dablink For the branch of model theory , see stable theory . In mathematics , stabilitytheory addresses the stability of solutions of differential equation s and of trajectories of dynamical system s under ... next whether a small change in the initial condition will lead to similar behavior. Stabilitytheory ... , and then stabilitytheory does not give sufficient information about the dynamics. One of the key ideas in stabilitytheory is that the qualitative behavior of an orbit under perturbations can be analyzed ..., The Wolfram Demonstrations Project . Category Stabilitytheory Category Limit sets de Stabilit tstheorie ... distance . In Dynamical Systems, an orbit dynamics orbit is called Lyapunov stability Lyapunov stable ..., larger neighborhood. Various criteria have been developed to prove stability or instability of an orbit ... in Dynamical Systems Many parts of the qualitative theory of differential equations and dynamical ... stable and in the latter case, asymptotically stable , or attracting . Stability means that the trajectories ... decay exponential rate, cf Lyapunov stability and exponential stability . If none ..., positive. Analogous statements are known for perturbations of more complicated orbits. Stability ... that may or may not converge to the original state. There are useful tests of stability for the case of a linear system. Stability of a nonlinear system can often be inferred from the stability ... information is needed in order to decide stability. There is an analogous criterion for a continuously ... systems The stability of fixed points of a system of constant coefficient linear differential ... for t &rarr &infin . Application of this result in practice, in order to decide the stability of the origin for a linear system, is facilitated by the Routh Hurwitz stability criterion . The eigenvalues ... that avoids computing the roots. Non linear autonomous systems Asymptotic stability of fixed ... Lyapunov stability or asymptotic stability of a dynamical system is by means of Lyapunov function ... more details
Cleanup rewrite date September 2009 Hegemonic StabilityTheory , or HST , is a theory of international ... economy. The theory is about more than economics though the central idea behind HST is that the stability ... to develop and enforce the rules of the system. ref Vincent Ferraro. The Theory of Hegemonic Stability ... figures in the development of hegemonic stabilitytheory include Modelski, Gilpin, Robert Keohane ... StabilityTheory An Empirical Assessment , Review of International Studies 1989 15 , 183 98 ref ref Barry Eichengreen , http repositories.cdlib.org iber cider C96 080 Hegemonic StabilityTheory and Economic .... A superior navy, or air force is. ref Vincent Ferraro. The Theory of Hegemonic Stability. http www.mtholyoke.edu ... StabilityTheory. http faculty.maxwell.syr.edu merupert Teaching Hegemonic 20Stability 20Theory.htm ref Modelski s long cycle theory, however, states that war and other destabilizing events are a natural .... Two dominant theories have emerged from each school. What Robert Keohane first called the theory of hegemonic stability, ref Robert Gilpin. The Political Economy of International Relations . Princeton Princeton University Press, 1987. 86. ref joins A. F. K. Organski s Power Transition Theory as the two dominant approaches to the realist school of thought. Long Cycle Theory , espoused by George Modelski , and World Economy Theory , espoused by Immanuel Wallerstein , have emerged as the two dominant ... Economy Beyond Hegemonic Stability, Foreign Policy , 1998 ref Kindleberger argued, in his 1973 book ... to do so. Without the ability to force stability on the international system, Great Britain was able .... Seattle University of Washington Press, 1987 ref Competing Theories of Hegemonic Stability Hegemony ... Theory George Modelski, who presented his ideas in the book, Long Cycles in World Politics 1987 , is the chief architect of long cycle theory. In a nut shell, long cycle theory describes the connection ... world system . Under the terms of long cycle theory, five hegemonic long cycles have taken place ... more details
wiktionary stabilityStability may refer to Mathematics Stabilitytheory , the study of the stability of solutions to differential equations and dynamical systems Lyapunov stability Structural stability geometric invariant theoryStabilityStability of a point in geometric invariant theory. Numerical stability , a property of numerical algorithms which describes how errors in the input data propagate through the algorithm Stability probability , a property of probability distributions Stability radius , a property of continuous polynomial functions Stable theory , concerned with the notion of stability in model theory Engineering In atmospheric fluid dynamics, Air pollution dispersion terminology The Pasquill atmospheric stability atmospheric stability , a measure of the turbulence in the ambient atmosphere BIBO stability Bounded Input, Bounded Output stability , in signal processing and control theoryStability control theory , part of electrical engineering Directional stability , the tendency ... system Social sciences Economic