a new stochastic cellular automaton model on traffic flow and its jamming phase transition a general stochastic traffic cellular automaton ca model which includes the slow to start effect and driver s perspective is proposed in this paper it is shown that this model includes well known traffic ca models such as the nagel schreckenberg model the quick start model and the slow to start model as specific cases fundamental diagrams of this new model clearly show metastable states around the critical density even when the stochastic effect is present we also obtain analytic expressions of the phase transition curve in phase diagrams by using approximate flow density relations at boundaries these phase transition curves are in excellent agreement with numerical results

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

tdgl and mkdv equations for jamming transition in the lattice models of traffic abstract the lattice models of traffic are proposed to describe the jamming transition in traffic flow on a highway in terms of thermodynamic terminology of phase transitions and critical phenomena they are the lattice versions of the hydrodynamic model of traffic two lattice models are presented one is described by the differential difference equation where time is a continuous variable and space is a discrete variable and the other is the difference equation in which both time and space variables are discrete we apply the linear stability theory and the nonlinear analysis to the lattice models it is shown that the time dependent ginzburg landau tdgl equation is derived to describe the traffic flow near the critical point a thermodynamic theory is formulated for describing the phase transitions and critical phenomena it is also shown that the perturbed modified korteweg de vries mkdv equation is derived to describe the traffic jam

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

empirical test for cellular automaton models of traffic flow based on a detailed microscopic test scenario motivated by recent empirical studies of single vehicle data several cellular automaton models for traffic flow are compared we find three levels of agreement with the empirical data 1 models that do not reproduce even qualitatively the most important empirical observations 2 models that are on a macroscopic level in reasonable agreement with the empirics and 3 models that reproduce the empirical data on a microscopic level as well our results are not only relevant for applications but also shed light on the relevant interactions in traffic flow

dynamic structure models for scalar flux and dissipation in large eddy simulation a new class of subgrid scale models dynamic structure models for large eddy simulation is proposed for subgrid scalar flux and dissipation terms the structure of the modeled terms is taken from the corresponding leonard terms by the use of the test filter size equal to the base filter size and a particular form of the scaling factor is proposed the models are evaluated using available direct numerical simulation data the evaluation results compare well with viscosity and similarity models the dynamic structure models have been found to be robust and to work well under various conditions including various test to base filter size ratios and filter skewnesses models for both terms employ the subgrid scalar variance as a part of the scaling factor

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

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

an analysis of numerical errors in large eddy simulations of turbulence the reliability of numerical simulations of turbulence depend on our ability to quantify and control discretization errors in the classical literature on error analysis typically simple linear equations are studied estimates of errors derived from such analyses depend on the assumption that each dependent variable can be characterized by a unique amplitude and scale of spatial variation that can be normalized to unity this assumption is not valid for strongly nonlinear problems such as turbulence where nonlinear interactions rapidly redistribute energy resulting in the appearance of a broad continuous spectrum of amplitudes in such situations the numerical error as well as the subgrid model can change with grid spacing in a complicated manner that cannot be inferred from the results of classical error analysis in this paper a formalism for analyzing errors in such nonlinear problems is developed in the context of finite difference approximations for the navier stokes equations when the flow is fully turbulent analytical expressions for the power spectra of these errors are derived by exploiting the joint normal approximation for turbulent velocity fields these results are applied to large eddy simulation of turbulence to obtain quantitative bounds on the magnitude of numerical errors an assessment of the significance of these errors in made by comparing their magnitudes with that of the nonlinear and subgrid terms one method of controlling the errors is suggested and its effectiveness evaluated through quantitative measures although explicit evaluations are presented only for large eddy simulation the expressions derived for the power spectra of errors are applicable to direct numerical simulation as well

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

analytical study on the criticality of the stochastic optimal velocity model in recent works we have proposed a stochastic cellular automaton model of traffic flow connecting two exactly solvable stochastic processes i e the asymmetric simple exclusion process and the zero range process with an additional parameter it is also regarded as an extended version of the optimal velocity model and moreover it shows particularly notable properties in this paper we report that when taking optimal velocity function to be a step function all of the flux density graph i e the fundamental diagram can be estimated we first find that the fundamental diagram consists of two line segments resembling an inversed form and next identify their end points from a microscopic behaviour of vehicles it is notable that by using a microscopic parameter which indicates a driver s sensitivity to the traffic situation we give an explicit formula for the critical point at which a traffic jam phase arises we also compare these analytical results with those of the optimal velocity model and point out the crucial differences between them

a two dimensional ca model for traffic flow with car origin and destination abstract dynamic phase transitions in a two dimensional traffic flow model defined on a decorated square lattice are studied numerically the square lattice point and the decorated site denote intersections and roads respectively in the present model a car has a finite deterministic path between the origin and the destination which is assigned to the car from the beginning in this new model we found a new phase between the free flow phase and the frozen jam phase that is absent from previous models the new model is characterized by the persistence of a macroscopic cluster furthermore the behavior in this macroscopic cluster phase is classified into three regions characterized by the shape of the cluster the boundary of the three regions is phenomenologically estimated when the trip length is short and the car density is high both ends of the belt like cluster connect to each other through the periodic boundary with some probability this type of cluster is classified topologically as a string on a two dimensional torus

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

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

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

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

euler lagrange correspondence of cellular automaton for traffic flow models we propose a euler lagrange transformation for cellular automata ca by developing new explicit transformation formulas this transformation is done in the fully discrete level of variables and corresponds to the well known continuous version of it which appears in continuous mechanics such as fluid dynamics and plasma physics applying this method to the traffic problem we have obtained the lagrange representation of a traffic model and also succeeded in clarifying the relation between different types of traffic models it is shown that the burgers ca which is a corresponding ca of the continuous burgers equation plays a central role in considering this relation

