1,295 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
Concentration for One and Two Species One-Dimensional Reaction-Diffusion Systems
We look for similarity transformations which yield mappings between different
one-dimensional reaction-diffusion processes. In this way results obtained for
special systems can be generalized to equivalent reaction-diffusion models. The
coagulation (A + A -> A) or the annihilation (A + A -> 0) models can be mapped
onto systems in which both processes are allowed. With the help of the
coagulation-decoagulation model results for some death-decoagulation and
annihilation-creation systems are given. We also find a reaction-diffusion
system which is equivalent to the two species annihilation model (A + B ->0).
Besides we present numerical results of Monte Carlo simulations. An accurate
description of the effects of the reaction rates on the concentration in
one-species diffusion-annihilation model is made. The asymptotic behavior of
the concentration in the two species annihilation system (A + B -> 0) with
symmetric initial conditions is studied.Comment: 20 pages latex, uuencoded figures at the en
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
Circadian Timing of Food Intake Contributes to Weight Gain
Studies of body weight regulation have focused almost entirely on caloric intake and energy expenditure. However, a number of recent studies in animals linking energy regulation and the circadian clock at the molecular, physiological, and behavioral levels raise the possibility that the timing of food intake itself may play a significant role in weight gain. The present study focused on the role of the circadian phase of food consumption in weight gain. We provide evidence that nocturnal mice fed a high‐fat diet only during the 12‐h light phase gain significantly more weight than mice fed only during the 12‐h dark phase. A better understanding of the role of the circadian system for weight gain could have important implications for developing new therapeutic strategies for combating the obesity epidemic facing the human population today
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
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
Correlation Functions for Diffusion-Limited Annihilation, A + A -> 0
The full hierarchy of multiple-point correlation functions for
diffusion-limited annihilation, A + A -> 0, is obtained analytically and
explicitly, following the method of intervals. In the long time asymptotic
limit, the correlation functions of annihilation are identical to those of
coalescence, A + A -> A, despite differences between the two models in other
statistical measures, such as the interparticle distribution function
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
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.
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