Статті в журналах: "Multispecies asymmetric simple exclusion processes"

1

Matsui, Chihiro. "Multi-state Asymmetric Simple Exclusion Processes." Journal of Statistical Physics 158, no. 1 (September 27, 2014): 158–91. http://dx.doi.org/10.1007/s10955-014-1121-9.

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2

Karimipour, V. "Multispecies asymmetric simple exclusion process and its relation to traffic flow." Physical Review E 59, no. 1 (January 1, 1999): 205–12. http://dx.doi.org/10.1103/physreve.59.205.

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3

Pronina, Ekaterina, and Anatoly B. Kolomeisky. "Two-channel totally asymmetric simple exclusion processes." Journal of Physics A: Mathematical and General 37, no. 42 (October 7, 2004): 9907–18. http://dx.doi.org/10.1088/0305-4470/37/42/005.

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4

Roy, Dipankar. "The phase diagram for a class of multispecies permissive asymmetric exclusion processes." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 1 (January 6, 2021): 013201. http://dx.doi.org/10.1088/1742-5468/abc7ba.

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5

Cai, Zhong-Pan, Yao-Ming Yuan, Rui Jiang, Mao-Bin Hu, Qing-Song Wu, and Yong-Hong Wu. "Asymmetric coupling in multi-channel simple exclusion processes." Journal of Statistical Mechanics: Theory and Experiment 2008, no. 07 (July 18, 2008): P07016. http://dx.doi.org/10.1088/1742-5468/2008/07/p07016.

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6

XIAO, SONG, MINGZHE LIU, and JING SHANG. "SINGLE ON-RAMP IN ASYMMETRIC SIMPLE EXCLUSION PROCESSES." Modern Physics Letters B 26, no. 06 (March 10, 2012): 1150036. http://dx.doi.org/10.1142/s0217984911500369.

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Анотація:

This paper studies the single on-ramp in a totally asymmetric simple exclusion processes (TASEPs). In our model, particles can only attach irreversibly with rate q to a bulk site k + 1, which is far away from boundaries. The model is investigated under random sequential update and open boundary conditions by using Monte Carlo simulations and mean-field calculations. In the case of hopping rate p = 1, when attachment rate q is fixed and q < 0.5, there are five phases in the system, while when q > 0.5, the system includes only four phases and the LD/LD phase vanishes.

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7

Pronina, Ekaterina, and Anatoly B. Kolomeisky. "Asymmetric coupling in two-channel simple exclusion processes." Physica A: Statistical Mechanics and its Applications 372, no. 1 (December 2006): 12–21. http://dx.doi.org/10.1016/j.physa.2006.05.006.

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8

Landim, C., and H. T. Yau. "Fluctuation-dissipation equation of asymmetric simple exclusion processes." Probability Theory and Related Fields 108, no. 3 (July 16, 1997): 321–56. http://dx.doi.org/10.1007/s004400050112.

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9

Tsekouras, K., and A. B. Kolomeisky. "Inhomogeneous coupling in two-channel asymmetric simple exclusion processes." Journal of Physics A: Mathematical and Theoretical 41, no. 9 (February 19, 2008): 095002. http://dx.doi.org/10.1088/1751-8113/41/9/095002.

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10

Tian, Bo, Rui Jiang, Mao-Bin Hu, Zhong-Jun Ding, and Bin Jia. "Totally asymmetric simple exclusion processes on two intersected lanes." EPL (Europhysics Letters) 128, no. 4 (January 24, 2020): 40005. http://dx.doi.org/10.1209/0295-5075/128/40005.

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11

Midha, Tripti, Luiza V. F. Gomes, Anatoly B. Kolomeisky, and Arvind Kumar Gupta. "Theoretical investigations of asymmetric simple exclusion processes for interacting oligomers." Journal of Statistical Mechanics: Theory and Experiment 2018, no. 5 (May 30, 2018): 053209. http://dx.doi.org/10.1088/1742-5468/aac139.

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12

Shaw, Leah B., Anatoly B. Kolomeisky, and Kelvin H. Lee. "Local inhomogeneity in asymmetric simple exclusion processes with extended objects." Journal of Physics A: Mathematical and General 37, no. 6 (January 28, 2004): 2105–13. http://dx.doi.org/10.1088/0305-4470/37/6/010.

