This work presents new parallelizable numerical schemes for the integration of dissipative particle dynamics with energy conservation. So far, no numerical scheme introduced in the literature is able to correctly preserve the energy over long times and give rise to small errors on average properties for moderately small time steps, while being straightforwardly parallelizable. We present in this article two new methods, both straightforwardly parallelizable, allowing to correctly preserve the total energy of the system. We illustrate the accuracy and performance of these new schemes both on equilibrium and nonequilibrium parallel simulations.

Abstract. We consider in this work the numerical computation of transport coefficients for Brownian dynamics. We investigate the discretization error arising when simulating the dynamics with the Smart MC algorithm (also known as Metropolis-adjusted Langevin algorithm). We prove that the error is of order one in the time step as ∆t goes to zero, when using either the Green-Kubo or the Einstein formula to estimate the transport coefficients. We illustrate our results with numerical simulations.Résumé. Nous nous intéressons dans cet article au calcul numérique des coefficients de transports pour des dynamiques browniennes. Nousétudions l'erreur de discrétisation qui apparait lorsqu'on simule la dynamique avec l'algorithme connu sous le nom de "Smart MC" dans la littérature. Nous prouvons que cette erreur est d'ordre un en le pas de temps lorsque ∆t tend vers zéro, lorsqu'on utilise la formule de Green-Kubo ou la formule d'Einstein pour estimer les coefficients de transport. Nous illustrons ces résultats avec des simulations numériques.

The determination of surface tension of curved interfaces is a topic that raised many controversies during the last century. Explicit liquid-vapor interface modelling (ELVI) was unable up to now to reproduce interfacial behaviors in drops due to ambiguities in the mechanical definition of the surface tension. In this work, we propose a thermodynamic approach based on the location of surface of tension and its use in the Laplace equation to extract the surface tension of spherical interfaces from ELVI modelling.

No abstract