stability Hegemonic stabilitytheory This slot is reserved for usage ... including longitudinal static stability Nyquist stability criterion , defining the limits of stability for pole zero analysis in control theory control systems Relaxed stability , the property of inherently unstable aircraft Ship stability in naval architecture includes Limit of Positive StabilityStability conditions watercraft of waterborne vessels. Slope stabilityStability Model of software design. Natural sciences Band of stability , in physics, the scatter distribution of isotopes which do not decay Chemical stability , occurring when a substance is in a dynamic chemical equilibrium with its environment Thermal stability of a chemical compound stability of a chemical stability constants of complexes complex Convective instability , a meteorological condition Ecological stability ... Plasma stability , a measure of how likely a perturbation in a plasma is to be damped out Exercise ... more details
Orbital stability may refer to The Orbital spaceflight Stabilitystability of orbits of planetary bodies Orbital resonance Resonance between said orbits The closure of the orbit of a reductive group, in Geometric invariant theoryStability geometric invariant theory A stable electron configuration dab ... more details
In mathematics , in the realm of group theory , stability group of normal series subnormal series is the group of automorphisms that act as identity on each quotient group . algebra stub Category Group theory ... more details
tame theories such as the theory of real closed fields. This shows that the stability spectrum is a relatively ... . The uncountable case For a general stable theory T in a possibly uncountable language, the stability ...In model theory , a branch of mathematical logic , a complete first order theory T is called stable in an infinite cardinal number , if the Type model theory Stone space of every structure mathematical logic model of T of size has itself size . T is called a stable theory if there is no upper bound for the cardinals such that T is stable in . The stability spectrum of T is the class of all cardinals such that T is stable in . For countable theories there are only four possible stability spectra. The corresponding dividing line model theory dividing line s are those for totally transcendental theory total transcendentality , superstable theory superstability and stable theorystability . This result is due to Saharon Shelah , who also defined stability and superstability. The stability spectrum theorem for countable theories Theorem. Every countable complete first order theory T falls ... transcendental theories main Totally transcendental theory A complete first order theory T is called ... is equivalent to stability in , and therefore countable totally transcendental theories are often called stable for brevity. A totally transcendental theory is stable in every T , hence a countable stable theory is stable in all infinite cardinals. Every Morley s categoricity theorem uncountably categorical countable theory is totally transcendental. This includes complete theories ... theories main Superstable theory A complete first order theory T is superstable if there is a rank ... theory. Every totally transcendental theory is superstable. A theory T is superstable if and only ... theory A theory that is stable in one cardinal T is stable in all cardinals that satisfy sup T sup . Therefore a theory is stable if and only if it is stable in some cardinal ... more details
In game theory , the price of stability PoS of a game is the ratio between the best objective function value of one of its equilibria and that of an optimal outcome. The PoS is relevant for games in which there is some objective authority that can influence the players a bit, and maybe help them converge to a good Nash equilibrium . When measuring how efficient a Nash equilibrium is in a specific game we often time also talk about the price of anarchy PoA . Examples Another way of expressing PoS is math text PoS frac text value of best Nash equilibrium text value of optimal solution , text PoS .... Algorithmic game theory By Noam Nisan br 2. The price of stability in selfish scheduling games by Lucas Agussurja and Hoong Chuin Lau br 3. An math O log n log log n math upper bound on the price of stability for undirected Shapely network design games by Jian Li . DEFAULTSORT Price of stability Category Game theory Category Fixed points Category Decision theory he ... Bottom 0,0 5,10 Background and milestones The price of stability was first studied by A. Schulzan ... equilibrium always exists and the price of stability of this game is at most the nth harmonic number ... of stability of 4 3 for a single source and two players case. Jian li has proved that for undirected graphs with a distinguished destination to which all players must connect the price of stability ... of players. Purpose The price of stability is used to measure inefficiency. It differentiates between .... Formally, for a game with multiple equilibria, the price of stability is at least as close to 1 as the price of anarchy . Use The price of stability is studied for two main reasons. The first ... one is that the price of stability has a natural interpretation in many network games. We can regard .... These can either accept it or not. The price of stability measures the benefit of such protocols. Because of this interpretation the price of stability is typically studied only for equilibrium ... more details
