Martial Mazars

Lekner summations and Ewald summations for quasi-two-dimensional systems

The purpose of this work is to carry out a comparison between the Ewald quasi-2D and Lekner summation methods. These methods were derived to treat the long-range electrostatic interactions in systems periodic in two directions, but bound in the third. The comparison is performed by Monte Carlo simulations on a very simple system, a bilayer of point ions; samplings of the phase space, average energies and structure functions are compared. When correctly implemented, the Lekner summation method is found to be in close agreement with the Ewald quasi-2D method; otherwise, a very complicated bias may plague computations.The purpose of this work is to carry out a comparison between the Ewald quasi-2D and Lekner summation methods. These methods were derived to treat the long-range electrostatic interactions in systems periodic in two directions, but bound in the third. The comparison is performed by Monte Carlo simulations on a very simple system, a bilayer of point ions; samplings of the phase space, average energies and structure functions are compared. When correctly implemented, the Lekner summation method is found to be in close agreement with the Ewald quasi-2D method; otherwise, a very complicated bias may plague computations.

Structure and thermodynamics of a ferrofluid bilayer.

We present extensive Monte Carlo simulations for the thermodynamic and structural properties of a planar bilayer of dipolar hard spheres for a wide range of densities, dipole moments, and layer separations. Expressions for the stress and pressure tensors of the bilayer system are derived. For all thermodynamic states considered, the interlayer energy is shown to be attractive and much smaller than the intralayer contribution to the energy. It vanishes at layer separations of the order of two hard sphere diameters. The normal pressure is negative and decays as a function of layer separation h as -1/h;{5} . Intralayer and interlayer pair distribution functions and angular correlation functions are presented. Despite the weak interlayer energy, strong positional and orientational correlations exist between particles in the two layers.

Monte Carlo study of the thermodynamic stability of the nematic phase of a semiflexible liquid crystal model

This paper reports a Monte Carlo (MC) study of the ordering in a semiflexible liquid crystal model designed to give a crude representation of 4‐n‐octyl‐4′‐cyanobiphenyl (PCB). A mechanically stable nematic phase is obtained and the question of its thermodynamic stability is addressed by comparing the free energy to that of the isotropic phase. The free energies are calculated by thermodynamic integration using an efficient configuration biased MC scheme. Pair distribution functions, orientational correlation functions, and conformational properties of the nematic and isotropic phases are contrasted. In the isotropic phase the equation of state is compared with theoretical predictions for systems of convex molecules and chains made up of tangent hard spheres.

Ewald methods for inverse power-law interactions in tridimensional and quasi-two-dimensional systems

In this paper, we derive the Ewald method for inverse power-law interactions in quasi-two-dimensional systems. The derivation is done by using two different analytical methods. The first uses Parrys limit that considers the Ewald methods for quasi-two-dimensional systems as a limit of the Ewald methods for tridimensional systems; the second uses Poisson–Jacobi identities for lattice sums. Taking into account the equivalence of both derivations, we obtain a new analytical Fourier transform integral involving an incomplete gamma function. Energies of the generalized restrictive primitive model of electrolytes (η-RPM) and of the generalized one-component plasma model (η-OCP) are given for the tridimensional, quasi-two-dimensional and monolayers systems. Few numerical results, using Monte Carlo simulations, for η-RPM and η-OCP monolayer systems are reported.

Bond orientational order parameters in the crystalline phases of the classical Yukawa-Wigner bilayers

We present a study of the structural properties of the crystalline phases for a planar bilayer of particles interacting via repulsive Yukawa potentials in the weak screening region. The study is done with Monte Carlo computations and the long-ranged contributions to energy are taken into account with the Ewald method for quasi–two-dimensional systems. Two first-order phase transitions (fluid-solid and solid-solid) and one second-order transition (solid-solid) are found when the surface density is varied at constant temperature. Particular attention is paid to the characteristics of the crystalline phases by the analysis of bond orientational order parameters and center-to-center correlations functions.

Comment on “Rapid calculation of the Coulomb component of the stress tensor for three-dimensional systems with two-dimensional periodicity” [J. Chem. Phys. 115, 4457 (2001)]

The Ewald-like method for quasi-two dimensional systems proposed by M. Kawata and co-workers [J. Chem. Phys. 115, 4457 (2001)] is examined and compared to the method proposed by Sphor, Yeh, Berkowitz and others. Both methods are found numerically equivalent.

Freely jointed chains in external potentials: analytical computations

Freely jointed chains in external potentials are crude representations of macromolecular systems in interaction with electrostatic fields, surfaces, walls and interfaces. We show how the canonical partition function of these models can be computed analytically and how the independent motion approximation (IMA) may be applied. In particular, the chain stretched at both ends is studied with IMA and new results are obtained for entropic elastic constants and force/extension relations, including the dependence on the degree of polymerization. These new results are in good agreement with molecular dynamics computations.

Ewald sums for Yukawa potentials in quasi-two-dimensional systems

In this article, the author derive Ewald sums for Yukawa potential for three-dimensional systems with two-dimensional periodicity. This sums are derived from the Ewald sums for Yukawa potentials with three-dimensional periodicity [G. Salin and J.-M. Caillol, J. Chem. Phys.113, 10459 (2000)] by using the method proposed by Parry for the Coulomb interactions [D. E. Parry, Surf. Sci.49, 433 (1975); 54, 195 (1976)].

Canonical partition functions of freely jointed chains

The freely jointed chain is a simple off-lattice ideal model of a heteropolymer. We show how to compute the canonical partition function of this model exactly for all physical primary structures, degree of polymerization and space dimensions greater than or equal to 2. The canonical partition function of this model of a heteropolymer has an analytical expression involving a complicated multiple hypergeometric function. To obtain some accurate approximations we develop and use the independent motion approximation (IMA).

Holonomic constraints: an analytical result

Systems subjected to holonomic constraints follow quite complicated dynamics that could not be described easily with Hamiltonian or Lagrangian dynamics. The influence of holonomic constraints in equations of motions is taken into account by using Lagrange multipliers. Finding the value of the Lagrange multipliers allows us to compute the forces induced by the constraints and therefore, to integrate the equations of motions of the system. Computing analytically the Lagrange multipliers for a constrained system may be a difficult task that depends on the complexity of systems. For complex systems it is, most of the time, impossible to achieve. In computer simulations, some algorithms using iterative procedures estimate numerically Lagrange multipliers or constraint forces by correcting the unconstrained trajectory. In this work, we provide an analytical computation of the Lagrange multipliers for a set of linear holonomic constraints with an arbitrary number of bonds of constant length. In the appendix explicit formulae are shown for Lagrange multipliers for systems having 1, 2, 3, 4 and 5 bonds of constant length, linearly connected.