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
In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity o ...
behavior.
In
structural engineering
Structural engineering is a sub-discipline of civil engineering in which structural engineers are trained to design the 'bones and muscles' that create the form and shape of man-made structures. Structural engineers also must understand and cal ...
, a structure can become unstable when excessive load is applied. Beyond a certain threshold, structural
deflection
Deflection or deflexion may refer to:
Board games
* Deflection (chess), a tactic that forces an opposing chess piece to leave a square
* Khet (game), formerly ''Deflexion'', an Egyptian-themed chess-like game using lasers
Mechanics
* Deflection ...
s magnify
stresses, which in turn increases deflections. This can take the form of
buckling
In structural engineering, buckling is the sudden change in shape ( deformation) of a structural component under load, such as the bowing of a column under compression or the wrinkling of a plate under shear. If a structure is subjected to a ...
or crippling. The general field of study is called
structural stability.
Atmospheric instability
Atmospheric instability is a condition where the Earth's atmosphere is generally considered to be unstable and as a result the weather is subjected to a high degree of variability through distance and time. Atmospheric stability is a measure of t ...
is a major component of all
weather system
In meteorology, a low-pressure area, low area or low is a region where the atmospheric pressure is lower than that of surrounding locations. Low-pressure areas are commonly associated with inclement weather (such as cloudy, windy, with possible ...
s on Earth.
Instability in control systems
In the theory of
dynamical systems, a
state variable
A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of a ...
in a system is said to be unstable if it evolves without bounds. A system itself is said to be unstable if at least one of its state variables is unstable.
In
continuous time
In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled.
Discrete time
Discrete time views values of variables as occurring at distinct, separate "po ...
control theory
Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...
, a system is unstable if any of the
roots
A root is the part of a plant, generally underground, that anchors the plant body, and absorbs and stores water and nutrients.
Root or roots may also refer to:
Art, entertainment, and media
* ''The Root'' (magazine), an online magazine focusing ...
of its
characteristic equation has
real part
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form ...
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. The equivalent condition in
discrete time is that at least one of the eigenvalues is greater than 1 in absolute value, or that two or more eigenvalues are equal and of unit absolute value.
Instability in solid mechanics
*
Buckling
In structural engineering, buckling is the sudden change in shape ( deformation) of a structural component under load, such as the bowing of a column under compression or the wrinkling of a plate under shear. If a structure is subjected to a ...
*
Elastic instability
Elastic instability is a form of instability occurring in elastic systems, such as buckling of beams and plates subject to large compressive loads.
There are a lot of ways to study this kind of instability. One of them is to use the method of in ...
*
Drucker stability Drucker stability (also called the Drucker stability postulates) refers to a set of mathematical criteria that restrict the possible nonlinear stress-strain relations that can be satisfied by a solid material. The postulates are named after Daniel ...
of a nonlinear constitutive model
* Biot instability (surface wrinkling in elastomers)
* Baroclinic instability
Fluid instabilities
Fluid instabilities occur in
liquids
A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, a ...
,
gases
Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma).
A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or ...
and
plasmas, and are often characterized by the shape that form; they are studied in
fluid dynamics and
magnetohydrodynamics
Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magnetofluids include plasmas, liquid metals, ...
. Fluid instabilities include:
*
Ballooning instability The ballooning instability (a.k.a. ballooning mode instability) is a type of internal pressure-driven plasma instability usually seen in tokamak fusion power reactors or in space plasmas. It is important in fusion research as it determines a set of ...
(some analogy to the Rayleigh–Taylor instability); found in the
magnetosphere
*
Atmospheric instability
Atmospheric instability is a condition where the Earth's atmosphere is generally considered to be unstable and as a result the weather is subjected to a high degree of variability through distance and time. Atmospheric stability is a measure of t ...
**
Hydrodynamic instability
In fluid dynamics, hydrodynamic stability is the field which analyses the stability and the onset of instability of fluid flows. The study of hydrodynamic stability aims to find out if a given flow is stable or unstable, and if so, how these ins ...
or
dynamic instability Dynamic instability may refer to any of several scientific phenomena:
* Aircraft dynamic modes, including aircraft dynamic instability
*Atmospheric instability, in meteorology
* Dynamic instability of microtubules, in biology
*Firehose instability ...
