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 compact can a thin shell be without collapsing?

I've heard of https://en.wikipedia.org/wiki/Buchdahl%27s_theorem. It states that as the ratio between a spheres radius a it's Schwarzschild radius approaches $9/8$. the pressure at the center tends to ...
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About why electrons in atom don't radiate(considering wave nature also) [duplicate]

It's said in textbooks that electrons won't radiate and fall into nucleus because matter wave of it's form a standing wave but could somebody explain why being a standing wave it doesn't radiate, even ...
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75 votes
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Why doesn't a nucleus-like body made up of just neutrons exist?

We know that neutrons exert short ranged nuclear forces over other nucleons in a nucleus, and these forces are only attractive in nature. Also this force is universal and doesn't differentiate between ...
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Why do elements, as they have more protons, need a higher amount of neutrons to stabilise them? [duplicate]

I've seen the graphs of the stability line but I can't find any reason as to why this happens, I understand radiation, just not why radiation needs to occur in the first place if that makes sense.
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Why does the stability of a nucleus depend on the binding energy $\textit{per nucleon}$ instead of the total binding energy?

The larger the total binding energy of a nucleus, the greater the minimum energy that must be added to infinitely separate the constituent nucleons. Shouldn't the total binding energy, then, be used ...
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Current status and reference request for the Black Hole Stability Conjecture

The Black Hole Stability Conjecture is one of the most important open problems in the field of General Relativity, and remains open in spite of the advances in the past half century. To test Einstein’...
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Are atoms still unstable in 4 spatial dimensions when the physical size of nuclei is accounted for?

Per this answer, depending on a dimensionless parameter hydrogen atoms in 4 spatial dimensions can be either unbound (i.e., nonexistent), stably bound dependent on boundary conditions, or unstable ...
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Pointers for dealing with instability in fluid simulation?

I have been working on a 2D fluid simulator, and I have fallen victim to the problem of jumping in before doing enough research. I naively implemented a finite difference form of the continuity and ...
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Gas bubble underwater explosion shape

In this paper looking at the behaviour of gas bubble in water, under increasing pressure. Question, why the water pierces the bubble inwards, not the other way round? (images B, C) (i.e. gas spike ...
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Stability of a crate lifted with a lifting beam and two slings when the center of gravity is above the attachment points of the slings

I have a hard time understanding the stability of a crate lift when using a lifting beam. Consider the system in the first figure, where a crate is suspended in two lines using a lifting beam. Presume ...
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Active Balance on L1

Could you have a spacecraft on L1 say the earth-moon system and then extend a weight on a string to the moon and a weight on a string to the earth and keep the spacecraft in balance at L1 just by ...
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Proving the Stability conditions in Thermodynamics

The stability condition derived in Kardan's Statistical Mechanics textbook given by $$\delta S\delta T+\delta J\delta X+\delta \mu \delta N\geq0$$ I'm trying to show from this $$\partial^2_S E|_V\geq ...
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Stability of Chemical Reactions [closed]

Given the following reactions: $$A + X \xrightarrow{k_{1}} 2 X$$ $$Y + X \xrightarrow{k_{2}} 2 Y$$ $$Y \xrightarrow{k_{3}} B$$ I was able to write the following rate equations for the concentrations: $...
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What is a quasibound state and how is it different from a bound state?

What is a quasibound state and how is it different from a bound state? I have read this term in nuclear physics in the context of compound nucleus formation. A compound nucleus $C$ is formed by the ...
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Electrons remaining in an orbit and the emission of photons?

Electrons are not stationary around a nucleus, even if it remains in the same excitation state / in the same 'orbit'. As moving electrons should stir the EM field, they should be creating EM waves/...
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How can I show that the action of a SHO is a saddle-point solution if $t_{f} - t_{0} > T/2$?

In this post and in this post, QMechanic claims that a simple harmonic oscillator with Dirichlet boundary conditions has saddle-point solutions if $t_{f} - t_{0} > T/2$ where $T$ is the ...
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What does it mean that the vacuum is unstable?

This book I'm reading states that the Klein-Gordon equation, for $m^2<0$ has an "unstable" vacuum $\phi=0$. It's talking about tachyons and how their presence is a sign of instability. ...
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Graph Interpretation of Fold of Cyclic Bifurcation

I was studying about local bifurcations of cycles, and the basic type of it was the cyclic fold. According to the textbook, cyclic fold bifucation was the meaning of one of those that is, for two ...
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Criteria for Kelvin-Helmholtz Instability

I am presently engaged on a project to model elements of the behavior of Jupiter's atmosphere. I have been given by my authority some readings on fluid dynamics to raise awareness for the code. ...
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Extreme oscillations and values in heat equation on a 1D closed ring

I am trying to create a (very) simple model of heat diffusion along a closed rod (e.g., a ring) with an initial condition in which one segment is hotter than the rest. I'm using the following formula: ...
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Why is stable rotation achieved about the long axis of a skateboard? [duplicate]

I've been preparing a video for my mechanics assignment and I've hit a deadlock. Basically, I want to prove that the long axis of a skateboard takes the least force to move around it.I figured that a ...
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Deformation convert stresses to others

