exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

exact solution and asymptotic behaviour of the asymmetric simple exclusion process on a ring in this paper we study an exact solution of the asymmetric simple exclusion process on a periodic lattice of finite sites with two typical updates i e random and parallel then we find that the explicit formulae for the partition function and the average velocity are expressed by the gauss hypergeometric function in order to obtain these results we effectively exploit the recursion formula for the partition function for the zero range process the zero range process corresponds to the asymmetric simple exclusion process if one chooses the relevant hop rates of particles and the recursion gives the partition function in principle for any finite system size moreover we reveal the asymptotic behaviour of the average velocity in the thermodynamic limit expanding the formula as a series in system size

the asymmetric exclusion process and brownian excursions we consider the totally asymmetric exclusion process tasep in one dimension in its maximal current phase we show by an exact calculation that the non gaussian part of the fluctuations of density can be described in terms of the statistical properties of a brownian excursion numerical simulations indicate that the description in terms of a brownian excursion remains valid for more general one dimensional driven systems in their maximal current phase

understanding the edge effect in tasep with mean field theoretic approaches we study a totally asymmetric simple exclusion process tasep with one defect site hopping rate q 1 near the system boundary regarding our system as a pair of uniform tasep s coupled through the defect we study various methods to match a finite tasep and an infinite one across a common boundary several approximation schemes are investigated utilizing the finite segment mean field fsmf method we set up a framework for computing the steady state current j as a function of the entry rate and q for the case where the defect is located at the entry site we obtain an analytical expression for j q which is in good agreement with monte carlo simulation results when the defect is located deeper in the bulk we refined the scheme of macdonald et al 1968 biopolymers 6 1 and find reasonably good fits to the density profiles before the defect site we discuss the strengths and limitations of each method as well as possible avenues for further studies

phase transitions in an exactly soluble one dimensional exclusion process we consider an exclusion process with particles injected with rate at the origin and removed with rate at the right boundary of a one dimensional chain of sites the particles are allowed to hop onto unoccupied sites to the right only for the special case of 1 the model was solved previously by derridaet al here we extend the solution to general the phase diagram obtained from our exact solution differs from the one predicted by the mean field approximation

totally asymmetric exclusion processes with particles of arbitrary size the steady state currents and densities of a one dimensional totally asymmetric exclusion process tasep with particles that occlude an integer number d of lattice sites are computed using various mean field approximations and monte carlo simulations taseps featuring particles of arbitrary size are relevant for modelling systems such as mrna translation vesicle locomotion along microtubules and protein sliding along dna we conjecture that the nonequilibrium steady state properties separate into low density high density and maximal current phases similar to those of the standard d 1 tasep a simple mean field approximation for steady state particle currents and densities is found to be inaccurate however we find local equilibrium particle distributions derived from a discrete tonks gas partition function yield apparently exact currents within the maximal current phase for the boundary limited phases the equilibrium tonks gas distribution cannot be used to predict currents phase boundaries or the order of the phase transitions however we employ a refined mean field approach to find apparently exact expressions for the steady state currents boundary densities and phase diagrams of the d 1 tasep extensive monte carlo simulations are performed to support our analytic mean field results

probabilistic analysis of a generalized bin packing problem and applications we give a unified probabilistic analysis for a general class of bin packing problems by directly analyzing corresponding mathematical programs in this general class of packing problems objects are described by a given number of attribute values some attributes may be discrete others may be continuous bins are sets of objects and the collection of feasible bins is merely required to satisfy some general consistency properties we characterize the asymptotic optimal value as the value of an easily specified linear program whose size is independent of the number of objects to be packed or as the limit of a sequence of such linear program values we also provide bounds for the rate of convergence of the average cost to its asymptotic value the analysis suggests an a s asymptotically optimal heuristic that runs in linear time the heuristics can be designed to be asymptotically optimal while still running in polynomial time we also show that in several important cases the algorithm has both po

the convergence of euler products abstract an interpretation of the euler product is made in the theory of certain hilbert spaces whose elements are entire functions the main results are stated for those dirichlet zeta functions which are associated with nonprincipal characters but they apply also in modified form to the classical zeta function which is associated with a principal character

prolate spheroidal wave functions sonine spaces and the riemann zeta function abstract in this paper we study underlying spaces associated with a connes trace formula see connes 1999 3 li 2010 14 in particular the explicit formula in the theory of prime numbers is expressed as the trace of an operator acting on a hilbert space which is a direct sum of a sonine space the space of prolate spheroidal wave functions and a variant of the space of prolate spheroidal wave functions a formula is obtained for the orthogonal projection of the hilbert space onto the sonine space a base is given for the variant space of the space of prolate spheroidal wave functions

