We investigate micelle formation in a system containing two or more different amphiphiles with different geometries using a stochastic molecular-dynamics (MD) simulation method. For a binary system containing two amphiphiles, we calculate the critical micelle concentration (CMC) and cluster distribution for the mixture at several mole fractions and compare the simulation results with those pred...

Within this thesis, we consider Brownian dynamics simulations of anisotropic colloids modeled by elliptic disks. At first, a mathematical framework is developed in order to describe ellipses and to derive corresponding collision laws. Then, we introduce the conception of an event-driven algorithm. Within this scope, the collision time of two elliptic disks has to be determined. For this purpose...

This paper derives a complete analytical solution for the probability distribution of the configuration of a non-holonomic vehicle that moves in two spatial dimensions by satisfying the unicycle kinematic constraints and in presence of Brownian noises. In contrast to previous solutions, the one here derived holds even in the case of arbitrary linear and angular speed. This solution is obtained ...

We study interacting systems of linear Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. Our main objective has been to study the long range behavior of the spacings between the Brownian motions arranged in increasing order. For finitely many Brownian motions interacting in this manner, we characterize drifts fo...

Theoretical approaches to nonequilibrium many-body dynamics generally rest upon an adiabatic assumption, whereby the true dynamics is represented as a sequence of equilibrium states. Going beyond this simple approximation is a notoriously difficult problem. For the case of classical Brownian many-body dynamics, we present a simulation method that allows us to isolate and precisely evaluate supe...

We present a newly adapted Brownian-Dynamics (BD)-based protein docking method for predicting native protein complexes. The approach includes global BD conformational sampling, compact complex selection, and local energy minimization. In order to reduce the computational costs for energy evaluations, a shell-based grid force field was developed to represent the receptor protein and solvation ef...

We endow a system of interacting particles with two distinct, local, Markovian, and reversible microscopic dynamics that both converge to the Boltzmann-Gibbs equilibrium of standard liquids. While the first, standard, one leads to glassy dynamics, we use field-theoretical techniques to show that the latter displays no sign of glassiness. The approximations we use, akin to the mode-coupling appr...

We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust, space efficient, and easy to accumulate. We construct a system of overdamped Langevin equations in the quaternion representation that accounts for hydrodynamic ...

Classical density functional theory (DFT) provides an exact variational framework for determining the equilibrium properties of inhomogeneous fluids. We report a generalization of DFT to treat the non-equilibrium dynamics of classical many-body systems subject to Brownian dynamics. Our approach is based upon a dynamical functional consisting of reversible free energy changes and irreversible po...

We study the asymptotic behavior of a class of stochastic dynamics on interlacing particle configurations (also known as Gelfand-Tsetlin patterns). Examples of such dynamics include, in particular, a multilayer extension of TASEP and particle dynamics related to the shuffling algorithm for domino tilings of the Aztec diamond. We prove that the process of reflected interlacing Brownian motions i...