# What is Instability: Definition and 56 Discussions

In numerous fields of study, the component of instability within a system is generally characterized by some of the outputs or internal states growing without bounds. Not all systems that are not stable are unstable; systems can also be marginally stable or exhibit limit cycle behavior.
In structural engineering, a structure can become unstable when excessive load is applied. Beyond a certain threshold, structural deflections magnify stresses, which in turn increases deflections. This can take the form of buckling or crippling. The general field of study is called structural stability.
Atmospheric instability is a major component of all weather systems on Earth.

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1. ### I Fourier transform of the density fluctuation

There is a Fourier transform that I don't really understand in my textbook. I have the following equation: ##\ddot{\delta} + 2H\dot{\delta} -\frac{3}{2} \Omega_m H^2 \delta = 0## Then using the Fourier transform: ##\delta_{\vec{k}} = \frac{1}{V} \int \delta(\vec{r}) e^{i \vec{k} \cdot \vec{r}}...
2. ### Stability test for Feedback Amplifiers

Does the following simple test deduced from Nyquist criterion also apply to positive feedback or it needs to be modified? If magnitude of loop gain i.e. |T (jω)| > 1 at the frequency where phase(T (jω))= −180◦, then the amplifier is unstable. Reference: Analysis and Design of Analog...
3. ### I Electron-Positron Pair Instability Supernova

How does the formation of electron positron pairs increase the energy density and softens the EOS? I trrying to understand the pair instability supernova. In many texts and articles, it is written that the formation of electron positron pairs lead to instability, the energy density is increased...
4. ### Plasma thruster - plasma instability in magnetic nozzle

Plasma instability may be a solution for magnetic nozzle plasma thrusters https://phys.org/news/2022-12-plasma-instability-solution-magnetic-nozzle.html Kazunori Takahashi (Tohoku University), Christine Charles (ANU, Canberra, AU) & Rod W. Boswell (Tohoku University) Wave-driven electron...
5. ### Fractals/Dendrites and the Dissolving of Phenoxyethanol in Water

I shot some high speed footage of phenoxyethanol dissolving into water and observed some fractal/dendrite like patters at the edge of thin droplets that float on the surface of the water. I suspect that the water under the droplet becomes saturated very quickly as the phenoxyethanol is not...
6. ### Frequency of boundary layer instability

I've been searching the net but can not find any freely available literature. Can someone give me a quick lesson on boundary layer instability and its frequencies? I have an equation that claims to scale the instability frequency by: F = U/2*delta U is leading edge velocity delta is layer...
7. ### A Lagrange with Higher Derivatives (Ostrogradsky instability)

In class our teacher told us that, if a Lagrangian contain ##\ddot{q_i}## (i.e., ##L(q_i, \dot{q_i}, \ddot{q_i}, t)##) the energy will be unbounded from below and it can take any lower values (in other words be unstable). In this type of systems can we show that the energy is conserved ? Or in...
8. ### B Pair Instability Supernovae & Electron Capture Supernovae

Hi! I've been browsing the internet for information about supernovae and I came across this chart describing 4 types of core collapse causes (the chart may have copied weirdly because not all the information fits into this text box): Cause of collapse Progenitor star approximate initial mass...
9. ### MHB Diffusion-driven instability conditions

Is anyone able to help with a diffusion-driven instability condition question I've got: I think I've got the DDI's: So DDI 1 = -pi^2 DDI 2 = 6pi^2 DDI 3= 7pi^2 DDI4 = 49^4 Which I believe satisfies the DDI conditions, however I'm not sure what it means by calculate the range of unstable...
10. ### I Jeans Instability in an Expanding Universe

I am trying to derive the equation for a case, where we have a dust(zero-pressure) in an expanding universe. There are 4 equations but I think exercising on one of them would be helpful for me. I am trying to derive the equation for a case, where we have a dust(zero-pressure) in an expanding...
11. ### I How is the viscosity of a plasma produced?

