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

finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple lie algebra let g be a complex simple lie algebra we show that whent is not a root of 1 all finite dimensional representations of the quantum analogu t g are completely reducible and we classify the irreducible ones in terms of highest weights in particular they can be seen as deformations of the representations of the classical u g

complementarity of suq 3 and uq 2 and q boson realization of the suq 3 irreducible representations the complementarity relationship also termed duality that arises between the irreps of the su 3 and u 2 lie algebras when their direct sum su 3 u 2 is embedded into a larger u 6 algebra and single row irreps of the latter are considered is extended to the corresponding q algebras suq 3 and uq 2 it is demonstrated by explicitly constructing the unique q boson state that is simultaneously maximal in suq 3 and uq 2 for a given u q 2 weight in addition the relations between the suq 3 and uq 2 casimir operators resulting from their complementarity are explicitly found together with the q bargmann representation of q boson operators the complementarity relationship is then used to construct a gel fand tseitlin basis for arbitrary suq 3 irreps in terms of q boson operators

exact solution of the zero range process fundamental diagram of the corresponding exclusion process in this paper we propose a general way of computing expectation values in the zero range process zrp using an exact form of the partition function as an example we provide the fundamental diagram the flux density plot of the asymmetric exclusion process corresponding to the zrp we express the partition function for the steady state by the lauricella hypergeometric function and thereby have two exact fundamental diagrams each for the parallel and random sequential update rules meanwhile from the viewpoint of equilibrium statistical mechanics we work within the canonical ensemble but the result obtained is certainly in agreement with previous works done in the grand canonical ensemble

q deformation of the lorentz group we describe a q deformation of the lorentz group in terms of a q deformation of the van der waerden spinor algebra

analysis of car following model considering driver s physical delay in sensing headway abstract an extended car following model is proposed by taking into account the delay of the driver s response in sensing headway the stability condition of this model is obtained by using the linear stability theory the results show that the stability region decreases when the driver s physical delay in sensing headway increases the kdv equation and mkdv equation near the neutral stability line and the critical point are respectively derived by applying the reductive perturbation method the traffic jams could be thus described by soliton solution and kink antikink soliton solution for the kdv equation and mkdv equation respectively the numerical results in the form of the space time evolution of headway show that the stabilization effect is weakened when the driver s physical delay increases it confirms the fact that the delay of driver s response in sensing headway plays an important role in jamming transition and the numerical results are in good agreement with the theoretical analysis

harish chandra isomorphisms for quantum algebras the center of the quantum algebra is studied especially an analogue of the harish chandra isomorphism is established

kdv and kink antikink solitons in car following models abstract the jams in the congested traffic are related with various density waves which might be governed by the nonlinear wave equations such as the korteweg de vries kdv equation the burgers equation and the modified korteweg de vries mkdv equation three different versions of optimal velocity models are examined the stability conditions of the models are obtained by using the linear stability theory the kdv equation near the neutral stability line and the mkdv equation around the critical point are derived by applying the reductive perturbation method respectively the traffic jams could be thus described by the kdv and kink antikink soliton solutions for the two kinds of equations the general solutions are given for which can lead to specific solutions in previous work moreover they are applied to solve a new model the full velocity difference model and the corresponding kdv and kink antikink soliton solutions could be quickly obtained which demonstrates the general solutions presented herein are useful

algorithms for the integration and derivation of chebyshev series general formulas for the mth integral and derivative of a chebyshev polynomial of the first or second kind are presented the result is expressed as a finite series of the same kind of chebyshev polynomials these formulas permit to accelerate the determination of such integrals or derivatives besides it is presented formulas for the mth integral and derivative of finite chebyshev series and a numerical algorithm for the direct evaluation of the mth derivative of such a series

