Equilibrium may refer to: Equilibrium or sense of balance, which maintains physical balance in humans and animals In the physical sciences Thermodynamic equilibrium, when internal processes of a system cause no overall change in temperature or pressure Dynamic equilibrium, when two reversible processes (in thermodynamics) occur at the same rate Chemical equilibrium, when a chemical reaction proceeds at the same rate as its reverse reaction, with no change in the amount o ...

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Adaptive optics is a technology to improve the performance of (usually) astronomical telescopes by reducing the effects of atmospheric distortion, or astronomical seeing. Adaptive optics works by measuring the distortion and rapidly compensating for it either using deformable mirrors or material with variable refractive properties. While the technique was theoretically understood for some time, it was only advances in computer technology during the 1990s that finally made the technique practical. Adaptive optics should not be confused ...

Including:

• Adaptive optics - Introduction
• Adaptive optics - Uses of adaptive optics
• Adaptive optics - Beam stabilization

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Lyapunov stability theorems give only sufficient condition. Lyapunov stability - Lyapunov second theorem on stability. Consider a function V(x) : Rn → R such that (positive definite) (negative definite) Then V(x) is called a Lyapunov function candidate and the system is asymptotically stable in the sense of Lyapunov. It is easier to visualise this method of analysis by thinking of a physical system (e.g. vibrating sp ...

See also:

Lyapunov stability, Lyapunov stability - Lyapunov stability theorems, Lyapunov stability - Lyapunov second theorem on stability, Lyapunov stability - Stability for state space models, Lyapunov stability - Barbalat's lemma and stability of time-varying systems

Read more here: » Lyapunov stability: Encyclopedia II - Lyapunov stability - Lyapunov stability theorems

AEGEE, (French: Association des Etats Généraux des Etudiants de l’Europe), the European Students' Forum, is one of Europe's largest interdisciplinary student organisations. It takes its name from the Aegean sea, one of the birthplaces of democracy, and from the first parliament established at the dawn of the French Revolution, the "Etats Généraux." AEGEE - Description. The association was established in 1985, and now has about 15 000 members in 204 university cities in 40 countries throughout E ...

Including:

• AEGEE - Description
• AEGEE - History
• AEGEE - Activities
• AEGEE - Active Citizenship
• AEGEE - Higher Education
• AEGEE - Peace and Stability
• AEGEE - Cultural Exchange

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The most familiar stable distribution is the normal distribution with PDF and characteristic function: Note that the stability property can be immediately seen by noting that the product of two characteristic functions is of the same form: where ...

See also:

Stability probability, Stability probability - Definition, Stability probability - Calculating the PDF for the linear combination, Stability probability - Examples, Stability probability - Relationships for μ and c

Read more here: » Stability probability: Encyclopedia II - Stability probability - Examples

Different methods are used to calculate the factor of safety of a potential slip surface depending on the geometry of the slip surface. For the simplified model of a circular surface, the Bishop’s Simplified Solution may be used. Bishop’s method uses the method of slices and limit equilibrium. In the method of slices, the soil mass lying above the trial failure surface is divided, by vertical planes, into a series of slices of equal width. Bishop (1954) outlines the process by which this method is undertaken. The calculated factor ...

See also:

Slope stability, Slope stability - Slope stability analysis, Slope stability - Shapes in slopes, Slope stability - The use of piles in slope stability, Slope stability - Pile design, Slope stability - Other methods

Read more here: » Slope stability: Encyclopedia II - Slope stability - Slope stability analysis

A random variable represents the possible outcomes of a set of events or a process. If it is a real-valued random variable, for any particular instance this value will be a real number. Let's restrict ourselves to continuous distributions. (The results may be easily extended to discrete distributions.) The probability that the value will be between x and x + dx will be given by the pro ...

See also:

Stability probability, Stability probability - Definition, Stability probability - Calculating the PDF for the linear combination, Stability probability - Examples, Stability probability - Relationships for μ and c

Read more here: » Stability probability: Encyclopedia II - Stability probability - Definition

Assume that f is function of time only. If does not imply that f(t) has a limit at If f(t) has a limit as does not imply that . If f(t) is lower bounded and decreasing (), then it converges to a limit. But it does not say whether or not as . Barbalat's Lemma says that If f(t) has a finite limit as and if is uniformly conti ...