Image Saturn Kelvin Helmholtz.jpg thumb right Kelvin Helmholtz instability on Saturn , caused by the interaction between two bands of the planet s atmosphere . In fluid dynamics , hydrodynamic stability is the field of study field which analyses the stability and the onset of instability of fluid flows. Instabilities may develop further into turbulence . ref name p1 See Drazin 2002 , Introduction to hydrodynamic stability , p. 1. ref The foundations of hydrodynamic stability, both theoretical and experimental, were laid by notably Hermann von Helmholtz Helmholtz , William Thomson, 1st Baron Kelvin Kelvin , John Strutt, 3rd Baron Rayleigh Rayleigh and Osborne Reynolds Reynolds during the nineteenth century. ref name p1 See also List of hydrodynamic instabilities G rtler vortices Kelvin Helmholtz instability Plasma stability Rayleigh Taylor instability Taylor Couette flow Taylor Goldstein equation Orr Sommerfeld equation Notes reflist References citation title Introduction to hydrodynamic stability first P. G. last Drazin publisher Cambridge University Press year 2002 isbn 0 521 00965 0 citation first1 P.G. last1 Drazin first2 W.H. last2 Reid title Hydrodynamic stability publisher Cambridge University Press year 1981 isbn 0 521 28980 7 citation first C.C. last Lin authorlink Chia Chiao Lin title The theory of hydrodynamic stability publisher Cambridge University Press year 1966 edition corrected citation first D.D. last Joseph authorlink Daniel D. Joseph title Stability of fluid motions I publisher Springer Verlag volume 27 series Tracts in Natural Philosophy year 1976 isbn 3 540 07541 3 br citation first D.D. last Joseph title Stability of fluid motions II publisher Springer Verlag volume 28 series Tracts in Natural Philosophy year 1976 isbn 3 540 07516 X citation first S.S. last Sritharan title Invariant manifold theory for hydrodynamic transition publisher Wiley year 1990 series Pitman research notes in mathematics series volume 241 isbn 0582067812 External links c ... more details
part is also zero jw 0 means w 0 rad sec . See also Lyapunov stability DEFAULTSORT Marginal Stability Category Dynamical systems Category Stabilitytheory de Grenzstabilit t ...Unreferenced date December 2009 technical date March 2011 In the theory of dynamical systems , and control theory , a continuous linear system linear time invariant system is marginally stable if and only if the real part of every eigenvalue or pole mathematics pole in the system s transfer function is non positive , and all eigenvalues with zero real value are simple root s i.e. the eigenvalues on the complex plane imaginary axis are all distinct from one another . If all the poles have strictly negative real parts, the system is instead exponential stability asymptotically stable . A discrete linear time invariant system is marginally stable if and only if the transfer function s spectral radius is 1. That is, the greatest magnitude of any of the eigenvalues or poles of the transfer function is 1. The values of the poles must also be distinct. If the spectral radius is less than 1, the system is instead asymptotically stable. Practical Consequences A marginally stable system is one that, if given an dirac delta function 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 Heaviside step function 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 system is not a BIBO stability Bounded Input Bounded Output system the information in this para must be verified from other sources . A system having imaginary poles, i.e having zero real part in the pole s , will produce sustained oscillations ... spring damper , from where damper has been removed and spring is ideal i.e. no friction is there, then in theory ... more details
convenient to define the stability radius slightly different. For example, in many applications in control theory the radius of stability is defined as the size of the smallest destabilizing perturbation ...The stability radius of an object system, function, matrix, parameter at a given nominal point is the radius ... pre determined stability conditions. The picture of this intuitive notion is this Image Radius of stability 1.png 500px where math hat p math denote the nominal point, math P math denote the space ... the set of points that satisfy the stability conditions. Abstract definition The formal definition ... ref name MS10 Sniedovich, M. 2010 . A bird s view of info gap decision theory. Journal of Risk Finance ..., 9 1 , 64 70. ref . In the 1980s it became popular in control theory ref name Hindrichsen86 Hindrichsen, D. and Pritchard, A.J. 1986 . Stability radii of linear systems, Systems and Control ... of interest. Relation to Wald s maximin model It was shown ref name MS10 that the stability radius ... to force the math max math player not to perturb the nominal value beyond the stability radius of the system. It is an indication that the stability model is a model of local stability robustness, rather than a global one. Info gap decision theory Info gap decision theory is a recent non probabilistic decision theory. It is claimed to be radically different from all current theories of decision ... hat alpha q, tilde u max alpha ge 0 r c le R q,u , forall u in U alpha, tilde u math is actually a stability radius model characterized by a simple stability requirement of the form math r c le R q,u ... robustness.png 500px Since stability radius models are designed to deal with small perturbations ... the theory is unsuitable for the treatment of severe uncertainty characterized by a poor ... 