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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236 views

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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40 views

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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83 views

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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Chua's Circuit: an inequality ensuring that the equilibrium is not stable

According to Kennedy's Robust op-amp realization of Chua's circuit(1992), the differential equations satisfied by several physical quantities in Chua's circuit are $$\begin{aligned} C_{1} \frac{d v_{...
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159 views

Why doesn't the Lagrangian depend on higher-order derivatives of position?

This isn't a duplicate of already-answered questions, but rather a follow-up of this answer. The author presents a field-theoretical argument whereby a problematic run-away particle creation is ...
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418 views

Dzhanibekov effect in quantum systems

Dzhanibekov- or Tennis racket effect is what happens when an object with three diferent moments of inertia doesnt spin around the axis with highest or lowest moment of inertia. The object starts to ...
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271 views

Sign of the coupling constant for a $\phi^4$ interaction

The vacuum-vacuum transition for a simple bosonic $\phi^4$ theory is typically written as $$ \langle0|0\rangle = \int[D\phi]\ \exp\left[i\int (L_0+L_\mathrm{int}) d^4x \right], \tag{1} $$ Where $L_0$ ...
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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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27 views

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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100 views

Spiral galaxy stability

Is there a limit of baryonic masses $M_{B}$ ($M_{B}=M_{\star}+M_{g}$), beyond which a spiral galaxy is no longer rotationally supported? Like for example: Could spiral galaxies of baryonic masses $M_{...
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Looknig for resources on finding periodic orbit and stability on multidimensional Hamiltonian systems

I am looking for resources (books, papers, algorithms, codes) that explicitly explain the computation and analysis (using the monodromy matrix) of periodic orbits of multidimensional Hamiltonian ...
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53 views

How to calculate precision of Pound-Drever-Hall technique?

When I read the fifth section (Noise and fundamental limits: how well can you do?) of Eric's article, I have question. In this section(page 85 and 86), Eric discussed the shot noise, and gave the ...
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117 views

Examples of systems with stable equilibria on the boundary of the phase space

An example of bounded gradient flows are Hopfield networks, which are gradient dynamical systems, used (among other things) to solve combinatorial optimization problems, because stable equilibria are ...
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1answer
72 views

Coexistence at Lagrange points

I was wondering how precise the location of an object in a Lagrange point needs to be to maintain stability, since it seems that several natural objects (asteroids) exists together in some of these ...
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Calculations to Determine Force Required for Gyroscopic Stabalization

I am currently undertaking a project involving gyroscopes, the aim of which is to stabilize a large object. I have read that gyroscopes work because of conservation of angular momentum, and if you ...
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Stability condition for AdS background (when gravity coupled to matter fields)

In finding the stability condition for AdS background (when gravity coupled to matter fields), why the conserved energy should be positive?
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1answer
68 views

Does rotating our hands reduce the possibility to fall?

I was trying to balance on a thin wooden plank and when I was about to fall I would rotate my hands in vertical circles. I did not realize why I and other people I see trying not to fall on the plank ...
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Procedure to check stability of a metric against perturbation

What are broadly the procedures one needs to undertake to check the stability of a metric against small perturbations? Any review in this regard will also be helpful.
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What is the problem of higher-order time derivatives with causality?

I've heard that equations of motion with third- or higher-order time derivatives have problems with causality, but can't seem to find any proof or reasoning for this. Could anyone please help me? I ...
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Has any one seen an application of the virial theorem (say with magnetic fields) for non-self gravitating system?

Here is the version of the theorem I am most familiar with - consider an ideal magneto-fluid with density $\rho$, bulk velocity field $\mathbf v$, with magnetic field $\mathbf B$ and (isotropic gas) ...
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1answer
19 views

Linear stability analysis of a 2-cycle

In a discrete $N$-dimensional Hamiltonian map $\mathbf{X}^{(n+1)}=f(\mathbf{X}^{(n)})$, we often find a 2-cycle which shows oscillation between two points in phase space. In such a Hamiltonian map we ...
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1answer
69 views

Does Earnshaw's theorem apply to electrostatic + gravitational systems?

I've been learning about particle traps and Earnshaw's theorem. When dealing purely with electrostatic forces the theorem makes intuitive sense to me. But does it really apply to systems involving ...
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2answers
55 views

Necessary and Sufficient Conditions for an Equilibrium to be Stable

In the 4th section The condition that convection be absent of the book Fluid Mechanics by Landau and Lifshitz, they give the following statement: For the (mechanical) equilibrium to be stable, it is ...
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1answer
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Balance of an non-homogeneous object

Would a pencil balanced on its tip, remain balanced if the the tip was made of a material twice as heavy than the rest of the pencil?
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1answer
41 views

Can a position variable have an infintesimal in it?

I've been pondering unstable systems, such as a perfectly round rock atop a smooth hill. At the top of the hill is a metastable point where the rock could roll either way after an arbitrary amount of ...
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Stability of soap membranes when passing hot water through them

I noticed earlier today whilst washing a wire rack with dish soap that when running hot tap water through some soap membranes that formed in the rack, although most of the membranes broke immediately (...
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36 views

Is a satellite orbit around the Earth Lyapunov stable?

Presume there is a satellite orbiting the Earth in an orbit that follows a closed path around the planet (that is, escape orbits are not permitted here). As I understand it, there are two ...
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53 views

Instability of coupled non-linear oscillators

Consider a bunch of interacting oscillators (e.g., a chain of atoms), interacting due to anharmonicity in the potential energy. You can Taylor expand the force on each oscillator about equilibrium ...
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What can one conclude about the stability of limit cycles without the use of numerical methods?

Let's assume one asserts the existence of a closed orbit by applyling the Poincaré-Bendixson theorem to a trapping region $R$ that is constructed such that all phase vectors on its boundary point ...
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72 views

Vorticity of Fourier Expanded Velocity

I have been reading some papers which find all three components of the vorticity vector for a Fourier expanded (perturbation) velocity field i.e $\mathbf{u'}(x,y,z,t)=\int\mathbf{\hat{u}}(x,y,t)e^{...
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45 views

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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1answer
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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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190 views

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?
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240 views

Pendulum with friction: La Sall's Invariance Theorem

I am trying to understand la Sall's Invariance Theorem, which is used to proove that a system is aysmptotically stable. Can someone help me to understand it, by making an example of how to use it. ...
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1answer
213 views

Righting moment for object submerged in water

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 ...