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Results tagged with physics
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user 11260
For questions about mathematical problems arising from physics, the natural science studying general properties of matter, radiation and energy.
3
votes
Conserved quantities for the Cauchy momentum equation
1) conserved quantity for incompressible flow:
$$\frac{d\rho}{dt}=\frac{\partial\rho}{\partial t}+\bar{v}\cdot\nabla\rho=0$$
so if the flow is stationary, $\partial\rho/\partial t=0$, the density $\ …
- 188k
6
votes
Accepted
Mathematical difference between solitons and traveling waves for a non-linear dispersive PDE
A necessary requirement for a traveling wave $u(x,t)=f(x-ct)$ to be a "solitary wave" or "soliton" is that the two limits $\lim_{s\rightarrow\pm\infty}f(s)=\alpha_\pm$ exist. This is the condition of …
- 188k
7
votes
Accepted
How are spatial coordinate systems in physics defined?
This question has been explored in the context of global positioning systems, which need to account for general relativity. The traditional Minkowski coordinates $(t,x,y,z)$ of flat space-time do not …
- 188k
2
votes
Accepted
Why is the physical space equivalent to $\mathbb{R}^3$
this is basically a question on the granularity of space, which is an active topic of research in physics: space appears to be continuous, but does it actually come in discrete chunks on some very small …
- 188k
1
vote
orthotropic materials solution of boundary value problems
Analytical methods of solution are typically restricted to two-dimensional geometries, see for example
Applications of symmetry methods in basic problems of orthotropic elasticity (1999)
We discus …
- 188k
6
votes
Accepted
Why are discreteness and smoothness in physics inversed with respect to geometry?
The "manifold picture" can be applied to physics in the context of the Brillouin zone, see for example On Brillouin Zones. …
- 188k
5
votes
Why are solenoidal fields called solenoidal?
[To expand on Wojowu's comment.]
Q: "Why the description of a divergence-free field as solenoidal? I expect that this name had historical origins but its unlikely that it was so named without some lin …
- 188k
13
votes
Accepted
How does a Masters student of math learn physics by self?
I can recommend Leonard Susskind's Theoretical Minimum:
A number of years ago I became aware of the large number of physics
enthusiasts out there who have no venue to learn modern physics and
cosmology … So I started a series
of courses on modern physics at Stanford University where I am a
professor of physics. …
- 188k
12
votes
Representation theory and elementary particles
The Algebra of Grand Unified Theories, by John Baez and John Huerta may well be to your liking:
A full-fledged treatment of particle physics requires quantum field
theory, which uses representations … This brings
in a lot of analytical subtleties, which make it hard to formulate
theories of particle physics in a mathematically rigorous way. …
- 188k
6
votes
Applications of Hamiltonian formalism to classical mechanics
The Poincaré-von Zeipel method in celestial mechanics relies on canonical transformations of the Hamiltonian to separate fast and slow degrees of freedom in a solar system. See, for example, A note on …
- 188k
11
votes
Accepted
Does current follow the path(s) of least (total) resistance?
Perhaps to resolve this issue it helps to work out a simple example.
Take a region $D$ consisting of the strip $|x|<1$, $0<y<1$, and a $y$-independent conductivity profile
$$\sigma(x)=\begin{cases}
1 …
- 188k
5
votes
Accepted
Gadgets as primality tests
The gadgets use effects from chemistry (Biochemical identification of prime numbers), biology ( A Biological Generator of Prime Numbers, and physics An optical Eratosthenes' sieve for large prime numbers …
- 188k
3
votes
Quantum tunneling on the line with non-symmetric double well potential
Tunnel splitting of the spectrum and bilocalization of eigenfunctions in an asymmetric double well has a "theorem" on the bilocalization phenomenon (wave function localized in both asymmetric wells); …
- 188k
18
votes
Applications of complex exponential
Early applications of $e^{i\omega t}$ in the context of electromagnetism were understood as a mathematical device: the physical fields are real, and the complex exponential is a convenient method to i …
- 188k
28
votes
When exactly and why did matrix multiplication become a part of the undergraduate curriculum?
The article by J.-L. Dorier in On the Teaching of Linear Algebra suggests the answer to your question will be different for the UK and for continental Europe:
In an attempt to answer your questio …
- 188k