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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Nonlinear oscillations and stability [closed]

Hi all, Can anyone try to help to solve the following problem in detail, please?
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Why does uniform flow become unstable when the Seddon celerity is greater than the Lagrangian celerity?

Uniform flow down an inclined open channel becomes unsteady under certain conditions. Vedernikov's number > 1 is a generally accepted necessary condition for this type of instability. Vedernikov's ...
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Why every system tends to be more stable? [duplicate]

An entire topic of inorganic chemistry, i.e. chemical bonding, which is also one of the most important topics, is based on the idea of stability. But whenever I ask why every system tends to get ...
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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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Stability and Nuclear Binding Energy

I've read that the cause of Nuclear fission and nuclear fusion lies in the fact that Nuclear Binding Energy confers stability to a nucleus. This is why too heavy or too light nuclei resort to these ...
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Laser interferometry for relative movements between two mirrors

I have been struggling in the past weeks to understand how should I setup a laser interferometer for my experiment. I am not a physicist, and I am quite new to optics. I have a Cassegrain telescope ...
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Tower of building blocks

Why does a tower of building blocks (cubes) fall? Theoretically, as long as the center-of-mass is above the blocks' bottom faces, and as long as one does not shake the tower too much, it should not ...
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Why is the universe so stable and consistent? [closed]

Why is it we can discover patterns? Like math, chemistry, physics, biology, etc. Why does the universe never fail us? For example in one second I'm standing next to you, the next I'm still standing ...
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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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Newtonian mechanics in higher dimensions [duplicate]

Once in a book ( I think title was Mathematical Physics, no idea who the author was) saw the proof of instability of planetary orbits in 4 dimensions, cant remember the details of derivations only the ...
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Energy of a star in hydrostatic equilibrium

A star in hydrostatic equilibrium, considering only the gas pressure that provide a force to balance the gravitational attraction, the total energy is the sum of thermal and gravitational energy and ...
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Hydrogen atom in quantum field theory

In principle, how would we demonstrate the existence of the hydrogen atom in quantum field theory and the standard model? Has it been done in practice? Some naive ideas: Demonstrate that the familiar ...
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Why an electron does not get stuck to nucleus?

An electron remains in its orbit because of electrostatic and centrifugal force. But when a reaction takes place some electrons are gained or removed. Then how they still are stable?
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Why are tricycles inherently unstable? [closed]

I ride a velomobile which is a fared tricycle . The trike is a recumbent to enhance aerodynamics so my knees are over the front axle which supports two front wheels and my head partially lies above ...
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Difference between bound and unbound nuclear states?

What are the differences between bound and unbound nuclear states? What does bound or unbound excited states mean? Please explain in nuclear sense.
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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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Can 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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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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