arXiv subjects

Peter V. Coveney

Publications and source records attributed to Peter V. Coveney.

89 records · Page 5Linked to original sources

arXiv2000

Foundations of Dissipative Particle Dynamics

We derive a mesoscopic modeling and simulation technique that is very close to the technique known as dissipative particle dynamics. The model is derived from molecular dynamics by means of a systematic coarse-graining procedure. Thus the rules governing our new form of dissipative particle dynamics reflect the underlying molecular dynamics; in particular all the underlying conservation laws carry over from the microscopic to the mesoscopic descriptions. Whereas previously the dissipative particles were spheres of fixed size and mass, now they are defined as cells on a Voronoi lattice with variable masses and sizes. This Voronoi lattice arises naturally from the coarse-graining procedure which may be applied iteratively and thus represents a form of renormalisation-group mapping. It enables us to select any desired local scale for the mesoscopic description of a given problem. Indeed, the method may be used to deal with situations in which several different length scales are simultaneously present. Simulations carried out with the present scheme show good agreement with theoretical predictions for the equilibrium behavior.

cond-mat.soft↗

arXiv1999

A Particulate Basis for an Immiscible Lattice-Gas Model

We show that a phenomenological hydrodynamic lattice-gas model of two-phase flow, developed by Rothman and Keller in 1988 and used extensively for numerical simulations since then, can be derived from an underlying model of particle interactions. From this result, we elucidate the nature of the hydrodynamic limit of the Rothman-Keller model.

cond-mat.soft↗

arXiv1999

Spinodal decomposition of off-critical quenches with a viscous phase using dissipative particle dynamics in two and three spatial dimensions

We investigate the domain growth and phase separation of hydrodynamically-correct binary immiscible fluids of differing viscosity as a function of minority phase concentration in both two and three spatial dimensions using dissipative particle dynamics. We also examine the behavior of equal-viscosity fluids and compare our results to similar lattice-gas simulations in two dimensions.

cond-mat.soft↗

arXiv1999

A Ternary Lattice Boltzmann Model for Amphiphilic Fluids

A lattice Boltzmann model for amphiphilic fluid dynamics is presented. It is a ternary model, in that it conserves mass separately for each chemical species present (water, oil, amphiphile), and it maintains an orientational degree of freedom for the amphiphilic species. Moreover, it models fluid interactions at the microscopic level by introducing self-consistent forces between the particles, rather than by positing a Landau free energy functional. This combination of characteristics fills an important need in the hierarchy of models currently available for amphiphilic fluid dynamics, enabling efficient computer simulation and furnishing new theoretical insight. Several computational results obtained from this model are presented and compared to existing lattice-gas model results. In particular, it is noted that lamellar structures, which are precluded by the Peierls instability in two-dimensional systems with kinetic fluctuations, are not observed in lattice-gas models, but are easily found in the corresponding lattice Boltzmann models. This points out a striking difference in the phenomenology accessible to each type of model.

cond-mat.soft↗

arXiv1999

Cluster renormalization in the Becker-Doring equations

We apply ideas from renormalization theory to models of cluster formation in nucleation and growth processes. We study a simple case of the Becker-Doring system of equations and show how a novel coarse-graining procedure applied to the cluster aggregation space affects the coagulation and fragmentation rate coefficients. A dynamical renormalization structure is found to underlie the Becker-Doring equations, nine archetypal systems are identified, and their behaviour is analysed in detail. These architypal systems divide into three distinct groups: coagulation-dominated systems, fragmentation-dominated systems and those systems where the two processes are balanced. The dynamical behaviour obtained for these is found to be in agreement with certain fine-grained solutions previously obtained by asymptotic methods. This work opens the way for the application of renormalization ideas to a wide range of non-equilibrium physicochemical processes, some of which we have previously modelled on the basis of the Becker-Doring equations.

cond-mat.stat-mech↗

arXiv1999

From Molecular Dynamics to Dissipative Particle Dynamics

A procedure is introduced for deriving a coarse-grained dissipative particle dynamics from molecular dynamics. The rules of the dissipative particle dynamics are derived from the underlying molecular interactions, and a Langevin equation is obtained that describes the forces experienced by the dissipative particles and specifies the associated canonical Gibbs distribution for the system.

