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

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

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 $g$, 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 $T$ is lowered. This is a transition from a high-$T$ regime in which all paths contribute to the MFPT to a low-$T$ 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 $g$ but crosses-over, beyond a molecular-specific and $T$-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 $g$, 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

Percolation and cluster distribution. II. layers, variable-range interactions, and exciton cluster model

Monte Carlo simulations for the site percolation problem are presented for lattices up to 64 x 10 6 sites. We investigate for the square lattice the variable-range percolation problem, where distinct trends with bond-length are found for the critical concentrations and for the critical exponents β and γ . We also investigate the layer problem for stacks of square lattices added to approach a simple cubic lattice, yielding critical concentrations as a functional of layer number as well as the correlation length exponent ν . We also show that the exciton migration probability for a common type of ternary lattice system can be described by a cluster model and actually provides a cluster generating function.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45139/1/10955_2005_Article_BF01011724.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

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