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Vezzani A, Muñoz MA, Burioni R. Anomalous finite-size scaling in higher-order processes with absorbing states. Phys Rev E 2023; 107:014105. [PMID: 36797930 DOI: 10.1103/physreve.107.014105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2022] [Accepted: 12/21/2022] [Indexed: 01/09/2023]
Abstract
Here we study standard and higher-order birth-death processes on fully connected networks, within the perspective of large-deviation theory [also referred to as the Wentzel-Kramers-Brillouin (WKB) method in some contexts]. We obtain a general expression for the leading and next-to-leading terms of the stationary probability distribution of the fraction of "active" sites as a function of parameters and network size N. We reproduce several results from the literature and, in particular, we derive all the moments of the stationary distribution for the q-susceptible-infected-susceptible (q-SIS) model, i.e., a high-order epidemic model requiring q active ("infected") sites to activate an additional one. We uncover a very rich scenario for the fluctuations of the fraction of active sites, with nontrivial finite-size-scaling properties. In particular, we show that the variance-to-mean ratio diverges at criticality for [1≤q≤3], with a maximal variability at q=2, confirming that complex-contagion processes can exhibit peculiar scaling features including wild variability. Moreover, the leading order in a large-deviation approach does not suffice to describe them: next-to-leading terms are essential to capture the intrinsic singularity at the origin of systems with absorbing states. Some possible extensions of this work are also discussed.
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Affiliation(s)
- Alessandro Vezzani
- Istituto dei Materiali per l'Elettronica ed il Magnetismo (IMEM-CNR), Parco Area delle Scienze, 37/A-43124 Parma, Italy; Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università degli Studi di Parma, Parco Area delle Scienze 7/A, 43124 Parma, Italy; and INFN, Gruppo Collegato di Parma, Parco Area delle Scienze 7/A, 43124 Parma, Italy
| | - Miguel A Muñoz
- Departamento de Electromagnetismo y Física de la Materia and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada. E-18071 Granada, Spain
| | - Raffaella Burioni
- Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università degli Studi di Parma, Parco Area delle Scienze 7/A, 43124 Parma, Italy and INFN, Gruppo Collegato di Parma, Parco Area delle Scienze 7/A, 43124 Parma, Italy
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Bunzarova NZ, Pesheva NC. One-dimensional irreversible aggregation with dynamics of a totally asymmetric simple exclusion process. Phys Rev E 2017; 95:052105. [PMID: 28618542 DOI: 10.1103/physreve.95.052105] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2016] [Indexed: 11/07/2022]
Abstract
We define and study one-dimensional model of irreversible aggregation of particles obeying a discrete-time kinetics, which is a special limit of the generalized Totally Asymmetric Simple Exclusion Process (gTASEP) on open chains. The model allows for clusters of particles to translate as a whole entity one site to the right with the same probability as single particles do. A particle and a cluster, as well as two clusters, irreversibly aggregate whenever they become nearest neighbors. Nonequilibrium stationary phases appear under the balance of injection and ejection of particles. By extensive Monte Carlo simulations it is established that the phase diagram in the plane of the injection-ejection probabilities consists of three stationary phases: a multiparticle (MP) one, a completely filled (CF) phase, and a "mixed" (MP+CF) one. The transitions between these phases are: an unusual transition between MP and CF with jump discontinuity in both the bulk density and the current, a conventional first-order transition with a jump in the bulk density between MP and MP+CF, and a continuous clustering-type transition from MP to CF, which takes place throughout the MP+CF phase between them. By the data collapse method a finite-size scaling function for the current and bulk density is obtained near the unusual phase transition line. A diverging correlation length, associated with that transition, is identified and interpreted as the size of the largest cluster. The model allows for a future extension to account for possible cluster fragmentation.
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Affiliation(s)
- N Zh Bunzarova
- Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia.,Institute of Mechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
| | - N C Pesheva
- Institute of Mechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
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3
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Kinetics of aggregation with a finite number of particles and application to viral capsid assembly. J Math Biol 2014; 70:1685-705. [DOI: 10.1007/s00285-014-0819-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2014] [Revised: 06/09/2014] [Indexed: 10/24/2022]
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Abstract
ABSTRACTIt has been well established by theory and simulations that the reaction rates of diffusion-limited reactions can be affected by the spatial dimension in which they occur. The types of reactions A + B → C, A + A → A, and A + C→, C have been shown, theoretically and/or by simulation, to exhibit non-classical reaction kinetics in low and fractal dimensions. We present here experimental results from several 1D and fractal systems.An A+B → C type reaction was experimentally investigated in a long, thin capillary tube in which the reactants, A and B, are initially segregated. This initial segregation of reactants means that the net diffusion is along the length of the capillary only, making the system effectively 1D and allowing some of the properties of the resulting reaction front to be studied. The reaction rate of excitonic fusion, A + A →A, as well as trapping, A + C→ C, reactions were observed via phosphorescence(P) and delayed fluorescence(F) of naphthalene within the channels of Vycor glass, in isotopically mixed naphthalene crystals and in the isolated chains of dilute polymer blends. In these experiments, the non-classical kinetics are measured in terms of the heterogeneity exponent, h, from the equation: Rate ∼ F =; kt-hpn,, which gives the time dependence of the rate coefficient. Classically h =; 0, while h =; 1/2 in 1D, as well as in the fractal dimensions discussed here, for A + A → A as well as A + C →C type reactions.