totally asymmetric simple exclusion process with a shortcut in this paper we study the interplay of a totally asymmetric simple exclusion process tasep with a shortcut in its bulk under open boundary conditions two different models are introduced i model a for molecular motor motion and ii model b for vehicular traffic the phase diagrams and density profiles of both models are studied it is found that although the phase diagrams of both models can be classified into three regions the phases corresponding to these regions and the phase boundaries between these regions are quite different in these two models moreover the approximate stationary state solutions of model a have been carried out and it is shown that the analytical results are in good agreement with the results of monte carlo simulations

twenty five years after kls a celebration of non equilibrium statistical mechanics when lenz proposed a simple model for phase transitions in magnetism he couldn t have imagined that the ising model was to become a jewel in field of equilibrium statistical mechanics its role spans the spectrum from a good pedagogical example to a universality class in critical phenomena a quarter century ago katz lebowitz and spohn found a similar treasure by introducing a seemingly trivial modification to the ising lattice gas they took it into the vast realms of non equilibrium statistical mechanics an abundant variety of unexpected behavior emerged and caught many of us by surprise we present a brief review of some of the new insights garnered and some of the outstanding puzzles as well as speculate on the model s role in the future of non equilibrium statistical physics

exact solution of a cellular automaton for traffic we present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions e g cars can enter and leave a part of a highway with certain probabilities the model studied is the asymmetric exclusion process asep with simultaneous updating of all sites it is equivalent to a special case vmax 1 of the nagel schreckenberg model for highway traffic which has found many applications in real time traffic simulations the simultaneous updating induces additional strong short range correlations compared to other updating schemes the stationary state is written in terms of a matrix product solution the corresponding algebra which expresses a system size recursion relation for the weights of the configurations is quartic in contrast to previous cases in which the algebra is quadratic we derive the phase diagram and compute various properties such as density profiles two point functions and the fluctuations in the number of particles cars in the system the current and the density profiles can be mapped onto the asep with other time discrete updating procedures through use of this mapping our results also give new results for these models

analytic approach to the critical density in cellular automata for traffic flow the jamming transition in the stochastic traffic cellular automaton of nagel and schreckenberg j phys i 2 2221 1992 is examined we argue that most features of the transition found in the deterministic limit do not persist in the presence of noise and suggest instead to define the transition to take place at that critical density ensuremath rho c at which a large initial jam just fails to dissolve we show that ensuremath rho c v j v j v f where v f is the velocity of noninteracting vehicles and v j is the speed of the dissolution wave moving into the jam an approximate analytic calculation of v j in the framework of a simple renormalization scheme is presented which explicitly displays the effect of the interaction between vehicles during the acceleration stage of the nagel schreckenberg rules with maximum velocity v mathrm max g1 the analytic prediction is compared to numerical simulations we find a remarkable correspondence between the analytic expression for v j and a phase diagram obtained numerically by l ubeck et al phys rev e 57 1171 1998

application of cellular automata modeling to seismic elastodynamics abstract this article details application of a physics based cellular automata ca computational approach to model seismic events in an idealized linear elastic medium application of rectangular celled ca to the seismic problem is shown to yield discrete equations equivalent to the centered difference finite difference fd approach however it is emphasized that the discrete equations are arrived at from the bottom up using local rules vice top down discretization of global partial differential equations a further distinction between the two methods concerns the location of stresses and its impact on boundary conditions the ca approach assigns stresses to the cell faces while the fd approach assigns stress collocated with displacement components at a single node these differences may provide important perspective on modeling arbitrary geometry with a finite difference like approach based on cell assembly similar to finite element analysis implementation of the ca paradigm using autonomous local cells fits naturally with object oriented programming practices and lends itself readily to distributed computing results are provided for an example ground shock simulation in which a differentiated gaussian pulse acts on the surface of a linear elastic half space the ca perspective suggests a simple treatment for the free surface boundary condition comparison of the computed pressure shear and surface waves to those computed using a staggered grid finite difference approach demonstrates very good agreement in addition the simulation results suggest that the ca approach may exhibit less ringing as waves pass and more symmetry in left ward and right ward moving waves future directions exploiting attractive attributes of the ca approach are suggested to include large scale simulation multi resolution analysis and coupled field modeling

representations of the quadratic algebra and partially asymmetric diffusion with open boundaries we consider the one dimensional partially asymmetric exclusion model with open boundaries the model describes a system of hard core particles that hop stochastically in both directions with different rates at both boundaries particles are injected and extracted by means of the method of derrida et al the stationary probability measure can be expressed as a matrix product state involving two matrices forming a fock like representation of a general quadratic algebra we obtain the representations of this algebra which were unknown in the mathematical literature and use the two dimensional one to derive exact expressions for the density profile and correlation functions using the correspondence between the stochastic model and a quantum spin chain we obtain exact correlation functions for a spin heisenberg xxz chain with non diagonal boundary terms generalizations to other reaction diffusion models are discussed

