1,150 research outputs found
Finite-Size Scaling Studies of Reaction-Diffusion Systems Part III: Numerical Methods
The scaling exponent and scaling function for the 1D single species
coagulation model are shown to be universal, i.e. they are
not influenced by the value of the coagulation rate. They are independent of
the initial conditions as well. Two different numerical methods are used to
compute the scaling properties: Monte Carlo simulations and extrapolations of
exact finite lattice data. These methods are tested in a case where analytical
results are available. It is shown that Monte Carlo simulations can be used to
compute even the correction terms. To obtain reliable results from finite-size
extrapolations exact numerical data for lattices up to ten sites are
sufficient.Comment: 19 pages, LaTeX, 5 figures uuencoded, BONN HE-94-0
Diffusion-Limited Coalescence with Finite Reaction Rates in One Dimension
We study the diffusion-limited process in one dimension, with
finite reaction rates. We develop an approximation scheme based on the method
of Inter-Particle Distribution Functions (IPDF), which was formerly used for
the exact solution of the same process with infinite reaction rate. The
approximation becomes exact in the very early time regime (or the
reaction-controlled limit) and in the long time (diffusion-controlled)
asymptotic limit. For the intermediate time regime, we obtain a simple
interpolative behavior between these two limits. We also study the coalescence
process (with finite reaction rates) with the back reaction , and in
the presence of particle input. In each of these cases the system reaches a
non-trivial steady state with a finite concentration of particles. Theoretical
predictions for the concentration time dependence and for the IPDF are compared
to computer simulations. P. A. C. S. Numbers: 82.20.Mj 02.50.+s 05.40.+j
05.70.LnComment: 13 pages (and 4 figures), plain TeX, SISSA-94-0
Stochastic Ballistic Annihilation and Coalescence
We study a class of stochastic ballistic annihilation and coalescence models
with a binary velocity distribution in one dimension. We obtain an exact
solution for the density which reveals a universal phase diagram for the
asymptotic density decay. By universal we mean that all models in the class are
described by a single phase diagram spanned by two reduced parameters. The
phase diagram reveals four regimes, two of which contain the previously studied
cases of ballistic annihilation. The two new phases are a direct consequence of
the stochasticity. The solution is obtained through a matrix product approach
and builds on properties of a q-deformed harmonic oscillator algebra.Comment: 4 pages RevTeX, 3 figures; revised version with some corrections,
additional discussion and in RevTeX forma
Non-beneficial pediatric research : individual and social interests
Biomedical research involving human subjects is an arena of conflicts of interests. One of the most important conflicts is between interests of participants and interests of future patients. Legal regulations and ethical guidelines are instruments designed to help find a fair balance between risks and burdens taken by research subjects and development of knowledge and new treatment. There is an universally accepted ethical principle, which states that it is not ethically allowed to sacrifice individual interests for the sake of society and science. This is the principle of precedence of individual. But there is a problem with how to interpret the principle of precedence of individual in the context of research without prospect of future benefit involving children. There are proposals trying to reconcile non-beneficial research involving children with the concept of the best interests. We assert that this reconciliation is flawed and propose an interpretation of the principle of precedence of individual as follows: not all, but only the most important interests of participants, must be guaranteed; this principle should be interpreted as the secure participant standard. In consequence, the issue of permissible risk ceiling becomes ethically crucial in research with incompetent subjects
Soluble two-species diffusion-limited Models in arbitrary dimensions
A class of two-species ({\it three-states}) bimolecular diffusion-limited
models of classical particles with hard-core reacting and diffusing in a
hypercubic lattice of arbitrary dimension is investigated. The manifolds on
which the equations of motion of the correlation functions close, are
determined explicitly. This property allows to solve for the density and the
two-point (two-time) correlation functions in arbitrary dimension for both, a
translation invariant class and another one where translation invariance is
broken. Systems with correlated as well as uncorrelated, yet random initial
states can also be treated exactly by this approach. We discuss the asymptotic
behavior of density and correlation functions in the various cases. The
dynamics studied is very rich.Comment: 28 pages, 0 figure. To appear in Physical Review E (February 2001
Crossover from Rate-Equation to Diffusion-Controlled Kinetics in Two-Particle Coagulation