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

from modified kdv equation to a second order cellular automaton for traffic flow abstract we propose a cellular automaton ca model for traffic flow which is second order in time the model is derived from the modified korteweg de vries mkdv equation by use of the ultra discretization method udm proposed by tokihiro et al phys rev lett 76 1996 3247 this result can be seen as an analogue of the derivation of nonlinear evolution equations from differential and differential difference equation traffic models it is the intention of this paper to draw attention to exactly this analogy we show that the model exhibits a crossover from a freely moving regime to a jammed regime with increasing density

kink soliton characterizing traffic congestion we study traffic congestion by analyzing a one dimensional traffic flow model developing an asymptotic method to investigate the long time behavior near a critical point we derive the modified korteweg de vries mkdv equation as the lowest order model there is an infinite number of kink solitons to the mkdv equation while it has been found by numerical simulations that the kink pattern arising in traffic congestion is uniquely determined irrespective of initial conditions in order to resolve this selection problem we consider higher order corrections to the mkdv equation and find that there is a kink soliton that can deform continuously with the perturbation represented by the addition of these corrections with numerical confirmation we show that this continuously deformable kink soliton characterizes traffic congestion we also discuss the relationship between traffic congestion and the slugging phenomenon in granular flow

intermittent unstable structures induced by incessant constant disturbances in the full velocity difference car following model abstract in this paper we study traffic flow patterns induced by incessant constant disturbances in the full velocity difference car following model it is found that intermittent unstable structures may occur in the convectively unstable traffic flow under certain situations a phenomenological explanation of the phenomenon is given the incessant constant disturbances mainly function to maintain the stationary oscillating structure while the stationary oscillating structure is not always stable the intermittent instability of it leads to the intermittent unstable structures the similarity of the stationary oscillating structure to the transition layer in the local cluster effect is pointed out the dependence of the phenomenon on the headway of the initially uniform traffic the safety distance x c the sensitivity parameters and and the noise term is also investigated

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

singular vectors of representations of quantum groups the author gives explicit formulae for singular vectors of verma modules over uq g they give the general formula for g an for some cases when g dn and for some rank two subalgebras of g not an dn for this he uses a special basis of uq g where g is the negative root subalgebra of g which was introduced in his earlier work on the case q 1 this basis seems more economical than the poincare birkhoff witt type of basis used by malikov feigin and fuchs 1986 for the construction of singular vectors of verma modules in the case q 1 furthermore this basis turns out to be part of a general basis introduced recently for other reasons by lusztig 1988 for uq b where b is a borel subalgebra of g

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

exact solutions for a discrete system arising in traffic flow this paper concerns wave propagation in a discrete nonlinear system of equations proposed and studied by g f newell as a model for car following in traffic flow in particular newell found exact solutions for shock waves and related phenomena here exact solutions representing periodic waves and solitary waves are obtained the method relates travelling wave solutions to the toda and kac van moerbeke discrete systems in this and other ways much of the interest is in the general phenomena possible in discrete systems here including also a time lag rather than in just the specific traffic flow setting

modified kdv equation for jamming transition in the continuum models of traffic abstract continuum models of traffic are proposed to describe the jamming transition in traffic flow on a highway they are the simplified versions of the hydrodynamic model of traffic two continuum models are presented one is described by the partial differential equations and the other is the discrete lattice version the linear stability theory and the nonlinear analysis are applied to the continuum models the modified korteweg de vries equation kdv near the critical point is derived using the reduction perturbation method it is shown that the jamming transition and the density wave in the congested traffic flow are described by the modified kdv equation the solutions of the kdv equations obtained from the two models are compared with that of the optimal velocity model car following model

the korteweg de vries soliton in the lattice hydrodynamic model abstract the lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model but is also closely connected with the microscopic car following model the modified korteweg de vries mkdv equation about the density wave in congested traffic has been derived near the critical point since nagatani first proposed it but the korteweg de vries kdv equation near the neutral stability line has not been studied which has been investigated in detail in the car following model so we devote ourselves to obtaining the kdv equation from the lattice hydrodynamic model and obtaining the kdv soliton solution describing the traffic jam numerical simulation is conducted to demonstrate the nonlinear analysis result

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

phase transition in a difference equation model of traffic flow a difference equation is presented to describe traffic flow on a highway the difference equation model is derived from the optimal velocity models formulated in terms of the differential equations it is compared with the differential equation models we investigate phase transitions among the freely moving phase the coexisting phase in which jams appear and the uniform congested phase the linear stability theory is applied and the neutral stability line is obtained we find the critical point below which no jams appear to derive the modified korteweg de vries equation near the critical point we apply the reductive perturbation method we also compare the nonlinear analysis result with that of the optimal velocity model it is shown that the critical point and the amplitude of the jam are different from those of the optimal velocity model

