Instability

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Instability

Instability in systems is generally characterized by some of the outputs or internal states

State (controls)

In control theory, states are what characterize a system. With linear systems states are not unique, but can be transformed into equivalent states using certain linear transformations....
growing without bounds. Not all systems that are not stable

Stability

Stability may refer to:...
are unstable; systems can also be marginally stable

Marginal stability

In the theory of dynamical systems, and control theory, a continuous linear system time-invariant system is marginally stable if and only if the real part of every eigenvalue in the system's transfer-function is non-positive, and all eigenvalues with zero real value are simple roots ....
or exhibit limit cycle behavior.

In control theory

Control theory

Control theory is an interdisciplinary branch of engineering and mathematics, that deals with the behavior of dynamical systems. The desired output of a system is called the reference....
, a system is unstable if any of the roots

Root (mathematics)

In mathematics, a root of a complex-valued Function is a member of the Domain of such that vanishes at , that is,In other words, a "root" of a function is a value for that produces a result of zero ....
of its characteristic equation has real part

Real part

In mathematics, the real part of a complex number , is the first element of the ordered pair of real numbers representing , i.e. if , or equivalently, , then the real part of is ....
greater than zero.

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Encyclopedia

Instability in systems is generally characterized by some of the outputs or internal states

State (controls)

Stability

Stability may refer to:...
are unstable; systems can also be marginally stable

Marginal stability

Control theory

Root (mathematics)

Real part

State space (controls)

In control engineering, a state space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations....
having real part greater than zero.

In structural engineering

Structural engineering

Structural engineering is a field of engineering dealing with the analysis and design of structures that support or resist structural loads. Structural engineering is usually considered a specialty within civil engineering, but it can also be studied in its own right....
, a structure can become unstable when excessive load is applied. Beyond a certain threshold, structural deflection

Deflection

Deflection or deflexion may refer to:*Deflection *Deflection *Deflection *Electrostatic deflection*Deflection ...
s magnify stresses

Stress (physics)

In continuum mechanics, stress is a measure of the average amount of force exerted per unit area. It is a measure of the intensity of the total internal forces acting within a body across imaginary internal surfaces, as a reaction to external applied forces and body forces....
, which in turn increases deflections. This can take the form of buckling

Buckling

In engineering, buckling is a structural failure characterized by a sudden failure of a structural member subjected to high compressive stresses, where the actual compressive stress at the point of failure is less than the ultimate compressive stresses that the material is capable of withstanding....
or crippling. The general field of study is called structural stability

Structural stability

In mathematics, structural stability is an aspect of stability theory concerning whether a given function is sensitive to a small Perturbation theory....
.

Fluid instabilities

Fluid

A fluid is defined as a substance that continually deforms under an applied shear stress. All liquids and all gases are fluids. Fluids are a subset of the Phase and include liquids, gas, Plasma physics and, to some extent, plasticity ....
instabilities occur in liquids, gases and plasmas, and are often characterized by the shape that form; they are studied in fluid dynamics

Fluid dynamics

In physics, fluid dynamics is the sub-discipline of fluid mechanics dealing with fluid flow — the natural science of fluids in motion....
and magnetohydrodynamics

Magnetohydrodynamics

Magnetohydrodynamics is the academic discipline which studies the dynamics of electrical conduction fluids. Examples of such fluids include Plasma , liquid metals, and Brine....
. Fluid instabilities include:

Ballooning mode instability (some analogy to the Rayleigh–Taylor instability); found in the magnetosphere
Magnetosphere

A magnetosphere is a highly magnetized region around and possessed by an astronomical object. Earth is surrounded by a magnetosphere, as are the magnetized planets Mercury , Jupiter, Saturn, Uranus, and Neptune....
Atmospheric instability
Atmospheric instability

Atmospheric instability is a condition where the atmosphere is generally considered to be unstable and as a result the weather is subject to a high degree of variability through distance and time ....

