We discuss two fundamental reversible diffusion influenced reactions: ~i! A1B C and ~ii! A 1B C1D. In the pseudo-unimolecular case, we prove that reaction ~i! is a special case of ~ii!, which thus constitutes a unified reversible problem of multiparticle kinetics. For static A and C ~the ‘‘target’’ limit!, we suggest to treat this problem as follows. First we generalize the Smoluchowski theory ...

Quantum effects in the noninertial Brownian motion of a particle in a double well potential are treated via a semiclassical Smoluchowski equation for the time evolution of the reduced Wigner distribution function in configuration space allowing one to evaluate the position correlation function, its characteristic relaxation times, and dynamic susceptibility using matrix continued fractions and ...

Diffusion-limited reactions are usually described within the Smoluchowski theory, which neglects interparticle interactions. We propose a simple way to incorporate excluded-volume effects building on simulations of hard sphere in the presence of a sink. For large values of the sink-to-particle size ratio R(s), the measured encounter rate is in good agreement with a simple generalization of the ...

In all spatial dimensions d, we study the static and dynamical properties of a generalized Smoluchowski equation which describes the evolution of a gas obeying a logotropic equation of state, p = A ln ρ. A logotrope can be viewed as a limiting form of polytrope (p = Kρ γ , γ = 1 + 1/n), with index γ = 0 or n = −1. In the language of generalized thermodynamics, it corresponds to a Tsallis distri...

Speciation is fundamental to understanding the huge diversity of life on Earth. Although still controversial, empirical evidence suggests that the rate of speciation is larger for smaller populations. Here, we explore a biophysical model of speciation by developing a simple coarse-grained theory of transcription factor-DNA binding and how their co-evolution in two geographically isolated lineag...

A simplified, but non trivial, mechanical model—gas of N particles of mass m in a box partitioned by n mobile adiabatic walls of mass M—interacting with two thermal baths at different temperatures, is discussed in the framework of kinetic theory. Following an approach due to Smoluchowski, from an analysis of the collisions particles/walls, we derive the values of the main thermodynamic quantiti...

I. ABSTRACT A practical 1 imitation ·of the application of Smoluchowski 1 s classical estimate for the collision probability of two diffusing spherical particles in Brownian motion is the non-consideration of interparticle forces. For suspended particles in water such forces can arise from the disturbance the particle causes in the fluid {hydrodynamic forces), from the cloud of ions which surro...

We theoretically investigate general properties of driven (sheared) colloidal suspensions in confinement, based on methods of classical density functional theory. In the absence of an exact closed (Smoluchowski-) equation for the one-particle density under shear, we formulate a set of general conditions for approximations, and show that a simple closure fulfills them. The exact microscopic stre...

Considering systems of self-propelled polar particles with nematic interactions ("rods"), we compare the continuum equations describing the evolution of polar and nematic order parameters, derived either from Smoluchowski or Boltzmann equations. Our main goal is to understand the discrepancies between the continuum equations obtained so far in both frameworks. We first show that, in the simple ...