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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Stability and global symmetries of complex scalar field theory [closed]

Given the Lagrangian of a complex scalar field: $$ \mathcal L = \partial_{\mu} \phi^* \partial^{\mu} \phi - m^2 \phi^* \phi - \frac 12 \mu^{4-2n} \phi^{2n} - \frac 12 (\mu^*)^{4-2n} (\phi^*)^{2n} \, ,$...
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Eigenfrequencies of an Hamiltonian dynamical system in different bases

Consider the Hamiltonian $$ H=H(x,y,p_x,p_y) $$ which generates the dynamical system $$ \dot{x}=+\frac{\partial H}{\partial p_x} $$ $$ \dot{y}=+\frac{\partial H}{\partial p_y} $$ $$ \dot{...
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How to argue on physical grounds that a function is the ground state of a Hamiltonian?

$u_l(r) = Ar^{l+1}e^{-\kappa r}$ is provided as a solution to the radial wave equation for the Coulomb potential $$-\frac{\hbar^2}{2m}\frac{d^2}{dr^2}u_l(r)+\Bigl[\frac{\hbar^2}{2m}\frac{l(l+1)}{r^2} -...
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Unconditionally stable numerical method for 1st order non-linear coupled ODEs? [migrated]

I am attempting to numerically solve the following system of ODEs: $$\begin{gather}\frac{dT_1}{dt} = f_1(T_1,T_2), \quad T_1(t=0)=T_{1,0} \\[3pt] \frac{dT_2}{dt} = f_2(T_1,T_2), \quad T_2(t=0)=T_{2,0}...
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How wide is the $L_4$ and $L_5$ Moon-Earth Lagrangian point?

How far would an object need to be displaced from the $L_4$ and $L_5$ Lagrangian points so that it can escape returning to those points?
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Earth's orbit: chaotic but stable

The eccentricity of Earths orbit follows a bounded random walk-like pattern, see this chart. I presume most other planets are similar. One could think of eccentricity and argument of periapsis as "...
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A subtlety about Lyapunov stability of stationary rotations of rigid body

On Page 145 of Arnold's mechanics book there is the intermediate axis theorem: "The stationary solutions of the Euler equations corresponding to the largest and smallest principal axes [of the ...
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95 views

Why hasn't the false vacuum collapsed yet?

The Standard Model, and current measurements of the Higgs mass, suggest that our universe is in a metastable state, which may catastrophically collapse into a false vacuum. https://en.wikipedia.org/...
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Stabilizing a lightweight (empty) ship

Is it possible to stabilize an empty ship on high ocean waves with weights on long structures free to open up like wings by rotation on two vertical axis attached to the body of the ship simmilar to a ...
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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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Lattice stability

If one calculates the phonon dispersion function for cubic lattice in 3d or quadratic lattice in 2d, then it is seen that there exist impulses for which the frequency becomes imaginary. So it seems ...
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How to prove that atoms exist? More precisely - how come electrons and protons do not fall into each other? [duplicate]

Basically the question that I'm asking. Sure - There are few interactions that take the expected effect - electromagnetic, gravitational, strong and weak interactions. But how can we prove it, exactly?...
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Why can't we have trinary or multiple sytems, like binary systems?

We usually come across close binary systems in Astrophysics. Also, we can have hierarchical systems in which there is a close binary. The Alpha Centauri is an example of an hierarchical triple. But ...
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Is a square tube more resistant to bending than a round tube?

In considering tubular forms for aircraft construction, I am reasoning that a square form (or I-beam) would be more resistant to bending (if the load is directly perpendicular and in the plane of the ...
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Rigorous proof of Bertrand's Theorem for orbits under central force

I have read through several proofs of Bertrand's Theorem, including the one on Wikipedia. A typical proof can be found here (Santa Cruz Institute for Particle Physics). Almost all proofs using ...
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Why do all observed stable $n$-body systems have the largest mass at the center?

Comparing three different scales of $n$-body systems, atomic systems, solar systems and galactic systems, we find that all (observed) systems that exhibit long term stability have the largest mass at ...
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What is a “Doppler instability”?

In the paper "Flow-induced control of chemical turbulence" by Berenstein and Beta, the term "Doppler instability" is mentioned in the context of the Belousov-Zhabotinsky reaction. I am looking for a ...
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Solar system and $n$ body problem [duplicate]

How is possible for the solar system to be stable if has been proved that even the trhee body problem is chaotic with a very small amount of stable solutions? Do we need to consider the solar ...
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White dwarf stars: limits to stability

The Chandrasekhar mass limit $M_\text{Ch}$ for a cold, non-rotating white dwarf star is derived from the hydrostatic equilibrium assuming Newtonian gravity and a Lane-Emden polytrope with n=3. However,...
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Implication of Earnshaw theorem to the orbit of the moon

Can we apply Earnshaw theorem in circular/elliptical/hyperbolic orbits? I was wondering how did the moon stop at its current stationary orbit. It seems to me the fragments that gave origin to the moon ...
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Bicycle physics [duplicate]

From a long time, I have a question that bicycle is not stable at low speed or for that matter it's difficult to balance bicycle on its wheels in static position (with zero speed and no brakes). Can ...
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Can there be an atomic nucleus where there are more protons than neutrons?

