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1تقرير
المؤلفون: Boghosian, Bruce M., Love, Peter J., Coveney, Peter V., Karlin, Iliya V., Succi, Sauro, Yepez, Jeffrey
مصطلحات موضوعية: Condensed Matter - Statistical Mechanics
الوصف: We demonstrate that the requirement of galilean invariance determines the choice of H function for a wide class of entropic lattice Boltzmann models for the incompressible Navier-Stokes equations. The required H function has the form of the Burg entropy for D=2, and of a Tsallis entropy with q=1-2/D for D>2, where D is the number of spatial dimensions. We use this observation to construct a fully explicit, unconditionally stable, galilean invariant, lattice-Boltzmann model for the incompressible Navier-Stokes equations, for which attainable Reynolds number is limited only by grid resolution.
Comment: 4 pagesالوصول الحر: http://arxiv.org/abs/cond-mat/0211093Test
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2تقرير
المؤلفون: Wattis, Jonathan AD, Coveney, Peter V
الوصف: We study in detail the application of renormalisation theory to models of cluster aggregation and fragmentation of relevance to nucleation and growth processes. In particular, we investigate the Becker-Doring (BD) equations, originally formulated to describe and analyse non-equilibrium phase transitions, but more recently generalised to describe a wide range of physicochemical problems. We consider here rate coefficients which depend on the cluster size in a power-law fashion, but now perturbed by small amplitude random noise. Power-law rate coefficients arise naturally in the theory of surface-controlled nucleation and growth processes. The noisy perturbations on these rates reflect the effect of microscopic variations in such mean-field coefficients, thermal fluctuations and/or experimental uncertainties. In the present paper we generalise our earlier work that identified the nine classes into which all dynamical behaviour must fall by investigating how random perturbations of the rate coefficients influence the steady-state and kinetic behaviour of the coarse-grained, renormalised system. We are hence able to confirm the existence of a set of up to nine universality classes for such BD systems.
Comment: 30 pages, to appear in J Phys A Math Genالوصول الحر: http://arxiv.org/abs/cond-mat/0109111Test
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3تقرير
المؤلفون: Wattis, Jonathan AD, Coveney, Peter V
الوصف: We study in detail the application of renormalisation theory to models of cluster aggregation and fragmentation of relevance to nucleation and growth processes. We investigate the Becker-Dorging equations, originally formulated to describe and analyse non-equilibrium phase transitions, and more recently generalised to describe a wide range of physicochemical problems. In the present paper we analyse how the systematic coarse-graining renormalisation of the \BD system of equations affects the aggregation and fragmentation rate coefficients. We consider the case of power-law size-dependent cluster rate coefficients which we show lead to only three classes of system that require analysis: coagulation-dominated systems, fragmentation-dominated systems and those where coagulation and fragmentation are exactly balanced. We analyse the late-time asymptotics associated with each class.
Comment: 18 pages, to appear in J Phys A Math Genالوصول الحر: http://arxiv.org/abs/cond-mat/0109110Test
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4تقرير
المؤلفون: Nekovee, Maziar, Coveney, Peter V.
الوصف: We report the first results of our three-dimensional, mesoscopic, amphiphilic lattice-Boltzmann model, which has been used to simulate the dynamics of self-assembly of ordered cubic and lamellar phases in binary water-surfactant systems. Our results provide insight into the mechanism of ordering of such mesophases in terms of various molecular forces acting between water and surfactant molecules and the mechanism driving the transition from the lamellar to the cubic phase.
Comment: 2 pages, 2 figuresالوصول الحر: http://arxiv.org/abs/cond-mat/0101379Test
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5تقرير
المؤلفون: Coveney, Peter V., Wattis, Jonathan A. D.
مصطلحات موضوعية: Condensed Matter - Statistical Mechanics
الوصف: 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.
Comment: 10 pages, 1 figure, LaTeX2e, to appear in J. Phys. A, Math. Genالوصول الحر: http://arxiv.org/abs/cond-mat/9908402Test
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6تقرير
المؤلفون: Flekkoy, Eirik G., Coveney, Peter V.
الوصف: 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.
Comment: 5 pages, to appear in PRLالوصول الحر: http://arxiv.org/abs/cond-mat/9908334Test
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7تقرير
المؤلفون: Boghosian, Bruce M., Coveney, Peter V.
مصطلحات موضوعية: Nonlinear Sciences - Cellular Automata and Lattice Gases, Condensed Matter - Statistical Mechanics, Physics - Fluid Dynamics
الوصف: 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.
Comment: 12 pages, no figures, RevTeXالوصول الحر: http://arxiv.org/abs/comp-gas/9810001Test
