particlesin
Particlesin is a hypothetical modeling framework used to describe systems in which multiple particle species occupy a bounded region and interact through transport and chemical processes. In this framework, the state is represented by the set of number-density fields n_i(x,t) for each species i, defined inside a domain Ω with boundary ∂Ω. The evolution is typically expressed by a system of reaction-diffusion-advection equations: ∂t n_i = ∇·(D_i ∇n_i) - ∇·(v_i n_i) + R_i({n_j}). Here D_i are diffusion coefficients, v_i are advection velocities, and R_i denotes net production or loss due to reactions and interactions with other species. Boundary conditions may specify no-flux, fixed concentration, or reactive flux at ∂Ω, while the initial condition sets n_i(x,0).
The term gains its name from the idea of counting particles “in” a region; it has appeared
Applications of particlesin models include the design of chemical reactors in porous media, environmental transport and
Related concepts include reaction-diffusion systems, population balance modeling, and particle-in-cell methods. See also: diffusion equation, reaction