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13

XIAO, SONG, SHUYING WU, LIQIONG TANG, DONGSHENG ZHENG, and JING SHANG. "THEORETICAL INVESTIGATION OF ASYMMETRIC SIMPLE EXCLUSION PROCESSES WITH OFF-RAMP ON THE BOUNDARIES." Modern Physics Letters B 26, no. 24 (August 21, 2012): 1250155. http://dx.doi.org/10.1142/s0217984912501552.

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Анотація:

In this letter, asymmetric simple exclusion processes with off-ramp on the boundaries have been studied by asymmetric simple exclusion processes (ASEPs). In this model, particles can only detach from a single off-ramp on the boundaries of the system. The phase diagrams and density profiles are calculated by approximate mean field theory and have shown good agreement with the extensive Monte Carlo computer simulations.

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14

Landim, C., S. Olla, and H. T. Yau. "Some properties of the diffusion coefficient for asymmetric simple exclusion processes." Annals of Probability 24, no. 4 (1996): 1779–808. http://dx.doi.org/10.1214/aop/1041903206.

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15

Jiu-Ju, Cai, Xiao Song, Wang Ruo-Hui, and Liu Fei. "Successive defects asymmetric simple exclusion processes with particles of arbitrary size." Chinese Physics B 18, no. 12 (December 2009): 5097–102. http://dx.doi.org/10.1088/1674-1056/18/12/001.

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16

Tanaka, Ryokichi. "Hydrodynamic Limit for Weakly Asymmetric Simple Exclusion Processes in Crystal Lattices." Communications in Mathematical Physics 315, no. 3 (October 2, 2012): 603–41. http://dx.doi.org/10.1007/s00220-012-1574-0.

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17

Liu, MingZhe, XianGuo Tuo, RuiLi Wang, and Rui Jiang. "Recent developments in totally asymmetric simple exclusion processes with local inhomogeneity." Chinese Science Bulletin 56, no. 15 (April 26, 2011): 1527–31. http://dx.doi.org/10.1007/s11434-011-4449-4.

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18

Chang, Chih-Chung, Claudio Landim, and Stefano Olla. "Equilibrium fluctuations of asymmetric simple exclusion processes in dimension d≥3." Probability Theory and Related Fields 119, no. 3 (March 2001): 381–409. http://dx.doi.org/10.1007/pl00008764.

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19

Sethuraman, Sunder, S. R. S. Varadhan, and Horng-Tzer Yau. "Diffusive limit of a tagged particle in asymmetric simple exclusion processes." Communications on Pure and Applied Mathematics 53, no. 8 (2000): 972–1006. http://dx.doi.org/10.1002/1097-0312(200008)53:8<972::aid-cpa2>3.0.co;2-#.

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20

Wang, Yu-Qing, Rui Jiang, Qing-Song Wu, and Hai-Yi Wu. "Phase transitions in coupled exclusion processes constituted by TASEP and two-lane SEPs." Modern Physics Letters B 28, no. 08 (March 26, 2014): 1450064. http://dx.doi.org/10.1142/s021798491450064x.

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Анотація:

This paper studies the periodic one-dimensional exclusion processes constituted by totally asymmetric simple exclusion process (TASEP) and two-lane simple exclusion processes (SEP). TASEP and SEP compete with each other. Complemented by Monte Carlo simulations, mean-field analysis has been performed. Varying current splitting parameter θ, diffusivity rate D1 (or D2) and the global particle density np, we have studied phase diagrams, typical density profiles and current diagrams.

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21

XIAO, SONG, and JIN-YI BAI. "INVESTIGATION OF ASYMMETRIC SIMPLE EXCLUSION PROCESSES WITH ZONED INHOMOGENEITY AND ON-RAMP." Modern Physics Letters B 27, no. 09 (March 15, 2013): 1350062. http://dx.doi.org/10.1142/s0217984913500620.

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In this paper, theoretical analysis and extensive simulations are used to investigate asymmetric simple exclusion processes (ASEPs) with zoned inhomogeneity and on-ramp in a single-lane system. There are five possible phase diagrams with different hopping rate p and on-ramp rate q. Interestingly, the MC/MC, MC/LD and MC/HD phase can exist in the phase diagram with different hopping rate p and on-ramp rate q. When the on-ramp rate is fixed, with the decreasing of hopping rate, the HD/HD phase shrinks, it implies the heavy traffic in the system.