1998 . Analysis of the Local Robustness of Stability for Flows. Mathematics of Control, Signals, and Systems, 11, 289 302. ref . The picture is this Image Radius of stability 3.png 500px More formally ... more details
Stability Pact can mean The Stability and Growth Pact of the Economic and Monetary Union of the European Union The Stability Pact for South Eastern Europe disambig ... more details
In probability theory , the stability of a random variable is the property that a linear combination of two Statistical independence independent copies of the variable has the same probability distribution distribution , up to location parameter location and scale parameter scale parameters. ref Lukacs, E. 1970 Section 5.7 ref The distributions of random variables having this property are said to be stable distributions . Results available in probability theory show that all possible distributions having this property are members of a four parameter family of distributions. The article on the stable distribution describes this family together with some of the properties of these distributions. The importance in probability theory of stability and of the stable family of probability distributions is that they are attractors for properly normed sums of independent and identically distributed random variables. Important special cases of stable distributions are the normal distribution , the Cauchy distribution and the Levy distribution . For details see stable distribution . Definition There are several basic definitions for what is meant by stability. Some are based on summations of random variables and others on properties of characteristic function s. Definition via distribution functions Feller 1971 ref Feller 1971 , Section VI.1 ref makes the following basic definition. A random variable X is called stable has a stable distribution if, for n independent copies X sub i sub of X ... distributional identity to hold for n 2 and n 3 only. ref Feller 1971 , Problem VI.13.3 ref Stability in probability theory There are a number of mathematical results that can be derived for distributions which have the stability property. That is, all possible families of distributions which have ... if it is assumed that it has the stability property. The following results can be obtained for univariate ... Theory and Its Applications , Volume 2. Wiley. ISBN 0 471 25709 5 Category Theory of probability distributions ... more details
Category Stabilitytheory fr Stabilit asymptotique ...See Lyapunov stability , which gives a definition of asymptotic stability for more general dynamical systems . All exponentially stable systems are also asymptotically stable. In control theory , a continuous LTI system theory linear time invariant system is exponentially stable if and only if the system has eigenvalue s i.e., the pole complex analysis pole s of input to output systems with strictly negative real parts. i.e., in the left half of the complex plane . ref David N. Cheban 2004 , Global Attractors Of Non autonomous Dissipative Dynamical Systems . p. 47 ref A discrete time input to output LTI system is exponentially stable if and only if the poles of its transfer function lie strictly within the unit circle centered on the origin of the complex plane. Exponential stability is a form of asymptotic stability . Systems that are not LTI are exponentially stable if their convergence is bounded function bounded by exponential growth exponential decay . Practical consequences An exponentially stable LTI system is one that will not blow up i.e., give an unbounded output when given a finite input or non zero initial condition. Moreover, if the system is given a fixed, finite input i.e., a Heaviside step function step , then any resulting oscillations in the output will decay at an exponential growth exponential rate , and the output will tend asymptote asymptotically to a new final, steady state value. If the system is instead given a Dirac delta function Dirac delta impulse as input, then induced oscillations will die away and the system will return to its previous value ... is applied, the system is instead marginal stability marginally stable . Example exponentially ... stable over a certain range of inputs . See also Control theory State space controls References reflist External links http www.princeton.edu ap stability.pdf. Parameter estimation and asymptotic stability ... more details
