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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 ...
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 ...
A vacuum is defined as a space with as little energy in it as possible. Despite the name, the vacuum still has quantum fields.A true vacuum is stable because it is at a global minimum of energy, and is commonly assumed to coincide with the physical vacuum state we live in.
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.
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
For stability, the cloud must be in hydrostatic equilibrium, which in case of a spherical cloud translates to = (), where () is the enclosed mass, is the pressure, () is the density of the gas (at radius ), is the gravitational constant, and is the radius. The equilibrium is stable if small perturbations are damped and unstable if they are ...
Elasticity (physics) – Physical property when materials or objects return to original shape after deformation; Elastic modulus – Physical property that measures stiffness of material; Elastography – Set of imaging methods for determining soft-tissue hardness; Hardness – Measure of a material's resistance to localized plastic deformation
Floquet theory shows stability in Hill differential equation (introduced by George William Hill) approximating the motion of the moon as a harmonic oscillator in a periodic gravitational field. Bond softening and bond hardening in intense laser fields can be described in terms of solutions obtained from the Floquet theorem.