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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Do elementary particles last forever?

I have heard that not even black holes last forever, because of Hawking radiation. But what about elementary particles? Will an electron, for example, exist for all time?
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MHD instability: $\boldsymbol{k}\cdot\boldsymbol{B}=0$?

In this paper, on page 3, it states that to trigger an instability, a disturbance needs to have a wave vector, $\boldsymbol{k}$, which satisfies, $$\boldsymbol{k}\cdot\boldsymbol{B}=0,$$ where $\...
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Stability of energy levels in quantum mechanics

Does QM explain the fact that in nature electrons in atoms tend to be in the lowest energy level? Why are excited states unstable? And are excited states always more energetic than stable ones?
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Do Binary Stars Escape Each Other?

updated 8/27/2020 While the recession of our Moon from the Earth may slow and even stop, (see When will the Moon reach escape velocity?) binary star systems will (1) never stop experiencing mutual ...
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Is action maximized for a system in stable equilibrium?

Others have asked in general about cases in which the action integral is not minimized, but my question is specific: Can we show that the conventional action integral is always maximized for a system ...
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How does a bullet achieve its stability when fired?

As far as I know, darts, arrows, and airplanes have the center of gravity(CG) ahead of their center of pressure(CP) and often have fins at the rear to achieve stability. Contrary to these, bullets ...
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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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What is the physics explanation for why an object with a larger base is more “stable” or and more able to “balance”?

What is the physics explanation for why an object with a larger base is more "stable" or more able to "balance"? For example - two pyramids, one on its tip (less stable) VS one on ...
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Why a mechanical balance can balance? [duplicate]

In the above diagram, assume that the level is solid and massless: In the left setup, both mass are fixed on the level. As we know, it is not a stable mechanical balance. For any tilt, the level ...
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What does it mean when an isotope is stable?

Does stable mean that an isotope has a very long half life, for example xenon-124 has a half life of 1.8 x 10^22 years, or does it mean that fissure is theoretically not possible, or does it mean that ...
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Stability and topological charge of kink (anti-kink) solutions (soliton)

I am reading the book << Gauge theory of elementary particle physics >>. In chapter 15, it presents a model having finite-energy solution. First, we have a $1+1D$ spacetime model \begin{...
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If mass is homogeneously distributed why would there be gravitational attraction between bodies? [duplicate]

Assuming the mass of the universe was spread completely evenly throughout space why would gravitational attraction happen? All bodies in the universe would feel gravitational tug equally in all ...
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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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Is an infinite set of positive and negative charges next to each other $… - + - + …$ a position of equilibrium?

Suppose we have an infinite set of positive and negative charges next to each other: $$... + - + - + - ...$$ I am wondering if this a position of equilibrium. Intuitively I would say that it is a ...
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One third of Lyapunov exponents are zero? What does it mean?

This may be quite a straightforward question, but I have a dynamical system with a high dimensional phase-space. I calculated the Lyapunov spectrum for it and saw that one third of my Lyapunov ...
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How Bohr's model explains the stability of atoms?

How Bohr's model explains the stability of atoms? From Maxwell's equation, we know that an electron or any other charge will radiate energy on acceleration. This problem is said to be solved by Bohr ...
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Why does a book leaned up against a wall sometimes fall over after being stable for many hours?

This problem has been vexing me for years. Sometimes, you lean a book up against a wall and it stays there (the static frictional force balancing gravity, etc), but then after a long time (hours or ...
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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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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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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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