the stochastic randomization effect in the on ramp system single lane main road and two lane main road situations in this paper we investigate the effect of the stochastic randomization in the on ramp system using the cellular automata traffic flow model both single lane main road and two lane main road situations are studied the variation of the phase diagram with the randomization probability p is studied a new phase i e the maximum flow phase is reported in the two lane main road situation the capacity of the on ramp system under different p and vmax is discussed

garden of eden states in a traffic model revisited a modified mean field theory is framed to adjoin two successful mean field theories cluster approximation and paradisical mean field theory the results do not give an improvement in describing the fundamental diagram we point out that the success of paradisical mean field theory is accidental and cannot be improved systematically as the cluster approximation can

local inhomogeneity in asymmetric simple exclusion processes with extended objects totally asymmetric simple exclusion processes tasep with particles which occupy more than one lattice site and with a local inhomogeneity far away from the boundaries are investigated these non equilibrium processes are relevant for the understanding of many biological and chemical phenomena the steady state phase diagrams currents and bulk densities are calculated using a simple approximate theory and extensive monte carlo computer simulations it is found that the phase diagram for tasep with a local inhomogeneity is qualitatively similar to homogeneous models although the phase boundaries are significantly shifted the complex dynamics is discussed in terms of domain wall theory for driven lattice systems

exact solution of the asymmetric exclusion model with particles of arbitrary size a generalization of the simple exclusion asymmetric model is introduced in this model an arbitrary mixture of molecules with distinct sizes s 0 1 2 dots in units of lattice space diffuses asymmetrically on the lattice a related surface growth model is also presented variations of the distribution of the molecules sizes may change the excluded volume almost continuously we solve the model exactly through the bethe ansatz and the dynamical critical exponent z is calculated from the finite size corrections of the mass gap of the related quantum chain our results show that for an arbitrary distribution of molecules the dynamical critical behavior is on the kardar parizi zhang universality

exclusion process for particles of arbitrary extension hydrodynamic limit and algebraic properties the behaviour of extended particles with exclusion interaction on a one dimensional lattice is investigated the basic model is called l asep as a generalization of the asymmetric exclusion process asep to particles of arbitrary length l stationary and dynamical properties of the l asep with periodic boundary conditions are derived in the hydrodynamic limit from microscopic properties of the underlying stochastic many body system in particular the hydrodynamic equation for the local density evolution and the time dependent diffusion constant of a tracer particle are calculated as a fundamental algebraic property of the symmetric exclusion process the su 2 symmetry is generalized to the case of extended particles

exact results for one dimensional totally asymmetric diffusion models several types of totally asymmetric diffusion models with and without exclusion are considered for some models conditional probabilities of finding n particles on lattice sites at time t with initial occupation at time t 0 are expressed in a determinant form on the other hand the q boson totally asymmetric diffusion model is introduced which interpolates the free boson model and the model with exclusion like interaction the effects of the interaction are compared for the case of two particle diffusion

partially asymmetric exclusion process with open boundaries exclusive diffusion on a one dimensional lattice is studied in the model particles hop stochastically in both directions but with different rates at the ends of the lattice particles are injected and removed the exact stationary probability measure is represented in the form of a matrix product as a generalization of the solution given by derrida et al j phys a 26 1493 1993 for the fully asymmetric process the phase diagram of the current on the infinite lattice is obtained analytic expressions for the current in the different phases are derived the model is equivalent to an xxz heisenberg chain with a certain type of boundary terms the ground state of which corresponds to the stationary solution of the master equation

probabilistic analysis of the capacitated vehicle routing problem with unsplit demands in the capacitated vehicle routing problem with unsplit demands the demand of a customer may not be divided over more than one vehicle the objective is to find tours for the vehicles such that the amount delivered by a vehicle does not exceed its capacity each customer receives its demand and the total distance traveled is as small as possible we find the asymptotic optimal solution value of the capacitated vehicle routing problem with unsplit demands for any distribution of the demands when customers are independently and identically distributed in a given region we also develop polynomial time heuristics for the problem and show that under certain assumptions on the distribution of customer locations and demands the heuristics produce solutions that are asymptotically optimal in addition we give a tight bound on the rate of convergence for the case when customers are uniformly distributed in a rectangular region

around probabilistic cellular automata we survey probabilistic cellular automata with approaches coming from combinatorics statistical physics and theoretical computer science each bringing a different viewpoint some of the questions studied are specific to a domain and some others are shared most notably the ergodicity problem

