In this paper we use theoretical analysis and extensive simulations to study zone inhomogeneity with the random asymmetric simple exclusion process （ASEP）. In the inhomogeneous zone, the hopping probability is less ...In this paper we use theoretical analysis and extensive simulations to study zone inhomogeneity with the random asymmetric simple exclusion process （ASEP）. In the inhomogeneous zone, the hopping probability is less than 1. Two typical lattice geometries are investigated here. In case A, the lattice includes two equal segments. The hopping probability in the left segment is equal to 1, and in the right segment it is equal to p, which is less than 1. In case B, there are three equal segments in the system; the hopping probabilities in the left and right segments are equal to 1, and in the middle segment it is equal to p, which is less than 1. Through theoretical analysis, we can discover the effect on these systems when p is changed.展开更多
Local inhomogeneity in totally asymmetric simple exclusion processes （TASEPs） with different hopping rates was studied. Many biological and chemical phenomena can be described by these non-equilibrium processes. A s...Local inhomogeneity in totally asymmetric simple exclusion processes （TASEPs） with different hopping rates was studied. Many biological and chemical phenomena can be described by these non-equilibrium processes. A simple approximate theory and extensive Monte Carlo computer simulations were used to calculate the steady-state phase diagrams and bulk densities. It is found that the phase diagram for local inhomogeneity in TASEP with different hopping rates p is qualitatively similar to homogeneous models. Interestingly, there is a saturation point pair （a＊, fl＊） for the system, which is decided by parameters p and q. There are three stationary phases in the system, when parameter p is fixed （i.e., p=0.8）, with the increase of the parameter q, the region of LD/LD and HD/HD phase increases and the HD/LD is the only phase which the region shrinks. The analytical results are in good agreement with simulations.展开更多
In this paper, the effects of unequal injection rates and different hopping rates on the asymmetric simple exclusion process （ASEP） with a 2-input 1-output junction are studied by using a simple mean-field approach ...In this paper, the effects of unequal injection rates and different hopping rates on the asymmetric simple exclusion process （ASEP） with a 2-input 1-output junction are studied by using a simple mean-field approach and extensive computer simulations. The steady-state particle currents, the density profiles, and the phase diagrams are obtained. It is shown that with unequal injection rates and different hopping rates, the phase diagram structure is qualitatively changed. The theoretical calculations are in good agreement with Monte Carlo simulations.展开更多
In this paper, we investigate the effect of unequal injection rates on totally asymmetric simple exclusion processes （TASEPs） with a 2-input 1-output junction and parallel update. A mean-field approach is developed ...In this paper, we investigate the effect of unequal injection rates on totally asymmetric simple exclusion processes （TASEPs） with a 2-input 1-output junction and parallel update. A mean-field approach is developed to deal with the junction that connects two sub-chains and the single main chain. We obtain the stationary particle currents, density profiles and phase diagrams. Interestingly, we find that the number of stationary-state phases is changeable depending on the value of a1 （a1 is the injection rate on the first sub-chain）. When a1 〉 1/3, there are seven stationary-state phases in the system, however when a1 〈 1/3, only six stationary-state phases exist in the system. The theoretical calculations are shown to be in agreement with Monte Carlo simulations.展开更多
We study two-lane totally asymmetric simple exclusion processes(TASEPs)with an intersection.Monte Carlo simulations show that only symmetric phases exist in the system.To verify the existence of asymmetric phases,we c...We study two-lane totally asymmetric simple exclusion processes(TASEPs)with an intersection.Monte Carlo simulations show that only symmetric phases exist in the system.To verify the existence of asymmetric phases,we carry out a cluster mean-field analysis.Analytical results show that the densities of the two upstream segments of the intersection site are always equal,which indicates that the system is not in asymmetric phases.It demonstrates that the spontaneous symmetry breaking does not exist in the system.The density profiles and the boundaries of the symmetric phases are also investigated.We find that the cluster mean-field analysis shows better agreement with simulations than the simple mean-field analysis where the correlation of sites is ignored.展开更多
