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, states are what characterize a system. ... A bound can be: an upper bound - mathematics Bound (movie) This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ... The word stability has a number of technical meanings, all related to the common meaning of the word. ... In the theory of dynamical systems, a linear time-invariant system is marginally stable if every eigenvalue in the systems transfer-function is non-positive, and all eigenvalues with zero real value are simple roots. ... A limit-cycle is a closed trajectory in phase space exhibited by nonlinear systems. ...

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. For the application to living systems, see perceptual control theory. ... Roots is: The plural of Root Roots (album) Roots (TV miniseries), a mini-series based on a novel by Alex Haley Roots: The Saga of an American Family, a novel by Alex Haley Roots Canada Ltd. ... In linear algebra, the characteristic equation of a square matrix A is the equation in one variable λ where I is the identity matrix. ... In mathematics, the real part of a complex number , is the first element of the ordered pair of real numbers representing , i. ... In linear algebra, a scalar λ is called an eigenvalue (in some older texts, a characteristic value) of a linear mapping A if there exists a nonzero vector x such that Ax=λx. ... 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. ...

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 is can take the form of buckling or crippling. The general field of study is called structural stability. Taipei 101, the worlds tallest building as of 2004. ... [[ Deflection happens when an object hits a plane surface In physics In physics deflection is the event where an object collides and bounces against a plane surface. ... Figure 1  Stress tensor In physics, stress is a measure of the internal distribution of force per unit area within a body that balances and reacts to the loads applied to it. ... In engineering, buckling is a failure mode of a structural member characterised by a failure to react to the bending moment generated by a compressive load. ... Given a metric space and a homeomorphism , we say that is structurally stable if there is a neighborhood of in (the space of all homeomorphisms mapping to itself endowed with the compact-open topology) such that every element of is topologically conjugate to . ...

Fluid instabilities

Fluid instabilities occur in liquids, gases and plasmas, and are often characterised by the shape that form; they are studied in fluid dynamics and magnetohydrodynamics. Fluid instabilities include: A liquid will assume the shape of its container. ... -1... A Plasma lamp In physics and chemistry, a plasma is an ionized gas, and is usually considered to be a distinct phase of matter. ... Fluid dynamics is the subdiscipline of fluid mechanics that studies fluids (liquids and gases) in motion. ... Magnetohydrodynamics (MHD) (magnetofluiddynamics or hydromagnetics), is the academic discipline which studies the dynamics of electrically conducting fluids. ...

• Ballooning mode instability (some analogy to the Rayleigh-Taylor instability); found in the magnetosphere
• Baroclinic Instability
• Benard Instability
• Drift mirror instability
• Kelvin-Helmholtz instability (similar, but different to the diocotron instability in plasmas)
• Rayleigh-Taylor instability

Schematic of Earths magnetosphere. ... Baroclinic Instability is a fluid dynamic instability which helps to understand some important features of the so-called large scale waves in the mid-latitude atmosphere. ... A KHI on the planet Saturn, formed at the interaction of two bands of the planets atmosphere 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. ... RT fingers evident in the Crab Nebula Hydrodynamics simulation of the Rayleigh-Taylor instability [1] The Rayleigh-Taylor instability, or RT instability, or, less commonly, the Richtmyer-Meshkov instability, occurs any time a dense, heavy fluid is being accelerated by light fluid. ...

Plasma instabilities

Plasma instabilities can be divided into two general groups (1) hydrodynamic instabilities (2) kinetic 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, but different to the Kelvin-Helmholtz instability).
• Disruptive instability (in tokamaks)
• Double emission instability
• Drift wave instability
• Edge-localised modes [1]
• 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
• Modulation instability
• Non-Abelian instability
• Non-linear coalescence instability
• Oscillating two stream instability, see two stream instability
• Pair instability
• Parker 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

The Z machine at Sandia National Laboratories in Albuquerque, New Mexico. ... A KHI on the planet Saturn, formed at the interaction of two bands of the planets atmosphere 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. ... A split image of the largest tokamak in the world, the JET, showing hot plasma in the right image during a shot. ... A helix (pl: helices), from the Greek word έλικας/έλιξ, is a twisted shape like a spring, screw or a spiral staircase. ... Critical ionization velocity experiment onboard space shuttle Discovery (STS-39), releasing a plume of nitrous oxide gas. ... In mathematics, an abelian group is a commutative group, i. ... A toroid is a doughnut-shaped object whose surface is a torus. ... The two-stream instability is a very common instability in plasma physics. ... The Z machine at Sandia National Laboratories in Albuquerque, New Mexico. ...

External links

• eFluids Fluid Flow Image Gallery