MODELING AND SIMULATION OF NEW MATERIALS: Proceedings of Modeling and Simulation of New Materials: Tenth Granada Lectures

Molecular simulation methods for soft matter
View Description Hide DescriptionMolecular simulation methods that are relevant to the study of soft condensed matter are reviewed. A short discussion of molecular interaction potentials is followed by an discussion of molecular dynamics algorithms, stochastic dynamics, and thermostarting methods. The standard Metropolis Monte Carlo algorithm is described, and a short introduction given to weighted and biased sampling methods. Throughout, examples are chosen from the field of soft condensed matter, including colloidal systems, liquid crystals, and biopolymers.

Pattern formation in systems with competing interactions
View Description Hide DescriptionThere is a growing interest, inspired by advances in technology, in the low temperature physics of thin films. These quasi‐2D systems show a wide range of ordering effects including formation of striped states, reorientation transitions, bubble formation in strong magnetic fields, etc. The origins of these phenomena are, in many cases, traced to competition between short ranged exchange ferromagnetic interactions, favoring a homogeneous ordered state, and the long ranged dipole‐dipole interaction, which opposes such ordering on the scale of the whole sample. The present theoretical understanding of these phenomena is based on a combination of variational methods and a variety of approximations, e.g., mean‐field and spin‐wave theory. The comparison between the predictions of these approximate methods and the results of MonteCarlo simulations are often difficult because of the slow relaxation dynamics associated with the long‐range nature of the dipole‐dipole interactions. In this note we will review recent work where we prove existence of periodic structures in some lattice and continuum model systems with competing interactions. The continuum models have also been used to describe micromagnets, diblock polymers, etc.

Introduction to Monte Carlo simulations of polymers
View Description Hide DescriptionIn this lecture the basic aspects of Monte Carlo simulations are introduced, choosing models of polymers as examples. First the distinction between simple sampling and the Metropolis importance sampling algorithm is discussed, and the main limitations of the latter are discussed: lack of information on the partition function; “dynamical” correlation of “observations” and the resulting interpretation in terms of master equations, which also is the basis for applications to simulate the dynamics of fluctuations, diffusion processes and relaxation processes far from equilibrium; finite size effects, and their analysis in the context of simulations of second‐order and first‐order phase transitions. Examples discussed will include the dynamics of polymer melts, dynamics of translocation of polymers through membranes, and mixing of symmetrical binary mixtures, as well as asymmetrical polymer solutions. Also an introduction to path integral quantum Monte Carlo will be given, mentioning the application to crystalline orthorhombic polyethylene as an example.

From micro to macro scales using simulation: examples from hydrodynamics, elasticity and plasticity
View Description Hide DescriptionMolecular dynamics and Monte‐Carlo simulations, based on the knowledge of molecular interactions, have long been used to obtain information of simple bulk properties of materials, such as equation of state, elastic constants or transport coefficients. In this chapter, I will review several examples in which simulations are used to investigate intermediate length scales associated e.g. with interfaces, or with nanoscale heterogeneous behavior of materials. I will show how the resulting information can be used to infer macroscale properties of materials or interfaces.

On the relaxation dynamics of glass‐forming systems: Insights from computer simulations
View Description Hide DescriptionWe discuss the relaxation dynamics of a simple lattice gas model for glass‐forming systems and show that with increasing density of particles this dynamics slows down very quickly. By monitoring the trajectory of tagged particles we find that their motion is very heterogeneous in space and time, leading to regions in space in which there is a fast dynamics and others in which it is slow. We determine how the geometric properties of these quickly relaxing regions depend on density and time. Motivated by this heterogeneous hopping dynamics, we use a simple model, a variant of a continuous time random walk, to characterize the relaxation dynamics. In particular we find from this model that for large displacements the self part of the van Hove function shows an exponential tail, in agreement with recent findings from experiments and simulations of glass‐forming systems.

Fluctuations of a piston on top of a fluidized granular gas
View Description Hide DescriptionA fluidized granular gas in presence of a gravitational field is considered. It is enclosed in a box with a movable piston on the top. Molecular dynamics simulation results show that, if the box is not too wide, the system reaches a stationary state with gradients only in the direction of the field. Here, attention is focussed on the velocity fluctuations of the piston, that are observed to be Gaussian. The relationship between the second moment of this distribution and the granular temperature of the gas just below it is investigated. The ratio between the mean square velocities of the pisto and the gas can be larger or smaller than unity depending on the parameters of the system. A kinetic theory is formulated and its predictions compared with the simulation data.