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22

Bryc, Włodzimierz, and Yizao Wang. "Limit fluctuations for density of asymmetric simple exclusion processes with open boundaries." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 55, no. 4 (November 2019): 2169–94. http://dx.doi.org/10.1214/18-aihp945.

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23

Xiao, Song, Shuying Wu, and Jing Shang. "Asymmetric Coupling Two-lane with Same Hopping Probabilities p Simple Exclusion Processes." Procedia Engineering 31 (2012): 941–48. http://dx.doi.org/10.1016/j.proeng.2012.01.1125.

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24

Xiao, Song, Shu-ying Wu, Dong-sheng Zheng, and Ming-zhe Liu. "Local inhomogeneity in totally asymmetric simple exclusion processes with different hopping rates." Journal of Central South University 19, no. 10 (October 2012): 3012–16. http://dx.doi.org/10.1007/s11771-012-1371-0.

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25

Xiao, Song, Ming-Zhe Liu, Jing Shang, and Hua Wang. "Theoretical investigation of total-asymmetric simple exclusion processes with attachment and detachment." Chinese Physics B 21, no. 2 (February 2012): 020514. http://dx.doi.org/10.1088/1674-1056/21/2/020514.

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26

WANG, XIONG, RUI JIANG, MAO-BIN HU, KATSUHIRO NISHINARI, and QING-SONG WU. "TOTALLY ASYMMETRIC EXCLUSION PROCESSES ON LATTICES WITH A BRANCHING POINT." International Journal of Modern Physics C 20, no. 12 (December 2009): 1999–2012. http://dx.doi.org/10.1142/s0129183109014886.

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Анотація:

We study totally asymmetric simple exclusion process (TASEP) where particles move on a single-chain lattice which diverges into two parallel lattice branches. At the branching point, the particles move to one of the two branches with equal rate r/2. The phase diagram and density profiles are investigated by using mean-field approximation and Monte Carlo simulations. It is found that the phase diagram can be classified into three regions at any value of r. However, a threshold [Formula: see text] is identified. In cases of r > rc and r < rc, the phase diagram exhibits qualitatively different phases. The analytical results are in good agreement with the results of Monte Carlo simulations.

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27

Wang, Yu-Qing, Jia-Wei Wang, and Bing-Hong Wang. "Physical mechanisms in impacts of interaction factors on totally asymmetric simple exclusion processes." International Journal of Modern Physics B 33, no. 20 (August 10, 2019): 1950217. http://dx.doi.org/10.1142/s0217979219502175.

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Анотація:

Exclusion processes are hot study issues in statistical physics and corresponding complex systems. Among fruitful exclusion processes, totally asymmetric simple exclusion process (namely, TASEP) attracts much attention due to its insight physical mechanisms in understanding such nonequilibrium dynamical processes. However, interactions among isolated TASEP are the core of controlling the dynamics of multiple TASEPs that are composed of a certain amount of isolated one-dimensional TASEP. Different from previous researches, the interaction factor is focused on the critical characteristic parameter used to depict the interaction intensity of these components of TASEPs. In this paper, a much weaker constraint condition [Formula: see text] is derived as the analytical expression of interaction factor. Self-propelled particles in the subsystem [Formula: see text] of multiple TASEPs can perform hopping forward at [Formula: see text], moving into the target site of the (i − 1)th TASEP channel at [Formula: see text] or updating into the (i + 1)th TASEP channel at [Formula: see text]. The comparison of this proposed interaction factor and other previous factors is performed by investigating the computational efficiency of obtaining analytical solutions and simulation ones of order parameters of the proposed TASEP system. Obtained exact solutions are observed to match well with Monte Carlo simulations. This research attempts to have a more comprehensive interpretation of physical mechanisms in the impact of interaction factors on TASEPs, especially corresponding to stochastic dynamics of self-propelled particles in such complex statistical dynamical systems.

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28

Yuan, Yao-Ming, Rui Jiang, Ruili Wang, Qing-Song Wu, and Jin-Qiu Zhang. "Spontaneous symmetry breaking in totally asymmetric simple exclusion processes on two intersected lattices." Journal of Physics A: Mathematical and Theoretical 41, no. 3 (January 4, 2008): 035003. http://dx.doi.org/10.1088/1751-8113/41/3/035003.

