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Numerical stability, a property of numerical algorithms which describes how errors in the input data propagate through the algorithm; Stability radius, a property of continuous polynomial functions; Stable theory, concerned with the notion of stability in model theory; Stability, a property of points in geometric invariant theory
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation , for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature ...
The state is neutral to the lowest order and nearly remains in equilibrium if displaced a small amount. To investigate the precise stability of the system, higher order derivatives can be examined. The state is unstable if the lowest nonzero derivative is of odd order or has a negative value, stable if the lowest nonzero derivative is both of ...
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 analysis goes back to the work of Henri Poincaré on the three-body problem in celestial mechanics .
In nuclear physics, the island of stability is a predicted set of isotopes of superheavy elements that may have considerably longer half-lives than known isotopes of these elements. It is predicted to appear as an "island" in the chart of nuclides , separated from known stable and long-lived primordial radionuclides .
We can thus define the power system stability as the ability of the power system to return to steady state without losing synchronicity. Usually power system stability is categorized into steady state, transient and dynamic stability. Steady State Stability studies are restricted to small and gradual changes in the system operating conditions.
Classical physics predicts that such systems should be inherently unstable due to attractive and repulsive electrostatic forces between charges, and thus the stability of matter was a theoretical problem that required a quantum mechanical explanation.
In nuclear physics, the valley of stability (also called the belt of stability, nuclear valley, energy valley, or beta stability valley) is a characterization of the stability of nuclides to radioactivity based on their binding energy. [1] Nuclides are composed of protons and neutrons.