Summary: I'm interested in knowing more about instabilities within plasma. Is the viscosity of plasma produced by thermal, magnetic, or gravitational effects (or even something else)? I had the opportunity to talk with multiple Ph.D. students during the summer and was especially interested in...
12. ### A Sufficient conditions for Rayleigh-Taylor instability

I was reading the paper entitled "The Rayleigh—Taylor instability in astrophysical fluids" by Allen & Hughes (1984), and they discuss relativistically hot plasmas in the context of weak magnetic fields which are presumed to have no dynamic influence, so they take a fluid approach. In this paper...
13. ### Exploring Reyleigh-Taylor Instability with Variable Density and Viscosity

Homework Statement import time import numpy as np from Output import * from PoissonSolver import * tmps1=time.clock() # Physical parameters Re = 10. # Numerical parameters CFL = 0.9 dt = 0.001/4 t = 0.0 tmax = 1.5 # Make mesh from MeshGeneration import * mesh = Mesh(2.0,1.0,50,25) #...
14. ### I Instability of the Solar System

Hello! I read in some books that the behavior of the Solar system can't be predicted indefinitely (up to several hundreds of million of years). Is this a numerical limitation, in trying to simulate it or is it some physics responsible for it? (I guess that this assumes that no other bodies...
15. P

### I Instability of a Rigid Untethered Ring Around a Planet

I had this discussion while driving home to California from a trip to Washington state with a friend. We were discussing the stability of a completely rigid, untethered, ring-structure around Earth, and I did not know how to explain to him that such a thing must be tethered by rigid towers lest...
16. ### Design of High Pass filter to eliminate an instability in my control system

HI, i have a first order controller (ts/ks+k) which contain some oscillations and its settling time is very huge, i wanted the controller to have settling time of 10seconds and remove the oscillations. in order to remove the noise and get the expected settling time i added a filter ( s/cs+1)...
17. W

### Charged liquid jet instability

I am dealing with a problem of instability of an infinitely long charged liquid jet. When there is a change is surface profile(which originally is a column with radius R), it surface charge density changes, thus the electric energy change of the liquid jet is E (due to surface charge density...
18. ### I Why Does a Fluid Jet Become Unstable at Wavelengths Exceeding Its Perimeter?

Why a fluid jet becomes unstable only when the wavelength of the perturbation exceeds the value of jet perimeter? Do you imagine any physical reason behing this?
19. ### B How can you justify that the degree of instability inside a

How does the degree of instability relates with the Energy released and the binding energy?
20. ### I Instability of the Higgs particle

In the multiverse paradigm, the Higgs particle is said to be unstable. What does the instability of the Higgs particle mean? Could it spontaneously disappear? What are the conditions for something like that to happen? And what would be the fate of the universe if that were to happen - keeping in...
21. ### A Instability of Cosmology with Quantum Corrections

A good year ago, quantum corrections have been proposed to the very early Universe. It was concluded that these quantum corrections contain a precise estimation for the cosmological constant and the so-called radiation term. The authors even have interpreted the latter as evading the big-bang...
22. ### Modeling plasma instability with electric arc discharges

I was reading a paper recently about guiding electric arc discharges with lasers. http://loa.ensta-paristech.fr/ilm/uploads/ILM/134_Forestier_discharge_AIPAdvances_2_012151_2012.pdf Since electric arcs are plasmas and they seem to be stabilized by lasers, could the same principle be applied to...
23. ### Instability of a 1D material due to Fermi surface nesting

Consider the Lindhard response function: \chi(\vec{q})=\int\frac{d\vec{k}}{(2\pi)^d}\frac{f_\vec{k}-f_{\vec{k}+\vec{q}}}{\epsilon_\vec{k}-\epsilon_{\vec{k}+\vec{q}}} where ##\vec{q}## is the wavevector, ##\epsilon## is the free electron energy and ##f## is Fermi-Dirac distribution function. For...
24. ### Instability of free rigid body rotation about middle axis