headway oscillations and phase transitions for diffusing particles with increased velocity a totally asymmetric exclusion process with n particles on a periodic one dimensional lattice of l sites is considered where particles can move one or two sites per infinitesimal timestep an exact analysis for n 2 and a mean field theory in comparison with simulations show even odd oscillations in the headway distribution of particles the expression headway is understood as the number of empty sites in front of a particle oscillations become maximal if particles only move at their maximum possible speed a phase transition separates two density profiles around a generated perturbation that plays the role of a defect the matrix product ansatz is generalized to obtain the exact solution for finite n and l thermodynamically the headway distribution yields the mean field result as n while it is not described generally by a product measure

scaling behaviour in discrete traffic models we investigate the noisy discrete single lane highway traffic model proposed by nagel and schreckenberg 1992 and demonstrate by computer simulations that as a function of the car density there is a dynamical transition from laminar flow to jammed traffic in the system related to the divergence of the relaxation time of average car velocity the critical density is close to the position of the maximum in the fundamental diagram we give estimates of the critical exponents related to this jamming transition the critical density of the geometrical 1 1 dimensional percolation transition of jammed regions can be rather far from the jamming point depending on the strength of the noise which indicates that cooperativity leading to the jamming transition can be long range in character

jamming transition in two dimensional pedestrian traffic abstract jamming transitions of pedestrian traffic are investigated under the periodic boundary condition on the square lattice by the use of the lattice gas model of biased random walkers without the back step the two cases are presented the one with two types of walkers and the other with four types of walkers in the two types of walkers the first is the random walker going to the right and the second is the random walker going up in the four types of walkers the first second third and fourth are respectively the random walkers going to the right left up and down it is found that the dynamical jamming transitions occur at the critical densities the transition points do not depend on the system size for large system but depend strongly on the strength of drift the jamming transitions are compared with that obtained by the cellular automaton model of car traffic

generalized online routing new competitive ratios resource augmentation and asymptotic analyses we consider online routing optimization problems where the objective is to minimize the time needed to visit a set of locations under various constraints the problems are online because the set of locations are revealed incrementally over time we consider two main problems 1 the online traveling salesman problem tsp with precedence and capacity constraints and 2 the online tsp with m salesmen for both problems we propose online algorithms each with a competitive ratio of 2 for the m salesmen problem we show that our result is best possible we also consider polynomial time online algorithms we then consider resource augmentation where we give the online servers additional resources to offset the powerful offline adversary advantage in this way we address a main criticism of competitive analysis we consider the cases where the online algorithm has access to faster servers servers with larger capacities additional servers and or advanced information we derive improved competitive ratios we also give lower bounds on the competitive ratios under resource augmentation which in many cases are tight and lead to best possible results finally we study online algorithms from an asymptotic point of view we show that under general stochastic structures for the problem data unknown and unused by the online player the online algorithms are almost surely asymptotically optimal furthermore we provide computational results that show that the convergence can be very fast

disordered exclusion process revisited some exact results in the low current regime we study the steady state of the totally asymmetric simple exclusion process with inhomogeneous hopping rates associated with sites site wise disorder using the fact that the non normalized steady state weights which solve the master equation are polynomials in all the hopping rates we propose a general method for calculating their first few lowest coefficients exactly in the case of binary disorder where all slow sites share the same hopping rate r 1 we apply this method to calculate the steady state current up to the quadratic term in r for some particular disorder configurations for the most general non binary disorder we show that in the low current regime the current is determined solely by the current minimizing subset of equal hopping rates provided all other slow rates are much larger our approach can be readily applied to any other driven diffusive system with unidirectional hopping if one can identify a hopping rate such that the current vanishes when this rate is set to zero

a probabilistic analysis of tour partitioning heuristics for the capacitated vehicle routing problem with unsplit demands in the capacitated vehicle routing problem with unsplit demands a customer s demand may not be divided over more than one vehicle we analyze the asymptotic performance of a class of heuristics called route first cluster second and in particular the empirically well studied sweep algorithm and optimal partitioning heuristic for any distribution of the demands and when customers are independent and identically distributed in a given region we show a strong relationship between this class of heuristics and the familiar next fit bin packing heuristic

a cellular automaton model for two lane traffic we present some long time limit properties of a cellular automaton that models traffic of cars on a infinite two lane road this model called tl184 is a natural generalization of the cellular automaton classified as 184 by wolfram to be abbreviated by ca184 and studied before as a model for one lane traffic tl184 models cars motions on each lane by particles that interact via the ca184 rules and cars lane changes by a possibility for particles to flip from one ca184 to another we calculate the infinite time limit of the particle current in tl184 starting from a translation invariant measure and use this result to show how the possibility of lane changes may enhance the current of cars in tl184 compared to that in a corresponding model of two non interacting one lane roads we provide examples which demonstrate that even though the rules that regulate lane changes are completely symmetric the system does not evolve to an equipartition of cars among both lanes from a given initially asymmetric distribution moreover the asymptotic car velocities and currents may be different on different lanes we also show that for a particular class of initial distributions the asymptotic car density on a lane may be a non monotonic function of the initial car density on this lane finally we derive the current density relation for an extended continuous time version of tl184 with asymmetric lane changing rules