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Yuste SB, Ruiz-Lorenzo JJ, Lindenberg K. Coagulation reactions in low dimensions: Revisiting subdiffusive A+A reactions in one dimension. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:051114. [PMID: 20364954 DOI: 10.1103/physreve.80.051114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2009] [Indexed: 05/29/2023]
Abstract
We present a theory for the coagulation reaction A+A-->A for particles moving subdiffusively in one dimension. Our theory is tested against numerical simulations of the concentration of A particles as a function of time ("anomalous kinetics") and of the interparticle distribution function as a function of interparticle distance and time. We find that the theory captures the correct behavior asymptotically and also at early times, and that it does so whether the particles are nearly diffusive or very subdiffusive. We find that, as in the normal diffusion problem, an interparticle gap responsible for the anomalous kinetics develops and grows with time. This corrects an earlier claim to the contrary on our part.
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Affiliation(s)
- S B Yuste
- Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain
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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
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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.
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Affiliation(s)
- S B Yuste
- Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain
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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]
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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.
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Affiliation(s)
- M Mobilia
- Institute of Theoretical Physics, Swiss Federal Institute of Technology of Lausanne, CH-1015 Lausanne EPFL, Switzerland
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Mobilia M, Bares PA. Solution of a one-dimensional stochastic model with branching and coagulation reactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:045101. [PMID: 11690073 DOI: 10.1103/physreve.64.045101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2001] [Indexed: 05/23/2023]
Abstract
We solve a one-dimensional stochastic model of interacting particles on a chain. Particles can have branching and coagulation reactions; they can also appear on an empty site and disappear spontaneously. This model, which can be viewed as an epidemic model and/or as a generalization of the voter model, is treated analytically beyond the conventional solvable situations. With help of a suitably chosen string function, which is simply related to the density and the noninstantaneous two-point correlation functions of the particles, exact expressions of the density and of the noninstantaneous two-point correlation functions, as well as the relaxation spectrum are obtained on a finite and periodic lattice.
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Affiliation(s)
- M Mobilia
- Institute of Theoretical Physics, Swiss Federal Institute of Technology of Lausanne, CH-1015 Lausanne, Switzerland
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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.
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Affiliation(s)
- S B Yuste
- Department of Chemistry and Biochemistry 0340, University of California San Diego, La Jolla, California 92093-0340, USA
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Habib S, Lindenberg K, Lythe G, Molina-Parı́s C. Diffusion-limited reaction in one dimension: Paired and unpaired nucleation. J Chem Phys 2001. [DOI: 10.1063/1.1372763] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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de Oliveira MJ. Exact density profile of a stochastic reaction-diffusion process. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:2563-7. [PMID: 11970056 DOI: 10.1103/physreve.60.2563] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/1999] [Indexed: 04/18/2023]
Abstract
We calculate exactly the time dependent density profile of a one-dimensional stochastic reaction-diffusion process of hard-core particles subjected to the reactions AA <--> OO and AO <--> OA. The solution is based on the fundamental property that the evolution operator, defined over an appropriate vector space, transforms vectors with n kinks into vectors with n or n+2 kinks, only. In this space, a basis vector is represented by a string of plus and minus signs and a kink is defined as a pair of opposite signs. The exact time dependent profiles are calculated for the cases of uncorrelated initial states that are translational invariant as well as initial states that are inhomogeneous in space.
