We revisit the hard-spheres lattice gas model in the spherical approximation proposed by Lebowitz and Percus. Although no disorder is present in the model, we find that the short-range dynamical restrictions in the model induce glassy behaviour. We examine the offequilibrium Langevin dynamics of this model and study the relaxation of the density as well as the correlation, response and overlap ...

We propose a nonequilibrium sampling method for computing free energy profiles along a given reaction coordinate. The method consists of two parts: a controlled Langevin sampler that generates nonequilibrium bridge paths conditioned by the reaction coordinate, and Jarzynski’s formula for reweighting the paths. Our derivation of the equations of motion of the sampler is based on stochastic pertu...

In this paper, we generalize a result by Rubin and Ungar on Hamiltonian systems with a strong constraining potential to thermally embedded systems, i.e. to Langevin dynamics. Such highly oscillatory systems arise, for example, in the context of molecular dynamics. We derive averaged equations of motion for the slowly varying solution components. This includes in particular the derivation of a c...

Here I discuss the dynamics of microscopic systems, primarily for spin models, in thermal equilibrium, where the temperature causes random forces or torques, which are in competition with a damping force. This includes summarizing Langevin dynamics and finding methods for integrating the Landau-Gilbert equation of micromagnetics in time, with damping & temperature. The goal is to understand how...

In the coarse grained Brownian Dynamics simulation method the many solvent molecules are replaced by random thermal kicks and an effective friction acting on the particles of interest. For Brownian Dynamics the friction has to be so strong that the particles’ velocities are damped much faster than the duration of an integration timestep. Here we show that this conceptual limit can be dropped wi...

The statistical and dynamical properties of ions in the selectivity filter of the KcsA ion channel are considered on the basis of molecular dynamics (MD) simulations of the KcsA protein embedded in a lipid membrane surrounded by an ionic solution. A new approach to the derivation of a Brownian dynamics (BD) model of ion permeation through the filter is discussed, based on unbiased MD simulation...

The reaction A + B −→ B is studied when the reactants diffuse in phase space, i.e. their dynamics is described by the Langevin equation. The steadystate rate constants are calculated for both the target (static A and mobile B’s) and trapping (mobile A and static B’s) problems when the reaction is assumed to occur at the first contact. For Brownian dynamics (i.e., ordinary diffusion), the rate c...

The statistical and dynamical properties of ions in the selectivity filter of the KcsA ion channel are considered on the basis of molecular dynamics (MD) simulations of the KcsA protein embedded in a lipid membrane surrounded by an ionic solution. A new approach to the derivation of a Brownian dynamics (BD) model of ion permeation through the filter is discussed, based on unbiased MD simulation...