1
|
Chakraborti S, Chakraborty T, Das A, Dandekar R, Pradhan P. Transport and fluctuations in mass aggregation processes: Mobility-driven clustering. Phys Rev E 2021; 103:042133. [PMID: 34005942 DOI: 10.1103/physreve.103.042133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2020] [Accepted: 03/31/2021] [Indexed: 11/07/2022]
Abstract
We calculate the bulk-diffusion coefficient and the conductivity in nonequilibrium conserved-mass aggregation processes on a ring. These processes involve chipping and fragmentation of masses, which diffuse on a lattice and aggregate with their neighboring masses on contact, and, under certain conditions, they exhibit a condensation transition. We find that, even in the absence of microscopic time reversibility, the systems satisfy an Einstein relation, which connects the ratio of the conductivity and the bulk-diffusion coefficient to mass fluctuation. Interestingly, when aggregation dominates over chipping, the conductivity or, equivalently, the mobility of masses, is greatly enhanced. The enhancement in the conductivity, in accordance with the Einstein relation, results in large mass fluctuations and can induce a mobility-driven clustering in the systems. Indeed, in a certain parameter regime, we show that the conductivity, along with the mass fluctuation, diverges beyond a critical density, thus characterizing the previously observed nonequilibrium condensation transition [Phys. Rev. Lett. 81, 3691 (1998)10.1103/PhysRevLett.81.3691] in terms of an instability in the conductivity. Notably, the bulk-diffusion coefficient remains finite in all cases. We find our analytic results in quite good agreement with simulations.
Collapse
Affiliation(s)
- Subhadip Chakraborti
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India.,International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
| | - Tanmoy Chakraborty
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Arghya Das
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
| | - Rahul Dandekar
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India.,Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Punyabrata Pradhan
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| |
Collapse
|
2
|
Dandekar R, Chakraborti S, Rajesh R. Hard core run and tumble particles on a one-dimensional lattice. Phys Rev E 2021; 102:062111. [PMID: 33466079 DOI: 10.1103/physreve.102.062111] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2020] [Accepted: 11/16/2020] [Indexed: 11/07/2022]
Abstract
We study the large scale behavior of a collection of hard core run and tumble particles on a one-dimensional lattice with periodic boundary conditions. Each particle has persistent motion in one direction decided by an associated spin variable until the direction of spin is reversed. We map the run and tumble model to a mass transfer model with fluctuating directed bonds. We calculate the steady-state single-site mass distribution in the mass model within a mean field approximation for larger spin-flip rates and by analyzing an appropriate coalescence-fragmentation model for small spin-flip rates. We also calculate the hydrodynamic coefficients of diffusivity and conductivity for both large and small spin-flip rates and show that the Einstein relation is violated in both regimes. We also show how the nongradient nature of the process can be taken into account in a systematic manner to calculate the hydrodynamic coefficients.
Collapse
Affiliation(s)
- Rahul Dandekar
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai-600113, India.,Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai-400094, India
| | | | - R Rajesh
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai-600113, India.,Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai-400094, India
| |
Collapse
|
3
|
Kawagoe K, Huber G, Pradas M, Wilkinson M, Pumir A, Ben-Naim E. Aggregation-fragmentation-diffusion model for trail dynamics. Phys Rev E 2017; 96:012142. [PMID: 29347086 DOI: 10.1103/physreve.96.012142] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2017] [Indexed: 06/07/2023]
Abstract
We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine to form a larger one, and also one trail may split into two. In addition, trails move diffusively. The model is defined by two parameters which quantify the fragmentation rate and the fragment size. In the long-time limit, the system reaches a steady state, and our focus is the limiting distribution of trail weights. We find that the density of trail weight has power-law tail P(w)∼w^{-γ} for small weight w. We obtain the exponent γ analytically and find that it varies continuously with the two model parameters. The exponent γ can be positive or negative, so that in one range of parameters small-weight trails are abundant and in the complementary range they are rare.
