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Derbyshev AE, Povolotsky AM, Priezzhev VB. Emergence of jams in the generalized totally asymmetric simple exclusion process. Phys Rev E Stat Nonlin Soft Matter Phys 2015; 91:022125. [PMID: 25768476 DOI: 10.1103/physreve.91.022125] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2014] [Indexed: 06/04/2023]
Abstract
The generalized totally asymmetric exclusion process (TASEP) [J. Stat. Mech. (2012) P05014] is an integrable generalization of the TASEP equipped with an interaction, which enhances the clustering of particles. The process interpolates between two extremal cases: the TASEP with parallel update and the process with all particles irreversibly merging into a single cluster moving as an isolated particle. We are interested in the large time behavior of this process on a ring in the whole range of the parameter λ controlling the interaction. We study the stationary state correlations, the cluster size distribution, and the large-time fluctuations of integrated particle current. When λ is finite, we find the usual TASEP-like behavior: The correlation length is finite; there are only clusters of finite size in the stationary state and current fluctuations belong to the Kardar-Parisi-Zhang universality class. When λ grows with the system size, so does the correlation length. We find a nontrivial transition regime with clusters of all sizes on the lattice. We identify a crossover parameter and derive the large deviation function for particle current, which interpolates between the case considered by Derrida-Lebowitz and a single-particle diffusion.
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Affiliation(s)
- A E Derbyshev
- Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia and Moscow Institute of Physics and Technology, Dolgoprudny, Russia
| | - A M Povolotsky
- Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia and Laboratory of Mathematical Physics, NRU HSE, Moscow, Russia
| | - V B Priezzhev
- Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia
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Alcaraz FC, Brankov JG, Priezzhev VB, Rittenberg V, Rogozhnikov AM. Noncontractible loops in the dense O(n) loop model on the cylinder. Phys Rev E Stat Nonlin Soft Matter Phys 2014; 90:052138. [PMID: 25493770 DOI: 10.1103/physreve.90.052138] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2014] [Indexed: 06/04/2023]
Abstract
A lattice model of critical dense polymers O(n) is considered for finite cylinder geometry. Due to the presence of noncontractible loops with a fixed fugacity ξ, the model at n=0 is a generalization of the critical dense polymers solved by Pearce, Rasmussen, and Villani. We found the free energy for any height N and circumference L of the cylinder. The density ρ of noncontractible loops is obtained for N→∞ and large L. The results are compared with those found for the anisotropic quantum chain with twisted boundary conditions. Using the latter method, we derived ρ for any O(n) model and an arbitrary fugacity.
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Affiliation(s)
- F C Alcaraz
- Instituto de Física de São Carlos, Universidade de São Paulo, Casixa Postal 369, 13560-590, São Carlos, SP, Brazil
| | - J G Brankov
- Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia and Institute of Mechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
| | - V B Priezzhev
- Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia
| | - V Rittenberg
- Physikalisches Institut, Universität Bonn, Nussallee 12, 53115 Bonn, Germany
| | - A M Rogozhnikov
- National Research University Higher School of Economics, 101000 Moscow, Russia
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Poghosyan SS, Poghosyan VS, Priezzhev VB, Ruelle P. Numerical study of the correspondence between the dissipative and fixed-energy Abelian sandpile models. Phys Rev E Stat Nonlin Soft Matter Phys 2011; 84:066119. [PMID: 22304167 DOI: 10.1103/physreve.84.066119] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2011] [Revised: 09/06/2011] [Indexed: 05/31/2023]
Abstract
We consider the Abelian sandpile model (ASM) on the square lattice with a single dissipative site (sink). Particles are added one by one per unit time at random sites and the resulting density of particles is calculated as a function of time. We observe different scenarios of evolution depending on the value of initial uniform density (height) h(0). During the first stage of the evolution, the density of particles increases linearly. Reaching a critical density ρ(c)(h(0)), the system changes its behavior and relaxes exponentially to the stationary state of the ASM with density ρ(s). Considering initial heights -1 ≤ h(0) ≤ 4, we observe a dramatic decrease of the difference ρ(c)(h(0)) - ρ(s) when h(0) is zero or negative. In parallel with the ASM, we consider the conservative fixed energy sandpile (FES). The extensive Monte Carlo simulations show that the threshold density ρ(th)(h(0)) of the FES converges rapidly to ρ(s) for h(0) < 1.