Elastic instability (also known generically as buckling) can be interpreted as the phenomena in which deformation converts axial stress(compression) into bending moment. OK. Also, if we deform an ...
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Equation of Hill sphere when the mass ratio is not large

I know of the equation for determining the Hill sphere. Which is $a(1-e)(m/3M)^{1/3}$. However I noticed that during the derivation of this formula that the assumption that $m\ll M$ is used. But what ...
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To prove mathematically that a tip standing vertically will fall exponentially as soon as it deviates from its original position. (Homework Problem) [closed]

This is one of my questions from Homework for Quantum Mechanics. I know the answer quantitatively but cannot find any mathematical explanation. Question: Consider a thin needle of total mass m and ...
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Why is there no stable nucleus with two or more neutrons but no protons? [duplicate]

Why is there no stable nucleus with two or more neutrons but no protons?
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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 "magnetic instability"?

I saw "magnetic instability" many times in papers about superconductivity, but what is magnetic instability exactly? like this paper 10.1103/PhysRevB.40.10816 They only mentioned "...
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When you say "stability of soliton in energy space" what is energy space?

I am reading this (https://arxiv.org/abs/0802.2408) excellent review of the stability of the solutions of the differential equations. However, I don't quite understand what the author means when ...
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1 vote
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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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Why is Kerr Spacetime unstable?

How do we know from the Kerr Metric that it is unstable near the Cauchy Horizon? What causes this unstability?
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What exactly robustness of a solution mean?

One usually comes across many research papers that talk about robustness, but since I have never been introduced to this term formally in my education, I am not sure what distinguishes a robust ...
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Is a 3 body system with a permanent eclipse possible and stable?

Is it possible to have a star, planet and moon where the moon orbits the planet in the opposite direction with the same period of the planet orbiting the star? So that there would be a never-ending ...
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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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1 answer
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How to determine stability of shocks in hydrodynamics?

Shock waves are very common in relativistic as well as non-relativistic hydrodynamics. The stability of the shocks are usually studies using numerical simulations. However, I am interested to know ...
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Higgs field, phase transitions and false vacuum

Consider the familiar $\phi^4$ theory Lagrangian for a complex scalar field $$\mathcal{L} = \frac{1}{2}|\partial_{\mu}\phi |^2+\frac{1}{2}m_0^2| \phi | ^2 - \frac{\lambda}{4!}| \phi | ^4$$ with $m_0^...
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What the response of unstable limit cycles look like?

Stable limit cycles generate oscillations, i was wondering what the unstable limit cycles behaviours look like? From the picture in the left, the system shows a stable limit cycle and it generates ...
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Stable nuclear isotopes

It appears that all stable nuclei may be seen to be composed of pairs of smaller, stable nuclei, e.g., the Li-7 nucleus seemingly is composed of H-3 and He-4, i.e., 1(3) + 2(4) -> 3(7). What if any ...
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Is there a highest possible atomic number?

I know that atoms with higher atomic numbers tend to become more and more unstable and decay quicker the higher the atomic number goes. Is there a limit to this where the time it takes for the atom to ...
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0 votes
1 answer
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Why don't motorcycles have as good a turning radius as bicycles? [closed]

The question is about why are motorcycles not manufactured with handlebars that can turn to great degrees like a bicycle. In most motorcycles, you hardly have a steering angle of about 20-30 degrees, ...
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7 votes
2 answers
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Why are vortices stable?

Vortices persist over time, but change their shape. I am used to a structure that persists being “stable” as in it is robust against small perturbations. How can one define stability of a Vortex? For ...
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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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Is passive magnetic levitation without moving parts possible without the use of diamagnets?

So, I looked at the Wikipedia page on magnetic levitation and it described lots of ways of levitating things magnetically, but they were all stabilized by either electronic feed-back loops, ...
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2 votes
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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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Will a platform only supported by a column in the center fall? (Excluding weather)

My friend told me that without wind, a building with a platform that only has a column supporting it would be balanced and not fall, given that there is no wind. I said that the platform would fall ...
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Clarification in the definition of stable and unstable equilibrium

I am studying about types of equilibrium which are stable, unstable and neutral. In the definitions of these equilibriums they used the term "position of equilibrium". Like in stable ...
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Extrema in the Table of Nuclides [closed]

Symbolic picture of a nuclid chart: I would like to know for which $Z$ the area in the nuclide map has the greatest width and for which $N$ and the greatest height. Does anyone know? Note: I don't ...
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10 votes
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Why is the number of isotopes of an element bounded?

Is there a known reason why any given element has finitely many isotopes? Here I mean both stable and unstable isotopes. If we know this, do we have a reason why, for a given element, are the isotopes ...
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6 votes
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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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Is $\phi^4$ theory unstable?

I tried to write a simulation of a $\phi^4$ theory for 2+1 dimensions. But whatever values I gave for the coupling constant it always seems to blow up. i.e. a wave-like equation with a mass and ...
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Stability analysis of ODEs containing non-linear terms

I am currently reading this lecture notes on non-linear dynamics. If you look at equation (7) it is easy to write the ODEs, $\dot{x} = y$ and $\dot{y} = -x$ into a matrix form $\dot{\vec{x}}=A\vec{x}$...
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