# Questions tagged [stability]

Stability theory addresses the stability of potentials, solutions of differential equations, and of trajectories of dynamical systems under small perturbations of initial conditions.

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### How can we deduce that a hydrogen atom is stable in relativistic QED?

Consider relativistic quantum electrodynamics (QED) with three quantum fields: the electromagnetic field $A_\mu$, one fermion field $\psi$ for electrons/positrons, and one fermion field $\psi'$ for ...
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### Nonlinear stability question

I am looking for a simple example where a system is linearly unstable, but nonlinearly unstable or stable, depending on the sign of the initial perturbation. For instance, assume the linear normal ...
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### Regularization: What is so special about the Coulomb/Newtonian and harmonic potential?

I wanted to know if the procedure for regularization of the Coulomb potential outlined in Celletti (2003): Basics of regularization theory could be generalized to arbitrary polynomial potentials. So ...
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### Is classical Kaluza Klein theory stable or not?

Set Up In the original classical Kaluza Klein theory, you have a $d+1$ dimensional manifold where one space dimension is a circle $S^1$. In the "low energy limit," none of the metric ...
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### Plum-pudding atomic physics in higher dimensions?

It is established that "normal" electron orbitals are not stable in more than 3 spatial dimensions, as the available energy levels become unbounded from below. However, this result only applies given ...
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### Is this wire-melting phenomenon a manifestation of the Plateau–Rayleigh instability; have I done my maths right?

In LECTURE 5: Fluid jets from MIT's 1.63J/2.26J Advanced Fluid Dynamics equation 23 is $$\omega^2 =\frac{\sigma}{\rho R_0^3} k R_0 \frac{I_1(k R_0)}{I_0(k R_0)}\left(1 - k^2 R_0^2 \right)$$ and is ...
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### Stability of D-Branes and Coupling to Fields

I've been brushing up on my string theory using Becker, Becker, Schwarz (p. 208 in particular). They state that some D-branes can couple to R-R fields from closed string excitations. They then go on ...
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### Do laser filaments propagate in a straight line over long distances?

In so-called filament propagation, a powerful laser beam can propagate through a medium without diffraction. This occurs because the beam focuses itself through non-linear optical effects. Self-...
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### Stability of a dipole magnet undergoing eddy current braking in a cylindrical tube

Consider a cylindrical dipole magnet with strength $B$ undergoing eddy current braking in a conductive cylindrical tube with the axis of the magnet aligned with the axis of the tube. The magnet ...
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### Name of the Rayleigh–Taylor demonstrator toy

There is a common physics "toy" consisting of two liquids sealed into the space between two sheets of plexiglass. When turned upside down, it demonstrates the Rayleigh–Taylor instability. I ...
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### How do you check the stability of a kink solution?

I am reading a nice introductory note by Hugo Laurell (http://uu.diva-portal.org/smash/get/diva2:935529/FULLTEXT01.pdf) but got confused on section 3.2. He claims the stability of kink by expanding a ...
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### How weighing balance works and can balance itself?

i am new in this community and i was not able to answer in a similar post "how does a weighing balance that has 2 identical mass on both sides is capable of balancing after being tilted". i ...
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### What is the intuition behind a high Froude number causing instability in uniform flow?

Uniform flow in an inclined plane becomes unstable for high froude numbers. I can follow the spectral analysis, but I am curious why I would expect high froude numbers to cause instability. What is ...
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### How do electrons stay in orbitals in Bohmian Mechanics?

I've been reading various realist interpretations of quantum mechanics and in Bohmian Mechanics, I found that the "wave" aspect of a quantum particle is removed from the particle to preserve ...
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### Why are so few inclined circumbinary planets known?

For a research project I'm studying the orbits of circumbinary planets, most of these planets orbits are coplanar. However I was wondering if orbits with a high inclination could be stable. I made a ...
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### Increased Stability of Vortex Rings by Pushing it

I've noticed in playing around with smoke rings that they are substantially more stable in their axial motion if pushed from behind by a hand, as can be seen in various Youtube videos. I was wondering ...
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### What if $\omega =0$, which is the frequency of the perturbation term?

In analytic mechanics, when we found a equilibrium position of the system, to determine the stability of that configuration, we apply $q \to q_0 + \epsilon \eta$ with $|\eta| \ll 1$ s.t $q_0$ is the ...
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### What is the "special time dependence" that develops in an Ostrogradskian instability?

I've been reading papers that deal with Lagrangians containing second- and higher- order derivatives of field variables. In this paper in Section 3.1, I found this very interesting quote: The ...
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### Usage of Floquet's Method

I'm treating with a nonlinear system of ODE, in which one of my fixed points is non-hyperbolic, that is, its eigenvalues has ($\Re(\lambda_{1,2}) = 0$). Therefore, I cannot say anything about its ...
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### Wheel rolling leaned against a vertical wall

I'm new with rigid problems about. I'm trying to solve this: A massive circular disk of mass m, radius R, and negligible thickness is leaned against a vertical wall, slanting by 45 . In the ...
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### What is the physical interpretation of Rayleigh's inflection point theorem?

Let $\boldsymbol{u} = U(z)\,\mathbf{e}_x$ be the velocity profile of an inviscid parallel flow. Rayleigh's inflection point theorem states that this flow may be linearly unstable to perturbations only ...
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### Stability of Electromagnetic Waves

Is there currently any theory or set of equations which describe the stability of electromagnetic waves in gravity wells of compact objects such as neutron star or a white dwarf star . Weather the ...
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### overstability vs resonance: what is the difference?

Reading about discs, I encountered the word 'overstability' that its difference with resonance is not clear to me. Does anyone know the difference?
I am looking to determine the lateral angle at which an underwater camera system will no longer right itself. When on the ocean floor it is $-24.30~\text{kg}$ buoyant with the difference between its ...