# Tagged Questions

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### Rayleigh-Taylor Instability dependence on acceleration direction

I'm trying to bolster my understanding of the Rayleigh-Taylor instability, and I've gotten stuck on the point of which fluid (more or less dense) is being accelerated into the other. Cases of uniform ...
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### 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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### Examining the presence of persistent domain from time series data

There are three variables, $X_t$, $Y_t$, and $Z_t$ that are dependent of each other, and I have the time series data of those variables from replicated experiments. The stochastic dynamics look quite ...
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### Is an elastic, gravitating object stable?

As I understand, an object can contract under its own gravitantional pull. Then as it does so, different parts of the object must move with some velocity. This in turn means that their relativistic ...
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### 2D room with electron-point-charges (stability)

Is there a fast way to find out stable #"point charges" & constellation for this kind of Simulation. The 2D repeating itselve in each direction till infinity, so i've a kind of symetrie here. ...
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### Temporal properties of a photon

Naively, one can attempt to consider the (impossible) light-speed inertial frame. From there you arrive at nonsense conclusions like 'the universe is flattened in the direction of travel' which must '...
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### Lyapunov stability of circular orbits

I'm studying Classical mechanics on Arnold's "Mathematical Methods of Classical Mechanics". In a problem i'm asked to find for which $\alpha$ the circular orbits in the central field problem are ...
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### Why is the orbital resonance of the Galilean moons stable?

It is well known that the orbits of Ganymede, Europa and Io are in a 4:2:1 resonance. Most online sources (including but not limited to Wikipedia) say that such an orbital resonance, along with the 3:...
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### Does the maximally-extended Schwarzschild horizon see the entire past of the parallel universe?

I've seen similar discussions for the inner horizons of Kerr and Reissner-Nordstöm metrics, but I've never seen mention for the simple maximally extended Schwarzschild geometry: As an infalling ...
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### Bottle stableness optimization

A few days ago me and some friends played a game where you need to upset a bottle with a ball(flunkyball). Then a question occured: "How much water do we need to put into the bottle that its ...
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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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### 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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### 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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### Why are symmetrical structures highly stable?

What makes symmetrical structures(geometry) highly stable? It is perfect to say that the forces acting on a symmetrical structure is balanced and hence stable. But why is it so? To be more specific, ...
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### Imaginary part of the stress-energy tensor

I just encountered in an article of D. G. Boulware ("Quantum Field Theory in Schwarzschild and Rindler Spaces", Phys. Rev. D 11, 1404, 1975, in the last paragraph of the Introduction) the statement ...
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### Can a spheromak propagate in vacuum?

I recently learned about (and am now fascinated by) spheromaks. I am no expert on plasma physics, but as I understand they are analogous to propagating toroidal vortices (smoke rings), but with plasma ...
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### Recursion relations and stability analysis

I have a recursion relation in the form of the following two equations: $X_{t+1} = X_t + V_{t+1} \\ V_{t+1} = wV_t + cy(g-X_t)$ I want to write these two equations into a matrix form so that I can ...
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### Measure of stability

Is there a measure of stability of different systems? What I mean by stability is the ability of a system to return to its original position, even when inputted with high amounts of energy. The more ...
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### Argument for stability of journal bearing via inertial and viscous forces?

As I understand a journal bearing, a rotor is levitated by hydraulic forces from the lubricant. While these are lots of studies on this subject, I can't manage to find a paper that coherently breaks ...
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### What is the criterion of stability of thick-walled spherical shell?

Is there the formula (if someone already has discovered it) or what is the algorithm (if a particular formula was not deduced), to calculate the critical pressure of thick-walled spherical shell $−$ ...
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### Stability of fix-point of a system of 3 non linear first order ODE, when one of the eigenvalues of Jacobian is zero

I have been working on a mean-field solution for am open quantum system model, to compare with the numerical solution of the exact solution. I have solved the system for steady state, but am now ...
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### Generalized Eigenvalue Problem from linear stability analysis

I am trying to solve a generalized eigenvalue problem raised by linear stability analysis $$AV=\lambda BV.$$ $A$ and $B$ are non-symmetric complex valued matrices. The set of equations I am trying to ...
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### Would it be correct to state that all the forms of everyday matter (mountains, tables, buildings, people, etc.) are in a metastable state?

We had a fire going in the backyard of a friends house this weekend, and after thinking about the chemical reactions occurring in the wood (and anything else we threw into the pit), I started to ...
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### Stability of a complex valued system using Jacobian

I want to find the conditions for stability of a system by constructing the Jacobian matrix and finding what values of my parameters will give me negative eigenvalues. My system is of the form \$ \dot{...
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### Stabilizing a shaft with only one electromagnet

I have recently come across Earnshaw's theorem in my research which states that it is not possible to stabilize an object using only static permanent magnets. I understand that and it makes sense to ...
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### Stabilizing a rotating wheel with a changing center of mass

Imagine a rotating wheel. For simplicity's sake let's assume it's not under the influence of any significant external forces (including gravity). This wheel is hollow, and objects inside are ...
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### Is it possible that any spatial variation in press disturbance without gravity?

When gravity (and buoyancy), acting as the only body force of a liquid, is ignored. Is it possible that any spatial variations in pressure perturbation are the result of fluid motion or some other ...
I tried this on Math Stack Exchange. I'm trying to find initial conditions to ensure systems of the form stay bounded $$\ddot{x}_i+\sum_{j=1}^N k_{ij} x_j = 0, \quad k_{ij} \in \mathbb{C}.$$ For ...