Questions tagged [physics]
For questions about mathematical problems arising from physics, the natural science studying general properties of matter, radiation and energy.
193 questions
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Ghost cycles in dynamical systems
I'm reading a paper under the title Ghost channels and ghost cycles guiding long transients in dynamical systems, here or here.
The authors state that by examining simple ordinary differential ...
user571116
2
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0
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109
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Approximate solutions to $x''(t)=-cx + f(t)x$
I recently studied a problem which involved two particles joined by a harmonic spring moving in a potential and through some manipulation, I obtained the equation
$x''(t) = -\omega^2x + f(t)x$,
where $...
- 3,808
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Some details about relationship between central charges and second cohomology group of the Lie algebra
S. Weinberg in his book "The quantum theory of fields" talks about central charge that appear in Lie algebra of a given Lie group. To be more precise, on page 83 in the book, he computes the ...
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Is the topological dimension of spacetime fixed for causally isomorphic spacetimes?
Suppose time-oriented spacetimes $(M_1 , g_1)$ and $(M_2, g_2)$ are not homeomorphic under their manifold topologies $\mathcal{M}_1$ and $\mathcal{M}_2$ respectively.
The Lorentzian metrics $g_1$ and $...
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1
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Can the Causal Structure recover the manifold topology for non-chronological spacetimes?
Given a time-oriented spacetime $(M,g)$, a binary relation $\ll$ can be defined on this spacetime where $p \ll q$ for $p, q \in M$ if and only if there exists a time-like path connecting $p$ and $q$.
...
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33
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8
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Motivation and physical interpretation of the Laplace transform
Concerning the one-sided Laplace transform,
$$\mathcal{L}\{f\}(s) = \int_0^\infty f(t)e^{-st} dt$$
what is a motivation to come up with that formula? I am particularly interested in "physical&...
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Qualitative values between two electrons in an atom or how to interpret these values?
This question is a little bit trying to understand physics through geometry of simplex:
Let $E_{i,j}$ be the ionization energy in times the number of hydrogen ionization energy for an element with ...
- 3,761
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Temporal evolution of a globally hyperbolic spacetime
Any globally hyperbolic spacetime can be assigned a global function of time as Hawking has demonstrated for stably causal spacetime. (Any globally hyperbolic spacetime is also stably causal).
For ...
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Biot-Savart-like integral for a toroidal helix
The following problem originates from Physics, so I apologize if I will not use a rigorous mathematical jargon.
Let us consider a toroidal helix parametrized as follows:
$$
x=(R+r\cos(n\phi))\cos(\phi)...
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3
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359
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Interesting question about the Thomson problem for arbitrary number of electrons
This question is crossposted from here I believe this is a pretty hard question and so I decided to repost the question in the Math Overflow forum. If there is something wrong with doing this, I am ...
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Inverse square-law as a positive definite kernel?
Newtons law for gravity states that:
$$F_{12} = \frac{G m_1 m_2} {|x_1-x_2|^2}$$
The function :
$$k(x,y):=\exp(-| x-y|^2)$$
is known to be a positive definite function, called the RBF-kernel.
It ...
- 3,761
4
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1
answer
788
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Mathematical difference between solitons and traveling waves for a non-linear dispersive PDE
I see many mathematicians conflating the definitions of traveling waves and solitons, and I am unable to understand, from a mathematical point of view, the differences between these two types of ...
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9
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1
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698
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D'Alembert's Principle: rigorous formulation using notions from modern differential geometry
Is there a rigorous definition of D'Alembert's principle of virtual dynamic work in the language of differential geometry? Some questions I'm hoping to answer are:
How to view the configuration space ...
- 91
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248
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polynomial approximation of hypergeometric function 2F1
I have the following function $T(k_1,k_2)$ resulting from multiphoton transition matrix elements calculations:
$T(k_1,k_2)=\gamma^{-k_2}\sum_{j=0}^{k_1}(j+2)_{l+1}\binom{k_1}{j}(k_1+1)_3(\gamma-1)^{j}{...
- 11
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Particles sent into the same direction with uniformly distributed speed
Fix a positive integer $n$. Every second, a particle is sent along a straight line from a fixed position in a fixed direction, at a random integer speed chosen uniformly in $\{1,\ldots, n\}$ meters ...
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2
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1
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Examples of ODEs with complex constant coefficients and applications to physics?
This question is asked on stackexchange: Are there examples for ODEs with complex coefficients with applications in physics?
but received no answers. I am reposting it here on the hope that it catches ...
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Why are discreteness and smoothness in physics inversed with respect to geometry?
In a closed (say differentiable) Riemannian manifold you see only continuous features when looking at small neighbourhoods of points. From afar,
discrete features appear ((co)homology, closed ...
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4
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148
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Superspace derivation of supersymmetric non-linear sigma model in Supersolutions by Deligne and Freed
I am having a little trouble understanding passage from the linear to the non-linear sigma model in Section 4.1 of Supersolutions by Deligne and Freed. Most of my confusion comes down to the ...
user482049
16
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1
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817
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From a physicist: How do I show certain superelliptic curves are also hyperelliptic?
As the title suggests, I am a physicist and have a question about how to show certain superelliptic curves are also hyperelliptic. The superelliptic Riemann surfaces in question has the form $$w^n = \...
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How are spatial coordinate systems in physics defined?
Grothendieck once asked "What is a meter?" (https://golem.ph.utexas.edu/category/2006/08/letter_from_grothendieck.html). This innocent sounding question, made me to think about how ...
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-1
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Harmonic function in infinite domain in $\mathbb{R}^3$, constant on the boundary and decaying as $1/r^2$
EDIT: Let $\Omega\subset \mathbb{R}^3$ be a bounded domain with smooth connected boundary. Let $f\colon \mathbb{R}^3\backslash \Omega \to \mathbb{R}$ be a continuous function which is harmonic in $\...
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The specific connection between the Hecke operator and the t'Hooft Operator
As I was reading some articles concern about the Selberg trace formula and its general form, I have noticed that the Selberg trace formula and its general form can be understand as the energy spectrum ...
8
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Is there any physics theory which is similar to these analogies?
Since I am doing this little "research" project on my spare time and in my physical neighborhood there are not many people to discuss these ideas, I wanted to share with you a small point of ...
- 3,761
4
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1
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Formula involving Wigner's 3j symbols and integration over irreducible representations of SU(2)
$\DeclareMathOperator\SU{SU}$In some calculations, I saw the following formula
$$\int_{\SU(2)}\,\mathrm{d}g\,D^{j_{1}}_{m_{1}n_{1}}(g)D^{j_{2}}_{m_{2}n_{2}}(g)D^{j_{3}}_{m_{3}n_{3}}(g)=(-1)^{j_{1}+j_{...
user199422
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0
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Angular velocity from rotation matrix difference [closed]
I am working on something for a game. I need to calculate the angular velocity, however in my situation I only have access to the previous rotation matrix and the current rotation matrix. My angular ...
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