530 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
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
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
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
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
Weighted decomposition in high-performance lattice-Boltzmann simulations: Are some lattice sites more equal than others?
Obtaining a good load balance is a significant challenge in scaling up lattice-Boltzmann simulations of realistic sparse problems to the exascale. Here we analyze the effect of weighted decomposition on the performance of the HemeLB lattice-Boltzmann simulation environment, when applied to sparse domains. Prior to domain decomposition, we assign wall and in/outlet sites with increased weights which reflect their increased computational cost. We combine our weighted decomposition with a second optimization, which is to sort the lattice sites according to a space filling curve. We tested these strategies on a sparse bifurcation and very sparse aneurysm geometry, and find that using weights reduces calculation load imbalance by up to 85 %, although the overall communication overhead is higher than some of our runs.This work has received funding from the CRESTA and MAPPER projects within the EC-FP7 (ICT-2011.9.13) under Grant Agreements nos. 287703 and 261507, and from EPSRC Grants EP/I017909/1 (www.2020science.net) and EP/I034602/1
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
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.
A comparison of the Bravyi-Kitaev and Jordan-Wigner transformations for the quantum simulation of quantum chemistry
The ability to perform classically intractable electronic structure
calculations is often cited as one of the principal applications of quantum
computing. A great deal of theoretical algorithmic development has been
performed in support of this goal. Most techniques require a scheme for mapping
electronic states and operations to states of and operations upon qubits. The
two most commonly used techniques for this are the Jordan-Wigner transformation
and the Bravyi-Kitaev transformation. However, comparisons of these schemes
have previously been limited to individual small molecules. In this paper we
discuss resource implications for the use of the Bravyi-Kitaev mapping scheme,
specifically with regard to the number of quantum gates required for
simulation. We consider both small systems which may be simulatable on
near-future quantum devices, and systems sufficiently large for classical
simulation to be intractable. We use 86 molecular systems to demonstrate that
the use of the Bravyi-Kitaev transformation is typically at least approximately
as efficient as the canonical Jordan-Wigner transformation, and results in
substantially reduced gate count estimates when performing limited circuit
optimisations.Comment: 46 pages, 11 figure
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