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Results tagged with mp.mathematical-physics
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user 171439
Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.
6
votes
2
answers
602
views
Non-linear hyperbolic PDE
I have the following PDE in two dimensions
$$
2\partial_x\partial_y\sqrt{1-u^2}+\left(\partial^2_x-\partial^2_y \right)u=0,
$$
with $u=u(x,y)$ with values between $-1$ and $1$, or alternatively
$$
2\p …
- 134
6
votes
0
answers
158
views
Nonlinear-PDE arising from flat conformal Chebyshev nets
Consider a flat, simply connected surface endowed with the Riemannian metric $g_0=e^{2\Omega(u,v)}\left(\mathbb{d}^2u +\mathbb{d}^2v \right)$, so that $\Omega(u,v)$ is an arbitrary harmonic function. …
- 134
5
votes
1
answer
365
views
Systems of (hyperbolic) 2nd order PDEs with lower order constraints
Certain surfaces in mechanics are endowed with the fundamental forms
\begin{align}
\text{I} &= \mathrm{d}u^2+\mathrm{d}v^2+2\cos\gamma\: \mathrm{d}u\: \mathrm{d}v \\
\text{II} &= \alpha\left(\gamma \r …
- 134
4
votes
0
answers
235
views
Generalising Bäcklund transform to solve $\omega''(t)=t\sin\omega(t)$
Bäcklund transformations may be used also in ODE to solve non-linear problems; for instance, it's well known that for the equation
$$
\frac{\mathrm{d}^2\omega}{\mathrm{d}t^2}=\sin\omega
\tag{*}\label{ …
- 134
4
votes
Mathematical predictions of AdS/CFT
New exact solutions in classical general relativity have been found using AdS/CFT methods. It may sound trivial since there are already encyclopedias of exact solutions, but those new ones have quite …
- 134
3
votes
0
answers
170
views
Non-linear, hyperbolic, 2nd order system of PDEs
This is a cross-post.
In the context of two dimensional elasticity theory, when considering deformations of flat membranes into spherical caps, one encounters the following hyperbolic system
\begin{al …
- 134
3
votes
2
answers
221
views
$2\mathrm{d}$ area maximizing short embeddings
Think of a beach ball on an pool of water or sand.
Let $\left(\mathcal{M}^2,g\right)$ be a surface homeomorphic to a sphere, endowed with a Riemannian metric $g$, and $\left(\mathcal{N}^2,h\right)$ a …
- 134
2
votes
1
answer
182
views
Signs of curvatures of integrals lines of frames with constant principal values
Let $D\subset\mathbb{R}^2$ be a planar domain (maybe simply connected) and consider all the mappings $f:D\to\mathbb{R}^2$ with constant, fixed, positive singular values. Let $E=(E_1,E_2)$ be the ortho …
- 134
1
vote
How are Clifford algebras and spinors used to study the Ising model?
The section 12.2 of Huang's treatise on Statistical Mechanics (1963) gives hints of possible connections between the Ising model and Clifford algebras, but of course $\textit{under the physicist poin …
- 134
1
vote
On the “Non-conservation of parity in weak interactions”
If some interaction acts differently on the right-handed and left-handed components of a particle, the interaction is automatically parity violating. So you just need to look at the Lagrangian and not …
- 134