We study the one-dimensional asymmetric simple exclusion process （ASEP） with generic open boundaries （in- cluding current-counting deformation）, and obtain the exact solutions of this ASEP via the off-diagonal Bet...We study the one-dimensional asymmetric simple exclusion process （ASEP） with generic open boundaries （in- cluding current-counting deformation）, and obtain the exact solutions of this ASEP via the off-diagonal Bethe ansatz method. In particular, numerical results for the small size asymmetric simple exclusion process indicate that the spectrum obtained by the Bethe ansatz equations is complete. Moreover, we present the eigenvalue of the totally asymmetric exclusion process and the corresponding Bethe ansatz equations.展开更多
This paper investigates the effect of both unequal injection rates and different hopping rates on two-lane asymmetric simple exclusion processes(ASEPs) with asymmetric coupling. When the hopping rates of both lanes ar...This paper investigates the effect of both unequal injection rates and different hopping rates on two-lane asymmetric simple exclusion processes(ASEPs) with asymmetric coupling. When the hopping rates of both lanes are different, the system includes six steady phases, however, when the hopping rates of both lanes are same, the seventh phase(MC, MC) will exist in the system. Interestingly, with different hopping rates of both lanes, the densities of the system cannot be influenced by the non-zero vertical transition rate. Our theoretical arguments are in well agreement with extensively performed Monte Carlo simulations.展开更多
This paper uses various mean-field approaches and the Monte Carlo simulation to calculate asymmetric simple exclusion processes with particles of arbitrary size in the successive defects system. In this system, the ho...This paper uses various mean-field approaches and the Monte Carlo simulation to calculate asymmetric simple exclusion processes with particles of arbitrary size in the successive defects system. In this system, the hopping probability p （p 〈 1） and the size d of particles are not constant, Through theoretical calculation and computer simulation, it obtains the exact theoretical results and finds that the theoretical results are in agreement with the computer simulation. These results are helpful in analysing the effect of traffic with different hopping probabilities p and sizes d of particle.展开更多
We study an exclusion process with multiple dynamic roadblocks.Each roadblock can move diffusively forward or backward with different rates,as well as unbind from/rebind to a free site.By Monte Carlo simulations,the t...We study an exclusion process with multiple dynamic roadblocks.Each roadblock can move diffusively forward or backward with different rates,as well as unbind from/rebind to a free site.By Monte Carlo simulations,the two moving types are investigated in combination of roadblock number.The case of only diffusive roadblocks shows an asymmetric current-density relation.The case of only long-range jumping roadblocks presents that flux decreases with increasing roadblock number.展开更多
Totally asymmetric exclusion processes at constrained m-input n-output junction points under random update are studied by theoretical calculation and computer simulation in this paper. At the junction points, the hopp...Totally asymmetric exclusion processes at constrained m-input n-output junction points under random update are studied by theoretical calculation and computer simulation in this paper. At the junction points, the hopping rate of particles from m-input parallel lattices to n-output parallel lattices is assumed to be equal to r/n （0 〈 r 〈 1 ）. The mean-field approach and Monte Carlo simulations show that the phase diagram can be classified into three regions at any value of r. More interestingly, there is a threshold rc = n（ 1 - √1 - m/n）/m. In the cases of r 〉 re and r 〈 rc, qualitatively different phases exist in the system. With the increase of the value of m/n, the regions of （LD, LD） and （MC, LD） or （HD, LD） decrease, and the （HD, HD） is the only phase that increases in the region （LD stands for low density, HD stands for high density, and MC for maximal current）. Stationary current and density profiles are calculated, showing that they are in good agreement with Monte Carlo simulations.展开更多
In this paper we investigate the dynamics of an asymmetric exclusion process on a one-dimensional lattice with long- range hopping and random update via Monte Carlo simulations theoretically. Particles in the model wi...In this paper we investigate the dynamics of an asymmetric exclusion process on a one-dimensional lattice with long- range hopping and random update via Monte Carlo simulations theoretically. Particles in the model will firstly try to hop over successive unoccupied sites with a probability q, which is different from previous exclusion process models. The probability q may represent the random access of particles. Numerical simulations for stationary particle currents, density profiles, and phase diagrams are obtained. There are three possible stationary phases： the low density （LD） phase, high density （HD） phase, and maximal current （MC） in the system, respectively. Interestingly, bulk density in the LD phase tends to zero, while the MC phase is governed by α,β, and q. The HD phase is nearly the same as the normal TASEP, determined by exit rate β. Theoretical analysis is in good agreement with simulation results. The proposed model may provide a better understanding of random interaction dynamics in complex systems.展开更多