Brazil nut effect: Influence of friction and jamming on the transition line
View Description Hide DescriptionWe report a molecular dynamics study of the behavior of a bidimensional system consisting of a large disk (the intruder) immersed in a bed of many small disks. All collisions are instantaneous and inelastic and all possible parameters of the system are kept fixed except for two dimensionless parameters determining the frequency and amplitude of the vibrating base. A systematic exploration of this parameter space leads to determining a transition line separating a zone in which the Brazil nut effect is observed and one in which it is not. It is observed for the BNE to be present it is necessary that the characteristic velocity of the vibrating base is above a certain threshold. This threshold increases as the characteristic acceleration of the base gets larger. The results strongly suggest that, in the region of the parameter space in which the study is made, there is a minimum amplitude and a maximum frequency for the Brazil nut effect to take place. The shape of the transition line is understood in connection with the friction of the system with the lateral walls and with jamming. Friction with the lateral walls produces a net downward force, eventually leading to a convective current that pushes the intruder up. Although the energy injection rate, that helps the development of the convective current, is proportional mainly to the square of the velocity of the base, it is found that the average frictional force decreases when increasing the base acceleration. Therefore, for large base accelerations, higher values of the base velocity are needed to produce a convective current sufficiently strong. But if the system is not excited enough the friction which would produced convective currents are balanced by the reaction forces that result from jamming.

Molecular ordering at an interface by molecular dynamics
View Description Hide DescriptionIn this paper, we present results obtained by Molecular Dynamics on the molecular ordering at a liquid‐vapor interface. Molecules are made of simple diatomics: while entering the interface from the gas phase, the prefered molecular orientations shifts from parallel to perpendicular to the plane of the liquid‐vapor interface. We mention possible extension of those properties in biological membranes.

Modeling and simulation of macrocapillarity
View Description Hide DescriptionMacroscopic capillarity, or macrocapillarity for short, refers to capillary phenomena occurring during twophase and multiphase flow in porous media. Wetting phenomena and hysteresis in porous media are at present poorly understood in the sense that neither in physics nor in engineering a fully predictive theory seems to exist, that can describe or predict all observations. This paper extends the consitutive assumptions of a recent approach based on the concept of hydraulic percolation of fluid phases. The theory proposed here allows prediction of residual saturations. It can describe displacement processes in which imbibition and drainage occur simultaneously. This contrasts with the established traditional theory where capillary forces are lumped into capillary pressure function and relative permeabilities, and these functions need to be specified for each displacement process as input. Contrary to the traditional theory the approach advanced here allows to predict capillary pressure saturation relations as output.

Monte Carlo simulation of the equilibrium spin glass phase in disordered assemblies of magnetic nanoparticles
View Description Hide DescriptionThis chapter is about the collective effects that are brought about by dipole‐dipole interactions in disordered assemblies of magnetic nanoparticles (NP). We focus on NPs which have single magnetic domains and large uniaxial anisotropics. We first discuss time dependent properties of these systems, such as the zero field cooled (ZFC) and field cooled (FC) magnetic susceptibility and aging, and report some results we obtain making use of the Metropolis Monte Carlo algorithm. For equilibrium behavior, we turn to the parallel tempered Monte Carlo method. A brief introduction to the method is followed by equilibrium results we have recently obtained, mainly, systems of magnetic dipoles with random anisotropy axes have, (a) below some non‐zero temperature a thermodynamic spin glass phase in three dimensions, but (b) in one layer assemblies, a spin glass phase only at or near zero temperature.

Domain growth in 2d: exact results, simulations and experiments
View Description Hide DescriptionWe obtain the exact distribution of the areas enclosed by domain boundaries (‘hulls’) during the coarsening dynamics of a two‐dimensional nonconserved scalar field. This result represents the first analytical demostration of the dynamical scaling hypothesis for this system. The experimental data for the formation of chiral domains in liquid crystals are in very good agreement with the theory.

