Search results
Results From The WOW.Com Content Network
The dispersion relation of phonons is also non-trivial and important, being directly related to the acoustic and thermal properties of a material. For most systems, the phonons can be categorized into two main types: those whose bands become zero at the center of the Brillouin zone are called acoustic phonons , since they correspond to ...
A nonlinear dispersion relation (NDR) is a dispersion relation that assigns the correct phase velocity to a nonlinear wave structure. As an example of how diverse and intricate the underlying description can be, we deal with plane electrostatic wave structures ϕ ( x − v 0 t ) {\displaystyle \phi (x-v_{0}t)} which propagate with v 0 ...
The distributions of a wide variety of physical, biological, and human-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, [2] cloud sizes, [3] the foraging pattern of various species, [4] the sizes of activity patterns of neuronal populations, [5] the frequencies of words in most languages ...
In the mid-1990s, in the study of dynamics of spin glass models, a generalization of the fluctuation–dissipation theorem was discovered that holds for asymptotic non-stationary states, where the temperature appearing in the equilibrium relation is substituted by an effective temperature with a non-trivial dependence on the time scales. [9]
As the relation is linear, the wave equation is said to be non-dispersive. To simplify, consider the one-dimensional wave equation with ω(k) = ±kc . Then the general solution is u ( x , t ) = A e i k ( x − c t ) + B e i k ( x + c t ) , {\displaystyle u(x,t)=Ae^{ik(x-ct)}+Be^{ik(x+ct)},} where the first and second term represent a wave ...
The magnitude of a complex number must be a non-negative number, so only ψ = 0 solves the Ginzburg–Landau equation. Below the superconducting transition temperature, T < T c, the right hand side of the equation above is positive and there is a non-trivial solution for ψ.
Dispersion of gravity waves on a fluid surface. Phase and group velocity divided by √ gh as a function of h / λ . A: phase velocity, B: group velocity, C: phase and group velocity √ gh valid in shallow water. Drawn lines: based on dispersion relation valid in arbitrary depth. Dashed lines: based on dispersion relation valid in deep ...
These wave solutions are interesting as, notwithstanding we started with an equation with a wrong mass sign, the dispersion relation has the right one. Besides, Jacobi function d n {\displaystyle \,{\rm {dn}}\!} has no real zeros and so the field is never zero but moves around a given constant value that is initially chosen describing a ...