Hi everyone, I was recently talking to someone with a non-maths background about rotational stability, in particular how rotation is stable around the largest and smallest principal moments but not the intermediate one. He asked me if there was any 'obvious' reason for this, but one didn't...
25. ### Pair instability supernova pressure and temperature question

I read a scientific journal article that discusses pair instability supernova - I am puzzled about something discussed in the article. If the collision of atomic nuclei and energetic gamma rays produces electron and positron pairs which reduces the pressure inside a supermassive star's core -...
26. ### Instability of classical system of point charges

Earnshaw's theorem http://en.wikipedia.org/wiki/Earnshaw's_theorem gives a straightforward reason why we can't have a static equilibrium for a system of point charges. For some time I've been trying to find out if anyone's worked out a similar proof for the impossibility of a dynamic...
27. ### What does it by parametric instability?

Hi, I'm majoring in fluid mechanics. I notice some researchers are using the phrase parametric instability. I googled it, it seems this comes from the solid mechanics (vibration). Can you explain to me what's the difference between parametric instability and the resonance? They seem the same...
28. ### Can Weibel Instability Generate Cosmic Magnetic Fields?

http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys3178.html Collisionless shocks can be produced as a result of strong magnetic fields in a plasma flow, and therefore are common in many astrophysical systems. The Weibel instability is one candidate mechanism for the generation of...
29. ### Mass Inflation Instability in Kerr and Reisnerr black holes.

What exactly is this mass inflation instability phenomenon that is said to happen near the inner horizon of black holes? http://jila.colorado.edu/~ajsh/insidebh/realistic.html I got the nutshell of it, but I think I need someone to really explain this.
30. ### Question on the Inherent Instability of Lagrangian points

The question revokes around my personal hypothesis that there is two forces connected with the Gravitational Field one obviously attraction between two bodies that is linear and the second is a less powerful repulsive force that emanates in a spiral motion off of rotating bodies that causes the...
31. ### Snake instability and vortex pair

Dark soliton is a general phynomenon in broad physics subjects. In higher dimensions, dark soliton exhibits instable except one special kind as vortex. The fundamental instability of a single dark soliton in two dimensions is to eventually decay into a number of quantized vortics through what is...
32. ### MHB Determining critical values which cause multi-solutions and instability

I have the motion of a forced spring: $$x'' + \kappa x' + x - x^3 = \varGamma \cos(\omega t) \ \ \cdots \ \ (1)$$ and I am investigating the stability of its solutions with forcing period $T = \frac{2\pi}{\omega}$. I am given the asymptotic radius of the solutions: R_0(\kappa,t,\omega) =...
33. ### Attenuation numerical instability via numerical diss. nonlinear ODE

Hi, I'm solving a problem numerically that takes the form Q_{ij} \ddot{y}_j +S_{ijk}\dot{y}_j\dot{y}_k +V_i=0, where (Q_{ij},S_{ijk},V_i) are all functions of the dependent variables y_i. The dependent variables are all functions of the variable t. The resolution of this spectral...
34. ### Higgs mechanism and vacuum instability

Does the shape of the Higgs potential change if the energy of the vacuum changes? According to Wikipedia, If a more stable vacuum state were able to arise, then existing particles and forces would no longer arise as they presently do. Different particles or forces would arise from (and be...
35. ### Is the Higgs Mass Linked to Vacuum Instability?

Various news outlets are reporting a AAAS talk by Joe Lykken which appears to be about vacuum instability based on the mass of the Higgs. Frustratingly, there appears to be no info on the web apart from these crap popularizations. Can anyone provide any insight? The best info I have is the...
36. ### The Ostrogradski instability and f(R) theory

I am studying modified gravity theories, these days, and I have learned from many papers that, among various modified gravity theories, f(R) theory can avoid the Ostrogradski instability. Most of these papers cited Woodard's paper in 2007 (Lect. Notes. Phys. 720, 403 (2007)), which just gives a...
37. ### Understanding Jeans Instability & Masses

