"Mathematical physics consists of the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories." (from Journal of Mathematical Physics) This tag is intended for questions on methods used ...

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116 views

Is this equal ? (I found it on this website)

I found this equation on this website! I would like to know it its true or not? And how can proof or disprove it?! Euler-Mascheroni constant expression, further simplification ...
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0answers
85 views

How can we proof that this is equal? About $ln(n)$

I found this on this website (Euler-Mascheroni constant expression, further simplification) without any explaining why this is equal can someone give me that? ...
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0answers
34 views

Green's function in the context of classical mechanics

I am following this paper entitled "The classical mechanics of non-conservative systems". I would like to discuss equation (2) since I cannot get what the autor says. This is the problem: let's ...
1
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1answer
27 views

Parameters in the Hamilton-Jacobi Equation

I'm reading through Gelfand and Fomin's 'Calculus of Variations', and they've just derived the Hamilton-Jacobi Equation: $$\frac{\partial S}{\partial x} + H \left(x, y_1, \ldots, y_n , \frac{\partial ...
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1answer
47 views

maximum position uncertainty of particle in a box

I want to verify mathematically for wave function $\psi(x)$ satisfying $\psi(x)=0$ for $\lvert x \rvert \ge \frac{L}{2} $ and $\int_{- \frac{L}{2}}^{\frac{L}{2}} \lvert \psi(x) \rvert ^2 dx = 1 $ ...
3
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1answer
86 views

What is the prerequisite knowledge for Navier–Stokes Existence and Smoothness problem?

I am highly interested in the Millennium Problem of Navier–Stokes Existence and Smoothness (also here) and my aim is to reach some level of knowledge to do research on it. The problem seems simple to ...
1
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3answers
74 views

Finding initial value of differential equation

Given, $$ mdv/dt = mg - kv $$ Question is: Find the velocity $v(t)$ that satisfies this initial value problem. Also, by letting $t$ approach positive infinity, determine the terminal velocity ...
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36 views

Blow-Up for Semi-Linear Wave Equation

I am reading C. D. Sogge's book "Lectures on Non-Linear Wave Equations". As an exercise, I attempted to fill out the details of the proof of Theorem 5.1 (Local Existence of Solutions for Semilinear ...
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0answers
42 views

Kahler-Einstein Metrics in Physics - Topic Suggestions

I am hoping to get some topic suggestions for a presentation I have to give in a couple of weeks. The course the presentation is for is called Kahler-Einstein metrics. I would really like the ...
3
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0answers
80 views

Regge symmetry and outer automorphisms of Dynkin diagrams

Quantum $6j$-symbols are the coefficients of the change of basis matrix in the central extension of Temperley-Lieb algebra(see the book by Kauffman and Lins). It is my understanding that Ocneanu has ...
0
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0answers
51 views

Function $\int_0^1 x^{a}(1-x)^{n}~dx$ used for Gamma Function

I was reading a historical note on Euler and found that below given function is used to find Gamma Function: $$ \int_0^1 x^{a}(1-x)^{n} dx .$$ And I could not understand that why this function ...
3
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2answers
91 views

What are BesselJ functions?

I solved an integration on mathematica which gives BesselJ functions and some other terms. I explored mathematica help and google but could not understand the difference between different types of ...
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0answers
36 views

partial differential equation applicational problem

As a Maths student with not much knowledge in physics, I dont understand how the "string" can be "cut" into half at x=L/2. Also, how many initial conditions(data) does this question have apart from ...
2
votes
1answer
43 views

How invariance is formulated mathematically?

Consider $M$ a smooth manifold of dimension $n$, then a vector at the point $a\in M$ can be defined without any reference to any coordinate system. Indeed, we define a vector $v\in T_aM $ usually as ...
3
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3answers
117 views

What a reference frame is mathematically?

Physicists usually talk about reference frames and more specially inertial reference frames. This is particularly important in Mechanics and Relativity. Now, from the Physics standpoint there's no ...
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0answers
69 views

For Riemann Hypothesis, many people seek physics intuition, why not for Goldbach Conjecture ?

All: As we all know, for Riemann Hypothesis research, many people seek physics intuition, to understand more fundamental reasons why Riemann Hypothesis shall hold. In this direction, we have ...
5
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0answers
67 views

Could you explain the failure of the Hodge decomposition to exist for non-compact manifolds?

