Yukawa potentials in systems with partial periodic boundary conditions I : Ewald sums for quasi-two dimensional systems

Yukawa potentials are often used as effective potentials for systems as colloids, plasmas, etc. When the Debye screening length is large, the Yukawa potential tends to the non-screened Coulomb potential ; in this small screening limit, or Coulomb limit, the potential is long ranged. As it is well known in computer simulation, a simple truncation of the long ranged potential and the minimum image convention are insufficient to obtain accurate numerical data on systems. The Ewald method for bulk systems, i.e. with periodic boundary conditions in all three directions of the space, has already been derived for Yukawa potential [cf. Y., Rosenfeld, {\it Mol. Phys.}, \bm{88}, 1357, (1996) and G., Salin and J.-M., Caillol, {\it J. Chem. Phys.}, \bm{113}, 10459, (2000)], but for systems with partial periodic boundary conditions, the Ewald sums have only recently been obtained [M., Mazars, {\it J. Chem. Phys.}, {\bf 126}, 056101 (2007)]. In this paper, we provide a closed derivation of the Ewald sums for Yukawa potentials in systems with periodic boundary conditions in only two directions and for any value of the Debye length. A special attention is paid to the Coulomb limit and its relation with the electroneutrality of systems.Comment: 40 pages, 5 figures and 4 table

Structural Anisotropy in Polar Fluids Subjected to Periodic Boundary Conditions

A heuristic model based on dielectric continuum theory for the long-range solvation free energy of a dipolar system possessing periodic boundary conditions (PBCs) is presented. The predictions of the model are compared to simulation results for Stockmayer fluids simulated using three different cell geometries. The boundary effects induced by the PBCs are shown to lead to anisotropies in the apparent dielectric constant and the long-range solvation free energy of as much as 50%. However, the sum of all of the anisotropic energy contributions yields a value that is very close to the isotropic one derived from dielectric continuum theory, leading to a total system energy close to the dielectric value. It is finally shown that the leading-order contribution to the energetic and structural anisotropy is significantly smaller in the noncubic simulation cell geometries compared to when using a cubic simulation cell

A software framework for the portable parallelization of particle-mesh simulations

We present a software framework for the transparent and portable parallelization of simulations using particle-mesh methods. Particles are used to transport physical properties and a mesh is required in order to reinitialize the distorted particle locations, ensuring the convergence of the method. Field quantities are computed on the particles using fast multipole methods or by discretizing and solving the governing equations on the mesh. This combination of meshes and particles presents a challenging set of parallelization issues. The present library addresses these issues for a wide range of applications, and it enables orders of magnitude increase in the number of computational elements employed in particle methods. We demonstrate the performance and scalability of the library on several problems, including the first-ever billion particle simulation of diffusion in real biological cell geometries