Instability

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 control theory, a system is unstable if any of the roots of its characteristic equation has real part greater than zero (or if zero is a repeated root). This is equivalent to any of the eigenvalues of the state matrix having either real part greater than zero, or, for the eigenvalues on the imaginary axis, the algebraic multiplicity being larger than the geometric multiplicity.

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.

Contents 1 Fluid instabilities 2 Plasma instabilities 3 Instabilities of stellar systems 4 See also 5 Notes 6 External links

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 - see this paragraph in plasma stability.

Instabilities of stellar systems

Galaxies and star clusters 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
• Firehose instability^[2]
• Gravothermal instability
• Radial-orbit instability
• Various instabilities in cold rotating disks

See also

Plasma stability

Notes

External links

• eFluids Fluid Flow Image Gallery