I'm a physicist and the mathematics around the Hodge Decomposition is way formal than I can currently follow (I'm trying to better myself but it'll take a while). Specifically what I'm ...
0
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0answers
23 views

Thermodynamics: find exit temp and velocity of air out of a nozzle?

I don't know if I can really ask a thermodynamics question here on this math site but I need help and this was the best site for when I needed help in math class. Concerning thermodynamics, I have ...
1
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2answers
63 views

How can I scale a value from -255 to 255 or -100 to 100 to a scale of 0-100?

For Brightness, I have a formula that takes in a value from -255 to 255 and contrast from -100 to 100. What if I wanted to use the same formula but I wanted to convert/adjust the scaling so that I ...
0
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1answer
52 views

Vectors Velocity, Physics Word Problem.

A bird is flying from Hamilton ON to Waterloo ON. There is a heavy wind traveling at 5.0km/h (S11°E). What should its heading be? How long will it take? That is all the information I get and ...
2
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0answers
19 views

Analytic solution to wave equation on a hollow cylinder

Is it possible to find an analytic solution for the modes of vibration of a hollow cylinder, assuming azimuthal symmetry? That is can the following PDE be evaluated: ...
6
votes
1answer
91 views

Surveys: problems, conjectures, and questions in some areas of nonlinear analysis

I would like to create a "big-list" of resources (e.g., survey papers, webpages, conference proceedings, monographs, etc.) that collect and offer some context and ...
0
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2answers
66 views

Notion of contraction in tensor algebra

Assuming a vector space V and it's basis set $\{\vec{e}_\nu\}$. A vector $\vec{v}$ can be written as: $\vec{v}=x^\nu\vec{e}_\nu$ where $x^\nu$ is the corresponding contravariant coordinate. We can ...
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1answer
63 views

Can an integral of a function that is not well behaved be finite?

Consider the following integral which gives the time period of simple pendulum where $\theta_0$ is the initial inclination of pendulum with vertical. ...
3
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0answers
77 views

Wave equation for a string nonuniform (PDE)

I have tried to solve this exercise from Applied Partial Differential Equations-Richard Haberman , but I have been impossible these paragraphs. The displacement $u$ of a nonuniform string ...
0
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1answer
54 views

Understanding derivatives in simple terms

Im am trying to understand the idea of derivatives and how they relate to the real world. I understand if i have function, in pkysics first derivative is the velocity, and the second derivative is ...
7
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1answer
165 views

Stefan-Boltzmann Constant and Stefan's Law

The following argument is from my textbook, An Introduction to Thermal Physics by Daniel Schroeder. If you are familiar with the derivation of Stefan's Law from the energy density of a photon gas, you ...
2
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0answers
67 views

Index notation confusion in tensor algebra

I have some confusions regarding index notation in tensor algebra. Let's assume $\vec{v}$ is a vector belonging to vector space $V$. Choosing a basis set $\{\vec{e}_\nu\}$, $\vec{v}=x^\nu\vec{e}_\nu$ ...
0
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0answers
32 views

Flow through a viscous fluid, “reflections method”

does anyone know about the "reflections method" on determining the velocity field around a small assemblage of spheres moving through a viscous fluid with small Reynolds Number? [ch. 6 Happel & ...
0
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0answers
55 views

complex potentials in plane polar coordinates - stream function

Determine the stream function and the potential in plane polar coordinates and sketching streamlines We need to take the value of m=1. I have an idea on how to do the parts and i know what a ...
0
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0answers
21 views

Modelling: Use Newton's law to write down an equation for the position $x$ of the mass.

Here is the background for the question: Consider a one-dimensional frictionless spring-mass system, where the forces acting on the mass $m$ at position $x$ are the forces of gravity $F_g =-mg$ with ...
1
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1answer
38 views

Justifying the use of real numbers for measuring length

I am not sure if this is the most appropriate place to post this but here goes nothing: Assume we were trying to come up with system of numbers $S$ to model our intuition of length. We want $S$ to ...
0
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0answers
15 views

How do you calculate certain variables of two or more events that occur simultaneously compared to the same events happening subsequently.

Say you have two hoses, A and B, that fill up a pool of equal size at different rates. Hose A fills up a pool in 10 mins, hose B in 20 mins. Thus A = 1p/10m, B = 1p/20m. Lets say that Hose A filling ...
2
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1answer
136 views

Generalized Functions (Distributions) over Manifolds

What is the right way of making sense of generalized functions over manifolds? For concreteness, let me restrict my question to the dirac delta function. The article on Wikipedia on Dirac delta ...
0
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1answer
15 views

Show that the current in a cylindrical conductor is uniformly distributed across its cross section

Using relevant equations for E and J, show that the current in a steady current I in a cylindrical conductor with uniform conductivity $\sigma$ is uniformly distributed across its cross-section. I ...
0
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1answer
24 views

Interpretation of integral.