the asymmetric exclusion process comparison of update procedures the asymmetric exclusion process asep has attracted a lot of interest not only because of its many applications e g in the context of the kinetics of biopolymerization and traffic flow theory but also because it is a paradigmatic model for nonequilibrium systems here we study the asep for different types of updates namely random sequential sequential sublattice parallel and parallel in order to compare the effects of the different update procedures on the properties of the stationary state we use large scale monte carlo simulations and analytical methods especially the so called matrix product ansatz mpa we present in detail the exact solution for the model with sublattice parallel and sequential updates using the mpa for the case of parallel update which is important for applications like traffic flow theory we determine the phase diagram the current and density profiles based on monte carlo simulations we furthermore suggest an mpa for that case and derive the corresponding matrix algebra

correlation functions in the nagel schreckenberg model we investigate the effect of the jamming transition on short range correlation functions in the nagel schreckenberg cellular automaton model of single lane traffic at high densities the structure of the time dependent correlation functions is double peaked one peak corresponds to moving cars the other to blocked cars the emergence of the latter peak as well as the occurrence of short range anticorrelations behind the propagating peak is related to the jamming transition at even higher densities the peak corresponding to moving cars disappears which is an indication of a superjamming transition

a relationship of mean field theory for a driven lattice gas to an exact equilibrium density functional we consider the totally asymmetric exclusion process tasep of particles on a one dimensional lattice that interact with site exclusion and are driven into one direction only the mean field approximation of the dynamical equation for the one particle density of this model is shown to be equivalent to the exact euler lagrange equations for the equilibrium density profiles of a binary mixture in this mixture particles occupy one two lattice sites and correspond to resting moving particles in the tasep despite the strict absence of bulk phase transitions in the equilibrium mixture the influence of density dependent external potentials is shown to induce abrupt changes in the one body density that are equivalent to the exact out of equilibrium phase transitions between steady states in the tasep with open boundaries

jamming transitions and the modified korteweg de vries equation in a two lane traffic flow abstract the two lattice models are presented to simulate the traffic flow on a two lane highway they are the lattice versions of the hydrodynamic model of traffic the one model a is described by the differential difference equation where time is a continuous variable and space is a discrete variable and the other model b is the difference equation in which both time and space variables are discrete the jamming transitions among the freely moving phase the coexisting phase and the uniform congested phase are studied by using the nonlinear analysis and the computer simulation the modified korteweg de vries mkdv equations are derived from the lattice models near the critical point the traffic jam is described by a kink antikink solution obtained from the mkdv equation it is found that the critical point the coexisting curve and the neutral stability line decrease with increasing the rate of lane changing also the computer simulation is performed for the model b it is shown that the coexisting curves obtained from the mkdv equation are consistent with the simulation result

two dimensional city traffic model with periodically placed blocks abstract a new two dimensional cellular automaton traffic model is proposed where blocks are placed periodically the present model includes the model of two crossing roads in the limit of maximum sized blocks and the bml model in the limit of zero sized blocks new phases of traffic flow appear between the free flow phase and the jam phase in the bml model the boundaries between these phases come closer as the size of the block decreases and converge into one phase boundary at a density around 0 19 which is in fair agreement with the critical density in the bml model

probabilistic analysis of a combined aggregation and math programming heuristic for a general class of vehicle routing and scheduling problems we propose and analyze a heuristic that uses region partitioning and an aggregation scheme for customer attributes load size time windows etc to create a finite number of customer types a math program is solved based on these aggregated customer types to generate a feasible solution to the original problem the problem class we address is quite general and defined by a number of general consistency properties problems in this class include vrps with general distance norms capacitated problems time window vrps pick up and delivery problems combined inventory control and routing problems and arc routing we provide a probabilistic analysis of this heuristic under very general probabilistic assumptions in particular we do not require independence between customer locations and their various attributes the heuristic is a s optimal as the number of customers n tends to infinity further it runs in o n log n time for a fixed relative error and can be designed to be asymptotically optimal w

car oriented mean field theory for traffic flow models we present a new analytical description of the cellular automaton model for single lane traffic in contrast to previous approaches we do not use the occupation number of sites as dynamical variable but rather the distance between consecutive cars therefore certain longer ranged correlations are taken into account and even a mean field approach yields non trivial results in fact for the model with the exact solution is reproduced for the fundamental diagram shows a good agreement with results from simulations