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

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

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

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

central limit theorem for a class of relativistic diffusions two similar minkowskian diffusions have been considered on one hand by debbasch and co workers j math phys 40 2891 2001 eur phys j 19 37 2001 23 487 2001 j stat phys 88 945 1997 90 1179 1998 and on the other hand by dunkel and hanggi phys rev e 71 016124 2005 72 036106 2005 we address here two questions asked by debbasch and rivet j stat phys 90 1179 1998 and by dunkel and hanggi phys rev e 71 016124 2005 72 036106 2005 respectively about the asymptotic behavior of such diffusions more generally we establish a central limit theorem for a class of minkowskian diffusions to which the two above ones belong as a consequence we correct a partially wrong guess by dunkel and hanggi phys rev e 71 016124 2005

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

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 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

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

phase transitions in a cellular automaton model of a highway on ramp we introduce a lattice gas model for the merging of two single lane automobile highways the merging rules for traffic on the two lanes are deterministic but the inflow on both lanes is stochastic analysing the stationary distribution of this stochastic cellular automaton we find a discontinuous phase transition from a free flow phase which depends on the initial state of the road to a jammed phase where all memory of the initial state is lost inside the jammed phase we identify dynamical phase transitions in the approach to stationarity each dynamical phase is characterized by a fixed number of relaxation cycles which is decreasing as one moves deeper into the jammed phase in each cycle step the number of desperate drivers who force their way onto the main road when they reach the end of the on ramp increases until stationarity

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

multi value cellular automaton models and metastable states in a congested phase in this paper a family of multi value cellular automaton ca associated with traffic flow is presented the family is obtained by extending the rule 184 ca which is an ultradiscrete analogue to the burgers equation ca models in the family show both metastable states and stop and go waves which are often observed in real traffic flow metastable states in the models exist not only on a prominent part of a free phase but also in a congested phase

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

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

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

diffusion on a curved surface a geometrical approach abstract we propose a new model of 2d free particle diffusion on a possibly curved surface this model is a generalization of the standard ornstein uhlenbeck process and is completely determined by writing down the transport equation describing the diffusion in the phase space of the diffusing particle this transport equation is then used to show that curvature effects can profoundly affect the phenomenology of diffusion in the hydrodynamic limit a specific pedagogical example is also worked out

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

analytical properties of ultradiscrete burgers equation and rule 184 cellular automaton in this paper we propose an ultradiscrete burgers equation of which all the variables are discrete the equation is derived from a discrete burgers equation under an ultradiscrete limit and reduces to an ultradiscrete diffusion equation through the cole hopf transformation moreover it becomes a cellular automaton ca under appropriate conditions and is identical to rule 184 ca in a specific case we show shock wave solutions and asymptotic behaviours of the ca exactly via the diffusion equation finally we propose a particle model expressed by the ca and discuss a mean flux of particles

a diffusion process in curved space time we construct a curved space time generalization of the special relativistic ornstein uhlenbeck process this is done by deriving a manifestly covariant kolmogorov equation that describes diffusion in curved space times the simple case of diffusion in a spatially flat friedmann robertson walker universe is then considered it is proven that at least in these space times kolmogorov equation admits as possible solution a natural generalization of the flat space time juttner equilibrium solution the first correction to juttner s distribution in a slowly expanding universe is also obtained explicitly

dynamic one equation nonviscosity large eddy simulation model anew approach for a nonviscosity large eddy simulation les subgrid stress model is presented theapproach uses a scaling that is provided by the subgrid kinetic energy and a tensor coefe cient that is obtained from the dynamic modeling approach hence a dynamic structure model mathematical and conceptual issues motivating the development of this new model are explored attention is focused on dynamic modeling approaches the basic equations that originate in dynamic modeling approaches are fredholm integral equations of the second kind these equations have solvability requirements that have not been previously addressed in the context of les models these conditionsare examined for traditional dynamic smagorinksy modeling that is zero equation approaches and one equation subgrid models it is shown that standard approaches do not always satisfy the integral equation solvability condition it is also shown that traditional les models that use the resolved scale strain rate to estimatethesubgrid stressesscalepoorly with e lterlevel leading to signie cant errorsin themodeling of the subgrid scale stress the poor scaling in traditional les approaches can result in not only weak models but can also cause nonrealizability of the subgrid stresses a better scaling based on the subgrid kinetic energy is proposed that leads to a new one equation nonviscosity model that does satisfy the solvability conditions and appears to maintain realizability both integral and algebraic formulations of the new one equation nonviscosity model are presented the resolved and subgrid kinetic energies are shown to compare well to a direct numerical simulation of decaying isotropic turbulence

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

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

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

hydrodynamic behavior of brownian particles in a position dependent constant force field the diffusion equation in physical space time for a brownian particle driven by an external force field has been derived by smoluchowski in the two particular cases where the external field is uniform or varies linearly with position elastic force in more general cases correction terms must be added to the smoluchowski equation we show here how to use a multi scale chapman enskog expansion to obtain in the hydrodynamic limit the first corrective terms to the smoluchowski equation without any restriction on the friction coefficient and for any sufficiently small position dependent constant force field we also compare our approach with the works of wilemski titulaer and van kampen

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 lagrange representation of cellular automaton traffic flow models a new cellular automaton ca model of traffic flow in the lagrange form is proposed in this paper we study the algebraic relationship between models with the lagrange form and the euler form of burger s ca which is constructed from burger s equation using the ultradiscrete method it is found that the lagrange form has made the description of traffic flow in one lane simpler thus we have extended a simple lagrange model to include the effects of inertia of cars and drivers perspective the extended model shows metastable states and complex phase transition from a free to congested state which is similar to the observed data for expressways

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

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