Static and dynamic properties of a reversible gel
View Description Hide DescriptionWe study a microscopically realistic model of a physical gel and use computer simulations to investigate its static and dynamic properties at thermal equilibrium. The phase diagram comprises a sol phase, a coexistence region ending at a critical point, a gelation line, and an equilibrium gel phase unrelated to phase separation. The global structure of the gel is homogeneous, but the stress is supported by a fractal network. Gelation results in a dramatic slowing down of the dynamics, which can be used to locate the transition, which otherwise shows no structural signatures. Moreover, the equilibrium gel dynamics is highly heterogeneous as a result of the presence of particle families with different mobilities. An analysis of gel dynamics in terms of mobile and arrested particles allows us to elucidate several differences between the dynamics of equilibrium gels and that of glass‐formers.

Liquid‐glass transition in suspensions of charged liposomes
View Description Hide DescriptionWe report the first observation of a transition from the ergodic liquid state to the nonergodic glass in concentrated charged liposomes suspensions. In consequence, the measured dynamic structure factors, determined by means of a three‐dimensional dynamic light scattering scheme, evolve to nondecaying components as the liposomes volume fraction is increased. Our experimental data agree reasonably well with the predictions obtained from the numerical resolution of a hard sphere mode‐coupling model.

Effective temperature in Coulomb glasses
View Description Hide DescriptionWe have developed a Monte Carlo algorithm to simulate relaxation of disordered electronic systems with long range Coulomb interactions at low temperatures. The algorithm can integrate out exactly fast transitions avoiding repetitive hops characteristic of metastable states. The present implementation of the method can follow the dynamics of systems with up to 1000 sites to times of the order of one second. This method is quite general and can be extended to most slow discrete relaxation systems.

Influence of intramolecular couplings in a model for hydrogen‐bonded liquids
View Description Hide DescriptionA brief review of recent work on the unique and unusual properties of water is given through results obtained from a simple cell model that reproduces qualitatively the behavior observed in experiments and molecular dynamics simulations. The attention is focused on results that help establish which theoretic scenario better describes the phase diagram of water.

Hydrodynamic description for ballistic annihilation systems
View Description Hide DescriptionThe problem of the validity of a hydrodynamic description for a system in which there are no collisional invariants is addressed. Hydrodynamic equations have been derived and successfully tested against simulation data for a system where particles annihilate with a probability p, or collide elastically otherwise. The response of the system to a linear perturbation is analyzed as well.

Global fluctuations in dissipative systems
View Description Hide DescriptionOur goal here is to investigate the influence of velocity correlations on the fluctuations of several global quantities for two different systems. In the first case, we study the fluctuations of the total number of particles, momentum and energy in a probabilistic ballistic annihilation model. For this model, when there is a binary encounter, the particles annihilate with certain probability. In the second case, we analyze the fluctuations of the total energy in a granular system which is driven by a stochastic thermostat. The theoretical analysis is based on the study of the equation for the two‐particle distribution function. The predictions are in very good agreement with simulations results.

Boundary‐induced heterogeneous absorbing states
View Description Hide DescriptionWe study two different types of systems with many absorbing states (with and without a conservation law) and scrutinize the effect of walls/boundaries (either absorbing or reflecting) into them. In some cases, non‐trivial structured absorbing configurations (characterized by a background field) develop around the wall. We study such structures using a mean‐field approach as well as computer simulations. The main results are: i) for systems in the directed percolation class, a very fast (exponential) convergence of the background to its bulk value is observed; ii) for systems with a conservation law, power‐law decaying landscapes are induced by both types of walls: while for absorbing walls this effect is already present in the mean‐field approximation, for reflecting walls the structured background is a noise‐induced effect. The landscapes are shown to converge to their asymptotic bulk values with an exponent equal to the inverse of the bulk correlation length exponent. Finally, the implications of these results in the context of self‐organizing systems are discussed.

Simulation of large deviation functions using population dynamics
View Description Hide DescriptionIn these notes we present a pedagogical account of the population dynamics methods recently introduced to simulate large deviation functions of dynamical observables in and out of equilibrium. After a brief introduction on large deviation functions and their simulations, we review the method of Giardinà et al. for discrete time processes and that of Lecomte et al. for the continuous time counterpart. Last we explain how these methods can be modified to handle static observables and extract information about intermediate times.