comment on garden of eden states in a traffic model revisited recently huang and lin suggested a combination of two successful mean field theories the 2 cluster approximation and paradisical mean field for the nagel schreckenberg cellular automaton model of traffic flow we argue that this new approximation is inconsistent since it violates the kolmogorov conditions

jamming transition of high dimensional traffic dynamics phase transition and critical phenomenon are investigated in high dimensional traffic flow numerically and analytically the two dimensional lattice traffic model is extended to the three and d dimensional traffic flows it is shown that the phase transition among the freely moving phase the coexisting phase and the uniformly congested phase occurs below the critical point in the two three and four dimensional traffic simulations the phase separation line and the critical point of the d dimensional traffic are consistent with those of the one dimensional traffic the time dependent ginzburg landau tdgl equation for the d dimensional traffic is derived by the use of the nonlinear analysis the phase separation line the spinodal line and the critical point are calculated from the tdgl equation it is found that the phase transition and critical phenomenon are independent of the space dimension

jamming transition in traffic flow on triangular lattice abstract phase transitions and critical phenomena are investigated in the two dimensional traffic flow on the triangular lattice numerically and analytically the two dimensional traffic model on the square lattice is extended to the traffic flow on the triangular lattice where the three roads cross on a site it is shown that the jamming transition between the freely moving and jammed phases depends on the configuration of car moving directions it is found that the three distinct jamming transitions occur the conventional jamming transition to the kink jams the jamming transition to the chaotic jams and the jamming transition to the oscillating jams the conventional jamming transition to the kink jams is analyzed by the use of the linear stability theory and the nonlinear method the coexisting curve between the freely moving and jammed phases is calculated from the solution of the modified korteweg de vries kdv equation

the effect of traffic light on accident probability in open and periodic boundaries system in this paper we numerically study the dependence of car accident probability pac per site and per time step on cycle time t of traffic light both in open and periodic boundaries system in this study one traffic light is placed in the middle of the system this work is based on nagel and schreckenberg nasch model nagel and schreckenberg 1992 in parallel dynamics the pac dependence on t and the phase diagrams are established and are the injecting and extracting rates of cars in the traffic lane respectively the increase of the cycle time light t causes an important decrease of the accident probability pac both in the open and periodic cases

particle hopping models of vehicular traffic distributions of distance headways and distance between jams we calculate the distribution of the distance headways i e the instantaneous gap between successive vehicles as well as the distribution of instantaneous distance between successive jams in the nagel schreckenberg ns model of vehicular traffic when the maximum allowed speed vmax of the vehicles is larger than unity over an intermediate range of densities of vehicles our monte carlo mc data for the distance headway distribution exhibit two peaks which indicate the coexistence of free flowing traffic and traffic jams our analytical arguments clearly rule out the possibility of occurrence of more than one peak in the distribution of distance headways in the ns model when vmax 1 as well as in the asymmetric simple exclusion process modifying and extending an earlier analytical approach for the ns model with vmax 1 and introducing a novel transfer matrix technique we also calculate the exact analytical expression for the distribution of distance between the jams in this model the corresponding distributions for vmax 1 have been computed numerically through mc simulation

martingale inequalities and np complete problems we use martingale inequalities in the probabilistic analysis of stochastic models of np complete problems we give examples of applications to the bin packing and traveling salesman problems in both cases we obtain sharp bounds on pr un eun t where un is the objective function value of the problem with n random data

discrete stochastic models for traffic flow we investigate a probabilistic cellular automaton model which has been introduced recently this model describes single lane traffic flow on a ring and generalizes the asymmetric exclusion process models we study the equilibrium properties and calculate the so called fundamental diagrams flow versus density for parallel dynamics this is done numerically by computer simulations of the model and by means of an improved mean field approximation which takes into account short range correlations for cars with a maximum velocity of 1 the simplest nontrivial approximation gives the exact result for higher velocities the analytical results obtained by iterated application of the approximation scheme are in excellent agreement with the numerical simulations

hard rod gas with long range interactions exact predictions for hydrodynamic properties of continuum systems from discrete models one dimensional hard rod gases are explicitly constructed as the limits of discrete systems exclusion processes involving particles of arbitrary length those continuum many body systems in general do not exhibit the same hydrodynamic properties as the underlying discrete models considering as examples a hard rod gas with additional long range interaction and the generalized asymmetric exclusion process for extended particles it is shown how a correspondence between continuous and discrete systems must be established instead this opens up a possibility to exactly predict the hydrodynamic behavior of this continuum system under eulerian scaling by solving its discrete counterpart with analytical or numerical tools as an illustration simulations of the totally asymmetric exclusion process are compared to analytical solutions of the model and applied to the corresponding hard rod gas the case of short range interaction is treated separately

