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

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

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 the Parry's 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 intregral involving incomplete gamma function. Energies of the generalized restrictive primitive model of electrolytes ($\eta$-RPM) and of the generalized one component plasma model ($\eta$-OCP) are given for the tridimensional, quasi-two dimensional and monolayers systems. Few numerical results, using Monte-Carlo simulations, for $\eta$-RPM and $\eta$-OCP monolayers systems are reported.Comment: to be published in Journal of Physics A: Mathematical and Theoretical (19 pages, 2 figures and 3 tables

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. A particular attention is pay to the characteristics of the crystalline phases by the analysis of bond orientational order parameters and center-to-center correlations functions.Comment: 6 pages, 6 figures, 2 table

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

Lekner summations and Ewald summations for quasi-two dimensional systems

Using the specific model of a bilayer of classical charged particles (bilayer Wigner crystal), we compare the predictions for energies and pair distribution functions obtained by Monte Carlo simulations using three different methods available to treat the long range Coulomb interactions in systems periodic in two directions but bound in the third one. The three methods compared are: the Ewald method for quasi-two dimensional systems [D.E. Parry, Surf. Sci. $\bm{49}$, 433 (1975); \it{ibid.}, $\bm{54}$, 195 (1976)], the Hautman-Klein method [J. Hautman and M.L. Klein, Mol. Phys. $\bm{75}$, 379 (1992)] and the Lekner summations method [J. Lekner, Physica A$\bm{176}$, 485 (1991)]. All of the three method studied in this paper may be applied to any quasi-two dimensional systems, including those having not the specific symmetry of slab systems. For the particular system used in this work, the Ewald method for quasi-two dimensional systems is exact and may be implemented with efficiency; results obtained with the other two methods are systematically compared to results found with the Ewald method. General recommendations to implement with accuracy, but not always with efficiency, the Lekner summations technique in Monte Carlo algorithms are given.Comment: 50 pages, 9 figures, 4 table

Seismic vulnerability reduction: numerical modeling of FRP reinforcement using multifiber beams elements

This paper presents a simplified modeling strategy for reproducing the behavior of beam-column structures reinforced with Polymer Reinforced Fibers (FRP). A 1D concrete constitutive model has been recently proposed, suitable for both monotonic and cycling loadings. The model is inspired on two well-known concrete laws, one based on damage mechanics theory (La Borderie concrete damage model) and one based on experimental studies (Eid & Paultre's confined concrete model). Spatial discretization is done using multifiber Timoshenko beam elements. Validation of the strategy is provided using two case studies: a retrofitted bridge pier and a vulnerability analysis on an existing building

Shaking table tests of lightly RC walls: Numerical simulations

International audienceIn the framework of the European consortium ECOLEADER, a seismic research project has been performed on specimens tested on a shaking table. The specimens were representative of reinforced concrete buildings with bearing walls. The mock-up studied in particular in this article is composed of two parallel walls linked with a perpendicular one that has openings. The walls are reinforced according to the current design practice in France with a small amount of reinforcement. Two kinds of finite element simulations have been performed: a refined one using a detailed 3D description of the specimen and a simplified one, based on multifiber beams. The comparison between the experimental and numerical results not only demonstrates the accuracy of the time-history analysis models, but also allows obtaining more detailed information about the behavior of the specimen for more complex seismic excitations. It is shown that both models are able to describe quantitatively the global and qualitatively the local behavior of the structure. The simplified model is furthermore used to investigate the behavior of the specimen under a 3D earthquake loading