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29

Xiao, Song, Mingzhe Liu, and Jiu-ju Cai. "Asymmetric coupling in two-lane simple exclusion processes: Effect of unequal injection rates." Physics Letters A 374, no. 1 (December 2009): 8–12. http://dx.doi.org/10.1016/j.physleta.2009.10.022.

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30

Yang, Xian-Qing, Kang Qiu, Wei Zhang, Lin Ren, Wen-Tao Xu, and You-Jin Deng. "Effects of detachment and size of particles in totally asymmetric simple exclusion processes." Physica A: Statistical Mechanics and its Applications 379, no. 2 (June 2007): 595–606. http://dx.doi.org/10.1016/j.physa.2007.01.007.

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31

Wang, Ruili, Mingzhe Liu, and Rui Jiang. "Local inhomogeneity in two-lane asymmetric simple exclusion processes coupled with Langmuir kinetics." Physica A: Statistical Mechanics and its Applications 387, no. 2-3 (January 2008): 457–66. http://dx.doi.org/10.1016/j.physa.2007.09.042.

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32

Wang, Ya Fei, Bing Qi Liu, Gang Yang, and Xu Cao. "Zoned Inhomogeneity in Asymmetric Exclusion Processes with Random Update and Off-Ramp." Advanced Materials Research 1049-1050 (October 2014): 1586–94. http://dx.doi.org/10.4028/www.scientific.net/amr.1049-1050.1586.

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Анотація:

In this letter, we investigate asymmetric simple exclusion processes (ASEPs) with zoned inhomogeneity and off-ramp by the means of theoretical analysis and simulations. According to the theoretical analysis, we can find that the phase diagrams existing in this one-lane system varies with different hopping rate p and off-ramp rate q and the condition for p<0.5 and p>0.5 is distinctly different . It should be noticed that LD/LD, LD/HD and MC/HD can exist in this system no matter how hopping rate p and off-ramp rate q change.

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33

Sun, Xiaoyan, Yanbo Xie, Zhiwei He, and Binghong Wang. "Shocks induced by junctions in totally asymmetric simple exclusion processes under periodic boundary condition." Physics Letters A 375, no. 28-29 (July 2011): 2699–703. http://dx.doi.org/10.1016/j.physleta.2011.06.007.

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34

Liu, Ming-Zhe, Shao-Da Li, and Wang Rui-Li. "Asymmetric simple exclusion processes with complex lattice geometries: A review of models and phenomena." Chinese Physics B 21, no. 9 (September 2012): 090510. http://dx.doi.org/10.1088/1674-1056/21/9/090510.

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35

Xiao, Song, Xiao-Yu Chen, and Yan-Na Liu. "Asymmetric Coupling in Two-Lane Asymmetric Simple Exclusion Processes with Unequal Injection Rates: Effect of Different Hoping Rates." Communications in Theoretical Physics 63, no. 5 (May 1, 2015): 581–87. http://dx.doi.org/10.1088/0253-6102/63/5/581.

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36

XIAO, SONG, JIU-JU CAI, FEI LIU, and MINGZHE LIU. "THEORETICAL INVESTIGATION OF SYNCHRONOUS TOTALLY ASYMMETRIC EXCLUSION PROCESSES ON LATTICES WITH A SHORTCUT." International Journal of Modern Physics B 24, no. 28 (November 10, 2010): 5539–46. http://dx.doi.org/10.1142/s021797921005689x.

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Анотація:

In this paper, a synchronous totally asymmetric simple exclusion process (TASEP) with a shortcut under open boundary conditions is investigated. The shortcut is located in the bulk and characterized by shortcut probability q. The phase diagram and density profiles of the model are obtained. It is found that the phase diagram of the model includes three regions, similar to the normal synchronous TASEP. Interestingly, the phase diagram does not change with q. Monte Carlo simulations are used to obtain the bulk density of different phases and they are in good agreement with the approximate stationary state solutions of the model.

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37

Landim, C., S. Olla, and H. T. Yau. "First-order correction for the hydrodynamic limit of asymmetric simple exclusion processes in dimensiond ? 3." Communications on Pure and Applied Mathematics 50, no. 2 (February 1997): 149–203. http://dx.doi.org/10.1002/(sici)1097-0312(199702)50:2<149::aid-cpa2>3.0.co;2-c.

