# Instability

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Instability

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Hydrodynamics simulation of the Rayleigh–Taylor instability [Shengtai Li, Hui Li "Parallel AMR Code for Compressible MHD or HD Equations" (Los Alamos National Laboratory) [http://math.lanl.gov/Research/Highlights/amrmhd.shtml] ] ] 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 are 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 alongthe beam axis n=0 Axial hollowing n=1 Standard sausaging n=2 Axial bunching m=1 "Sinuous", "kink" or "hose" instability:represents transversedisplacements 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 breakupof the beam into separate filaments. Gives an elliptic cross-section m=3 Gives a pyriform (pear-shaped) cross-section
Source: Andre Gsponer, " [http://arxiv.org/abs/physics/0409157 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, [Buneman, O., " [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1958PhRvL...1....8B&db_key=PHY&data_type=HTML&format= Instability, Turbulence, and Conductivity in Current-Carrying Plasma] " (1958) "Physical Review Letters", vol. 1, Issue 1, pp. 8-9] (same as Farley-Buneman instability?)* Cherenkov instability, [Kho, T. H.; Lin, A. T., " [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1990ITPS...18..513K&db_key=PHY&data_type=HTML&format=&high=4521318e0232018 Cyclotron-Cherenkov and Cherenkov instabilities] " (1990) "IEEE Transactions on Plasma Science" (ISSN 0093-3813), vol. 18, June 1990, p. 513-517] * Chute instability* Coalescence instability, [Finn, J. M.; Kaw, P. K., " [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1977PhFl...20...72F&db_key=PHY&data_type=HTML&format=&high=4521318e0202808 Coalescence instability of magnetic islands] " (1977) "Physics of Fluids", vol. 20, Jan. 1977, p. 72-78. ( [http://adsabs.harvard.edu/cgi-bin/nph-abs_connect?db_key=AST&db_key=PHY&qform=AST&sim_query=YES&ned_query=YES&aut_logic=OR&obj_logic=OR&author=&object=&start_mon=&start_year=&end_mon=&end_year=&ttl_logic=OR&title=%22Diocotron+instability%22&txt_logic=OR&text=&nr_to_return=100&start_nr=1&jou_pick=ALL&ref_stems=&data_and=ALL&group_and=ALL&start_entry_day=&start_entry_mon=&start_entry_year=&end_entry_day=&end_entry_mon=&end_entry_year=&min_score=&sort=SCORE&data_type=SHORT&aut_syn=YES&ttl_syn=YES&txt_syn=YES&aut_wt=1.0&obj_wt=1.0&ttl_wt=0.3&txt_wt=3.0&aut_wgt=YES&obj_wgt=YES&ttl_wgt=YES&txt_wgt=YES&ttl_sco=YES&txt_sco=YES&version=1 More citations] )] * 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, [Uhm, H. S.; Siambis, J. G., " [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1979PhFl...22.2377U&db_key=PHY&data_type=HTML&format=&high=4521318e0204112 Diocotron instability of a relativistic hollow electron beam] " (1979) "Physics of Fluids", vol. 22, Dec. 1979, p. 2377-2381. ] (similar to the Kelvin-Helmholtz fluid instability).* Disruptive instability (in tokamaks)* Double emission instability* Drift wave instability* Edge-localised modes [http://news.bbc.co.uk/1/hi/sci/tech/3260985.stm] *Electrothermal instability* 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

Notes

* [http://www.efluids.com/efluids/pages/gallery.htm eFluids Fluid Flow Image Gallery]

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### Look at other dictionaries:

• Instability — In sta*bil i*ty, n.; pl. {Instabilities}. [L. instabilitas: cf. F. instabilit[ e].] [1913 Webster] 1. The quality or condition of being unstable; lack of stability, firmness, or steadiness; liability to give way or to fail; insecurity;… …   The Collaborative International Dictionary of English

• instability — UK US /ˌɪnstəˈbɪləti/ noun [U or C] (plural instabilities) ► ECONOMICS, POLITICS the fact of a situation being likely to change, in a way that is worrying, or the changes that happen: political/economic instability »Investors should keep in mind… …   Financial and business terms

• instability — [in΄stə bil′ə tē] n. 1. lack of stability; unstableness; specif., a) lack of firmness or steadiness b) lack of determination; irresolution 2. tendency to behave or react violently or erratically [the instability of a chemical compound, emotional… …   English World dictionary

• instability — instability. См. нестабильность. (Источник: «Англо русский толковый словарь генетических терминов». Арефьев В.А., Лисовенко Л.А., Москва: Изд во ВНИРО, 1995 г.) …   Молекулярная биология и генетика. Толковый словарь.

• instability — index doubt (indecision), fault (weakness), frailty, inconsistency, indecision, jeopardy, risk …   Law dictionary

• instability — early 15c., from M.Fr. instabilite inconstancy, from L. instabilitatem (nom. instabilitas) unsteadiness, from instabilis unsteady, from in not, opposite of (see IN (Cf. in ) (1)) + stabilis (see STABLE (Cf. stable) (2)) …   Etymology dictionary

• instability — [n] imbalance, inconstancy alternation, anxiety, capriciousness, changeability, changeableness, disequilibrium, disquiet, fickleness, fitfulness, flightiness, fluctuation, fluidity, frailty, hesitation, immaturity, impermanence, inconsistency,… …   New thesaurus

• instability — ► NOUN (pl. instabilities) ▪ lack of stability …   English terms dictionary

• instability — noun ADJECTIVE ▪ increased ▪ growing, increasing ▪ inherent, internal ▪ the inherent instability of financial markets ▪ …   Collocations dictionary

• instability — [[t]ɪ̱nstəbɪ̱lɪti[/t]] instabilities N UNCOUNT: also N in pl Instability is the quality of being unstable. ...unpopular policies, which resulted in social discontent and political instability. ...Caligula s inherent mental instability... The… …   English dictionary