Instability Totally Explained

Everything about Unstable totally explained

Instability in systems 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 control theory, a system is unstable if any of the roots of its characteristic equation has real part greater than zero. This is equivalent to any of the eigenvalues of the state matrix having real part greater than zero.
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.

Fluid instabilities

Fluid instabilities occur in liquids, gases and plasmas, and are often characterized by the shape that form; they're studied in fluid dynamics and magnetohydrodynamics. Fluid instabilities include:

Ballooning mode instability (some analogy to the Rayleigh-Taylor instability); found in the magnetosphere
Atmospheric instability
- 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)
  - Conditional or static instability, buoyant instability, latent instability, nonlocal static instability, conditional-symmetric instability; convective, potential, or thermal instability, convective instability of the first and second kind; absolute or mechanical instability
- Bénard instability
- Drift mirror instability
- Kelvin-Helmholtz instability (similar, but different from the diocotron instability in plasmas)
- Rayleigh-Taylor instability
- Plateau-Rayleigh instability (similar to the Rayleigh-Taylor instability)
- Richtmyer-Meshkov instability (similar to the Rayleigh-Taylor instability)

Plasma instabilities

Plasma 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 crosssection 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, "Physics of high-intensity high-energy particle beam propagation in open air and outer-space plasmas

" (2004)

List of plasma instabilities

Bennett pinch instability (also called the z-pinch instability )

Beam acoustic instability

Bump-in-tail instability

Buneman instability, (same as Farley-Buneman instability?)

Cherenkov 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, (similar to the Kelvin-Helmholtz fluid instability).

Disruptive instability (in tokamaks)

Double emission instability

Drift wave instability

Edge-localised modes (External Link

)

Farley-Buneman instability

Fan instability

Filamentation instability

Firehose instability (also called Hose instability)

Flute instability

Free electron maser instability

Gyrotron instability

Helical instability (helix 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 mechanism)

Magnetic drift instability

Magnetic buoyancy instability (Parker instability)

Modulation instability

Non-Abelian instability (see also Chromo-Weibel Instability)

Chromo-Weibel Instability

Non-linear coalescence instability

Oscillating two stream instability, see two stream instability

Pair instability

Parker instability (magnetic buoyancy instability)

Peratt instability (stacked toroids)

Pinch instability

Sausage instability

Slow Drift Instability

Tearing mode instability

Two stream instability

Weak beam instability

Weibel instability

z-pinch instability, also called Bennett pinch instability

Further Information

Get more info on 'Unstable'.

External Link Exchanges

Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:

<a href="http://instability.totallyexplained.com">Instability Totally Explained</a>

Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned.