Brownian web Brownian web In probability theory, the Brownian web is an uncountable collection of one-dimensional coalescing Brownian motions, starting from every point in space and time. It arises as the diffusive space-time scaling limit of a collection of coalescing random walks, with one walk starting from each point of the integer lattice Z at each time. What is now known as the Brownian web was first conceived by Arratia in his Ph.D. thesis and a subsequent incomplete and unpublished manuscript. Arratia studied the voter model, an interacting particle system that models the evolution of a population's political opinions. The individuals of
Brownian motor bias the motion of a particle (like an ion or polypeptide); the result would essentially be diffusion of a particle whose net motion is strongly biased in one direction. The translocation of the particle would only be loosely coupled to hydrolysis of ATP. The dynamics and activity of Brownian motors are current topics of study in theoretical and experimental biophysics. Brownian motors are sometimes modeled using the Fokker-Planck equation or with Monte Carlo methods. Many researchers are presently engaged in understanding how molecular-scale motors operate in environments with non-negligible thermal noise. The thermodynamics of such motors is constrained by the