As far as I know, number of protons is less that or equal to the number of neutrons in any atomic nucleus. But is there any possibility that there exists a nucleus where the number of protons exceeds ...
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Intermediate axis theorem in higher dimensions

The intermediate axis theorem states that the rotation of an object around its first and third principal axes is stable, while rotation around its second principal axis (or intermediate axis) is not. ...
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Looking for a good book on star stability

Can anyone recommend me any resources from which I could learn about how stars maintain a stable form, maybe using some thermal and nuclear physics, and maybe fluid dynamics, but not so advanced. ...
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5 Lagrangian points: why isn't there a line of stability between $L_1$ and $L_4$ and $L_1$ and $L_5$ respectively? [duplicate]

Given the 5 Lagrangian points of two large orbiting bodies: (from wikipedia), why isn't there a line of stability between L1 and L4 and L1 and L5 respectively (as depicted in red in the modified ...
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How much water to put in cup for maximum stability? [closed]

I found this problem in ‘200 puzzling physics problems’ An empty cylindrical beaker of mass 100 g, radius 30 mm and negligible wall thickness, has its center of gravity 100 mm above its base. To ...
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Arnold's Mathematical Methods of Classical Mechanics and Lyapunov stability

In Arnold's Classical Mechanics of Classical Mechanics, he refers to Lyapunov stability in many of the problems in the second chapter. E.g. on page 20: "Problem: Consider a periodic motion along the ...
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Apparent contradictions in stability conditions for diamagnetic materials

I was looking at Herbert B Callen's book on thermodynamics, specially Chapter 8 on the Stability of Thermodynamic systems. In it, he states that for a system to be in a stable thermodynamical ...
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Can a Gyroscope be Used to Stop a Spinning Cable?

The scenario here is a helicopter attempting to hoist someone vertically into the air. When the person leaves the ground they begin to spin (sometimes slowly, other times quite fast if not stabilized ...
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How is Schrodinger's model of atom consistent with reference to Maxwell's Theory of Electromagnetic Radiation? [duplicate]

When Rutherford proposed his model of atom, he mentioned that "Nucleus is surrounded by electrons that move around the nucleus with very high speed in circular paths called orbits. James Maxwell ...
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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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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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Finding stable superheavy elements

Finding new stable superheavy elements is big interests in nuclear physics. Nuclides with $Z>92$ are not found in nature, but can be made artificially. Usually these nuclides become more unstable ...
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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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Is flipping a coin is a stable rotation?

If I rotate a coin with dimensions: 10X10X1 about 1 of the big axes(10) in space, where there is no torque, will the rotation will be stable just like a frisbee or a football regular rotations are? ...
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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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What is causing plasma confinement instability according to Erik Witalis?

Erik Witalis mentions problems with traditional plasma confinement like the one in tokamaks and particle beams. Instead he mentioned a different technique. What is the problem with plasma confinement ...
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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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Chua's circuit: Is $x=y=z=0$ a stable equilibrium?

According to this wikipedia page, the differential equations satisfied by several physical quantities in Chua's circuit is (What each letter represents doesn't matter that much in this question) For ...
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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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What does the Ostrogradsky instability have to do with stability?

Ostrogradsky's instability theorem says that under some conditions, a system governed by a Lagrangian which depends on time derivatives beyond the first is "unstable". In the proof, one computes the ...
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Stability/decay, are they boolean or not, or does QM probabilities overrule this?

This is not a duplicate, I am not asking whether the proton is a stable particle, or why it is. I am asking about the definition of stability/decay whether it is boolean or not. I have read this ...
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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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Why does a force divide equally on multiple supports/legs?

Imagine a bridge spanning across two pillars/supports with a weight of $80N$. {Any external forces affecting the system are assumed to be negligible.} We know that the force exerted on these 2 ...
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Orbital stability and inverse square law

It is well-known that orbits are stable under an inverse square law gravitational attraction. My question is, how far could gravitational attraction deviate from an exact inverse square law without ...
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Jupiter & Saturn

In his prog. on Jupiter, Brian Cox stated that the complex gravitational interplay, between Jupiter & Saturn, prevented Jupiter from drifting through the Asteroid Belt, and approaching our part of ...
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Railroad train on tracks [closed]

What keeps the railroad trains on the tracks? P.S: It is not the flanges, as already remarked by Dr. Richard Feynman. I want a detailed explanation of this question, if possible. Thanks.
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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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Is this wire-melting phenomenon a manifestation of the Plateau–Rayleigh instability; have I done my math 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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