Dispersionform

Dispersionform, occasionally written as dispersion form, is a term used across science to denote the mathematical description of how a quantity spreads as it propagates through space, time, or across a spectrum of frequencies.

In continuous media, dispersion is often modeled by equations such as the diffusion equation ∂u/∂t = D ∇^2 u or the advection-diffusion equation ∂u/∂t + v·∇u = D ∇^2 u, capturing spreading from random motion and transport by flow. In wave phenomena, dispersion relations relate frequency ω to wavenumber k, defining how phase and group velocities vary with frequency. In optics, refractive dispersion is represented by wavelength-dependent indices of refraction, often expressed through empirical or semi-empirical formulas.

Key properties include linear versus nonlinear dispersion, isotropy versus anisotropy, and local versus nonlocal forms. The chosen dispersion form depends on medium properties, scales, and whether spreading competes with other processes such as reaction, convection, or confinement.

Applications span environmental modeling of pollutant plumes, heat conduction in solids, acoustics and electromagnetism, and computer graphics for visual effects that simulate dispersion of light or motion.

The term is a descriptive label rather than a single universal concept; its precise meaning varies by field and context, but it generally refers to the mathematical structure that governs how a quantity spreads during propagation.