Hydrodynamic instability or dynamic instability (atmospheric dynamics)

Inertial instability; baroclinic instability; symmetric instability, conditional symmetric or convective symmetric instability; barotropic instability; Helmholtz or shearing instability; rotational instability

Hydrostatic instability or static instability/vertical instability (parcel instability), thermodynamic instability (atmospheric thermodynamics
Atmospheric thermodynamics

In the physical sciences, atmospheric thermodynamics is the study of heat and energy transformations in the earth?s atmospheric system. Following the fundamental laws of classical thermodynamics, atmospheric thermodynamics studies such phenomena as properties of moist air, formation of clouds, atmospheric convection, boundary layer meteorolo...
)

Conditional or static instability, buoyant instability, latent instability, nonlocal static instability, conditional-symmetric instability; convective
Convective instability

Convective instability is a form of fluid instability found in thermally stratified atmospheres in which a colder fluid overlies a warmer one....
, potential
Convective instability

Convective instability is a form of fluid instability found in thermally stratified atmospheres in which a colder fluid overlies a warmer one....
, or thermal instability
Convective instability

Convective instability is a form of fluid instability found in thermally stratified atmospheres in which a colder fluid overlies a warmer one....
, convective instability of the first and second kind; absolute or mechanical instability

Bénard instability
Bénard cells

B?nard cells are convection cells that appear spontaneously in a liquid layer when heat is applied from below. They can be obtained using a simple experiment first conducted by Henri B?nard, a French physicist, in 1900....
Drift mirror instability
Kelvin–Helmholtz instability (similar, but different from the diocotron instability
Diocotron instability

A diocotron instability is a Plasma instability created by two sheets of charge slipping past each other. Energy is dissipated in the form of two surface waves propagating in opposite directions, with one flowing over the other....
in plasmas)
Rayleigh–Taylor instability
Plateau-Rayleigh instability
Plateau-Rayleigh instability

The Plateau?Rayleigh instability, often just called the Rayleigh instability, explains why and how a falling stream of fluid breaks up into smaller packets with the same volume but less surface area....
(similar to the Rayleigh–Taylor instability)
Richtmyer-Meshkov instability
Richtmyer-Meshkov instability

The Richtmyer?Meshkov instability occurs when an interface between fluids of differing density is impulsively accelerated, e.g. by the passage of a shock wave....
(similar to the Rayleigh–Taylor instability)

Plasma instabilities

Plasma

Plasma (physics)

In physics and chemistry, plasma is a partially ionized gas, in which a certain proportion of electrons are free rather than being bound to an atom or molecule....
instabilities can be divided into two general groups (1) hydrodynamic instabilities (2) kinetic instabilities. Plasma instabilities are also categorised into different modes:

Mode (azimuthal wave number)	Note	Description	Radial modes	Description
m=0		Sausage instability: displays harmonic variations of beam radius with distance along the beam axis	n=0	Axial hollowing
			n=1	Standard sausaging
			n=2	Axial bunching
m=1		Sinuous, kink or hose instability: represents transverse displacements of the beam cross-section without change in the form or in a beam characteristics other than the position of its center of mass
m=2	Filamentation modes: growth leads towards the breakup of the beam into separate filaments.	Gives an elliptic cross-section
m=3		Gives a pyriform (pear-shaped) cross-section

Source: Andre Gsponer, "" (2004)

List of plasma instabilities

* Bennett pinch instability (also called the z-pinch

Z-pinch

In fusion power research, the Z-pinch, or zeta pinch, is a type of Plasma confinement system that uses an electrical current in the plasma to generate a magnetic field that compresses it ....
instability )
* Beam acoustic instability
* Bump-in-tail instability
* Buneman

Oscar Buneman

Oscar Buneman made advances in science, engineering, and mathematics. Buneman was a pioneer of computational plasma physics and Plasma simulation....
instability, (same as Farley-Buneman instability?)
* Cherenkov

Pavel Alekseyevich Cherenkov

Pavel Alekseyevich Cherenkov was a Soviet physicist who won the Nobel Prize in physics in 1958 for his scientific contributions....
instability,
* Chute instability
* Coalescence instability,
* Collapse instability
* Counter-streaming instability
* Cyclotron instabilities, including:
:*Alfven cyclotron instability
:*Electron cyclotron instability
:*Electrostatic ion cyclotron Instability
:*Ion cyclotron instability
:*Magnetoacoustic cyclotron instability
:*Proton cyclotron instability
:*Nonresonant Beam-Type cyclotron instability
:*Relativistic ion cyclotron instability
:*Whistler cyclotron instability
* Diocotron instability

Diocotron instability

A diocotron instability is a Plasma instability created by two sheets of charge slipping past each other. Energy is dissipated in the form of two surface waves propagating in opposite directions, with one flowing over the other....
, (similar to the Kelvin-Helmholtz fluid instability

Kelvin-Helmholtz instability

Kelvin?Helmholtz instability can occur when velocity shear is present within a continuous fluid or, when there is sufficient velocity difference across the interface between two fluids....
).
* Disruptive instability (in tokamak

Tokamak

A tokamak is a machine producing a torus magnetic field for plasma equilibria and stability a plasma . It is one of several types of magnetic fusion energy, and it is one of the most-researched candidates for producing controlled thermonuclear fusion power....
s)
* Double emission instability
* Drift wave instability
* Edge-localized modes

Edge-Localized Mode

DefinitionAn Edge-Localized Mode is a disruptive instability occurring in the edge region of a tokamak plasma due to the quasi-periodic relaxation of a transport barrier previously formed during an L --> H transition....

