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

Yukawa potentials may be long ranged when the Debye screening length is large. In computer simulations, such long ranged potentials have to be taken into account with convenient algorithms to avoid systematic bias in the sampling of the phase space. Recently, we have provided Ewald sums for quasi-two dimensional systems with Yukawa interaction potentials [M. Mazars, {\it J. Chem. Phys.}, {\bf 126}, 056101 (2007) and M. Mazars, {\it Mol. Phys.}, Paper I]. Sometimes, Lekner sums are used as an alternative to Ewald sums for Coulomb systems. In the present work, we derive the Lekner sums for quasi-two dimensional systems with Yukawa interaction potentials and we give some numerical tests for pratical implementations. The main result of this paper is to outline that Lekner sums cannot be considered as an alternative to Ewald sums for Yukawa potentials. As a conclusion to this work : Lekner sums should not be used for quasi-two dimensional systems with Yukawa interaction potentials.Comment: 25 pages, 5 figures and 1 tabl

The melting of the classical two dimensional Wigner crystal

We report an extensive Monte-Carlo study of the melting of the classical two dimensional Wigner crystal for a system of point particles interacting via the $1/r$-Coulomb potential. A hexatic phase is found in systems large enough. With the multiple histograms method and the finite size scaling theory, we show that the fluid/hexatic phase transition is weakly first order. No set of critical exponents, consistent with a Kosterlitz-Thouless transition and the finite size scaling analysis for this transition, have been found.Comment: 6 pages, 5 figures, 1 tabl

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 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 is depending 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 of the paper, one would find explicit formulas for Lagrange multipliers for systems having 1, 2, 3, 4 and 5 bonds of constant length, linearly connected.Comment: 13 pages, no figures. To appear in J. Phys. A : Math. The

Mixtures of Hard Ellipsoids and Spheres: Stability of the Nematic Phase

The stability of liquid crystal phases in presence of small amount of non-mesogenic impurities is of general interest for a large spectrum of technological applications and in the theories of binary mixtures. Starting from the known phase diagram of the hard ellipsoids systems, we propose a simple model and method to explore the stability of the nematic phase in presence of small impurities represented by hard spheres. The study is performed in the isobaric ensemble with Monte Carlo simulations

Analysis, by simulation, of the impact of a technical default of a payment system participant.

Payment systems play a very important role in ensuring the safe and efficient transfer of deposits and financial instruments. Consequently, the failure of these systems may have a destabilising impact. Business continuity plans have thus been developed to ensure their robustness. However, their smooth functioning is also contingent on the capacity of participants to submit their payment orders. The Banque de France, in its role of overseer of the French payment systems, conducted a study with a view to enhancing its understanding of the consequences and the impact of the technical default of a participant in such systems. This study, carried out using a simulator of the functioning of the Paris Net Settlement (PNS) large-value payment system, operated by the CRI (Centrale des Règlements Interbancaires), shows that the technical default of a participant in this system has negative consequences on the smooth running of the system. Indeed, a situation in which a major participant, in the wake of a technical incident, is unable to submit its payment orders in a normal fashion to its counterparties in PNS, could further exacerbate congestion in the system and result in almost 10% of payments being rejected among non-defaulting participants. The consequences of a technical default could nevertheless be greatly reduced if the participants set their bilateral sender limits at a lower level than that currently observed and if they reacted rapidly to information indicating a technical default by reducing their bilateral limits with the defaulting participant (defaulter).

Stress state influence on nonlocal interactions in damage modelling

This paper presents a modification of an integral nonlocal damage model used to describe concrete behaviour. It aims at providing a better treatment of areas close to a boundary and a fracture process zone where the interactions between points should vanish. Modifications on the original integral nonlocal model are introduced by considering the stress state of points in the weight function used to compute the nonlocal variables. Computations show that local information such as strain or damage profiles are significantly different, leading to a narrower region where damage equal to 1 in the case of the modified nonlocal model. It allows to better approach a discontinuity of the displacement field upon failure and thus, improves the estimation of the crack opening that has been developed in post-processing for this type of calculation

Taking one charge off a two-dimensional Wigner crystal

A planar array of identical charges at vanishing temperature forms a Wigner crystal with hexagonal symmetry. We take off one (reference) charge in a perpendicular direction, hold it fixed, and search for the ground state of the whole system. The planar projection of the reference charge should then evolve from a six-fold coordination (center of a hexagon) for small distances to a three-fold arrangement (center of a triangle), at large distances $d$ from the plane. The aim of this paper is to describe the corresponding non-trivial lattice transformation. For that purpose, two numerical methods (direct energy minimization and Monte Carlo simulations), together with an analytical treatment, are presented. Our results indicate that the $d=0$ and $d\to\infty$ limiting cases extend for finite values of $d$ from the respective starting points into two sequences of stable states, with intersecting energies at some value $d_t$; beyond this value the branches continue as metastable states.Comment: 17 pages, 11 figure