Collapse
Affiliation(s)
- Kyle Kawagoe
- Kavli Institute for Theoretical Physics, University of California Santa Barbara, California 93106, USA
- Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Greg Huber
- Kavli Institute for Theoretical Physics, University of California Santa Barbara, California 93106, USA
| | - Marc Pradas
- Kavli Institute for Theoretical Physics, University of California Santa Barbara, California 93106, USA
- School of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, England
| | - Michael Wilkinson
- Kavli Institute for Theoretical Physics, University of California Santa Barbara, California 93106, USA
- School of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, England
| | - Alain Pumir
- Kavli Institute for Theoretical Physics, University of California Santa Barbara, California 93106, USA
- Laboratoire de Physique, Ecole Normale Supérieure de Lyon, CNRS, Université de Lyon, F-69007 Lyon, France
| | - Eli Ben-Naim
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
4
|
Romero AH, Lacasta AM, Sancho JM, Lindenberg K. Numerical study of A+A→0 and A+B→0 reactions with inertia. J Chem Phys 2007; 127:174506. [DOI: 10.1063/1.2779327] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
5
|
Menyhárd N, Odor G. One-dimensional spin-anisotropic kinetic Ising model subject to quenched disorder. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:021103. [PMID: 17930002 DOI: 10.1103/physreve.76.021103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2006] [Revised: 06/04/2007] [Indexed: 05/25/2023]
Abstract
Large-scale Monte Carlo simulations are used to explore the effect of quenched disorder on one-dimensional, nonequilibrium kinetic Ising models with locally broken spin symmetry, at zero temperature (the symmetry is broken through spin-flip rates that differ for "+" and "-" spins). The model is found to exhibit a continuous phase transition to an absorbing state. The associated critical behavior is studied at zero branching rate of kinks, through analysis spreading of + and - spins, and of the kink density. Impurities exert a strong effect on the critical behavior only for a particular choice of parameters, corresponding to the strongly spin-anisotropic kinetic Ising model introduced by Majumdar [Phys Rev. Lett 86, 2301 (2001)]. Typically, disorder effects become evident for impurity strengths such that diffusion is nearly blocked. In this regime, the critical behavior is similar to that arising, for example, in the one-dimensional diluted contact process, with Griffiths-like behavior for the kink density. We find variable cluster exponents, which obey a hyperscaling relation, and are similar to those reported by Cafiero [Phys Rev. E 57, 5060 (1998)]. We also show that the isotropic two-component AB --> [symbol: see text] model is insensitive to reaction disorder, and that only logarithmic corrections arise, induced by strong disorder in the diffusion rate.
Collapse
Affiliation(s)
- Nóra Menyhárd
- Research Institute for Solid State Physics and Optics, H-1525 Budapest, P.O. Box 49, Hungary
| | | |
Collapse
|
6
|
Lawniczak AT. From reactive lattice gas automaton rules to its partial differential equations. ACTA ACUST UNITED AC 2006. [DOI: 10.1080/00411450008205875] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- A. T. Lawniczak
- a Departament of Mathematics and Statistics, Guelph-Waterloo Program for Graduate Work in Physics , University of Guelph , Guelph , Ontario , N1G 2W1 , Canada E-mail:
- b The Fields Institute for Research in Mathematical Sciences , 222 College Street, Toronto , Ont , M5T 3J1 , Canada E-mail:
| |
Collapse
|
7
|
Roshani F, Aghamohammadi A, Khorrami M. Static and dynamic phase transitions in multidimensional voting models on continua. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:056128. [PMID: 15600713 DOI: 10.1103/physreve.70.056128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2004] [Indexed: 05/24/2023]
Abstract
A voting model (or a generalization of the Glauber model at zero temperature) on a multidimensional lattice is defined as a system composed of a lattice, each site of which is either empty or occupied by a single particle. The reactions of the system are such that two adjacent sites, one empty, the other occupied, may evolve to a state where both of these sites are either empty or occupied. The continuum version of this model in a D-dimensional region with a boundary is studied, and two general behaviors of such systems are investigated, the stationary behavior of the system, and the dominant way of relaxation of the system toward its stationary state. Based on the first behavior, a static phase transition (discontinuous changes in the stationary profiles of the system) is studied. Based on the second behavior, a dynamical phase transition (discontinuous changes in the relaxation times of the system) is studied. It is shown that the static phase transition is induced by the bulk reactions only, while the dynamical phase transition is a result of both bulk reactions and boundary conditions.
