Mean-Field SPDE Model

Available identifiers

MaRDI QIDQ6775431

Mean Field mofel for clustering dynamics comprising of SPDEs

Description

Stochastic effects crucial for systems of finite size N, especially in the case of clustering behavior.

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List of mathematical expressions with quantities

Evolution Of The Concentration Of Particles SPDE	${\partial }_{t}c(x,t)={\partial }_x(c(x,t)(F^{\prime }*c(\cdot ,t))(x))+\frac{{\sigma }^2}{2}{\partial }_{xx}c(x,t)+\frac{\sigma }{\sqrt{N}}{\partial }_x\cdot (\sqrt{c(x,t)}\xi (x,t))$
$(F^{\prime }*c(\cdot ,t))$ symbol represents Convolution Between Interaction Force And Density
$N$ symbol represents Number of Particles
$\sigma$ symbol represents Diffusion Coefficient
$\xi$ symbol represents White Noise
$c$ symbol represents Concentration Of Particles
$t$ symbol represents Time