The height, in centimeters, of a bicycle pedal is given by $h(t)=30+16\sin t$ where $t$ is the time. Evaluate and interpret the following integral \begin{align} \dfrac{1}{2\pi}\int_0^{2\pi} h(t)\,dt. ...
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0answers
13 views

Calculating gain ratio from a dB value

In a practice problem I have: power gain = $\log_{10}(\frac{db}{20})$ The final answer for the ratio is 1. The dB value is $-3$. When I do $\log_{10}(\frac{3}{20})$ I get $-0.823$. Just wondering ...
0
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2answers
39 views

find travel time given path and velocity field

As I was studying refraction, I began wondering what path would light take when entering a non-homogeneous transparent medium, i.e. a certain material in which the refraction index $n$ varies ...
2
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2answers
59 views

Completeness of solutions and the separation of variables method

The method of separation of variables is introduced in every textbook on mathematical physics. A basic question is rarely addressed: does this method exhaust all the solutions? Is there any ...
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0answers
81 views

Multiple absorbing boundaries

I am interested in the relation between absorbing boundaries and the trajectories of particles (evolving according to a Brownian motion). The probability to hit a boundary at a given time can be ...
2
votes
1answer
45 views

Classification of All Maps $T^2 \to S^4$ up to homotopy

From my study of physics I have arrived at the question of how to classify all maps $\mathbb{T}^2\to S^4$ where $\mathbb{T}^2$ is the two-torus. The classification should be up to homotopies. The ...
0
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1answer
40 views

Sturm-Liouville and Bessel function identity

Given S-L equation $\dfrac{1}{x}[\dfrac{d}{dx}(xy')+(\dfrac{-m^2}{x})y]=-\lambda y$ Say $\mathcal{L}$ is the Sturm-Liouville operator, $y_k$ is eigenfunction $J_m(j_{mk}x)$ where $J_m$ is Bessel ...
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0answers
11 views

How to obtain the velocity sigma

Hi i have a set of results below but i don't understand how the value 4.4646x10^-4 is obtained. This is the part I'm specifically talking about. i hope someone can help. thank you
0
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0answers
95 views

Reflection of light from function graph

Let a positive convex decreasing differentiable function $f(x)$ be defined on $\mathbb{R}$ and $\lim_{x \to \infty}f(x)=0$. Let the point light source be placed at $P(x_0,y_0)$ with $y_0>0,\,y_0 ...
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0answers
25 views

Non-dimensionalization using Buckingham-$\pi$: example of the “bead on a rotating hoop, with viscous damping” problem

I am trying to find a way to non-dimensionalize known equations, using the Buckingham-$\pi$ theorem. Consider the "bead on a rotating hoop, with viscous damping" problem---if you are interested in ...
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0answers
15 views

Finding the expectation of momentum using density matrices.

I've been given the task of showing that $$ \bar{<p>}=\int\nabla_r\rho(r,r')|_{r=r'} dr$$ using the defition that the expectation of an operator $O$ is given by: $$ \bar{<O>}=\int\int ...
7
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0answers
94 views

Essential Selfadjointness of Quantum Harmonic Oscillator Hamiltonian

The Hamiltonian for the Quantum Harmonic Oscillator is (disregarding constants) the Hermite operator $$ Hf = -f''+x^{2}f, $$ where $\mathcal{D}(H)$ consists of all twice absolutely ...
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0answers
19 views

Question about DE related to physics; includes Hooke's Law and Newton's Second Law as well as system of DE equations and solutions, and a phase plane.

I mainly need help with part A, and a little bit on B and C. Thank you in advance for your answer or any comment or edit that helps!!! A second-order DE can be sometimes solved with clever ...
0
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1answer
51 views

Force between parallel conductors using amperes law

Two parallel conductors are 0.3m long, and 0.15m apart. They each carry 2.5A of current in the same direction. Calculate the force between them. I did (2 * 10^-7) (2.5^2) / (0.15) and got the ...
3
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1answer
44 views

Minkowski metric on a surface

Do closed surfaces admit a metric with lorentzian signature? Any reference?