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38

Srinivasan, Rengarajan. "Stochastic comparisons of density profiles for the road-hog process." Journal of Applied Probability 28, no. 4 (December 1991): 852–63. http://dx.doi.org/10.2307/3214688.

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Анотація:

We consider the asymmetric simple exclusion process which starts from a product measure such that all the sites to the left of zero (including zero) are occupied and the right of 0 (excluding 0) are empty. We label the particle initially at 0 as the leading particle. We study the long-term behaviour of this process near large sites when the leading particle's holding time is different from that of the other particles. In particular, we assume that the leading particle moves at a slower rate than the other particles. We call this modified asymmetric simple exclusion process the road-hog process. Coupling and stochastic ordering techniques are used to derive the density profile of this process. Road-hog processes are useful in modelling series of exponential queues with Poisson and non-Poisson input process. The density profiles dramatically illustrate the flow of customers through the queues.

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39

Srinivasan, Rengarajan. "Stochastic comparisons of density profiles for the road-hog process." Journal of Applied Probability 28, no. 04 (December 1991): 852–63. http://dx.doi.org/10.1017/s0021900200042765.

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Анотація:

We consider the asymmetric simple exclusion process which starts from a product measure such that all the sites to the left of zero (including zero) are occupied and the right of 0 (excluding 0) are empty. We label the particle initially at 0 as the leading particle. We study the long-term behaviour of this process near large sites when the leading particle's holding time is different from that of the other particles. In particular, we assume that the leading particle moves at a slower rate than the other particles. We call this modified asymmetric simple exclusion process the road-hog process. Coupling and stochastic ordering techniques are used to derive the density profile of this process. Road-hog processes are useful in modelling series of exponential queues with Poisson and non-Poisson input process. The density profiles dramatically illustrate the flow of customers through the queues.

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40

Tian, Bo, Ping Xia, Li Liu, Meng-Ran Wu, and Shu-Yong Guo. "Existence of spontaneous symmetry breaking in two-lane totally asymmetric simple exclusion processes with an intersection." Chinese Physics B 29, no. 5 (May 2020): 050505. http://dx.doi.org/10.1088/1674-1056/ab820e.

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41

Goldman, Carla, and Elisa T. Sena. "The dynamics of cargo driven by molecular motors in the context of asymmetric simple exclusion processes." Physica A: Statistical Mechanics and its Applications 388, no. 17 (September 2009): 3455–64. http://dx.doi.org/10.1016/j.physa.2009.04.038.

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42

Liu, Yanna, Wencan Xiao, Peng Dong, Yingjie Zhang, and Song Xiao. "The effect of single on-ramp with constrained resources on the density of asymmetric simple exclusion processes." Renewable and Sustainable Energy Reviews 62 (September 2016): 815–20. http://dx.doi.org/10.1016/j.rser.2016.05.038.

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43

Wang, Yu-Qing, Rui Jiang, Qing-Song Wu, and Hai-Yi Wu. "Phase transitions in three-lane TASEPs with weak coupling." Modern Physics Letters B 28, no. 15 (June 17, 2014): 1450123. http://dx.doi.org/10.1142/s0217984914501231.

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Анотація:

This paper studies three-lane totally asymmetric simple exclusion processes (TASEP) with weak coupling under open boundary conditions. Here, particles can hop along each lane or hop to the adjacent lane. Besides, the lane-changing rates are inversely proportional to the system size L. Complemented by Monte Carlo simulations, mean-field analysis has been performed. The phase diagrams, density profiles and current profiles have been calculated. Moreover, the bulk-induced shock has been found in the system.

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44

Tian, Bo, Rui Jiang, Mao-Bin Hu, Zhong-Jun Ding, and Bin Jia. "Cluster mean field analysis of spontaneous symmetry breaking in totally asymmetric simple exclusion processes on two intersected lattices." Physica A: Statistical Mechanics and its Applications 541 (March 2020): 123542. http://dx.doi.org/10.1016/j.physa.2019.123542.

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45

WANG, RUILI, RUI JIANG, MINGZHE LIU, JIMING LIU, and QING-SONG WU. "EFFECTS OF LANGMUIR KINETICS ON TWO-LANE TOTALLY ASYMMETRIC EXCLUSION PROCESSES OF MOLECULAR MOTOR TRAFFIC." International Journal of Modern Physics C 18, no. 09 (September 2007): 1483–96. http://dx.doi.org/10.1142/s0129183107011479.