Collapse
Affiliation(s)
- F Roshani
- Institute for Advanced Studies in Basic Sciences, P.O. Box 159, Zanjan 45195, Iran.
| | | | | |
Collapse
|
8
|
Khorrami M, Aghamohammadi A. Perturbative calculation of one-point functions of one-dimensional single-species reaction-diffusion systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:011103. [PMID: 15324038 DOI: 10.1103/physreve.70.011103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2004] [Indexed: 05/24/2023]
Abstract
Perturbations around autonomous one-dimensional single-species reaction-diffusion systems are investigated. It is shown that the parameter space corresponding to the autonomous systems is divided into two parts: In one part, the system is stable against the perturbations, in the sense that the largest relaxation time of the one-point functions changes continuously with perturbations. In the other part, however, the system is unstable against perturbations, so that any small perturbation drastically modifies the large-time behavior of the one-point functions.
Collapse
Affiliation(s)
- Mohammad Khorrami
- Department of Physics, Alzahra University, Tehran 19938-91167, Iran.
| | | |
Collapse
|
9
|
Yuste SB, Acedo L, Lindenberg K. Reaction front in an A+B-->C reaction-subdiffusion process. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:036126. [PMID: 15089380 DOI: 10.1103/physreve.69.036126] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2003] [Indexed: 05/24/2023]
Abstract
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.
Collapse
Affiliation(s)
- S B Yuste
- Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain
| | | | | |
Collapse
|
10
|
Buhot A. Kovacs effect and fluctuation–dissipation relations in 1D kinetically constrained models. ACTA ACUST UNITED AC 2003. [DOI: 10.1088/0305-4470/36/50/002] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
11
|
Oshanin G, Burlatsky SF. Adsorption of reactive particles on a random catalytic chain: an exact solution. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:016115. [PMID: 12636572 DOI: 10.1103/physreve.67.016115] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2002] [Indexed: 05/24/2023]
Abstract
We study equilibrium properties of a catalytically activated annihilation A+A-->0 reaction taking place on a one-dimensional chain of length N (N--> infinity ) in which some segments (placed at random, with mean concentration p) possess special, catalytic properties. Annihilation reaction takes place as soon as any two A particles land onto two vacant sites at the extremities of the catalytic segment, or when any A particle lands onto a vacant site on a catalytic segment while the site at the other extremity of this segment is already occupied by another A particle. Noncatalytic segments are inert with respect to reaction and here two adsorbed A particles harmlessly coexist. For both "annealed" and "quenched" disorder in placement of the catalytic segments, we calculate exactly the disorder-averaged pressure per site. Explicit asymptotic formulas for the particle mean density and the compressibility are also presented.
Collapse
Affiliation(s)
- G Oshanin
- Laboratoire de Physique Théorique des Liquides, Université Paris 6, 4 Place Jussieu, 75252 Paris, France
| | | |
Collapse
|
12
|
Tabatabaee F, Aghamohammadi A. Cluster approximation solution of a two-species annihilation model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:066136. [PMID: 12513376 DOI: 10.1103/physreve.66.066136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2002] [Indexed: 05/24/2023]
Abstract
A two-species reaction-diffusion model, in which particles diffuse on a one-dimensional lattice and annihilate when meeting each other, has been investigated. Mean-field equations for general choice of reaction rates have been solved exactly. The cluster mean-field approximation of the model is also studied. It is shown that the general form of large time behavior of one- and two-point functions of the number operators are determined by the diffusion rates of the two type of species, and is independent of annihilation rates.
Collapse
Affiliation(s)
- F Tabatabaee
- Department of Physics, Alzahra University, Tehran 19834, Iran.
| | | |
Collapse
|
13
|
|
14
|
Abad E, Masser T, ben-Avraham D. Lattice kinetics of diffusion-limited coalescence and annihilation with sources. ACTA ACUST UNITED AC 2002. [DOI: 10.1088/0305-4470/35/7/301] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|
15
|
Mobilia M, Bares PA. Generalized empty-interval method applied to a class of one-dimensional stochastic models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:066123. [PMID: 11736252 DOI: 10.1103/physreve.64.066123] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2001] [Indexed: 05/23/2023]
Abstract
In this work we study, on a finite and periodic lattice, a class of one-dimensional (bimolecular and single-species) reaction-diffusion models that cannot be mapped onto free-fermion models. We extend the conventional empty-interval method, also called interparticle distribution function (IPDF) method, by introducing a string function, which is simply related to relevant physical quantities. As an illustration, we specifically consider a model that cannot be solved directly by the conventional IPDF method and that can be viewed as a generalization of the voter model and/or as an epidemic model. We also consider the reversible diffusion-coagulation model with input of particles and determine other reaction-diffusion models that can be mapped onto the latter via suitable similarity transformations. Finally we study the problem of the propagation of a wave front from an inhomogeneous initial configuration and note that the mean-field scenario predicted by Fisher's equation is not valid for the one-dimensional (microscopic) models under consideration.
