65 research outputs found
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
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
Long-Time Behaviour and Self-Similarity in a Coagulation Equation with Input of Monomers
For a coagulation equation with Becker-Doring type interactions and
time-independent monomer input we study the detailed long-time behaviour of
nonnegative solutions and prove the convergence to a self-similar function.Comment: 30 pages, 5 Figures, now published in Markov Processes and Related
Fields 12, 367-398, (2006
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
Dissociation in a polymerization model of homochirality
A fully self-contained model of homochirality is presented that contains the
effects of both polymerization and dissociation. The dissociation fragments are
assumed to replenish the substrate from which new monomers can grow and undergo
new polymerization. The mean length of isotactic polymers is found to grow
slowly with the normalized total number of corresponding building blocks.
Alternatively, if one assumes that the dissociation fragments themselves can
polymerize further, then this corresponds to a strong source of short polymers,
and an unrealistically short average length of only 3. By contrast, without
dissociation, isotactic polymers becomes infinitely long.Comment: 16 pages, 6 figures, submitted to Orig. Life Evol. Biosp
Coagulation and fragmentation processes with evolving size and shape profiles : a semigroup approach
We investigate a class of bivariate coagulation-fragmentation equations. These equations describe the evolution of a system of particles that are characterised not only by a discrete size variable but also by a shape variable which can be either discrete or continuous. Existence and uniqueness of strong solutions to the associated abstract Cauchy problems are established by using the theory of substochastic semigroups of operators
Homochiral growth through enantiomeric cross-inhibition
The stability and conservation properties of a recently proposed
polymerization model are studied. The achiral (racemic) solution is linearly
unstable once the relevant control parameter (here the fidelity of the
catalyst) exceeds a critical value. The growth rate is calculated for different
fidelity parameters and cross-inhibition rates. A chirality parameter is
defined and shown to be conserved by the nonlinear terms of the model. Finally,
a truncated version of the model is used to derive a set of two ordinary
differential equations and it is argued that these equations are more realistic
than those used in earlier models of that form.Comment: 20 pages, 6 figures, Orig. Life Evol. Biosph. (accepted
Caring About the Shape of Mental Health Nursing: A survey investigating practitionerâs perceptions towards potential changes to undergraduate education
While there is a growing disquiet about the future of mental health nursing, there is little in the way of an organised, unified response from mental health nurses. The Health and Social Care Information Centre report a fall in the number of mental health nurses of more than 10% over the past five years. A survey was launched to explore stakeholders perspectives on the future of mental health nursing. The interest in and the analysis of this survey indicates that we are at the start of a key discussion rather than at the end point of consensus. It is vital that mental health nurses have opportunities to consider and test their opinions on these issues and the confidence to speak up and be hear
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