a parallel theory of stability for differentiable maps, which forms a key part of singularity theory . Thom envisaged applications of this theory to biological systems. When Smale started to develop the theory of hyperbolic dynamical systems, he hoped that structurally stable systems would be typical ... system s. See also Homeostasis Self stabilization , superstabilization Stabilitytheory References ... systems Category Stabilitytheory ar de Strukturelle Stabilit t ja pt Estabilidade ... mathematics fixed points and periodic orbit s but not their periods . Unlike Lyapunov stability , which considers perturbations of initial conditions for a fixed system, structural stability deals with perturbations ... stability of C sup 1 sup vector fields on the unit disk D that are transversal to the boundary and on the two ... by Henri Poincar . Structural stability of non singular smooth vector fields on the torus can be investigated using the theory developed by Poincar and Arnaud Denjoy . Using the Poincar recurrence map , the question is reduced to determining structural stability of diffeomorphisms of the circle ... . History and significance Structural stability of the system provides a justification for applying the qualitative theory of dynamical systems to analysis of concrete physical systems. The idea of such qualitative ... mechanics . Around the same time, Aleksandr Lyapunov rigorously investigated stability of small ... stability is due to Solomon Lefschetz , who oversaw translation of their monograph into English. Ideas of structural stability were taken up by Stephen Smale and his school in the 1960s in the context ... in the theory of differential equations series Grundlehren der Mathematischen Wissenschaften, 250 ... Rough system author D.V. Anosov Scholarpedia title Structural stability urlname Structural stability ... more details
stability and a domain of attraction from dynamical system s theory. Notes reflist References cite ...otheruses Stability disambiguation Ecological stability can refer to types of stability in a continuum ranging from resilience returning quickly to a previous state to constancy to persistence. The precise definition depends on the ecosystem in question, the variable or variables of interest, and the overall context. In the context of conservation biology conservation ecology , stable population s are often defined as ones that do not go extinct. Researchers applying mathematical model s from system Dynamics mechanics dynamics usually use Lyapunov stability . ref name autogenerated1 cite web url http philsci archive.pitt.edu archive 00002987 01 PSA 2006 Justus 10 15 06.pdf title Ecological and Lyanupov Stability last Justus first James publisher Paper presented at the Biennial Meeting of The Philosophy of Science Association , Vancouver, Canada year 2006 format PDF ref ref cite journal author Justus, J title Ecological and Lyanupov Stability journal Philosophy of Science volume 75 issue 4 pages 421 436 year 2008 doi 10.1086 595836 Published version of above paper ref Types of ecological stability Local stability indicates that a system is stable over small short lived disturbances, while global stability indicates a system highly resistant to change in species composition and or food web dynamics . Constancy and persistence Observational studies of ecosystems use constancy to describe living systems that can remain unchanged. Resistance and inertia persistence Resistance and inertia deal with a system s inherent response to some perturbation. A perturbation is any externally imposed change in conditions, usually happening in a short time period. Resistance is a measure of how little the variable of interest changes in response to external pressures. Inertia or persistence implies that the living system is able to resist external fluctuations. In the context of changing ... more details
Category Stabilitytheory Category Dynamical systems de Stabilit tstheorie eo Stabileco de dinamika ...Otheruses4 asymptotic stability of nonlinear systems stability of linear systems exponential stability no footnotes date May 2009 In mathematics , the notion of Lyapunov stability occurs in the study of dynamical ... stability guarantees a minimal rate of decay, i.e., an estimate of how quickly the solutions converge. The idea of Lyapunov stability can be extended to infinite dimensional manifolds, where it is known as structural stability , which concerns the behavior of different but nearby solutions to differential equations. Input to state stability ISS applies Lyapunov notions to systems with inputs ... are the following Lyapunov stability of an equilibrium means that solutions starting close enough to the equilibrium ... want to choose. Asymptotic stability means that solutions that start close enough not only remain close enough but also eventually converge to the equilibrium. Exponential stability means that solutions ... showing that attractivity does not imply asymptotic stability. Such examples are easy to create ... lim n to infty d f n x ,f n y 0 math whenever math d x,y delta math . Lyapunov stability theorems The general study of the stability of solutions of differential equations is known as stabilitytheory . Lyapunov stability theorems gives only sufficient condition. Lyapunov s second method for stability Lyapunov, in his original 1892 work proposed two methods for demonstrating stability. The first ... properness or radial unboundedness is required in order to conclude global asymptotic stability. It is easier ... systems or biological systems, the concept of energy may not be applicable. Lyapunov s realization was that stability ... function can be found to satisfy the above constraints. Stability for linear state space models ... stable in fact, Exponential stability exponentially stable if all real parts of the eigenvalue ... stable in fact, Exponential stability exponentially stable if all the eigenvalue s of math ... more details