Collapse
Affiliation(s)
- M Mobilia
- Institute of Theoretical Physics, Swiss Federal Institute of Technology of Lausanne, CH-1015 Lausanne EPFL, Switzerland
| | | |
Collapse
|
16
|
Alimohammadi M, Khorrami M, Aghamohammadi A. Exactly solvable models through the empty-interval method. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:056116. [PMID: 11736023 DOI: 10.1103/physreve.64.056116] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2001] [Indexed: 05/23/2023]
Abstract
The most general one dimensional reaction-diffusion model with nearest-neighbor interactions that can be solved exactly through empty-interval method has been introduced. Assuming translationally invariant initial conditions, the probability that n consecutive sites are empty, E(n), has been exactly obtained. Here, however, we do not consider reactions changing two empty neighboring sites. In the thermodynamic limit, the large-time behavior of the system has also been investigated. Releasing translationally invariance, the evolution equation for the probability that n consecutive sites, starting from the site k, are empty, E(k,n), is obtained. In the thermodynamic limit, the large time behavior of the system is also considered. Finally, the continuum limit of the model is considered and the empty-interval probability function is obtained.
Collapse
Affiliation(s)
- M Alimohammadi
- Physics Department, University of Tehran, North Karegar Avenue, Tehran, Iran.
| | | | | |
Collapse
|
17
|
Yuste SB, Lindenberg K. Subdiffusion-limited A+A reactions. PHYSICAL REVIEW LETTERS 2001; 87:118301. [PMID: 11531549 DOI: 10.1103/physrevlett.87.118301] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2001] [Indexed: 05/23/2023]
Abstract
We consider the coagulation dynamics A+A-->A and A+A <==> A and the annihilation dynamics A+A-->0 for particles moving subdiffusively in one dimension. This scenario combines the "anomalous kinetics" and "anomalous diffusion" problems, each of which leads to interesting dynamics separately and to even more interesting dynamics in combination. Our analysis is based on the fractional diffusion equation.
Collapse
Affiliation(s)
- S B Yuste
- Department of Chemistry and Biochemistry 0340, University of California San Diego, La Jolla, California 92093-0340, USA
| | | |
Collapse
|
18
|
Masser TO, ben-Avraham D. Method of intervals for the study of diffusion-limited annihilation, A+A-->0. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:066108. [PMID: 11415174 DOI: 10.1103/physreve.63.066108] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2001] [Indexed: 05/23/2023]
Abstract
We introduce a method of intervals for the analysis of diffusion-limited annihilation, A+A-->0, on the line. The method leads to manageable diffusion equations whose interpretation is intuitively clear. As an example, we treat the following cases: (a) annihilation in the infinite line and in infinite (discrete) chains; (b) annihilation with input of single particles, adjacent particle pairs, and particle pairs separated by a given distance; (c) annihilation, A+A-->0, along with the birth reaction A-->3A, on finite rings, with and without diffusion.