cond-mat.soft↗

arXiv1999

A three-dimensional lattice gas model for amphiphilic fluid dynamics

We describe a three-dimensional hydrodynamic lattice-gas model of amphiphilic fluids. This model of the non-equilibrium properties of oil-water-surfactant systems, which is a non-trivial extension of an earlier two-dimensional realisation due to Boghosian, Coveney and Emerton [Boghosian, Coveney, and Emerton 1996, Proc. Roy. Soc. A 452, 1221-1250], can be studied effectively only when it is implemented using high-performance computing and visualisation techniques. We describe essential aspects of the model's theoretical basis and computer implementation, and report on the phenomenological properties of the model which confirm that it correctly captures binary oil-water and surfactant-water behaviour, as well as the complex phase behaviour of ternary amphiphilic fluids.

cond-mat.soft↗

arXiv1999

The Origin of the RNA World: a Kinetic Model

The aims of this paper are to propose, construct and analyse microscopic kinetic models for the emergence of long chains of RNA from monomeric beta-D-ribonucleotide precursors in prebiotic circumstances. Our theory starts out from similar but more general chemical assumptions to those of Eigen, namely that catalytic replication can lead to a large population of long chains. In particular, our models incorporate the possibility of (i) direct chain growth, (ii) template-assisted synthesis and (iii) catalysis by RNA replicase ribozymes, all with varying degrees of efficiency. However, in our models the reaction mechanisms are kept `open'; we do not assume the existence of closed hypercycles which sustain a population of long chains. Rather it is the feasibility of the initial emergence of a self-sustaining set of RNA chains from monomeric nucleotides which is our prime concern. We confront directly the central nonlinear features of the problem, which have often been overlooked in previous studies. Our detailed microscopic kinetic models lead to kinetic equations which are generalisations of the Becker-Doring system (BD) for the step-wise growth of clusters or polymer chains; they lie within a general theoretical framework which has recently been successfully applied to a wide range of complex chemical problems. In fact, the most accurate model we consider has BD aggregation terms, together with a general Smoluchowski fragmentation term to model the competing hydrolysis of RNA polymer chains. We conclude that, starting from reasonable initial conditions of monomeric nucleotide concentrations within a prebiotic soup and in an acceptable timescale, it is possible for a self-replicating subset of polyribonucleotide chains to be selected, while less efficient replicators become extinct.

adap-org↗

arXiv1998

Inverse Chapman-Enskog Derivation of the Thermohydrodynamic Lattice-BGK Model for the Ideal Gas

A thermohydrodynamic lattice-BGK model for the ideal gas was derived by Alexander et al. in 1993, and generalized by McNamara et al. in the same year. In these works, particular forms for the equilibrium distribution function and the transport coefficients were posited and shown to work, thereby establishing the sufficiency of the model. In this paper, we rederive the model from a minimal set of assumptions, and thereby show that the forms assumed for the shear and bulk viscosities are also necessary, but that the form assumed for the thermal conductivity is not. We derive the most general form allowable for the thermal conductivity, and the concomitant generalization of the equilibrium distribution. In this way, we show that it is possible to achieve variable (albeit density-dependent) Prandtl number even within a single-relaxation-time lattice-BGK model. We accomplish this by demanding analyticity of the third moments and traces of the fourth moments of the equilibrium distribution function. The method of derivation demonstrates that certain undesirable features of the model -- such as the unphysical dependence of the viscosity coefficients on temperature -- cannot be corrected within the scope of lattice-BGK models with constant relaxation time.

comp-gas↗

arXiv1998

Finite-difference methods for simulation models incorporating non-conservative forces

We discuss algorithms applicable to the numerical solution of second-order ordinary differential equations by finite-differences. We make particular reference to the solution of the dissipative particle dynamics fluid model, and present extensive results comparing one of the algorithms discussed with the standard method of solution. These results show the successful modeling of phase separation and surface tension in a binary immiscible fluid mixture.

cond-mat.soft↗

arXiv1997

Simulation of Self-Reproducing Micelles using a Lattice-Gas Automaton

We simulate self-reproducing micellar systems using a recently introduced lattice-gas automaton. This dynamical model correctly describes the equilibrium and non-equilibrium properties of mixtures of oil, water and surfactants. The simulations reported here mimic the experiments of Luisi et al. in which caprylate micelles are formed by alkaline hydrolysis of immiscible ethyl caprylate ester. As in the laboratory experiments, we find an extended induction period during which the concentration of micelles remains small; thereafter the ester is consumed very rapidly with concomitant production of micelles.

cond-mat.soft↗

arXiv1997

Shear-Induced Isotropic-to-Lamellar Transition in a Lattice-Gas Model of Ternary Amphiphilic Fluids

Although shear-induced isotropic-to-lamellar transitions in ternary systems of oil, water and surfactant have been observed experimentally and predicted theoretically by simple models for some time now, their numerical simulation has not been achieved so far. In this work we demonstrate that a recently introduced hydrodynamic lattice-gas model of amphiphilic fluids is well suited for this purpose: the two-dimensional version of this model does indeed exhibit a shear-induced isotropic-to-lamellar phase transition.