Consider a generalized model of the facilitated exclusion process, which is a onedimensional exclusion process with a dynamical constraint that prevents the particle at site x from jumping to x+1 (or x-1) if the sites...Consider a generalized model of the facilitated exclusion process, which is a onedimensional exclusion process with a dynamical constraint that prevents the particle at site x from jumping to x+1 (or x-1) if the sites x-1, x-2 (or x+1, x+2) are empty. It is nongradient and lacks invariant measures of product form. The purpose of this paper is to identify the invariant measures and to show that they satisfy both exponential decay of correlations and equivalence of ensembles. These properties will play a pivotal role in deriving the hydrodynamic limit.展开更多
This paper studies two-lane asymmetric simple exclusion processes(ASEPs)with an intersection.In the upstream segments of the intersection,one particle can move to the next site with rate 1 if the site is empty,and the...This paper studies two-lane asymmetric simple exclusion processes(ASEPs)with an intersection.In the upstream segments of the intersection,one particle can move to the next site with rate 1 if the site is empty,and the other particle can move forward with rate p in the sites of downstream segments.The parameter p can represent the rate of slowing of motion,and the parameter is introduced to investigate spontaneous symmetry breaking(SSB)phenomenon.Extensive Monte Carlo simulations are carried out.It is shown that three symmetric phases exist and the SSB does not exist in the system.Simple mean field approach in which correlation of sites is ignored is firstly adopted to analyze the system,and the system is divided into four independent segments.It is found that the analytical results deviate from the simulation ones,especially when p is small.In addition,the inexsitence of SSB can only be explained qualitatively.Motivated by this,we carry out the cluster mean field analysis in which correlation of five sites is considered.It is shown that densities of the two upstream segments are equal,which demonstrates that the SSB does not exist.It is also shown that,as expected,the cluster mean field analysis performs much better than the simple mean field analysis.展开更多
In this paper, traffic systems with attachment and detachment have been studied by total-asymmetric simple exclusion processes （TASEPs）. Attachment and detachment in a one-dimensional system is a type of complex geo...In this paper, traffic systems with attachment and detachment have been studied by total-asymmetric simple exclusion processes （TASEPs）. Attachment and detachment in a one-dimensional system is a type of complex geometry that is relevant to biological transport with the random update rule. The analytical results are presented and have shown good agreement with the extensive Monte Carlo computer simulations.展开更多
The exclusion process,sometimes called Kawasaki dynamics or lattice gas model,describes a system of particles moving on a discrete square lattice with an interaction governed by the exclusion rule under which at most ...The exclusion process,sometimes called Kawasaki dynamics or lattice gas model,describes a system of particles moving on a discrete square lattice with an interaction governed by the exclusion rule under which at most one particle can occupy each site.We mostly discuss the symmetric and reversible case.The weakly asymmetric case recently attracts attention related to KPZ equation;cf.Bertini and Giacomin(Commun Math Phys 183:571–607,1995)for a simple exclusion case and Gonçalves and Jara(Arch Ration Mech Anal 212:597–644,2014)for an exclusion process with speed change,see also Gonçalves et al.(Ann Probab 43:286–338,2015),Gubinelli and Perkowski(J Am Math Soc 31:427–471,2018).In Sect.1,as a warm-up,we consider a simple exclusion process and discuss its hydrodynamic limit and the corresponding fluctuation limit in a proper space–time scaling.From this model,one can derive a linear heat equation and a stochastic partial differential equation(SPDE)in the limit,respectively.Section 2 is devoted to the entropy method originally invented by Guo et al.