996 research outputs found
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
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
Single and multiple random walks on random lattices: Excitation trapping and annihilation simulations
Random walk simulations of exciton trapping and annihilation on binary and ternary lattices are presented. Single walker visitation efficiencies for ordered and random binary lattices are compared. Interacting multiple random walkers on binary and ternary random lattices are presented in terms of trapping and annihilation efficiencies that are related to experimental observables. A master equation approach, based on Monte Carlo cluster distributions, results in a nonclassical power relationship between the exciton annihilation rate and the exciton density.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45145/1/10955_2005_Article_BF01012307.pd
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
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
Disorder and Funneling Effects on Exciton Migration in Tree-Like Dendrimers
The center-bound excitonic diffusion on dendrimers subjected to several types
of non-homogeneous funneling potentials, is considered. We first study the
mean-first passage time (MFPT) for diffusion in a linear potential with
different types of correlated and uncorrelated random perturbations. Increasing
the funneling force, there is a transition from a phase in which the MFPT grows
exponentially with the number of generations , to one in which it does so
linearly. Overall the disorder slows down the diffusion, but the effect is much
more pronounced in the exponential compared to the linear phase. When the
disorder gives rise to uncorrelated random forces there is, in addition, a
transition as the temperature is lowered. This is a transition from a
high- regime in which all paths contribute to the MFPT to a low- regime
in which only a few of them do. We further explore the funneling within a
realistic non-linear potential for extended dendrimers in which the dependence
of the lowest excitonic energy level on the segment length was derived using
the Time-Dependent Hatree-Fock approximation. Under this potential the MFPT
grows initially linearly with but crosses-over, beyond a molecular-specific
and -dependent optimal size, to an exponential increase. Finally we consider
geometrical disorder in the form of a small concentration of long connections
as in the {\it small world} model. Beyond a critical concentration of
connections the MFPT decreases significantly and it changes to a power-law or
to a logarithmic scaling with , depending on the strength of the funneling
force.Comment: 13 pages, 9 figure
Reaction Front in an A+B -> C Reaction-Subdiffusion Process
We study the reaction front for the process A+B -> C in which the reagents
move subdiffusively. Our theoretical description is based on a fractional
reaction-subdiffusion equation in which both the motion and the reaction terms
are affected by the subdiffusive character of the process. We design numerical
simulations to check our theoretical results, describing the simulations in
some detail because the rules necessarily differ in important respects from
those used in diffusive processes. Comparisons between theory and simulations
are on the whole favorable, with the most difficult quantities to capture being
those that involve very small numbers of particles. In particular, we analyze
the total number of product particles, the width of the depletion zone, the
production profile of product and its width, as well as the reactant
concentrations at the center of the reaction zone, all as a function of time.
We also analyze the shape of the product profile as a function of time, in
particular its unusual behavior at the center of the reaction zone
Organizational Culture and Physician Satisfaction with Dimensions of Group Practice
To assess the extent to which the organizational culture of physician group practices is associated with individual physician satisfaction with the managerial and organizational capabilities of the groups. Study Design and Methods . Physician surveys from 1997 to 1998 assessing the culture of their medical groups and their satisfaction with six aspects of group practice. Organizational culture was conceptualized using the Competing Values framework, yielding four distinct cultural types. Physician-level data were aggregated to the group level to attain measures of organizational culture. Using hierarchical linear modeling, individual physician satisfaction with six dimensions of group practice was predicted using physician-level variables and group-level variables. Separate models for each of the four cultural types were estimated for each of the six satisfaction measures, yielding a total of 24 models. Sample Studied . Fifty-two medical groups affiliated with 12 integrated health systems from across the U.S., involving 1,593 physician respondents (38.3 percent response rate). Larger medical groups and multispecialty groups were over-represented compared with the U.S. as a whole. Principal Findings . Our models explain up to 31 percent of the variance in individual physician satisfaction with group practice, with individual organizational culture scales explaining up to 5 percent of the variance. Group-level predictors: group (i.e., participatory) culture was positively associated with satisfaction with staff and human resources, technological sophistication, and price competition. Hierarchical (i.e., bureaucratic) culture was negatively associated with satisfaction with managerial decision making, practice level competitiveness, price competition, and financial capabilities. Rational (i.e., task-oriented) culture was negatively associated with satisfaction with staff and human resources, and price competition. Developmental (i.e., risk-taking) culture was not significantly associated with any of the satisfaction measures. In some of the models, being a single-specialty group (compared with a primary care group) and a group having a higher percent of male physicians were positively associated with satisfaction with financial capabilities. Physician-level predictors: individual physicians' ratings of organizational culture were significantly related to many of the satisfaction measures. In general, older physicians were more satisfied than younger physicians with many of the satisfaction measures. Male physicians were less satisfied with data capabilities. Primary care physicians (versus specialists) were less satisfied with price competition. Conclusion . Some dimensions of physician organizational culture are significantly associated with various aspects of individual physician satisfaction with group practice.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72696/1/j.1475-6773.2006.00648.x.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/72696/2/HESR+648+Appendix+A.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/72696/3/HESR+648+Appendix+C.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/72696/4/HESR+648+Appendix+B.pd
Geometry-controlled kinetics
It has long been appreciated that transport properties can control reaction
kinetics. This effect can be characterized by the time it takes a diffusing
molecule to reach a target -- the first-passage time (FPT). Although essential
to quantify the kinetics of reactions on all time scales, determining the FPT
distribution was deemed so far intractable. Here, we calculate analytically
this FPT distribution and show that transport processes as various as regular
diffusion, anomalous diffusion, diffusion in disordered media and in fractals
fall into the same universality classes. Beyond this theoretical aspect, this
result changes the views on standard reaction kinetics. More precisely, we
argue that geometry can become a key parameter so far ignored in this context,
and introduce the concept of "geometry-controlled kinetics". These findings
could help understand the crucial role of spatial organization of genes in
transcription kinetics, and more generally the impact of geometry on
diffusion-limited reactions.Comment: Submitted versio
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