Renormalisation-theoretic analysis of non-equilibrium phase transitions II: The effect of perturbations on rate coefficients in the Becker-Doring equations

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 Ge

Managing sleep and wakefulness in a 24 hour world

This article contributes to literature on the sociology of sleep by exploring the sleeping practices and subjective sleep experiences of two social groups: shift workers and students. It draws on data, collected in the UK from 25 semi-structured interviews, to discuss the complex ways in which working patterns and social activities impact upon experiences and expectations of sleep in our wired awake world. The data show that, typically, sleep is valued and considered to be important for health, general wellbeing, appearance and physical and cognitive functioning. However, sleep time is often cut back on in favour of work demands and social activities. While shift workers described their efforts to fit in an adequate amount of sleep per 24-hour period, for students, the adoption of a flexible sleep routine was thought to be favourable for maintaining a work–social life balance. Collectively, respondents reported using a wide range of strategies, techniques, technologies and practices to encourage, overcome or delay sleep(iness) and boost, promote or enhance wakefulness/alertness at socially desirable times. The analysis demonstrates how social context impacts not only on how we come to think about sleep and understand it, but also how we manage or self-regulate our sleeping patterns

Renormalisation-theoretic analysis of non-equilibrium phase transitions I: The Becker-Doring equations with power law rate coefficients

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 Ge

Continuum-particle hybrid coupling for mass, momentum and energy transfers in unsteady fluid flow

The aim of hybrid methods in simulations is to communicate regions with disparate time and length scales. Here, a fluid described at the atomistic level within an inner region P is coupled to an outer region C described by continuum fluid dynamics. The matching of both descriptions of matter is made across an overlapping region and, in general, consists of a two-way coupling scheme (C->P and P->C) which conveys mass, momentum and energy fluxes. The contribution of the hybrid scheme hereby presented is two-fold: first it treats unsteady flows and, more importantly, it handles energy exchange between both C and P regions. The implementation of the C->P coupling is tested here using steady and unsteady flows with different rates of mass, momentum and energy exchange. In particular, relaxing flows described by linear hydrodynamics (transversal and longitudinal waves) are most enlightening as they comprise the whole set of hydrodynamic modes. Applying the hybrid coupling scheme after the onset of an initial perturbation, the cell-averaged Fourier components of the flow variables in the P region (velocity, density, internal energy, temperature and pressure) evolve in excellent agreement with the hydrodynamic trends. It is also shown that the scheme preserves the correct rate of entropy production. We discuss some general requirements on the coarse-grained length and time scales arising from both the characteristic microscopic and hydrodynamic scales.Comment: LaTex, 12 pages, 9 figure

Three dimensional hysdrodynamic lattice-gas simulations of binary immiscible and ternary amphiphilic flow through porous media

We report the results of a study of multiphase flow in porous media. A Darcy's law for steady multiphase flow was investigated for both binary and ternary amphiphilic flow. Linear flux-forcing relationships satisfying Onsager reciprocity were shown to be a good approximation of the simulation data. The dependence of the relative permeability coefficients on water saturation was investigated and showed good qualitative agreement with experimental data. Non-steady state invasion flows were investigated, with particular interest in the asymptotic residual oil saturation. The addition of surfactant to the invasive fluid was shown to significantly reduce the residual oil saturation.Comment: To appear in Phys. Rev.

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.Comment: 34 pages (11 figures); accepted for publication in Phys. Rev.

Fluctuating lattice Boltzmann

The lattice Boltzmann algorithm efficiently simulates the Navier Stokes equation of isothermal fluid flow, but ignores thermal fluctuations of the fluid, important in mesoscopic flows. We show how to adapt the algorithm to include noise, satisfying a fluctuation-dissipation theorem (FDT) directly at lattice level: this gives correct fluctuations for mass and momentum densities, and for stresses, at all wavevectors $k$. Unlike previous work, which recovers FDT only as $k\to 0$, our algorithm offers full statistical mechanical consistency in mesoscale simulations of, e.g., fluctuating colloidal hydrodynamics.Comment: 7 pages, 3 figures, to appear in Europhysics Letter

Fluctuating hydrodynamic modelling of fluids at the nanoscale

A good representation of mesoscopic fluids is required to combine with molecular simulations at larger length and time scales (De Fabritiis {\it et. al}, Phys. Rev. Lett. 97, 134501 (2006)). However, accurate computational models of the hydrodynamics of nanoscale molecular assemblies are lacking, at least in part because of the stochastic character of the underlying fluctuating hydrodynamic equations. Here we derive a finite volume discretization of the compressible isothermal fluctuating hydrodynamic equations over a regular grid in the Eulerian reference system. We apply it to fluids such as argon at arbitrary densities and water under ambient conditions. To that end, molecular dynamics simulations are used to derive the required fluid properties. The equilibrium state of the model is shown to be thermodynamically consistent and correctly reproduces linear hydrodynamics including relaxation of sound and shear modes. We also consider non-equilibrium states involving diffusion and convection in cavities with no-slip boundary conditions