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Анотація:

In this paper, we study a two-lane totally asymmetric simple exclusion process (TASEP) coupled with random attachment and detachment of particles (Langmuir kinetics) in both lanes under open boundary conditions. Our model can describe the directed motion of molecular motors, attachment and detachment of motors, and free inter-lane transition of motors between filaments. In this paper, we focus on some finite-size effects of the system because normally the sizes of most real systems are finite and small (e.g., size ≤ 10 000). A special finite-size effect of the two-lane system has been observed, which is that the density wall moves left first and then move towards the right with the increase of the lane-changing rate. We called it the jumping effect. We find that increasing attachment and detachment rates will weaken the jumping effect. We also confirmed that when the size of the two-lane system is large enough, the jumping effect disappears, and the two-lane system has a similar density profile to a single-lane TASEP coupled with Langmuir kinetics. Increasing lane-changing rates has little effect on density profiles after the density reaches maximum. Also, lane-changing rate has no effect on density profiles of a two-lane TASEP coupled with Langmuir kinetics at a large attachment/detachment rate and/or a large system size. Mean-field approximation is presented and it agrees with our Monte Carlo simulations.

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46

Song, Minghua, and Yunxin Zhang. "Mean-field analysis of two-species totally asymmetric simple exclusion process (TASEP) with attachment and detachment." Canadian Journal of Physics 95, no. 4 (April 2017): 370–80. http://dx.doi.org/10.1139/cjp-2016-0644.

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Анотація:

In the field of statistical physics, unidirectional motion of a large number of particles along a single track can be described by totally asymmetric simple exclusion process (TASEP), from which many meaningful properties, such as the appearance of domain wall (defined as the borderline of high particle density and low particle density along the motion track) and boundary layers, can be obtained. However, it is biologically general that a single track may be occupied by different particle species. For example, in cells each microtubule protofilament is usually occupied by different species of motor protein. So previous studies about TASEP that included only one particle species may not be reasonable enough to describe more detailed properties of particle motion processes in a real cell environment. To address this problem, TASEP including two particle species is discussed in this study. Theoretical methods to get particle densities of each species are provided. By which, phase transition related properties of particle densities are obtained. Our analysis shows that domain wall and boundary layers of single species densities always appear simultaneously with those of the total particle density. The height of the domain wall of total particle density is equal to the summation of those of single particle species. Phase diagrams for typical model parameters are also presented. The methods presented in this study can be generalized to analyze TASEP with more particle species.

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47

Wang, Yu-Qing, Jia-Wei Wang, Zi-Ang Zhu, and Bing-Hong Wang. "Stochastic dynamics in nonequilibrium phase transitions of multiple totally asymmetric simple exclusion processes coupled with strong and weak interacting effects." International Journal of Modern Physics B 33, no. 20 (August 10, 2019): 1950229. http://dx.doi.org/10.1142/s0217979219502291.

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Анотація:

Totally asymmetric simple exclusion process (TASEP) is an important stochastic dynamic process in the area of statistical physics, which can be used to model microscopic transport in nonequilibrium processes. Due to its rich stochastic dynamics and nonequilibrium phase transition mechanisms, the importance of TASEP in statistical physics is similar with that of Ising model, which has attracted many attentions. In this paper, multiple TASEPs are introduced and coupled with various strong and weak interacting effects of self-driven particles. Both strong and weak couplings are calculated by means of mean-field analyses and Monte Carlo simulations. Tremendous cluster dynamics, evolution law of topological structures of phase diagrams and mechanisms of shock evolution are found in thermodynamic limit of proposed particle system. Monte Carlo simulation results like phase boundaries are found to be a good match with mean-field analyses, which reflect the validity of the research. The research work will be conducive to exploring the mechanisms of stochastic dynamics in the process of nonequilibrium phase transitions of multi-body interacting particle systems.

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48

CORWIN, IVAN. "THE KARDAR–PARISI–ZHANG EQUATION AND UNIVERSALITY CLASS." Random Matrices: Theory and Applications 01, no. 01 (January 2012): 1130001. http://dx.doi.org/10.1142/s2010326311300014.