stability. refend References reflist Category Signal processing Category Digital signal processing Category Articles containing proofs Category Stabilitytheory de BIBO Stabilit t fr Stabilit EBSB ja ... time sufficient condition For a discrete time LTI system, the condition for BIBO stability is that the impulse ... , the condition for stability is that the region of convergence ROC of the Laplace transform includes ... must be in the strict left half of the s plane for BIBO stability. This stability condition can be derived ... discrete time system , the condition for stability is that the region of convergence ROC of the z ..., all poles of the system must be inside the unit circle in the z plane for BIBO stability. This stability ... 1 math . The region of convergence must therefore include the unit circle . See also LTI system theory ... response IIR filter Nyquist plot Routh Hurwitz stability criterion Bode plot Gain margin and phase ... more details
Static stability is the ability of a robot to remain upright when at rest, or under acceleration and deceleration. Static stability may also refer to In aircraft or missiles Static margin a concept used to characterize the static stability and controllability of aircraft and missiles. Longitudinal static stability the stability of an aircraft in the longitudinal, or pitching, plane during static established conditions. In meteorology Fluid statics Static stability also called hydrostatic stability or vertical stability the ability of a fluid at rest to become turbulent or laminar due to the effects of buoyancy. In sailing Sailing Heeling Static stability the angle of roll, or heel, achieved under constant wind conditions. disambig ... more details
Orphan date March 2011 unreferenced date March 2011 In probability theory , to obtain a nondegenerate limiting distribution of the extreme value distribution , it is necessary to reduce the actual greatest value by applying a linear transformation with coefficients that depend on the sample size. If math X 1, X 2, dots , X n , math are independence probability theory independent random variable s with common probability density function math p X j x f x , math then the cumulative distribution function of math X n max ,X 1, ldots,X n , , math is math F X n F x n , math If there is a limiting distribution of interest, the stability postulate states the limiting distribution is some sequence of transformed reduced values, such as math a n X n b n , math , where math a n, b n , math may depend on n but not on x . To distinguish the limiting cumulative distribution function of the reduced greatest value from F x , we will denote it by G x . It follows that G x must satisfy the functional equation math G x n G a n x b n , math This equation was obtained by Maurice Ren Fr chet and also by Ronald Fisher . Boris Vladimirovich Gnedenko has shown there are no other distributions satisfying the stability postulate other than the following Gumbel distribution for the minimum stability postulate If math X i textrm Gumbel mu, beta , math and math Y min ,X 1, ldots,X n , , math then math Y sim a n X b n , math where math a n 1 , math and math b n beta log n , math In other words, math Y sim textrm Gumbel mu beta log n , beta , math Extreme value distribution for the maximum stability postulate If math X i textrm EV mu, sigma , math and math Y max ,X 1, ldots,X n , , math then math Y sim a n X b n , math where math a n 1 , math and math b n sigma log tfrac 1 n , math In other words, math Y sim textrm EV mu sigma log tfrac 1 n , sigma , math Fr chet distribution for the maximum stability ... Probability theory Category Extreme value data Statistics stub Probability stub ... more details