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Affiliation(s)
- M J de Oliveira
- Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05315-970 São Paulo, SP, Brazil
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Redner S, ben-Avraham D. Nearest-neighbour distances of diffusing particles from a single trap. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/23/22/003] [Citation(s) in RCA: 48] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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17
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Braunstein L, Martin HO, Grynberg MD, Roman HE. Effects of probability of reaction on annihilation reactions in one dimension. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/25/5/009] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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18
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Brilliantov NV, Krapivsky PL. Nonscaling and source-induced scaling behaviour in aggregation model of movable monomers and immovable clusters. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/24/20/014] [Citation(s) in RCA: 62] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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19
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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]
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20
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Derrida B. Exponents appearing in the zero-temperature dynamics of the 1D Potts model. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/28/6/006] [Citation(s) in RCA: 54] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Simon H. Concentration for one and two-species one-dimensional reaction-diffusion systems. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/28/23/013] [Citation(s) in RCA: 52] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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22
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Rey PA, Droz M. A renormalization group study of a class of reaction-diffusion models, with particles input. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/30/4/013] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Lin AL, Kopelman R, Argyrakis P. Diffusion-Controlled Elementary Reactions in Tubular Confinement: Extreme Nonclassicality, Segregation, and Anomalous Scaling Laws for Dimensional Crossovers. J Phys Chem A 1997. [DOI: 10.1021/jp9628904] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Anna L. Lin
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055
| | - Raoul Kopelman
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055
| | - Panos Argyrakis
- Department of Physics, University of Thessaloniki, 54006 Thessaloniki, Greece
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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]
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Lin AL, Kopelman R, Argyrakis P. Dimensional crossovers and anomalous scaling of single and reacting random walkers in baguettelike lattices: Monte Carlo simulations of the number of distinct sites visited and of bimolecular A+A and A+B reactions. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:R5893-R5896. [PMID: 9965939 DOI: 10.1103/physreve.54.r5893] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Mai J, Sokolov IM, Blumen A. Front Propagation and Local Ordering in One-Dimensional Irreversible Autocatalytic Reactions. PHYSICAL REVIEW LETTERS 1996; 77:4462-4465. [PMID: 10062544 DOI: 10.1103/physrevlett.77.4462] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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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]
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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]
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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]
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Lin A, Kopelman R, Argyrakis P. Nonclassical kinetics in three dimensions: Simulations of elementary A+B and A+A reactions. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:1502-1509. [PMID: 9964413 DOI: 10.1103/physreve.53.1502] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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31
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Balboni D, Rey PA, Droz M. Universality of a class of annihilation-coagulation models. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:6220-6226. [PMID: 9964138 DOI: 10.1103/physreve.52.6220] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Gonzalez AP, Pereyra VD, Milchev A, Zgrablich G. Kinetics of simple reactions in a dichotomic barrier model. PHYSICAL REVIEW LETTERS 1995; 75:3954-3957. [PMID: 10059773 DOI: 10.1103/physrevlett.75.3954] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Zumofen G, Klafter J. Reaction dynamics controlled by enhanced diffusion. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 50:5119-5122. [PMID: 9962599 DOI: 10.1103/physreve.50.5119] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Hoyuelos M, Mártin HO. Annihilation reaction A+A-->0 with diffusion and interaction between particles in disordered structures. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 50:600-603. [PMID: 9962006 DOI: 10.1103/physreve.50.600] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Krapivsky PL. Diffusion-limited-aggregation processes with three-particle elementary reactions. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 49:3233-3238. [PMID: 9961591 DOI: 10.1103/physreve.49.3233] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Kuzovkov V, Kotomin E. Pair and triple correlations in the A+B-->B diffusion-controlled reaction. PHYSICAL REVIEW LETTERS 1994; 72:2105-2108. [PMID: 10055789 DOI: 10.1103/physrevlett.72.2105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Clément E, Kopelman R, Sander L. The diffusion-limited reaction A + A →0 in the steady state: influence of correlations in the source. Chem Phys 1994. [DOI: 10.1016/0301-0104(93)e0413-p] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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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]
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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]
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Hoyuelos M, Mártin HO. Rate equation of the A+A-->A reaction with probability of reaction and diffusion. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 48:3309-3313. [PMID: 9960987 DOI: 10.1103/physreve.48.3309] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Lemarchand A, Lesne A, Perera A, Moreau M, Mareschal M. Chemical wave front in two dimensions. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 48:1568-1571. [PMID: 9960751 DOI: 10.1103/physreve.48.1568] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Hoyuelos M, Mártin HO. Annihilation reactions in two-dimensional percolation clusters: Effects of short-range interactions. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 48:71-76. [PMID: 9960569 DOI: 10.1103/physreve.48.71] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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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]
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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]
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ben-Avraham D. Universality classes of second-order dynamical phase transitions. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:711-713. [PMID: 9960047 DOI: 10.1103/physreve.47.711] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Chopard B, Droz M, Karapiperis T, Rácz Z. Properties of the reaction front in a reversible A+B. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:R40-R43. [PMID: 9960074 DOI: 10.1103/physreve.47.r40] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Shi ZY, Kopelman R. Reaction order versus reaction probability for bimolecular steady state reactions: A+A → A and A+A → 0 in one dimension. Chem Phys 1992. [DOI: 10.1016/0301-0104(92)80030-y] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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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]
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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]
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