Abstract The theory of stochastic processes impacts both physical and social sciences. At the molecular scale, dynamics is ubiquitous because thermal fluctuations. Fokker–Plank–Smoluchowski equation models time evolution probability density selected degrees freedom in diffusive regime it is, therefore, a workhorse chemistry. In this paper we report on development implementation variational quan...

Abstract. The dynamical density functional theory of Marconi and Tarazona [J. Chem. Phys., 110, 8032 (1999)], a theory for the non-equilibrium dynamics of the onebody density profile of a colloidal fluid, is applied to a binary fluid mixture of repulsive Gaussian particles confined in a spherical cavity of variable size. For this model fluid there exists an extremely simple Helmholtz free energ...

We calculate the escape rates of different dynamical processes for the case of a one-dimensional symmetric double-well potential. In particular, we compare the escape rates of a Smoluchowski process, i.e., a corresponding overdamped Brownian motion dynamics in a metastable potential landscape, with the escape rates obtained for a biologically motivated model known as the Fisher-Eigen process. T...

Many simulation algorithms have been developed to help model spatial structure in cellular systems, each of which is intended to represent reaction dynamics with high spatial resolution. In this study, we simulated the e ects of macromolecular crowding on biochemical reaction rates to investigate which method actually performs best in practice. All 5 simulators investigated showed that di usion...

Consider N particles, which merge into clusters according to the rule: a cluster of size x and a cluster of size y merge at (stochastic) rate K (x; y)=N , where K is a speciied rate kernel. This Marcus-Lushnikov model of stochastic coalescence, and the underlying deter-ministic approximation given by the Smoluchowski coagulation equations , have an extensive scientiic literature. Some mathemati...

We study the free diffusion in two dimensions of active Brownian swimmers subject to passive fluctuations on the translational motion and to active fluctuations on the rotational one. The Smoluchowski equation is derived from a Langevin-like model of active swimmers and analytically solved in the long-time regime for arbitrary values of the Péclet number; this allows us to analyze the out-of-eq...

∗ Department of Mathematics, The University of Chicago, Chicago, Il 60637. †Chemical Engineering, PACM and Mathematics, Princeton University, Princeton, NJ 08544. ‡Department of Mathematics, and Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697-3875, Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot 76100,...

We investigate nonlinear rheology of dilute liquid crystalline polymer solutions under time dependent two-directional shear flow. We analyze the Smoluchowski equation, which describes the dynamics of the orientation of a liquid crystalline polymer, by employing technique of the full counting statistics. In the adiabatic limit, we derive the expression for time integrated currents generated by a...

Abstract. Size-structured population models provide a popular means to mathematically describe phenomena such as bacterial aggregation, schooling fish, and planetesimal evolution. For parameter estimation, generalized sensitivity functions (GSFs) provide a tool that quantifies the impact of data from specific regions of the experimental domain. These functions help identify the most relevant da...

Ds of a dilute suspension of 0.15 J.t polystyrene spheres moving through concentrated suspensions of 0.038 J.t polystyrene spheres was determined with light scattering spectroscopy. Solutions from which small ions had been rigorously excluded were compared with suspensions containing such ions. If the concentration dependence of Ds is Ds = Do (1 + J..¢ ), ¢ being the volume fraction of 0.038 J....