See also:

Lyapunov stability, Lyapunov stability - Lyapunov stability theorems, Lyapunov stability - Lyapunov second theorem on stability, Lyapunov stability - Stability for state space models, Lyapunov stability - Barbalat's lemma and stability of time-varying systems

Read more here: » Lyapunov stability: Encyclopedia II - Lyapunov stability - Barbalat's lemma and stability of time-varying systems

Slope stability has been the subject of a great number of different works. A useful paper regarding the analysis of the stability of slopes is A.W. Bishop’s The Use of the Slip Circle in the Stability Analysis of Slopes. This allows calculations to be made for the stability of a slope for which the profile of the slip surface is circular. Much work has been undertaken regarding the use of piles to transfer vertical axial loads to a firmer stratum of soil beneath ground level. However, relatively little work related to piles is focused on the issu ...

See also:

Slope stability, Slope stability - Slope stability analysis, Slope stability - Shapes in slopes, Slope stability - The use of piles in slope stability, Slope stability - Pile design, Slope stability - Other methods

Read more here: » Slope stability: Encyclopedia II - Slope stability - The use of piles in slope stability

Beta is a measure of plasma pressure normalized to the magnetic field strength. (See magnetohydrodynamics for a full definition.) MHD stability at high beta is crucial for a compact, cost-effective magnetic fusion reactor. Fusion power density varies roughly as β2 at constant magnetic field, or as βN4 at constant bootstrap fraction in configurations with externally driven plasma current. (Here βN = β /(I/aB) is the normalized beta.) In many cases MHD stability represents the primary limitation ...

See also:

Plasma stability, Plasma stability - MHD Instabilities, Plasma stability - Ideal Instabilities, Plasma stability - Resistive Wall Modes, Plasma stability - Resistive instabilities, Plasma stability - Opportunities for Improving MHD Stability, Plasma stability - Configuration, Plasma stability - Internal Structure, Plasma stability - Feedback Control, Plasma stability - Disruption Mitigation

Read more here: » Plasma stability: Encyclopedia II - Plasma stability - MHD Instabilities

A marginally stable system is one that, if given an impulse of finite magnitude as input, will not "blow up" and give an unbounded output. However, oscillations in the output will persist indefinitely, and so there will, in general, be no final steady-state output. If the system is given a step as an input, the system's output will increase indefinitely, with the system effectively acting as an integrator on the input, and so a marginally stable syste ...

See also:

Marginal stability, Marginal stability - Practical Consequences

Read more here: » Marginal stability: Encyclopedia II - Marginal stability - Practical Consequences

The design of the piles involves increasing the available shear force in an attempt to increase the factor of safety (F) from, say, 1.0 to 1.4 (i.e. on the verge of failure to a conservative value). The calculation of the strength of soil mobilised is already conservative, and applying F makes doubly sure. Once F has been acquired for the slope, the additional resistant shear force required to stabilise the slope should be acquired from limit equilibrium analysis of the soil mass above the slip surface. By adding ...

See also:

Slope stability, Slope stability - Slope stability analysis, Slope stability - Shapes in slopes, Slope stability - The use of piles in slope stability, Slope stability - Pile design, Slope stability - Other methods

Read more here: » Slope stability: Encyclopedia II - Slope stability - Pile design

BIBO stability - Continuous-time necessary and sufficient condition. In continuous time, the condition for BIBO stability is that the impulse response be absolutely integrable, i.e., its L1 norm exist. BIBO stability - Discrete-time necessary and sufficient condition. In discrete time, the condition for BIBO stability is that the impulse response be absolutely summable, i.e., its norm exist. ...

See also:

BIBO stability, BIBO stability - Time domain condition, BIBO stability - Continuous-time necessary and sufficient condition, BIBO stability - Discrete-time necessary and sufficient condition, BIBO stability - Proof of sufficiency, BIBO stability - Frequency domain condition, BIBO stability - Continuous signals, BIBO stability - Discrete signals

Read more here: » BIBO stability: Encyclopedia II - BIBO stability - Time domain condition

BIBO stability - Continuous signals. For a causal, rational, continuous time system, the condition for stability is that the region of convergence (ROC) of the Laplace transform includes the imaginary axis. When the system is causal, the ROC is the open region to the right of a vertical line whose abscissa is the real part of the largest pole. (Largest here is defined so that the real part of the largest pole is greater than the real part of any other pole in the system.) The real part of the largest pole ...