(
atmospheric dynamics)
***
Inertial instability
In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration ...
;
baroclinic instability
In fluid dynamics, the baroclinity (often called baroclinicity) of a stratified fluid is a measure of how misaligned the gradient of pressure is from the gradient of density in a fluid. In meteorology a baroclinic flow is one in which the densi ...
;
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 is the study of heat-to-work transformations (and their reverse) that take place in the earth's atmosphere and manifest as weather or climate. Atmospheric thermodynamics use the laws of classical thermodynamics, to descr ...
)
***
Conditional or
static instability,
buoyant instability,
latent instability,
nonlocal static instability,
conditional-symmetric instability;
convective
Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convec ...
,
potential
Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple r ...
, or
thermal instability,
convective instability of the first and
second kind;
absolute or
mechanical instability
*
Bénard instability
* Drift mirror instability
*
Kelvin–Helmholtz instability
The Kelvin–Helmholtz instability (after Lord Kelvin and Hermann von Helmholtz) is a fluid instability that occurs when there is velocity shear in a single continuous fluid or a velocity difference across the interface between two fluids. K ...
(similar, but different from the
diocotron instability in plasmas)
*
Rayleigh–Taylor instability
The Rayleigh–Taylor instability, or RT instability (after Lord Rayleigh and G. I. Taylor), is an instability of an interface between two fluids of different densities which occurs when the lighter fluid is pushing the heavier fluid.
Drazin ( ...
*
Plateau-Rayleigh instability (similar to the Rayleigh–Taylor instability)
*
Richtmyer-Meshkov instability (similar to the Rayleigh–Taylor instability)
*
Shock Wave
In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a me ...
Instability
*
Benjamin-Feir Instability (also known as modulational 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
In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be needed to move an object to that location from a fixed reference location. It is analogous to the electric ...
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
In stellar physics, the Jeans instability causes the collapse of interstellar gas clouds and subsequent star formation, named after James Jeans. It occurs when the internal gas pressure is not strong enough to prevent gravitational collapse of ...
*
Firehose instability
The firehose instability (or hose-pipe instability) is a dynamical instability of thin or elongated galaxies. The instability causes the galaxy to buckle or bend in a direction perpendicular to its long axis. After the instability has run its ...
*
Gravothermal instability
*
Radial-orbit instability
* Various instabilities in cold rotating disks
Joint instabilities
The most common residual disability after any sprain in the body is instability. Mechanical instability includes insufficient stabilizing structures and mobility that exceed the physiological limits. Functional instability involves recurrent sprains or a feeling of giving way of the injured joint. Injuries cause
proprioceptive
Proprioception ( ), also referred to as kinaesthesia (or kinesthesia), is the sense of self-movement, force, and body position. It is sometimes described as the "sixth sense".
Proprioception is mediated by proprioceptors, mechanosensory neurons ...
deficits and impaired postural control in the joint. Individuals with muscular weakness, occult instability, and decreased postural control are more susceptible to injury than those with better postural control. Instability leads to an increase in postural sway, the measurement of the time and distance a subject spends away from an ideal
center of pressure. The measurement of a subject's postural sway can be calculated through testing center of pressure (CoP), which is defined as the vertical projection of center of mass on the ground. Investigators have theorized that if injuries to joints cause
deafferentation
Peripheral neuropathy, often shortened to neuropathy, is a general term describing disease affecting the peripheral nerves, meaning nerves beyond the brain and spinal cord. Damage to peripheral nerves may impair sensation, movement, gland, or o ...
, the interruption of sensory nerve fibers, and functional instability, then a subject's postural sway should be altered.
Joint stability can be enhanced by the use of an external support system, like a brace, to alter body mechanics. The mechanical support provided by a brace provides cutaneous afferent feedback in maintaining postural control and increasing stability.
Notes
{{Reflist
External links
eFluids Fluid Flow Image Gallery
Systems theory
Fluid mechanics
Plasma physics
Stability theory