with 10 pounds of paint. Immediately after it is filled, it is pulled up at a steady rate to the top of a building 30 feet high. While being pulled, ...
3
votes
2answers
28 views

What does it mean to use levi civita symbol with Poisson brackets in this way

I'm doing some studies in mathematical methods for physics and I came across something that I don't really understand. I have only been using the $\epsilon_{ijk}$ when I cross some vectors or ...
7
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3answers
273 views

Function to describe teardrop shape

If I fill a plastic ziploc-shaped bag with water, the cross section profile should be sort of teardrop shaped (assuming we ignore the edge effects of the bag being sealed on the sides as well as the ...
1
vote
1answer
28 views

Calculus Compress Spring

I have a question I cannot seem to get correct and am looking for some help. Suppose a force of $40~\text{N}$ is required to compress a spring $3~\text{cm}$ from its equilibrium length. How much ...
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1answer
1k views

Calculating the average force (mathematical physics)

I am trying to calculate the average force with regards to this question: Calculate the average force that USA gold medalist Allyson Felix (mass = $55.3$ kg, height = $168$ cm) exerted backwards on ...
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1answer
22 views

Numerical solver for maxwell equations?

Just curious if someone has come across a package where I can simply solve the basic maxwell equations(just the curl equations). I'm just interested in solving it on a 2-d plate out of interest. ...
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0answers
18 views

General Schrodingers Equation Quetions

I have som very general questions about the Schrodingers equation, 1) In seprating the variables into radial and angular, why do we equal it to $l(l+1)$, I can not seem to understand it from the books ...
3
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2answers
576 views

Definition: Mathematical way to define the “left” and the “right”

How do we define the left and the right, (such as left/right handness) from a mathematical way of definition? How can we explain this definition to some inhabitant of a distant stellar system who has ...
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0answers
39 views

How much does water cool in 1 second

I'm wondering if I've done my calculations correctly because the units I get are really weird... So.. I'm calculating how much the temperature change in $1$ second if the temperature difference is ...
4
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4answers
134 views

A Proportion Question

If $a$ is directly proportional to $b$ and also directly proportional to $c$, is it true that $a$ is directly proportional to $bc$.(It seems like it is true) Here is what I did and I have a feeling ...
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0answers
28 views

Dynamics of fluid

While reading on Wikipedia about the partial differential equations (https://en.wikipedia.org/wiki/Partial_differential_equation), I wondered how dynamics for the fluid occur in an ...
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2answers
30 views

Find an function that oscillates between a given upper and lower envelope

Suppose I'm given two real, continuous functions $f(x)$ and $g(x)$ such that $f(x)\ge g(x)$ for all real $x$. I'd like to determine an oscillating function $h(x)$ that has $f(x)$ as its upper-envelope ...
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3answers
29 views

Relative velocity from points' point of view

Edit: The terminology might be imprecise. Please pay attention to the picture I drew to explain my problems. I will appreciate an edit that will ensure the terminology is no longer disputable. This ...
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0answers
32 views

Calculate initial velocity

If I have the equation $y'' = -g -by'$, I know that a rock was thrown straight up from a specific height h, and hit the ground at time t, how do I calculate its initial velocity? I don't understand ...
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1answer
32 views

configuration spaces in mathematics and in physics

On the Wekipedia website Configuration space , there are two configuration spaces defined. One is Configuration spaces in physics, the other is Configuration spaces in mathematics. Question. Do ...
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1answer
35 views

Acceleration: If I know distance, time, and initial velocity, what's acceleration and final velocity?

So I know the Initial Velocity ($V_i$), Time ($t$), and Distance ($d$). I know that $$d = V_it + \frac{1}{2} at^2$$ If I rearrange this, would acceleration $a = \dfrac{2(d - V_it)}{t^2}$ ? Then ...
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1answer
26 views

Determining the most appropriate set of eigenmodes for a modal decomposition of an experimental data set

I have a complex vector of the transverse amplitude and phase distribution of a laser beam, derived from experimental data. When modelling these field distributions, ordinarily the eigenmodes of the ...
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1answer
14 views

Trigonometric function with a theoretical scenario used to find missing variables?

For my pre-calculus class I am given a theoretical scenario and I am tasked with finding the different time(s) an object within the scenario will be "x" inches above equilibrium. The prompt given to ...
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0answers
22 views

Power of a signature (sum of squares divided by number of elements)

I need to find some literature to study the theory of an exercise I am working on (it is from a course in digital image processing and pattern recognition). I have an $n\times n$ matrix, I have to ...
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0answers
23 views

How a “pillbox” can be considered as a Gaussian surface?

I'm currently practicing how to use Gauss's Law to evaluate electric flux passing through a Gaussian surface, but how a "pillbox" can be considered as a Gaussian surface, although it is not a smooth ...
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1answer
569 views

How to calculate solid angle of a rectangular detector of 20cm x 10cm?

I have an detector of $20\mathrm{cm}\times 10\mathrm{cm}$, how can I calculate the solid angle subtended by the detector if the detector is placed at $30\ \mathrm{cm}$ apart? Because directly I can ...
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0answers
21 views

Question about forever acceleration on a pendulum

So i'm a bit confused about something. If we take a mathematical pendulum and we apply a force to it. We ignore all friction and air resistance and only consider gravity and the force applied to bob. ...
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0answers
10 views

Finding the electric and magnetic field outside a cylindrical conductor.

A cylindrical conductor with constant circular cross-section and uniform conductivity $\sigma$ has a steady current I that is uniformly distributed across the cross-section flowing through it. Find ...
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2answers
384 views

Centre of Mass and Moment of Inertia of a sphere - spherical cap

I have been given a sphere of radius a, from this sphere a cap of hight h is cut off. 1) What is the centre of mass of the rest of the sphere? 2) What is the moment of inertia regarding the axis of ...