Collapse
Affiliation(s)
- T O Masser
- Physics Department, Clarkson University, Potsdam, New York 13699-5820, USA
| | | |
Collapse
|
19
|
Kim H, Joe Shin K. On the diffusion-influenced reversible trapping problem in one dimension. J Chem Phys 2000. [DOI: 10.1063/1.481436] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
20
|
|
21
|
Zhong D, Ben-Avraham D. Diffusion-limited coalescence with finite reaction rates in one dimension. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/28/1/010] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|
22
|
Braunstein LA, Buceta RC. Nucleation model for multiparticle reactions with finite reaction rates in one dimension. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:6125-6127. [PMID: 9965831 DOI: 10.1103/physreve.54.6125] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
23
|
Monthus C. Exponents appearing in heterogeneous reaction-diffusion models in one dimension. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:4844-4859. [PMID: 9965666 DOI: 10.1103/physreve.54.4844] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
24
|
Karzazi MA, Lemarchand A, Mareschal M. Fluctuation effects on chemical wave fronts. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:4888-4895. [PMID: 9965669 DOI: 10.1103/physreve.54.4888] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
25
|
Molski A. Fluctuation theory of the coupling between diffusion and reaction in 1D: coalescence with point reactivities. Chem Phys Lett 1996. [DOI: 10.1016/s0009-2614(96)00166-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
|
26
|
Braunstein LA, Buceta RC. Nucleation model for diffusion-limited coalescence with finite reaction rates in one dimension. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:3414-3419. [PMID: 9964650 DOI: 10.1103/physreve.53.3414] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
27
|
Riordan J, Doering CR, ben-Avraham D. Fluctuations and stability of fisher waves. PHYSICAL REVIEW LETTERS 1995; 75:565-568. [PMID: 10060053 DOI: 10.1103/physrevlett.75.565] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
28
|
Shipilevsky BM. Critical change of relaxation dynamics in a reaction-diffusion system. PHYSICAL REVIEW LETTERS 1994; 73:201-204. [PMID: 10056755 DOI: 10.1103/physrevlett.73.201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
29
|
Diffusion-limited many-body reactions in one dimension and the method of interparticle distribuion functions. Chem Phys 1994. [DOI: 10.1016/0301-0104(93)e0412-o] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
|
30
|
Lin JC, Taylor PL. Exact solution of a phase-separation model with conserved-order-parameter dynamics and arbitrary initial concentration. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 48:4305-4308. [PMID: 9961111 DOI: 10.1103/physreve.48.4305] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
31
|
ben-Avraham D. Diffusion-limited three-body reactions in one dimension. PHYSICAL REVIEW LETTERS 1993; 71:3733-3735. [PMID: 10055058 DOI: 10.1103/physrevlett.71.3733] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
32
|
Kroon R, Fleurent H, Sprik R. Diffusion-limited exciton fusion reaction in one-dimensional tetramethylammonium manganese trichloride (TMMC). PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:2462-2472. [PMID: 9960278 DOI: 10.1103/physreve.47.2462] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
33
|
Agmon N. Competitive and noncompetitive reversible binding processes. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:2415-2429. [PMID: 9960273 DOI: 10.1103/physreve.47.2415] [Citation(s) in RCA: 26] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
34
|
|
35
|
Huppert D, Goldberg SY, Masad A, Agmon N. Experimental determination of the long-time behavior in reversible binary chemical reactions. PHYSICAL REVIEW LETTERS 1992; 68:3932-3935. [PMID: 10045841 DOI: 10.1103/physrevlett.68.3932] [Citation(s) in RCA: 61] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
36
|
Horsthemke W, Doering CR, Ray TS, Burschka MA. Fluctuations and correlations in a diffusion-reaction system: Unified description of internal fluctuations and external noise. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:5492-5503. [PMID: 9907647 DOI: 10.1103/physreva.45.5492] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
|
37
|
Lin JC. Exact results for one-dimensional reversible coagulation in discrete spatial formalism. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:3892-3895. [PMID: 9907437 DOI: 10.1103/physreva.45.3892] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
38
|
Lin JC. Closure schemes for joint density functions in diffusion-limited reactions. PHYSICAL REVIEW A 1991; 44:6706-6722. [PMID: 9905799 DOI: 10.1103/physreva.44.6706] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
39
|
Lin JC. Symmetry between diffusion-limited coagulation and annihilation. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 43:5714-5716. [PMID: 9904890 DOI: 10.1103/physreva.43.5714] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
40
|
Sheu WS, Lindenberg K. Coagulation reaction in a one-dimensional gas. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 43:4401-4405. [PMID: 9905544 DOI: 10.1103/physreva.43.4401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
41
|
Sheu WS, Lindenberg K. Exact solution of the one-dimensional immobile trapping problem with and without sources. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 42:5025-5028. [PMID: 9904618 DOI: 10.1103/physreva.42.5025] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
|
42
|
|
43
|
Peak D, Greenlaw DC, Schick LA. Pair-correlation kinetics and the reversible diffusion-controlled reaction. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:5362-5365. [PMID: 9902923 DOI: 10.1103/physreva.41.5362] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
44
|
Doering CR, Burschka MA. Long crossover times in a finite system. PHYSICAL REVIEW LETTERS 1990; 64:245-248. [PMID: 10041930 DOI: 10.1103/physrevlett.64.245] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|