See also:

BIBO stability, BIBO stability - Time domain condition, BIBO stability - Continuous-time necessary and sufficient condition, BIBO stability - Discrete-time necessary and sufficient condition, BIBO stability - Proof of sufficiency, BIBO stability - Frequency domain condition, BIBO stability - Continuous signals, BIBO stability - Discrete signals

Read more here: » BIBO stability: Encyclopedia II - BIBO stability - Frequency domain condition

Any transfer function can be written in the form (Mason's Rule) where Δ(s) = 0 is known as the characteristic equation. Solving the characteristic equation for s yields the "Poles of the Closed-Loop Transfer Function." In a negative feedback loop, the characteristic equation Δ(s) is equal to where is known as the "Loop Transfer function", or in situations where there is only a single feedba ...

See also:

Nyquist stability criterion, Nyquist stability criterion - Background, Nyquist stability criterion - Terminology, Nyquist stability criterion - Stability Concerns, Nyquist stability criterion - The argument principle, Nyquist stability criterion - The Nyquist criterion

Read more here: » Nyquist stability criterion: Encyclopedia II - Nyquist stability criterion - Background

To determine if a family is stable, we need to be able to calculate the PDF for the Y variable. The probability that Y takes on a value from y to y + dy is the integral of the probability that X1 has value x1 + dx1 and X2 h ...

See also:

Stability probability, Stability probability - Definition, Stability probability - Calculating the PDF for the linear combination, Stability probability - Examples, Stability probability - Relationships for μ and c

Read more here: » Stability probability: Encyclopedia II - Stability probability - Calculating the PDF for the linear combination

An asymptotically stable system is one that, if given a finite input, will not "blow up" and give an unbounded output. Moreover, if the system is given a fixed, finite input (that is, a step), then any resulting oscillations in the output will decay, and the output will tend asymptotically to a new final, steady-state value. If the system is instead given an Dirac delta impulse as input, then induced oscillations will die away and the system will return to its previous value. If oscillations do not die away, or the system does not return to its original output when an impulse is ...

See also:

Asymptotic stability, Asymptotic stability - Practical consequences, Asymptotic stability - Example asymptotically stable systems, Asymptotic stability - Real-world example

Read more here: » Asymptotic stability: Encyclopedia II - Asymptotic stability - Practical consequences

Numerous critics have expressed concern about the theory. First, it is not just the hegemon’s existence that maintains order, but also some recognition of the hierarchy of states by other actors in the international community. As Wyatt Walters argues, it was the Soviet threat that led England, France and Germany to take a secondary role to the U.S.; it was not just the presence of the United States. Second, it has been argued that the absence of a hegemon during the interwar years was not responsible for the breakdown of the international economic system, i ...

See also:

Hegemonic stability theory, Hegemonic stability theory - Criticism, Hegemonic stability theory - Newer variations of the theory, Hegemonic stability theory - Is the U.S. still a hegemon?

Read more here: » Hegemonic stability theory: Encyclopedia II - Hegemonic stability theory - Criticism

██ criteria breach ██ criteria breach for 3 consequtive years, sanctions can be expected ...

See also:

Stability and Growth Pact, Stability and Growth Pact - Member states by SGP criteria, Stability and Growth Pact - Bibliography, Stability and Growth Pact - External link

Read more here: » Stability and Growth Pact: Encyclopedia II - Stability and Growth Pact - Member states by SGP criteria

The Nyquist Contour Nyquist proposed a contour in the s plane that goes as such: a path traveling up the jω axis, from to . a semicircular arc, with radius , that starts at and travels clock-wise to The Nyquist Criterion Given a Nyquist contour in the s plane, Γs, the resultant contour in the F(s< ...

See also:

Nyquist stability criterion, Nyquist stability criterion - Background, Nyquist stability criterion - Terminology, Nyquist stability criterion - Stability Concerns, Nyquist stability criterion - The argument principle, Nyquist stability criterion - The Nyquist criterion

Read more here: » Nyquist stability criterion: Encyclopedia II - Nyquist stability criterion - The Nyquist criterion

The graph on the right shows the impulse response of two similar systems. The green curve is the response of the system with impulse response , whilst the blue represents the system . Although one response is oscillatory, both return to the original value of 0 over time. Asymptotic stability - Real-world example. Imagine putting a marble in a ladle. It will settle itself into the lowest point of the ladle and, unless disturbed, will stay there. Now imagine giving the ball a push, which is an approximation ...

See also:

Asymptotic stability, Asymptotic stability - Practical consequences, Asymptotic stability - Example asymptotically stable systems, Asymptotic stability - Real-world example

Read more here: » Asymptotic stability: Encyclopedia II - Asymptotic stability - Example asymptotically stable systems