(Commun Math Phys 118:31–59,1988).We consider the exclusion process with speed change,in which the jump rate of a particle depends on the configuration nearby the particle.This gives a non-trivial interaction among particles.We study only the case that the jump rate satisfies the so-called gradient condition.The hydrodynamic limit,which leads to a nonlinear diffusion equation,follows from the local ergodicity or the local equilibrium of the system,and this is shown by establishing one-block and twoblock estimates.We also discuss the fluctuation limit which follows by showing the so-called Boltzmann–Gibbs principle.Section 3 explains the relative entropy method originally due to Yau(Lett Math Phys 22:63–80,1991).This is a variant of GPV method and gives another proof for the hydrodynamic limit.The difference between these two methods is as follows.Let N^(d)be the volume of the domain on which the system is defined(typically,d-dimensional discrete box with side length N)and denote the(relative)entropy by H.Then,H relative to a global equilibrium behaves as H=O(N^(d))(or entropy per volume is O(1))as N→∞.GPV method rather relies on the fact that the entropy production I,which is the time derivative of H,behaves as O(N^(d−2))so that I per volume is o(1),and this characterizes the limit measures.On the other hand,Yau’s method shows H=o(Nd)for H relative to local equilibria so that the entropy per volume is o(1)and this proves the hydrodynamic limit.In Sect.4,we considerKawasaki dynamics perturbed by relatively largeGlauber effect,which allows creation and annihilation of particles.This leads to the reaction–diffusion equation in the hydrodynamic limit.We discuss especially the equation with reaction term of bistable type and the problem related to the fast reaction limit or the sharp interface limit leading to the motion by mean curvature.We apply the estimate on the relative entropy due to Jara and Menezes(Non-equilibrium fluctuations of interacting particle systems,2017;Symmetric exclusion as a random environment:invariance principle,2018),which is actually obtained as a combination of GPV and Yau’s estimates.This makes possible to study the hydrodynamic limit for microscopic systems with another diverging factors apart from that caused by the space–time scaling.展开更多
The exclusive photoproduction of vector mesons(J/ψ/andφ)is investigated by considering the next-toleading order corrections in the framework of the color glass condensate.We compare the next-to-leading order modifie...The exclusive photoproduction of vector mesons(J/ψ/andφ)is investigated by considering the next-toleading order corrections in the framework of the color glass condensate.We compare the next-to-leading order modified dipole amplitude with the HERA data,finding a good agreement.Our studies show that theχ~2/d.o.f from the leading order,running coupling,and collinearly improved next-to-leading order dipole amplitudes are 2.159,1.097,and 0.932 for the elastic cross-section,and 2.056,1.449,and 1.357 for the differential cross-section,respectively.The results indicate that the higher-order corrections contribute significantly to the vector meson productions,and the description of the experimental data is dramatically improved once the higher order corrections are included.We extend the next-to-leading order exclusive vector meson production model to LHC energies using the same parameters obtained from HERA.We find that our model provides a rather good description of the J/ψandΦdata in proton-proton collisions at 7 TeV and 13 TeV in LHCb experiments.展开更多
基金Project supported by the State Key Program for Basic Research of China (Grant No 2005CB724206)
文摘In this paper we use theoretical analysis and extensive simulations to study zone inhomogeneity with the random asymmetric simple exclusion process （ASEP）. In the inhomogeneous zone, the hopping probability is less than 1. Two typical lattice geometries are investigated here. In case A, the lattice includes two equal segments. The hopping probability in the left segment is equal to 1, and in the right segment it is equal to p, which is less than 1. In case B, there are three equal segments in the system; the hopping probabilities in the left and right segments are equal to 1, and in the middle segment it is equal to p, which is less than 1. Through theoretical analysis, we can discover the effect on these systems when p is changed.
基金Project(2011FZ050) supported by Applied Basic Research Program of Yunnan Provincial Science and Technology Department,ChinaProject(2011J084) supported by Master Program of Yunnan Province Education Department,China
文摘Local inhomogeneity in totally asymmetric simple exclusion processes （TASEPs） with different hopping rates was studied. Many biological and chemical phenomena can be described by these non-equilibrium processes. A simple approximate theory and extensive Monte Carlo computer simulations were used to calculate the steady-state phase diagrams and bulk densities. It is found that the phase diagram for local inhomogeneity in TASEP with different hopping rates p is qualitatively similar to homogeneous models. Interestingly, there is a saturation point pair （a＊, fl＊） for the system, which is decided by parameters p and q. There are three stationary phases in the system, when parameter p is fixed （i.e., p=0.8）, with the increase of the parameter q, the region of LD/LD and HD/HD phase increases and the HD/LD is the only phase which the region shrinks. The analytical results are in good agreement with simulations.
