337 research outputs found
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
Dissipative Particle Dynamics with energy conservation
Dissipative particle dynamics (DPD) does not conserve energy and this
precludes its use in the study of thermal processes in complex fluids. We
present here a generalization of DPD that incorporates an internal energy and a
temperature variable for each particle. The dissipation induced by the
dissipative forces between particles is invested in raising the internal energy
of the particles. Thermal conduction occurs by means of (inverse) temperature
differences. The model can be viewed as a simplified solver of the fluctuating
hydrodynamic equations and opens up the possibility of studying thermal
processes in complex fluids with a mesoscopic simulation technique.Comment: 5 page
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
Two-dimensional hydrodynamic lattice-gas simulations of binary immiscible and ternary amphiphilic fluid flow through porous media
The behaviour of two dimensional binary and ternary amphiphilic fluids under
flow conditions is investigated using a hydrodynamic lattice gas model. After
the validation of the model in simple cases (Poiseuille flow, Darcy's law for
single component fluids), attention is focussed on the properties of binary
immiscible fluids in porous media. An extension of Darcy's law which explicitly
admits a viscous coupling between the fluids is verified, and evidence of
capillary effects are described. The influence of a third component, namely
surfactant, is studied in the same context. Invasion simulations have also been
performed. The effect of the applied force on the invasion process is reported.
As the forcing level increases, the invasion process becomes faster and the
residual oil saturation decreases. The introduction of surfactant in the
invading phase during imbibition produces new phenomena, including
emulsification and micellisation. At very low fluid forcing levels, this leads
to the production of a low-resistance gel, which then slows down the progress
of the invading fluid. At long times (beyond the water percolation threshold),
the concentration of remaining oil within the porous medium is lowered by the
action of surfactant, thus enhancing oil recovery. On the other hand, the
introduction of surfactant in the invading phase during drainage simulations
slows down the invasion process -- the invading fluid takes a more tortuous
path to invade the porous medium -- and reduces the oil recovery (the residual
oil saturation increases).Comment: 48 pages, 26 figures. Phys. Rev. E (in press
Symmetry-breaking in chiral polymerisation
We propose a model for chiral polymerisation and investigate its symmetric
and asymmetric solutions. The model has a source species which decays into
left- and right-handed types of monomer, each of which can polymerise to form
homochiral chains; these chains are susceptible to `poisoning' by the opposite
handed monomer. Homochiral polymers are assumed to influence the proportion of
each type of monomer formed from the precursor. We show that for certain
parameter values a positive feedback mechanism makes the symmetric steady-state
solution unstable. The kinetics of polymer formation are then analysed in the
case where the system starts from zero concentrations of monomer and chains. We
show that following a long induction time, extremely large concentrations of
polymers are formed for a short time, during this time an asymmetry introduced
into the system by a random external perturbation may be massively amplified.
The system then approaches one of the steady-state solutions described above.Comment: 26pages, 6 Figure
Prediction of the functional properties of ceramic materials from composition using artificial neural networks
We describe the development of artificial neural networks (ANN) for the
prediction of the properties of ceramic materials. The ceramics studied here
include polycrystalline, inorganic, non-metallic materials and are investigated
on the basis of their dielectric and ionic properties. Dielectric materials are
of interest in telecommunication applications where they are used in tuning and
filtering equipment. Ionic and mixed conductors are the subjects of a concerted
effort in the search for new materials that can be incorporated into efficient,
clean electrochemical devices of interest in energy production and greenhouse
gas reduction applications. Multi-layer perceptron ANNs are trained using the
back-propagation algorithm and utilise data obtained from the literature to
learn composition-property relationships between the inputs and outputs of the
system. The trained networks use compositional information to predict the
relative permittivity and oxygen diffusion properties of ceramic materials. The
results show that ANNs are able to produce accurate predictions of the
properties of these ceramic materials which can be used to develop materials
suitable for use in telecommunication and energy production applications
Using lambda networks to enhance performance of interactive large simulations
The ability to use a visualisation tool to steer large simulations provides innovative and novel usage scenarios, e.g. the ability to use new algorithms for the computation of free energy profiles along a nanopore [1]. However, we find that the performance of interactive simulations is sensitive to the quality of service of the network with variable latency and packet loss in particular having a detrimental effect The use of dedicated networks (provisioned in this case as a circuit-switched point-to-point optical lightpath or lambda) can lead to significant (50% or more) performance enhancement, When funning on say 128 or 256 processors of a high-end supercomputer this saving has a significant value. We perform experiments to understand the impact of network characteristics on the performance of a large parallel classical molecular dynamics simulation when coupled interactively to a remote visualisation tool. This paper discusses the experiments performed and presents the results from the systematic studies. © 2006 IEEE.Published versio
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.Comment: 18 pages, 7 figure
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