nonequilibrium steady states of matrix product form a solver s guide we consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model among other things biological transport and traffic flow we begin with a broad overview of this class of driven diffusive systems which includes exclusion processes focusing on interesting physical properties such as shocks and phase transitions we then turn our attention specifically to those models for which the exact distribution of microstates in the steady state can be expressed in a matrix product form in addition to a gentle introduction to this matrix product approach how it works and how it relates to similar constructions that arise in other physical contexts we present a unified pedagogical account of the various means by which the statistical mechanical calculations of macroscopic physical quantities are actually performed we also review a number of more advanced topics including nonequilibrium free energy functionals the classification of exclusion processes involving multiple particle species existence proofs of a matrix product state for a given model and more complicated variants of the matrix product state that allow various types of parallel dynamics to be handled we conclude with a brief discussion of open problems for future research

on the ubiquity of matrix product states in one dimensional stochastic processes with boundary interactions abstract recently it has been shown that the zero energy eigenstate corresponding to the stationary state of a stochastic hamiltonian with nearest neighbour interaction in the bulk and single site boundary terms can generically be written in the form of a so called matrix product state we generalize this result to stochastic hamiltonians with arbitrary but finite interaction range as an application two different particle hopping models with three site bulk interaction are studied for these models which can be interpreted as cellular automata for traffic flow we present exact solutions for periodic boundary conditions and some suitably chosen boundary interactions

exact results for car accidents in a traffic model within the framework of a recent model for car accidents on single lane highway traffic we study analytically the probability of the occurrence of car accidents exact results are obtained various scaling behaviours are observed the linear dependence of the occurrence of car accidents on density is understood as the dominance of a single velocity in the distribution

relation between primes and nontrivial zeros in the riemann hypothesis legendre polynomials modified zeta function and schrodinger equation we study the dependence between prime numbers and the real and imaginary parts of the nontrivial zeros of the riemann zeta function the legendre polynomials and the partial derivatives of the riemann zeta function are used to investigate the above dependence along with the riemann hypothesis with physical interpretations a modified zeta function with finite terms is defined as a new implement for the study of the zeta function and its zeros

an exact solution of a one dimensional asymmetric exclusion model with open boundaries a simple asymmetric exclusion model with open boundaries is solved exactly in one dimension the exact solution is obtained by deriving a recursion relation for the steady state if the steady state is known for all system sizes less thann then our equation 8 gives the steady state for sizen using this recursion we obtain closed expressions 48 for the average occupations of all sites the results are compared to the predictions of a mean field theory in particular for infinitely large systems the effect of the boundary decays as the distance to the power 1 2 instead of the inverse of the distance as predicted by the mean field theory

multi species asymmetric exclusion process in ordered sequential update a multi species generalization of the asymmetric simple exclusion process is studied with ordered sequential and sub lattice parallel updating schemes in this model particles hop with their own specific probabilities to their rightmost empty site and fast particles overtake slow ones with a definite probability using the matrix product ansatz technique we obtain the relevant algebra and study the uncorrelated stationary state of the model both for an open system and on a ring a complete comparison between the physical results in these updates and those of random sequential introduced in karimipour v 1999 a multi species asep and its relation to traffic flow phys rev e 59 205 and karimipour v 1998 a multi species asep steady state and correlation functions on a periodic lattice preprint cond mat 9809193 is made

worst case analysis of heuristics for the bin packing problem with general cost structures we consider the famous bin packing problem where a set of items must be stored in bins of equal capacity in the classical version the objective is to minimize the number of bins used motivated by several optimization problems that occur in the context of the storage of items we study a more general cost structure where the cost of a bin is a concave function of the number of items in the bin the objective is to store the items in such a way that total cost is minimized such cost functions can greatly alter the way the items should be assigned to the bins we show that some of the best heuristics developed for the classical bin packing problem can perform poorly under the general cost structure on the other hand the so called next fit increasing heuristic has an absolute worst case bound of no more than 1 75 and an asymptotic worst case bound of 1 691 for any concave and monotone cost function our analysis also provides a new worst case bound for the well studied next tit decreasing heuristic when

bounds and heuristics for capacitated routing problems in a capacitated routing problem the objective is to minimize the total distance travelled by vehicles of limited capacity to serve a set of customers that are located in the euclidean plane we develop asymptotically optimal bounds and heuristics for this problem under the assumption that the capacity of a vehicle is expressed in terms of an upper bound on the number of customers that it can serve the analysis culminates in an algorithm that for a given capacity and given will find a solution with relative error at most in time polynomial in the number of customers

