Single-particle diffusion, also known as Brownian motion, is the random motion of a particle in space due to collisions with its surrounding medium. The theory of diffusion in a homogeneous medium, one with a constant diffusion coefficient, is well established and recognized. The theoretical basis of diffusion in heterogeneous environments, where the diffusion coefficient varies in space, is fa...

Diffusion studies of adsorbates moving on a surface are often analyzed using 2D Langevin simulations. These simulations are computationally cheap and offer valuable insight into the dynamics, however, they simplify the complex interactions between the substrate and adsorbate atoms, neglecting correlations in the motion of the two species. The effect of this simplification on the accuracy of obs...

We study the influence of the bulk dynamics of a growing cluster of particles on the properties of its interface. First, we define a general bulk growth model by means of a continuum Master equation for the evolution of the bulk density field. This general model just considers an arbitrary addition of particles (though it can be easily generalized to consider subtraction) with no other physical...

We prove that incompressible two-dimensional nonequilibrium Langevin dynamics (NELD) converges exponentially fast to a steady-state limit cycle. use automorphism remapping periodic boundary conditions (PBCs) such as Lees–Edwards PBCs and Kraynik–Reinelt treat respectively shear flow planar elongational flow. The convergence is shown using technique similar (Joubaud et al. in J Stat Phys 158:1–3...

We consider Langevin dynamics associated with a modified kinetic energy vanishing for small momenta. This allows us to freeze slow particles, and hence avoid the re-computation of inter-particle forces, which leads to computational gains. On the other hand, the statistical error may increase since there are a priori more correlations in time. The aim of this work is first to prove the ergodicit...