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Affiliation(s)
- Su S Poghosyan
- Institute for Informatics and Automation Problems NAS of Armenia, 375044 Yerevan, Armenia
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Abstract
Following the recent proposal made by [J. Bouttier, Phys. Rev. E 76, 041140 (2007)], we study analytically the mobility properties of a single vacancy in the close-packed dimer model on the square lattice. Using the spanning web representation, we find determinantal expressions for various observable quantities. In the limiting case of large lattices, they can be reduced to the calculation of Toeplitz determinants and minors thereof. The probability for the vacancy to be strictly jammed and other diffusion characteristics are computed exactly.
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Affiliation(s)
- V S Poghosyan
- Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia
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Izmailian NS, Papoyan VV, Priezzhev VB, Hu CK. Self-organizing behavior in a lattice model for co-evolution of virus and immune systems. Phys Rev E Stat Nonlin Soft Matter Phys 2007; 75:041104. [PMID: 17500862 DOI: 10.1103/physreve.75.041104] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2006] [Revised: 01/12/2007] [Indexed: 05/15/2023]
Abstract
We propose a lattice model for the co-evolution of a virus population and an adaptive immune system. We show that, under some natural assumptions, both probability distribution of the virus population and the distribution of activity of the immune system tend during the evolution to a self-organized critical state.
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Affiliation(s)
- N Sh Izmailian
- Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan
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Izmailian NS, Priezzhev VB, Ruelle P, Hu CK. Logarithmic conformal field theory and boundary effects in the dimer model. Phys Rev Lett 2005; 95:260602. [PMID: 16486328 DOI: 10.1103/physrevlett.95.260602] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2005] [Indexed: 05/06/2023]
Abstract
We study the finite-size corrections of the dimer model on a square lattice with two different boundary conditions: free and periodic. We find that the finite-size corrections depend in a crucial way on the parity of ; we also show that such unusual finite-size behavior can be fully explained in the framework of the logarithmic conformal field theory.
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Affiliation(s)
- N Sh Izmailian
- Institute of Physics, Academia Sinica, Nankang, Taipei, Taiwan
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Brankov JG, Priezzhev VB, Shelest RV. Generalized determinant solution of the discrete-time totally asymmetric exclusion process and zero-range process. Phys Rev E Stat Nonlin Soft Matter Phys 2004; 69:066136. [PMID: 15244696 DOI: 10.1103/physreve.69.066136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2003] [Indexed: 05/24/2023]
Abstract
We consider the discrete-time evolution of a finite number of particles obeying the totally asymmetric exclusion process with backward-ordered update on an infinite chain. Our first result is a determinant expression for the conditional probability of finding the particles at given initial and final positions, provided that they start and finish simultaneously. The expression has the same form as the one obtained by J. Stat. Phys. 88, 427 (1997)] for the continuous-time process. Next we prove that under some sufficient conditions the determinant expression can be generalized to the case when the particles start and finish at their own times. The latter result is used to solve a nonstationary zero-range process on a finite chain with open boundaries.
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Affiliation(s)
- J G Brankov
- Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St. 4, 1113 Sofia, Bulgaria
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Avdeev MV, Khokhryakov AA, Tropin TV, Andrievsky GV, Klochkov VK, Derevyanchenko LI, Rosta L, Garamus VM, Priezzhev VB, Korobov MV, Aksenov VL. Structural features of molecular-colloidal solutions of C60 fullerenes in water by small-angle neutron scattering. Langmuir 2004; 20:4363-8. [PMID: 15969139 DOI: 10.1021/la0361969] [Citation(s) in RCA: 48] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Highly stable and reproducible molecular-colloidal water solutions of C60 fullerenes (FWS) obtained by transferring fullerenes from an organic solution into an aqueous phase with the help of ultrasonic treatment are investigated by means of small-angle neutron scattering (SANS). A polydispersity in the size of detected particles up to 84 nm is revealed. These particles are slightly anisotropic and have a characteristic size of approximately 70 nm. Along with it, there are some indications that a significant part of fullerenes composes particles with the size of the order of 1 nm. The contrast variation based on mixtures of light and heavy water shows that the mean scattering length density of the particles is close to that of the packed fullerene associates as well as that the characteristic size of possible fluctuations of the scattering length density within the particles does not exceed 2 nm. A smooth surface resulting in the Porod law for the scattering is detected. A number of models discussed in the literature are considered with respect to the SANS data.