derivation and empirical validation of a refined traffic flow model abstract the gas kinetic foundation of fluid dynamic traffic equations suggested in previous papers d helbing physica a 219 1995 375 and 391 is further refined by applying the theory of dense gases and granular materials to the boltzmann like traffic model by paveri fontana it is shown that despite the phenomenologically similar behaviour or ordinary and granular fluids the relations for these cannot directly be transferred to vehicular traffic the dissipative and anisotropic interactions of vehicles as well as their velocity dependent space requirements lead to a considerably different structure of the macroscopic traffic equations also in comparison with the previously suggested traffic flow models as a consequence the instability mechanisms of emergent density waves are different crucial assumptions are validated by empirical traffic data and essential results are illustrated by figures

steady state properties of a totally asymmetric exclusion process with periodic structure we study the steady state behavior of totally asymmetric simple exclusion processes taseps that contain periodically varying movement rates in this model particles move to the right at one of two rates p 2 if the particle occupies one of a periodically arranged set of lattice sites p 1 otherwise approximate mean field approaches are used to study the steady state currents and bulk densities of this model these mean field methods are found to provide results in good agreement with data derived from monte carlo simulations finally the condition for particle hole symmetry in the tasep with periodically varying movement rates is specified and the changes in the locations of the boundary limited to maximal current transition lines due to symmetry violation are investigated

totally asymmetric exclusion process with extended objects a model for protein synthesis the process of protein synthesis in biological systems resembles a one dimensional driven lattice gas in which the particles have spatial extent covering more than one lattice site we expand the well studied totally asymmetric exclusion process in which particles typically cover a single lattice site to include cases with extended objects exact solutions can be determined for a uniform closed system we analyze the uniform open system through two approaches first a continuum limit produces a modified diffusion equation for particle density profiles second an extremal principle based on domain wall theory accurately predicts the phase diagram and currents in each phase finally we briefly consider approximate approaches to a nonuniform open system with quenched disorder in the particle hopping rates and compare these approaches with monte carlo simulations

the noncommutative space of stochastic diffusion systems in the matrix product ground states approach to n species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process we show that the quadratic algebra defines a noncommutative space with a glq n quantum group action as its symmetry boundary processes account for the appearance of parameter dependent linear terms in the algebraic relations we argue that for systems with boundary conditions the diffusion algebras are also obtained either by a shift of basis in the n dimensional quantum plane or by an appropriate change of basis in a lower dimensional one which leads to a reduction of the glq n symmetry

is brownian motion sensitive to geometry fluctuations many situations of physical and biological interest involve diffusions on manifolds it is usually assumed that irregularities in the geometry of these manifolds do not influence diffusions the validity of this assumption is put to test by studying brownian motions on nearly flat 2d surfaces it is found by perturbative calculations that irregularities in the geometry have a cumulative and drastic influence on diffusions and that this influence typically grows exponentially with time the corresponding characteristic times are computed and discussed

a stochastic cellular automaton model for traffic flow with multiple metastable states a new stochastic cellular automaton ca model of traffic flow which includes slow to start effects and a driver s perspective is proposed by extending the burgers ca and the nagel schreckenberg ca model the flow density relation of this model shows multiple metastable branches near the transition density from free to congested traffic which form a wide scattering area in the fundamental diagram the stability of these branches and their velocity distributions are explicitly studied by numerical simulations

generalized determinant solution of the discrete time totally asymmetric exclusion process and zero range process 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 schutz 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

two channel totally asymmetric simple exclusion processes totally asymmetric simple exclusion processes consisting of two coupled parallel lattice chains with particles interacting with hard core exclusion and moving along the channels and between them are considered in the limit of strong coupling between the channels the particle currents density profiles and a phase diagram are calculated exactly by mapping the system into an effective one channel totally asymmetric exclusion model for intermediate couplings a simple approximate theory that describes the particle dynamics in vertical clusters of two corresponding parallel sites exactly and neglects the correlations between different vertical clusters is developed it is found that similarly to the case of one channel totally asymmetric simple exclusion processes there are three stationary state phases although the phase boundaries and stationary properties strongly depend on inter channel coupling extensive computer monte carlo simulations fully support the theoretical predictions

spontaneous symmetry breaking in totally asymmetric simple exclusion processes on two intersected lattices this paper studies totally asymmetric simple exclusion processes taseps on two intersected lattices three different models are introduced model a for molecular motor motion and models b and c for vehicle traffic extensive monte carlo simulations are carried out phase diagrams and density profiles of the three models are investigated it is shown that phase diagrams of all the three models are divided into three regions the phase boundaries are calculated by an approximate mean field approach it is found that the analytic solutions are in good agreement with the results of monte carlo simulations for models b and c spontaneous symmetry breaking is identified the particle density histograms and qualitative domain wall explanation are presented to describe the spontaneous symmetry breaking phenomenon finally in model c the effect of lane changing probability p on spontaneous symmetry breaking is investigated a threshold of p for the occurrence of symmetry breaking is obtained