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Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or regularity) and expanding the breadth of its universality class. Over the past 25 years a new universality class has emerged to describe a host of important physical and probabilistic models (including one-dimensional interface growth processes, interacting particle systems and polymers in random environments) which display characteristic, though unusual, scalings and new statistics. This class is called the Kardar–Parisi–Zhang (KPZ) universality class and underlying it is, again, a continuum object — a non-linear stochastic partial differential equation — known as the KPZ equation. The purpose of this survey is to explain the context for, as well as the content of a number of mathematical breakthroughs which have culminated in the derivation of the exact formula for the distribution function of the KPZ equation started with narrow wedge initial data. In particular we emphasize three topics: (1) The approximation of the KPZ equation through the weakly asymmetric simple exclusion process; (2) The derivation of the exact one-point distribution of the solution to the KPZ equation with narrow wedge initial data; (3) Connections with directed polymers in random media. As the purpose of this article is to survey and review, we make precise statements but provide only heuristic arguments with indications of the technical complexities necessary to make such arguments mathematically rigorous.

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49

HUANG, DING-WEI. "COMPLETE TRAFFIC PATTERNS AROUND A T-SHAPED INTERSECTION." International Journal of Modern Physics C 21, no. 02 (February 2010): 189–204. http://dx.doi.org/10.1142/s0129183110015063.

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We propose Asymmetric Simple Exclusion Processes to analyze the traffic states around a T-shaped intersection. The system consists of six roadways connected by the intersection. There are nine control-parameters separated into three categories: injection αi, removal βi, and turning Pi, (where i = 1, 2, 3). As these nine parameters change, traffic states on each roadway reveal a two-phase transition: free flow (F) and jam (J). Together, there can be 64 (=26) possible combinations for the traffic phases. We observe 63 distinct phases. We analyze three major causes of congestion: (1) increase of traffic demand simulated by injection αi; (2) decrease of roadway capacity simulated by removal βi; (3) redistribution of traffic pattern simulated by turning Pi. In case (1), congestion can be confined to the roadways heading toward the intersection. In case (2), spillovers can be observed and congestion will pervade the whole system. In case (3), congestion can be triggered by both increasing Pi and decreasing Pi. The phase diagram can be a convenient tool to summarize the results of numerical simulations. We also compare the unsignalized intersection to an intersection regulated by traffic signals. We find that the operation of traffic signals is very inefficient in resolving the congestion around a T-shaped intersection.

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50

Zarai, Yoram, Michael Margaliot, and Tamir Tuller. "Ribosome flow model with extended objects." Journal of The Royal Society Interface 14, no. 135 (October 2017): 20170128. http://dx.doi.org/10.1098/rsif.2017.0128.

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We study a deterministic mechanistic model for the flow of ribosomes along the mRNA molecule, called the ribosome flow model with extended objects (RFMEO). This model encapsulates many realistic features of translation including non-homogeneous transition rates along mRNA, the fact that every ribosome covers several codons, and the fact that ribosomes cannot overtake one another. The RFMEO is a mean-field approximation of an important model from statistical mechanics called the totally asymmetric simple exclusion process with extended objects (TASEPEO). We demonstrate that the RFMEO describes biophysical aspects of translation better than previous mean-field approximations, and that its predictions correlate well with those of TASEPEO. However, unlike TASEPEO, the RFMEO is amenable to rigorous analysis using tools from systems and control theory. We show that the ribosome density profile along the mRNA in the RFMEO converges to a unique steady-state density that depends on the length of the mRNA, the transition rates along it, and the number of codons covered by every ribosome, but not on the initial density of ribosomes along the mRNA. In particular, the protein production rate also converges to a unique steady state. Furthermore, if the transition rates along the mRNA are periodic with a common period T then the ribosome density along the mRNA and the protein production rate converge to a unique periodic pattern with period T , that is, the model entrains to periodic excitations in the transition rates. Analysis and simulations of the RFMEO demonstrate several counterintuitive results. For example, increasing the ribosome footprint may sometimes lead to an increase in the production rate. Also, for large values of the footprint the steady-state density along the mRNA may be quite complex (e.g. with quasi-periodic patterns) even for relatively simple (and non-periodic) transition rates along the mRNA. This implies that inferring the transition rates from the ribosome density may be non-trivial. We believe that the RFMEO could be useful for modelling, understanding and re-engineering translation as well as other important biological processes.

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