Diffusion-Limited Coalescence with Finite Reaction Rates in One Dimension

We study the diffusion-limited process $A+A\to A$ 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 $A\to A+A$, 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

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

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.

A Feasibility Study of Quantifying Longitudinal Brain Changes in Herpes Simplex Virus (HSV) Encephalitis Using Magnetic Resonance Imaging (MRI) and Stereology.

OBJECTIVES: To assess whether it is feasible to quantify acute change in temporal lobe volume and total oedema volumes in herpes simplex virus (HSV) encephalitis as a preliminary to a trial of corticosteroid therapy. METHODS: The study analysed serially acquired magnetic resonance images (MRI), of patients with acute HSV encephalitis who had neuroimaging repeated within four weeks of the first scan. We performed volumetric measurements of the left and right temporal lobes and of cerebral oedema visible on T2 weighted Fluid Attenuated Inversion Recovery (FLAIR) images using stereology in conjunction with point counting. RESULTS: Temporal lobe volumes increased on average by 1.6% (standard deviation (SD 11%) in five patients who had not received corticosteroid therapy and decreased in two patients who had received corticosteroids by 8.5%. FLAIR hyperintensity volumes increased by 9% in patients not receiving treatment with corticosteroids and decreased by 29% in the two patients that had received corticosteroids. CONCLUSIONS: This study has shown it is feasible to quantify acute change in temporal lobe and total oedema volumes in HSV encephalitis and suggests a potential resolution of swelling in response to corticosteroid therapy. These techniques could be used as part of a randomized control trial to investigate the efficacy of corticosteroids for treating HSV encephalitis in conjunction with assessing clinical outcomes and could be of potential value in helping to predict the clinical outcomes of patients with HSV encephalitis

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

Excitonic Funneling in Extended Dendrimers with Non-Linear and Random Potentials

The mean first passage time (MFPT) for photoexcitations diffusion in a funneling potential of artificial tree-like light-harvesting antennae (phenylacetylene dendrimers with generation-dependent segment lengths) is computed. Effects of the non-linearity of the realistic funneling potential and slow random solvent fluctuations considerably slow down the center-bound diffusion beyond a temperature-dependent optimal size. Diffusion on a disordered Cayley tree with a linear potential is investigated analytically. At low temperatures we predict a phase in which the MFPT is dominated by a few paths.Comment: 4 pages, 4 figures, To be published in Phys. Rev. Let

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