We develop an analytical diffusion-equation-type approximation scheme for the
one-dimensional coagulation reaction A+A->A with partial reaction probability
on particle encounters which are otherwise hard-core. The new approximation
describes the crossover from the mean-field rate-equation behavior at short
times to the universal, fluctuation-dominated behavior at large times. The
approximation becomes quantitatively accurate when the system is initially
close to the continuum behavior, i.e., for small initial density and fast
reaction. For large initial density and slow reaction, lattice effects are
nonnegligible for an extended initial time interval. In such cases our
approximation provides the correct description of the initial mean-field as
well as the asymptotic large-time, fluctuation-dominated behavior. However, the
intermediate-time crossover between the two regimes is described only
semiquantitatively.Comment: 21 pages, plain Te
Coupled Maps on Trees
We study coupled maps on a Cayley tree, with local (nearest-neighbor)
interactions, and with a variety of boundary conditions. The homogeneous state
(where every lattice site has the same value) and the node-synchronized state
(where sites of a given generation have the same value) are both shown to occur
for particular values of the parameters and coupling constants. We study the
stability of these states and their domains of attraction. As the number of
sites that become synchronized is much higher compared to that on a regular
lattice, control is easier to effect. A general procedure is given to deduce
the eigenvalue spectrum for these states. Perturbations of the synchronized
state lead to different spatio-temporal structures. We find that a mean-field
like treatment is valid on this (effectively infinite dimensional) lattice.Comment: latex file (25 pages), 4 figures included. To be published in Phys.
Rev.
Goal-oriented cognitive rehabilitation in early-stage dementia: study protocol for a multi-centre single-blind randomised controlled trial (GREAT).
yesBackground: Preliminary evidence suggests that goal-oriented cognitive rehabilitation (CR) may be a clinically
effective intervention for people with early-stage Alzheimer's disease, vascular or mixed dementia and their carers.
This study aims to establish whether CR is a clinically effective and cost-effective intervention for people with
early-stage dementia and their carers.
Methods/design: In this multi-centre, single-blind randomised controlled trial, 480 people with early-stage
dementia, each with a carer, will be randomised to receive either treatment as usual or cognitive rehabilitation
(10 therapy sessions over 3 months, followed by 4 maintenance sessions over 6 months). We will compare the
effectiveness of cognitive rehabilitation with that of treatment as usual with regard to improving self-reported and
carer-rated goal performance in areas identified as causing concern by people with early-stage dementia;
improving quality of life, self-efficacy, mood and cognition of people with early-stage dementia; and reducing stress
levels and ameliorating quality of life for carers of participants with early-stage dementia. The incremental
cost-effectiveness of goal-oriented cognitive rehabilitation compared to treatment as usual will also be examined.
Discussion: If the study confirms the benefits and cost-effectiveness of cognitive rehabilitation, it will be important
to examine how the goal-oriented cognitive rehabilitation approach can most effectively be integrated into routine
health-care provision. Our aim is to provide training and develop materials to support the implementation of this
approach following trial completion.
Trial registration: Current Controlled Trials ISRCTN2102748
Multiparticle Reactions with Spatial Anisotropy
We study the effect of anisotropic diffusion on the one-dimensional
annihilation reaction kA->inert with partial reaction probabilities when
hard-core particles meet in groups of k nearest neighbors. Based on scaling
arguments, mean field approaches and random walk considerations we argue that
the spatial anisotropy introduces no appreciable changes as compared to the
isotropic case. Our conjectures are supported by numerical simulations for slow
reaction rates, for k=2 and 4.Comment: nine pages, plain Te
Exact Solutions of Anisotropic Diffusion-Limited Reactions with Coagulation and Annihilation
We report exact results for one-dimensional reaction-diffusion models A+A ->
inert, A+A -> A, and A+B -> inert, where in the latter case like particles
coagulate on encounters and move as clusters. Our study emphasized anisotropy
of hopping rates; no changes in universal properties were found, due to
anisotropy, in all three reactions. The method of solution employed mapping
onto a model of coagulating positive integer charges. The dynamical rules were
synchronous, cellular-automaton type. All the asymptotic large-time results for
particle densities were consistent, in the framework of universality, with
other model results with different dynamical rules, when available in the
literature.Comment: 28 pages in plain TeX + 2 PostScript figure
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