Dec 20, 1894 Oct 19, 1961 , a student of geotechnical pioneer Karl von Terzaghi . See also Slope stability radar Slope stability analysis Mass wasting Mohr Coulomb theory Discontinuity layout optimization ...Image Slopslump2.jpg thumb 250px Figure 1 Simple slope slip section The field of slope stability encompasses the analysis of static and dynamic stability of slopes of earth and rock fill dams, slopes of other types of embankments, excavated slopes, and natural slopes in soil and soft rock. ref http web.archive.org web 20080528085404 http www.usace.army.mil publications eng manuals em1110 2 1902 entire.pdf US Army Corps of Engineers Manual on Slope Stability ref Slope stability investigation, analysis including modeling , and design mitigation is typically completed by geologists , engineering geologists , or geotechnical engineer s. Geologists and engineering geologists can also use their knowledge of earth process and their ability to interpret surficial geomorphology to determine relative slope stability based simply on site observations. As seen in Figure 1, earthen slopes can develop a cut spherical weakness area. The probability of this happening can be calculated in advance using ... Slope Stability Calculator accessdate 2006 12 14 work ref A primary difficulty with analysis is locating ... year 2002 title A method for locating critical slip surfaces in slope stability analysis journal ... have only been analyzed after the fact. More recently slope stability radar technology has been employed ... construction work . Stability can thus be significantly improved by installing drainage paths to reduce ... remains, which may then recur at the next monsoon. Slope stability issues can be seen with almost ... is a method for analyzing the stability of a slope in two dimensions. The sliding mass above the failure ... s Method is a method for calculating the stability of slopes. It is an extension of the Method of Slices ... slope stability in cohesive soils. It differs from Bishop s Method in that it uses a clothoid ... more details
is chosen sufficienty large. See also Asymptotic stability Lyapunov stability References references Category Stabilitytheory Category Solitons ...In mathematical physics or theory of partial differential equations , the soliton solitary wave solution of the form math u x,t e i omega t phi x , math is said to be orbitally stable if any solution with the initial data sufficiently close to math phi x , math forever remains in a given small neighborhood of the trajectory of math e i omega t phi x , math . Formal definition Formal definition is as follows ref Manoussos Grillakis, Jalal Shatah, Walter Strauss, Stabilitytheory of solitary waves in the presence of symmetry. I , J. Funct. Anal. 74 1987 , pp. 160 197. ref . Let us consider the dynamical system math frac du dt A u , qquad u t in X, quad t in R, math with math X , math a Banach space over math C , math , and math A , X to X math . We assume that the system is unitary invariance math mathrm U 1 , math invariant , so that math A e is u e is A u , math for any math u in X , math and any math s in R , math . Assume that math omega phi A phi , math , so that math u t e i omega t phi , math is a solution to the dynamical system. We call such solution a soliton solitary wave . We say that the solitary wave math e i omega t phi , math is orbitally stable if for any math epsilon 0 , math there is math delta 0 , math such that for any math v 0 in X math with math Vert phi v 0 Vert X delta , math there is a solution math v t , math defined for all math t ge 0 math such that math v 0 v 0 , math , and such that this solution satisfies math sup t ge 0 inf s in R Vert v t e is phi Vert X epsilon. math Example The solitary wave solution math e i omega t phi omega x , math to the nonlinear ..., is orbitally stable if the Vakhitov&ndash Kolokolov stability criterion is satisfied math frac ... t phi omega x , math is Lyapunov stability Lyapunov stable , with the Lyapunov function given by math ... more details
Plasma Instabilities Category Plasma physics Category Stabilitytheory ru ...An important field of plasma physics is the stability of the Plasma physics plasma . It usually only makes sense to analyze the stability of a plasma once it has been established that the plasma is in Mechanical ... any part of the plasma. If there are not, then stability asks whether a small perturbation will grow, oscillate, or be damped out. In many cases a plasma can be treated as a fluid and its stability analyzed with magnetohydrodynamics MHD . MHD theory is the simplest representation of a plasma, so MHD stability is a necessity for stable devices to be used for nuclear fusion , specifically magnetic ... field strength. See magnetohydrodynamics for a full definition. MHD stability at high beta is crucial ... cases MHD stability represents the primary limitation on beta and thus on fusion power density. MHD stability is also closely tied to issues of creation and sustainment of certain magnetic configurations ... the stability limits through the use of a variety of plasma configurations, and developing ... configurations exist, the underlying MHD physics is common to all. Understanding of MHD stability ... for predictive MHD stability codes, and advancing the development of active control techniques. The most fundamental and critical stability issue for magnetic fusion is simply that MHD instabilities ... stability boundaries is a disruption, a sudden loss of thermal energy often followed by termination ... are less well understood due to the computationally intensive nature of the stability calculations. The extensive beta limit database for tokamaks is consistent with ideal MHD stability limits, yielding ... measured. This good agreement provides confidence in ideal stability calculations for other ... modes RWM develop in plasmas that require the presence of a perfectly conducting wall for stability. RWM stability is a key issue for many magnetic configurations. Moderate beta values are possible without ... more details