ultradiscrete optimal velocity model a cellular automaton model for traffic flow and linear instability of high flux traffic in this paper we propose the ultradiscrete optimal velocity model a cellular automaton model for traffic flow by applying the ultradiscrete method for the optimal velocity model the optimal velocity model defined by a differential equation is one of the most important models in particular it successfully reproduces the instability of high flux traffic it is often pointed out that there is a close relation between the optimal velocity model and the modified korteweg de vries mkdv equation a soliton equation meanwhile the ultradiscrete method enables one to reduce soliton equations to cellular automata which inherit the solitonic nature such as an infinite number of conservation laws and soliton solutions we find that the theory of soliton equations is available for generic differential equations and the simulation results reveal that the model obtained reproduces both absolutely unstable and convectively unstable flows as well as the optimal velocity model

differential operators on quantized flag manifolds at roots of unity abstract the quantized flag manifold which is a q analogue of the ordinary flag manifold is realized as a non commutative scheme and we can define the category of d modules on it using the framework of non commutative algebraic geometry however when the parameter q is a root of unity lusztig s frobenius morphism allows us to handle d modules on the quantized flag manifold through modules over a certain sheaf of rings on the ordinary flag manifold in this paper we will show that this sheaf of rings on the ordinary flag manifold is an azumaya algebra over its center we also show that its restriction to certain subsets are split azumaya algebras these are analogues of some results of bezrukavnikov mirkovic rumynin on d modules on flag manifolds in positive characteristics

coexisting phases and lattice dependence of a cellular automaton model for traffic flow the biham middleton levine traffic model is perhaps the simplest system exhibiting phase transitions and self organization moreover it is an underpinning to extensive modern studies of traffic flow the general belief is that the system exhibits a sharp phase transition from freely flowing to fully jammed as a function of initial density of cars however we discover intermediate stable phases where jams and freely flowing traffic coexist the geometric structure of such phases is highly regular with bands of free flowing traffic intersecting at jammed wave fronts that propagate smoothly through the space instead of a phase transition as a function of density we see bifurcation points where intermediate phases begin coexisting with the more conventionally known phases we show that the regular geometric structure is in part a consequence of the finite size and aspect ratio of the underlying lattice and that for certain aspect ratios the asymptotic intermediate phase is on a periodic limit cycle the exact microscopic configuration recurs each tau time steps aside from describing these intermediate states which previously were overlooked we derive simple equations to describe the geometric constraints and predict their asymptotic velocities

traffic jams granular flow and soliton selection the flow of traffic on a long section of road without entrances or exits can be modeled by continuum equations similar to those describing fluid flow in a certain range of traffic density steady flow becomes unstable against the growth of a cluster or phantom traffic jam which moves at a slower speed than the otherwise homogeneous flow we show that near the onset of this instability traffic flow is described by a perturbed korteweg de vries kdv equation the traffic jam can be identified with a soliton solution of the kdv equation the perturbation terms select a unique member of the continuous family of kdv solitons these results may also apply to the dynamics of granular relaxation

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

quantum deformations of certain simple modules over enveloping algebras soit f un corps soit f 0 un sous corps de f soit u l algebre enveloppante universelle sur f 0 de l algebre de lie de kac moody correspondant a la matrice a d entiers on montre qu un module integrable de poids le plus eleve v de u admet une deformation quantique

solitons and kinks in a general car following model we study a general car following model of traffic flow on an infinitely long single lane road which assumes that a car s acceleration depends on time delayed values of its own speed the headway between it and the car ahead and the rate of change of headway but makes minimal assumptions about the functional form of that dependence we present a detailed characterization of the onset of linear instability in particular we find a specific limit on the delay time below which the marginal wave number at the onset of instability is zero and another specific limit on the delay time above which steady flow is always unstable crucially the threshold of absolute stability generally does not coincide with an inflection point of the steady state velocity function when the marginal perturbation at onset has wave number 0 we show that burgers and korteweg de vries kdv equations can be derived under the usual assumptions and that corrections to the kdv equation select a single member of the one parameter set of its one soliton solutions by driving a slow evolution of the soliton parameter while in previous models this selected soliton has always marked the threshold of a finite amplitude instability of linearly stable steady flow we find that it can alternatively be a stable small amplitude jam that occurs when steady flow is linearly unstable the model reduces to the usual modified korteweg de vries mkdv equation only in the special situation that the threshold of absolute stability coincides with an inflection point of the steady state velocity function in general near the threshold of absolute stability the model reduces instead to a kdv equation in the regime of small solitons while near an inflection point it reduces to a hayakawa nakanishi equation like the mkdv equation the hayakawa nakanishi equation admits a continuous family of kink solutions and the selection criterion arising from the corrections to this equation can be written down explicitly language en