cond-mat.soft↗

arXiv1997

Protein structure prediction as a hard optimization problem: the genetic algorithm approach

Protein structure prediction can be shown to be an NP-hard problem; the number of conformations grows exponentially with the number of residues. The native conformations of proteins occupy a very small subset of these, hence an exploratory, robust search algorithm, such as a genetic algorithm (GA), is required. The dynamics of GAs tend to be complicated and problem-specific. However, their empirical success warrants their further study. In this paper, guidelines for the design of genetic algorithms for protein structure prediction are determined. To accomplish this, the performance of the simplest genetic algorithm is investigated for simple lattice-based protein structure prediction models (which is extendible to real-space), using energy minimization. The study has led us to two important conclusions for `protein-structure-prediction-genetic-algorithms'. Firstly, they require high resolution building blocks attainable by multi-point crossovers and secondly they require a local dynamics operator to `fine tune' good conformations. Furthermore, we introduce a statistical mechanical approach to analyse the genetic algorithm dynamics and suggest a convergence criterion using a quantity analogous to the free energy of population.

physics.chem-ph↗

arXiv1997

Lattice-Gas Simulations of Minority-Phase Domain Growth in Binary Immiscible and Ternary Amphiphilic Fluid

We investigate the growth kinetics of binary immiscible fluids and emulsions in two dimensions using a hydrodynamic lattice-gas model. We perform off-critical quenches in the binary fluid case and find that the domain size within the minority phase grows algebraically with time in accordance with theoretical predictions. In the late time regime we find a growth exponent n = 0.45 over a wide range of concentrations, in good agreement with other simluations. In the early time regime we find no universal growth exponent but a strong dependence on the concentration of the minority phase. In the ternary amphiphilic fluid case the kinetics of self assembly of the droplet phase are studied for the first time. At low surfactant concentrations, we find that, after an early algebraic growth, a nucleation regime dominates the late-time kinetics, which is enhanced by an increasing concentration of surfactant. With a further increase in the concentration of surfactant, we see a crossover to logarithmically slow growth, and finally saturation of the oil droplets, which we fit phenomenologically to a stretched exponential function. Finally, the transition between the droplet and the sponge phase is studied.

cond-mat.soft↗

arXiv1996

Computer simulations of domain growth and phase separation in two-dimensional binary immiscible fluids using dissipative particle dynamics

We investigate the dynamical behavior of binary fluid systems in two dimensions using dissipative particle dynamics. We find that following a symmetric quench the domain size R(t) grows with time t according to two distinct algebraic laws R(t) = t^n: at early times n = 1/2, while for later times n = 2/3. Following an asymmetric quench we observe only n = 1/2, and if momentum conservation is violated we see n = 1/3 at early times. Bubble simulations confirm the existence of a finite surface tension and the validity of Laplace's law. Our results are compared with similar simulations which have been performed previously using molecular dynamics, lattice-gas and lattice-Boltzmann automata, and Langevin dynamics. We conclude that dissipative particle dynamics is a promising method for simulating fluid properties in such systems.

comp-gas↗

arXiv1996

Lattice-gas simulations of Domain Growth, Saturation and Self-Assembly in Immiscible Fluids and Microemulsions

We investigate the dynamical behavior of both binary fluid and ternary microemulsion systems in two dimensions using a recently introduced hydrodynamic lattice-gas model of microemulsions. We find that the presence of amphiphile in our simulations reduces the usual oil-water interfacial tension in accord with experiment and consequently affects the non-equilibrium growth of oil and water domains. As the density of surfactant is increased we observe a crossover from the usual two-dimensional binary fluid scaling laws to a growth that is {\it slow}, and we find that this slow growth can be characterized by a logarithmic time scale. With sufficient surfactant in the system we observe that the domains cease to grow beyond a certain point and we find that this final characteristic domain size is inversely proportional to the interfacial surfactant concentration in the system.

comp-gas↗

arXiv1995

A Lattice-Gas Model of Microemulsions

We develop a lattice gas model for the nonequilibrium dynamics of microemulsions. Our model is based on the immiscible lattice gas of Rothman and Keller, which we reformulate using a microscopic, particulate description so as to permit generalisation to more complicated interactions, and on the prescription of Chan and Liang for introducing such interparticle interactions into lattice gas dynamics. We present the results of simulations to demonstrate that our model exhibits the correct phenomenology, and we contrast it with both equilibrium lattice models of microemulsions, and to other lattice gas models.

comp-gas↗