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Affiliation(s)
- M V Avdeev
- Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia
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Povolotsky AM, Priezzhev VB, Hu CK. Transition from Kardar-Parisi-Zhang to tilted interface critical behavior in a solvable asymmetric avalanche model. Phys Rev Lett 2003; 91:255701. [PMID: 14754126 DOI: 10.1103/physrevlett.91.255701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2003] [Indexed: 05/24/2023]
Abstract
We use a discrete-time formulation of the asymmetric avalanche process (ASAP) [Phys. Rev. Lett. 87, 084301 (2001)]] of p particles on a finite ring of N sites to obtain an exact expression for the average avalanche size as a function of toppling probabilities and particle density rho=p/N. By mapping the model onto driven interface problems, we find that the ASAP incorporates the annealed Kardar-Parizi-Zhang and quenched tilted interface dynamics for rho<rho(c) and rho>rho(c), respectively, with rho(c) being the critical density for given toppling probabilities and N--> infinity. We analyze the crossover between two regimes and show which parameters are relevant near the transition point.
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Affiliation(s)
- A M Povolotsky
- Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan
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Abstract
The complete solution of the master equation for a system of interacting particles of finite density is presented. By using a new form of the Bethe ansatz, the totally asymmetric exclusion process on a ring is solved for arbitrary initial conditions and time intervals.
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Affiliation(s)
- V B Priezzhev
- Max-Planck Institute for the Physics of Complex Systems, Nöthnitzer strasse 38, D-01187 Dresden, Germany
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Priezzhev VB, Ivashkevich EV, Povolotsky AM, Hu CK. Exact phase diagram for an asymmetric avalanche process. Phys Rev Lett 2001; 87:084301. [PMID: 11497944 DOI: 10.1103/physrevlett.87.084301] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2001] [Indexed: 05/23/2023]
Abstract
The Bethe ansatz method and an iterative procedure based on detailed balance are used to obtain exact results for an asymmetric avalanche process on a ring. The average velocity of particle flow, v, is derived as a function of the toppling probabilities and the density of particles, rho. As rho increases, the system shows a transition from intermittent to continuous flow, and v diverges at a critical point rho(c) with exponent alpha. The exact phase diagram of the transition is obtained and alpha is found to depend on the toppling rules.
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Affiliation(s)
- V B Priezzhev
- Bogoliubov Laboratory of Theoretical Physics, J. I. N. R., Dubna 141980, Russia
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Hu CK, Ivashkevich EV, Lin CY, Priezzhev VB. Inversion symmetry and exact critical exponents of dissipating waves in the sandpile model. Phys Rev Lett 2000; 85:4048-4051. [PMID: 11056621 DOI: 10.1103/physrevlett.85.4048] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/29/1999] [Revised: 06/08/2000] [Indexed: 05/23/2023]
Abstract
By an inversion symmetry, we show that in the Abelian sandpile model the probability distribution of dissipating waves of topplings that touch the boundary of the system shows a power-law relationship with critical exponent 5/8 and the probability distribution of those dissipating waves that are also last in an avalanche has an exponent of 1. Our extensive numerical simulations not only support these predictions, but also show that inversion symmetry is useful for the analysis of the two-wave probability distributions.
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Affiliation(s)
- C K Hu
- Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan.
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Priezzhev VB, Dhar D, Dhar A, Krishnamurthy S. Eulerian Walkers as a Model of Self-Organized Criticality. Phys Rev Lett 1996; 77:5079-5082. [PMID: 10062709 DOI: 10.1103/physrevlett.77.5079] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Priezzhev VB, Ktitarev DV, Ivashkevich EV. Formation of avalanches and critical exponents in an Abelian sandpile model. Phys Rev Lett 1996; 76:2093-2096. [PMID: 10060604 DOI: 10.1103/physrevlett.76.2093] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Blagoveshchenskii NM, Bogoyavlenskii IV, Karnatsevich LV, Kozlov ZA, Kolobrodov VG, Priezzhev VB, Puchkov AV, Skomorokhov AN, Yarunin VS. Structure of the excitation spectrum of liquid 4He. Phys Rev B Condens Matter 1994; 50:16550-16565. [PMID: 9976042 DOI: 10.1103/physrevb.50.16550] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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