*Electrothermal instability

Electrothermal instability

The electrothermal instability is a magnetohydrodynamics instability appearing in Plasma #Magnetization Plasma #Temperatures Plasma used in MHD converters....

* Farley-Buneman instability
* Fan instability
* Filamentation instability
* Firehose instability (also called Hose instability)

* Flute instability
* Free electron maser instability
* Gyrotron instability
* Helical instability (helix

Helix

A helix is a special kind of space curve, i.e. a Differentiable manifold curve in three-space. As a mental image of a helix one may take the spring ....
instability)
* Helical kink instability
* Hose instability (also called Firehose instability)
* Interchange instability
* Ion beam instability
* Kink instability
* Lower hybrid (drift) instability (in the Critical ionization velocity

Critical ionization velocity

Critical ionization velocity is the relative velocity between a neutral gas and Plasma , at which the neutral gas will start to ionize. If more energy is supplied, the velocity of the atoms or molecules will not exceed the critical ionization velocity until the gas becomes almost fully ionized....
mechanism)
* Magnetic drift instability
* Magnetic buoyancy instability (Parker instability)
* Modulation instability
* Non-Abelian

Abelian

Abelian may refer to:* Abelians, a 4th century Christian sect* Hovhannes Abelian, an Armenian actor* A number of different mathematic terms named after Niels Henrik Abel::*Abelian group, a group in which the binary operation is commutative:**Category of abelian groups Ab has abelian groups as objects and group homomorphisms as morph...
instability (see also Chromo-Weibel instability

Chromo-Weibel instability

The Chromo-Weibel instability is a plasma instability present in homogeneous or nearly-homogeneous Non-abelian gauge theory Plasma which possess an anisotropy in momentum space....

* Non-linear coalescence instability
* Oscillating two stream instability, see two stream instability
* Pair instability
* Parker instability (magnetic buoyancy instability)
* Peratt instability (stacked toroid

Toroid

Toroid may refer to:*Toroid , a doughnut-like solid whose surface is a torus.*Toroidal inductors and transformers which have wire windings on circular ring shaped magnetic cores....
s)
* Pinch instability
* Sausage instability
* Slow Drift Instability
* Tearing mode instability
* Two stream instability

Two stream instability

The two-stream instability is a very common instability in Plasma physics. It can be induced by an energetic particle stream injected in a plasma, or setting a current along the plasma so different species can have different drift velocities....

* Weak beam instability
* Weibel instability

Weibel instability

The Weibel instability is a Plasma_instability present in homogeneous or nearly-homogeneous electromagnetic Plasma_%28physics%29 which possess an anisotropy in momentum space....

* z-pinch

Z-pinch

Instabilities of stellar systems

Galaxies and star cluster

Star cluster

Star clusters or star clouds are groups of stars which are gravity bound. Two types of star clusters can be distinguished: globular clusters are tight groups of hundreds of thousands of very old stars, while open clusters generally contain less than a few hundred members, and are often very young....
s can be unstable, if small perturbations in the gravitational potential cause changes in the density that reinforce the original perturbation. Such instabilities usually require that the motions of stars be highly correlated, so that the perturbation is not "smeared out" by random motions. After the instability has run its course, the system is typically "hotter" (the motions are more random) or rounder than before. Instabilities in stellar systems include:

Bar instability of rapidly-rotating disks
Jeans instability
Jeans instability

The Jeans instability causes the collapse of interstellar gas clouds and subsequent star formation. It occurs when the internal gas pressure is not strong enough to prevent gravitational collapse of a region filled with matter....
Firehose (bending) instability
Gravothermal instability
Radial-orbit instability
Various instabilities in cold rotating disks

Instability

Fluid instabilities

Plasma instabilities

List of plasma instabilities

Instabilities of stellar systems

See also

External links