Thermal stability is the stability of a molecule at high temperature s i.e. a molecule with more stability has more resistance to decomposition at high temperatures. Thermal stability also describes, as defined by Schmidt 1928 , the stability of a water body and his resistance to mixing. This is the amount of work needed to transform the waterbody e.g. a lake to an uniform water density. The Schmidt stability S is commonly measured in Joule per square meter or g cm cm . Compare Stratification water Stratification . References Unreferenced date January 2009 references Further reading cite book title Engineering Tribology author Gwidon W. Stachowiak and Andrew W. Batchelor pages 39&ndash 40 publisher Butterworth&ndash Heinemann date 2005 isbn 0750678364 isbn13 9780750678360 Schmidt, W. 1928. ber Temperatur und Stabilit tsverh ltnisse von Seen. Geogr. Ann 10 145 177. Category Molecular physics engineering stub chemistry stub ... more details
of Stability url http www.physorg.com news173028810.html accessdate 11 October 2009 ref Theory and origin The possibility of an island of stability was first proposed by Glenn T. Seaborg . The hypothesis ... New York Times Editorial by Oliver Sacks regarding the Island of Stabilitytheory Feb 2004 re ...Image Island of Stability.png thumb 500px right 3 dimensional rendering of the theoretical Island of Stability. The island of stability is a term from nuclear physics that describes the possibility of chemical ... to plant them upon an island of stability but with too few neutrons to even place them upon the island ... less than a minute. Fermium is the heaviest element that can be produced in a nuclear reactor . The stability ... to be at the beginning of the island of stability. The longest lived observed isotopes are shown ... heavier ones small The half life half lives of nuclei in the island of stability itself are unknown ... 2008 title Search for long lived heaviest nuclei beyond the valley of stability author P. Roy Chowdhury ... agreement with the available experimental data. Island of relative stability chem 232 Th thorium ... beyond the valley of stability author P. Roy Chowdhury, C. Samanta, and D. N. Basu journal Physical ... title On the nuclear structure and stability of heavy and superheavy elements author Sven G sta Nilsson ... ref name longlived ref name nuclear Synthesis problems The manufacturing of nuclei in the island of stability ... of stability Oct 26 2010, Physorg news http www.newscientist.com article mg19926661.200 hunting ... elements discovered and the island of stability sighted Aug 1999 includes report on article later retracted http cerncourier.com cws article cern 28067 First postcard from the island of nuclear stability 1999 http cerncourier.com cws article cern 28509 Second postcard from the island of stability Oct ... be formed in a supernova? Can we observe them? http www.pbs.org wgbh nova physics stability elements.html NOVA Island of Stability Ninov fraud not to be used http www.lbl.gov Science Articles Archive ... more details
equation, and its properties form the basis of much of control theory . Stability Analysis We ...Directional stability is stability of a moving body or vehicle about a vertical axis. Stability of a vehicle concerns itself with the tendency of a vehicle to return to its original direction in relation to the oncoming medium water, air, road surface, etc. when disturbed rotated away from that original direction. If a vehicle is directionally stable, a Yaw axis yawing torque moment is produced which is in a direction opposite to the rotational disturbance. This pushes the vehicle in rotation so as to return it to the original orientation, thus tending to keep the vehicle oriented in the original direction. Directional stability is frequently called weather vaning because a directionally stable vehicle free to rotate about its center of mass is similar to a weather vane rotating about its vertical ... and are designed so that the front points more or less in the direction of motion. Without this stability ... to achieve stability. A road vehicle does not have elements specifically designed to maintain stability, but relies primarily on the distribution of mass . Introduction These points are best illustrated ... the stability of a road vehicle is the derivation of a reasonable approximation to the equations ... axle are incapable of generating significant lateral force, the stability will obviously be affected. Assume to begin with that the rear tyres are faulty, what is the effect on stability? If the rear ... is more critical to directional stability than the state of the front tyres. Also, locking the rear ... 2 b a b IMV 2 eta math The steady state response is with all time derivatives set to zero. Stability ... increases both its directional stability, and its tendency to understeer. The result is an overpowered ... Ltd,3rd Edition, 1970. See also Relaxed stability Car handling Flight dynamics Longitudinal static stability Hunting oscillation Category Mechanics de Richtungsstabilit t ... more details
Encyclopedia
top