基金supported by the National Scientific and Technological Support Project,China (Grant No.2006BAE03A00)
文摘In this paper, the effects of unequal injection rates and different hopping rates on the asymmetric simple exclusion process （ASEP） with a 2-input 1-output junction are studied by using a simple mean-field approach and extensive computer simulations. The steady-state particle currents, the density profiles, and the phase diagrams are obtained. It is shown that with unequal injection rates and different hopping rates, the phase diagram structure is qualitatively changed. The theoretical calculations are in good agreement with Monte Carlo simulations.
基金Project supported by the National Scientific and Technological Support Project of China (Grant No. 2006BAE 03A 00)
文摘In this paper, we investigate the effect of unequal injection rates on totally asymmetric simple exclusion processes （TASEPs） with a 2-input 1-output junction and parallel update. A mean-field approach is developed to deal with the junction that connects two sub-chains and the single main chain. We obtain the stationary particle currents, density profiles and phase diagrams. Interestingly, we find that the number of stationary-state phases is changeable depending on the value of a1 （a1 is the injection rate on the first sub-chain）. When a1 〉 1/3, there are seven stationary-state phases in the system, however when a1 〈 1/3, only six stationary-state phases exist in the system. The theoretical calculations are shown to be in agreement with Monte Carlo simulations.
基金Project supported by the National Natural Science Foundation of China(Grant No.11802003).
文摘We study two-lane totally asymmetric simple exclusion processes(TASEPs)with an intersection.Monte Carlo simulations show that only symmetric phases exist in the system.To verify the existence of asymmetric phases,we carry out a cluster mean-field analysis.Analytical results show that the densities of the two upstream segments of the intersection site are always equal,which indicates that the system is not in asymmetric phases.It demonstrates that the spontaneous symmetry breaking does not exist in the system.The density profiles and the boundaries of the symmetric phases are also investigated.We find that the cluster mean-field analysis shows better agreement with simulations than the simple mean-field analysis where the correlation of sites is ignored.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11375141,11475135,11434013 and 11425522the Ministry of Education Doctoral Program Fund under Grant No 20126101110004the Northwest University Graduate Student Innovation Fund under Grant No YZZ14104
文摘We study the one-dimensional asymmetric simple exclusion process （ASEP） with generic open boundaries （in- cluding current-counting deformation）, and obtain the exact solutions of this ASEP via the off-diagonal Bethe ansatz method. In particular, numerical results for the small size asymmetric simple exclusion process indicate that the spectrum obtained by the Bethe ansatz equations is complete. Moreover, we present the eigenvalue of the totally asymmetric exclusion process and the corresponding Bethe ansatz equations.
基金Supported by National Natural Science Foundation of China under Grant No.21301079
文摘This paper investigates the effect of both unequal injection rates and different hopping rates on two-lane asymmetric simple exclusion processes(ASEPs) with asymmetric coupling. When the hopping rates of both lanes are different, the system includes six steady phases, however, when the hopping rates of both lanes are same, the seventh phase(MC, MC) will exist in the system. Interestingly, with different hopping rates of both lanes, the densities of the system cannot be influenced by the non-zero vertical transition rate. Our theoretical arguments are in well agreement with extensively performed Monte Carlo simulations.
基金Project supported by the National Key Fundamental Research and Development Project of China (Grant No 2005CB724206)
文摘This paper uses various mean-field approaches and the Monte Carlo simulation to calculate asymmetric simple exclusion processes with particles of arbitrary size in the successive defects system. In this system, the hopping probability p （p 〈 1） and the size d of particles are not constant, Through theoretical calculation and computer simulation, it obtains the exact theoretical results and finds that the theoretical results are in agreement with the computer simulation. These results are helpful in analysing the effect of traffic with different hopping probabilities p and sizes d of particle.
基金Project supported by the National Basic Research Program of China(Grant No.2012CB725404)the National Natural Science Foundation of China(Grant Nos.11422221,71171185,and 71371175)
文摘We study an exclusion process with multiple dynamic roadblocks.Each roadblock can move diffusively forward or backward with different rates,as well as unbind from/rebind to a free site.By Monte Carlo simulations,the two moving types are investigated in combination of roadblock number.The case of only diffusive roadblocks shows an asymmetric current-density relation.The case of only long-range jumping roadblocks presents that flux decreases with increasing roadblock number.