I'm trying to understand all the properties of the Jeans instability, the Jeans mass and the Jeans length. I understand the mathematics behind it, though not all the variables. There is a [itex]m_{H}[\itex] or I've also seen it as [itex]m_{p}[\itex] in the Jeans length and Jeans mass. The...
38. ### Instability of Liquid Jets: Incorporating a forcing function

Hi, I am working with a droplet generation system that is designed to produce monodisperse droplets. A periodic disturbance of appropriate frequency (kHz) is applied to a piezoelectric ceramic, transferred to an orifice disk (fitted within the ceramic by means of a Teflon O-ring), then sent to...
39. ### Instability of an atomic clock

Hi When I read "popular" papers on atomic clocks, many journalists write that the clock loses 1 second in XX million/billion years. But when I look at some professional papers, people talk about a fractional instability of e.g. 10-14t-1/2, the authors never use the former way of characterizing...
40. ### Deriving bar instability mode- formal definition of instability?

I am doing an undergraduate project on bars and I am trying to derive the bar instability mode given by Mo et al. It says "whether or not a disk is globally stable depends on the global properties of the disk... it is not possible to write down a universal dispersion relation or stability...
41. ### Crank-Nicolson instability in 3D

I have a perfectly working 2-D finite-difference thermal solver, using an alternating-direction implicit scheme (painfully written in Fortran 90 at my adviser’s insistence), that I have recently extended to 3-D. It is essentially a three step approximation to the Crank-Nicolson equation, which...
42. ### About the instability of wormholes

"The Einstein-Rosen bridge was discovered by Albert Einstein and his colleague Nathan Rosen, who first published the result in 1935. However, in 1962 John A. Wheeler and Robert W. Fuller published a paper showing that this type of wormhole is unstable, and that it will pinch off too quickly for...
43. ### 125 GeV Higgs and Vacuum Instability

125 GeV Higgs and "Vacuum Instability" So the Higgs has been http://press.web.cern.ch/press/pressreleases/Releases2011/PR25.11E.html (maybe). Nothing "beyond the standard model" about that of course; the Higgs is standard model. Except-- in the leadup to the LHC announcement, I repeatedly saw...
44. ### Understanding the Instability of Positronium: A Closer Look at K-Capture Decay

The 'reason' electrons do not collapse into the nucleus of atom is due to the standing wave nature of the electron. This is all fine and dandy. My question, essentially, is why the same does not hold true for positronium (in which an electron orbits a positron). Shouldn't the electron...
45. ### Hyperbolic Equation Instability

Hello, I'm trying to calculate the following equation which is the derivative in 'x' of a distribution function: d(dxF)/dt = d(Efield.(dvxF))/dx The problem comes because the right hand of the equation is solved by using central difference, but there is a zone where there is a...
46. ### What Does 'Superconducting Instability' Mean?

Could anyone please explain what 'Superconducting instability' means? If there are some good references to read, that would be really nice!
47. ### Unstable molecules - is the instability relative to environment?

Unstable molecules - is the instability "relative" to environment? There are many highly unstable chemical configurations. Most chemicals, after all, would prefer to move from high-energy states to low-energy states. This is usually possible due to the presence of a reaction pathway that makes...
48. ### Archeomagnetic jerks & Unexplained Geomagnetic Field Instability

Geomagnetic researchers have found in the last 10 years that the Earth's geomagnetic field abruptly changes in intensity with the non-dipole portion of the total field suddenly becoming stronger. These abrupt change events are referred to as archeomagnetic jerks, as one analysis method to find...
49. ### RC Aircraft Stability: Neutral or Instability?

For an RC aircraft which i am working on i was thinking about having static stability at the extreme limits of pitching to prevent stalling and further instability, but i was wondering what to have between the limits neutral static stability or static instability. Static instability may help the...
50. ### Fermi Surface Instability in Solid States: Explained

Hi Can somebody explain the meaning of the following sentence which is from Wikipedia: "Solids with a large density of states at the Fermi level become unstable at low temperatures and tend to form ground states where the condensation energy comes from opening a gap at the Fermi surface e.g...