基金supported by the National Natural Science Foundation of China (Grant No. 41274109)the Special Fund of the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection,China (Grant No. 2011Z006)+1 种基金the Scientific and Technological Support Program of Sichuan Province,China (Grant Nos. 2013FZ0021 and 2013FZ0022)the Creative Team Program of Chengdu University of Technology,China (Grant No. KYTD201301)
文摘Totally asymmetric exclusion processes at constrained m-input n-output junction points under random update are studied by theoretical calculation and computer simulation in this paper. At the junction points, the hopping rate of particles from m-input parallel lattices to n-output parallel lattices is assumed to be equal to r/n （0 〈 r 〈 1 ）. The mean-field approach and Monte Carlo simulations show that the phase diagram can be classified into three regions at any value of r. More interestingly, there is a threshold rc = n（ 1 - √1 - m/n）/m. In the cases of r 〉 re and r 〈 rc, qualitatively different phases exist in the system. With the increase of the value of m/n, the regions of （LD, LD） and （MC, LD） or （HD, LD） decrease, and the （HD, HD） is the only phase that increases in the region （LD stands for low density, HD stands for high density, and MC for maximal current）. Stationary current and density profiles are calculated, showing that they are in good agreement with Monte Carlo simulations.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.41274109 and 11104022)the Fund for Sichuan Youth Science and Technology Innovation Research Team(Grant No.2011JTD0013)the Creative Team Program of Chengdu University of Technology
文摘In this paper we investigate the dynamics of an asymmetric exclusion process on a one-dimensional lattice with long- range hopping and random update via Monte Carlo simulations theoretically. Particles in the model will firstly try to hop over successive unoccupied sites with a probability q, which is different from previous exclusion process models. The probability q may represent the random access of particles. Numerical simulations for stationary particle currents, density profiles, and phase diagrams are obtained. There are three possible stationary phases： the low density （LD） phase, high density （HD） phase, and maximal current （MC） in the system, respectively. Interestingly, bulk density in the LD phase tends to zero, while the MC phase is governed by α,β, and q. The HD phase is nearly the same as the normal TASEP, determined by exit rate β. Theoretical analysis is in good agreement with simulation results. The proposed model may provide a better understanding of random interaction dynamics in complex systems.
基金Supported in part by the National Natural Science Foundation of China(11731012, 11871425, 12271475)Fundamental Research Funds for Central Universities grant(2020XZZX002-03)。
文摘Consider a generalized model of the facilitated exclusion process, which is a onedimensional exclusion process with a dynamical constraint that prevents the particle at site x from jumping to x+1 (or x-1) if the sites x-1, x-2 (or x+1, x+2) are empty. It is nongradient and lacks invariant measures of product form. The purpose of this paper is to identify the invariant measures and to show that they satisfy both exponential decay of correlations and equivalence of ensembles. These properties will play a pivotal role in deriving the hydrodynamic limit.
基金Project supported by the National Natural Science Foundation of China(Grant No.11802003).
文摘This paper studies two-lane asymmetric simple exclusion processes(ASEPs)with an intersection.In the upstream segments of the intersection,one particle can move to the next site with rate 1 if the site is empty,and the other particle can move forward with rate p in the sites of downstream segments.The parameter p can represent the rate of slowing of motion,and the parameter is introduced to investigate spontaneous symmetry breaking(SSB)phenomenon.Extensive Monte Carlo simulations are carried out.It is shown that three symmetric phases exist and the SSB does not exist in the system.Simple mean field approach in which correlation of sites is ignored is firstly adopted to analyze the system,and the system is divided into four independent segments.It is found that the analytical results deviate from the simulation ones,especially when p is small.In addition,the inexsitence of SSB can only be explained qualitatively.Motivated by this,we carry out the cluster mean field analysis in which correlation of five sites is considered.It is shown that densities of the two upstream segments are equal,which demonstrates that the SSB does not exist.It is also shown that,as expected,the cluster mean field analysis performs much better than the simple mean field analysis.
基金supported by the National Natural Science Foundation of China-Yunnan Union Foundation (Grant No.U0937604)
文摘In this paper, traffic systems with attachment and detachment have been studied by total-asymmetric simple exclusion processes （TASEPs）. Attachment and detachment in a one-dimensional system is a type of complex geometry that is relevant to biological transport with the random update rule. The analytical results are presented and have shown good agreement with the extensive Monte Carlo computer simulations.
文摘The exclusion process,sometimes called Kawasaki dynamics or lattice gas model,describes a system of particles moving on a discrete square lattice with an interaction governed by the exclusion rule under which at most one particle can occupy each site.We mostly discuss the symmetric and reversible case.The weakly asymmetric case recently attracts attention related to KPZ equation;cf.Bertini and Giacomin(Commun Math Phys 183:571–607,1995)for a simple exclusion case and Gonçalves and Jara(Arch Ration Mech Anal 212:597–644,2014)for an exclusion process with speed change,see also Gonçalves et al.(Ann Probab 43:286–338,2015),Gubinelli and Perkowski(J Am Math Soc 31:427–471,2018).In Sect.1,as a warm-up,we consider a simple exclusion process and discuss its hydrodynamic limit and the corresponding fluctuation limit in a proper space–time scaling.From this model,one can derive a linear heat equation and a stochastic partial differential equation(SPDE)in the limit,respectively.Section 2 is devoted to the entropy method originally invented by Guo et al.(Commun Math Phys 118:31–59,1988).We consider the exclusion process with speed change,in which the jump rate of a particle depends on the configuration nearby the particle.This gives a non-trivial interaction among particles.We study only the case that the jump rate satisfies the so-called gradient condition.The hydrodynamic limit,which leads to a nonlinear diffusion equation,follows from the local ergodicity or the local equilibrium of the system,and this is shown by establishing one-block and twoblock estimates.We also discuss the fluctuation limit which follows by showing the so-called Boltzmann–Gibbs principle.Section 3 explains the relative entropy method originally due to Yau(Lett Math Phys 22:63–80,1991).This is a variant of GPV method and gives another proof for the hydrodynamic limit.The difference between these two methods is as follows.Let N^(d)be the volume of the domain on which the system is defined(typically,d-dimensional discrete box with side length N)and denote the(relative)entropy by H.Then,H relative to a global equilibrium behaves as H=O(N^(d))(or entropy per volume is O(1))as N→∞.GPV method rather relies on the fact that the entropy production I,which is the time derivative of H,behaves as O(N^(d−2))so that I per volume is o(1),and this characterizes the limit measures.On the other hand,Yau’s method shows H=o(Nd)for H relative to local equilibria so that the entropy per volume is o(1)and this proves the hydrodynamic limit.In Sect.4,we considerKawasaki dynamics perturbed by relatively largeGlauber effect,which allows creation and annihilation of particles.This leads to the reaction–diffusion equation in the hydrodynamic limit.We discuss especially the equation with reaction term of bistable type and the problem related to the fast reaction limit or the sharp interface limit leading to the motion by mean curvature.We apply the estimate on the relative entropy due to Jara and Menezes(Non-equilibrium fluctuations of interacting particle systems,2017;Symmetric exclusion as a random environment:invariance principle,2018),which is actually obtained as a combination of GPV and Yau’s estimates.This makes possible to study the hydrodynamic limit for microscopic systems with another diverging factors apart from that caused by the space–time scaling.
基金Supported by the National Natural Science Foundation of China(11765005,11947119,11305040,11847152,11775097)the Fund of Science and Technology Department of Guizhou Province([2018]1023,[2019]5653)+3 种基金the Education Department of Guizhou Province(KY[2017]004)Qian Kehe Platform Talents([2017]5736-027)the National key research and development program of China(2018YFE0104700,CCNU18ZDPY04)the 2018 scientific research startup foundation for the introduced talent of Guizhou University of Finance and Economics(2018YJ60)。
文摘The exclusive photoproduction of vector mesons(J/ψ/andφ)is investigated by considering the next-toleading order corrections in the framework of the color glass condensate.We compare the next-to-leading order modified dipole amplitude with the HERA data,finding a good agreement.Our studies show that theχ~2/d.o.f from the leading order,running coupling,and collinearly improved next-to-leading order dipole amplitudes are 2.159,1.097,and 0.932 for the elastic cross-section,and 2.056,1.449,and 1.357 for the differential cross-section,respectively.The results indicate that the higher-order corrections contribute significantly to the vector meson productions,and the description of the experimental data is dramatically improved once the higher order corrections are included.We extend the next-to-leading order exclusive vector meson production model to LHC energies using the same parameters obtained from HERA.We find that our model provides a rather good description of the J/ψandΦdata in proton-proton collisions at 7 TeV and 13 TeV in LHCb experiments.