gas kinetic derivation of navier stokes like traffic equations macroscopic traffic models have recently been severely criticized to base on lax analogies only and to have a number of deficiencies therefore this paper shows how to construct a logically consistent fluid dynamic traffic model from basic laws for the acceleration and interaction of vehicles these considerations lead to the gas kinetic traffic equation of paveri fontana its stationary and spatially homogeneous solution implies equilibrium relations for the fundamental diagram the variance density relation and other quantities which are partly difficult to determine empirically paveri fontana s traffic equation allows the derivation of macroscopic moment equations which build a system of non closed equations this system can be closed by the well proved method of chapman and enskog which leads to euler like traffic equations in zeroth order approximation and to navier stokes like traffic equations in first order approximation the latter are finally corrected for the finite space requirements of vehicles it is shown that the resulting model is able to withstand the above mentioned criticism

representations of kac moody algebras by step algebras representations of a kac moody algebra associated to a semisimple lie algebra g which decompose to a direct sum of finite dimensional representations of the subalgebra g are constructed using a step algebra method the cases g su 2 su 3 are considered in detail

solvable optimal velocity models and asymptotic trajectory in the optimal velocity model proposed as a new version of car following model it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density a well established congested flow obtained in a numerical simulation shows a remarkable repetitive property such that the velocity of a vehicle evolves exactly in the same way as that of its preceding one except a time delay t this leads to a global pattern formation in time development of vehicles motion and gives rise to a closed trajectory on delta x v headway velocity plane connecting congested and free flow points to obtain the closed trajectory analytically we propose a new approach to the pattern formation which makes it possible to reduce the coupled car following equations to a single difference differential equation rondo equation to demonstrate our approach we employ a class of linear models which are exactly solvable we also introduce the concept of asymptotic trajectory to determine t and v b the backward velocity of the pattern the global parameters associated with vehicles collective motion in a congested flow in terms of parameters such as the sensitivity a which appeared in the original coupled equations

density waves in the full velocity difference model density waves are investigated in the full velocity difference model fvdm analytically and numerically by the use of nonlinear analysis the burgers korteweg de vries kdv and modified kdv equations are derived for the triangular shock wave the soliton wave and the kink antikink wave respectively appearing in the stable region out of the coexisting curve near the spinodal line and in the unstable region within the spinodal line it is shown numerically that the triangular shock wave and the soliton wave are determined by the initial perturbation configuration and different initial perturbations will produce different waveforms in the stable region or near the spinodal line

traffic behavior in a mixture of different vehicles the car following models are extended to take into account the characteristics of different vehicles the characteristic of each car can be included in the parameter of the dimensionless delay time the traffic behavior is investigated analytically and numerically under the periodic boundary condition at a low density all the vehicles move at a constant velocity when the density is larger than the critical value the traffic flow becomes unstable and the density waves appear the jamming transition does not depend only on the mean value of the dimensionless delay time but also on the variation with increase in the variation of dimensionless delay time the jamming transition occurs at a higher value of the mean value it is found that the variation of vehicles stabilizes the traffic flow and suppresses the traffic jams the transition line obtained by the linear stability analysis is compared with the simulation result

stochastic optimal velocity model and its long lived metastability in this paper we propose a stochastic cellular automaton model of traffic flow extending two exactly solvable stochastic models i e the asymmetric simple exclusion process and the zero range process moreover it is regarded as a stochastic extension of the optimal velocity model in the fundamental diagram flux density diagram our model exhibits several regions of density where more than one stable state coexists at the same density in spite of the stochastic nature of its dynamical rule moreover we observe that two long lived metastable states appear for a transitional period and that the dynamical phase transition from a metastable state to another metastable stable state occurs sharply and spontaneously

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

numerical simulation of soliton and kink density waves in traffic flow with periodic boundaries abstract the soliton and kink antikink density waves are simulated with periodic boundaries by adding perturbation in the initial condition on single lane road based on a car following model they are reproduced in the form of the space time evolution of headway both of which propagate backwards it is found that the solitons appear only near the neutral stability line regardless of the boundary conditions and they exhibit upward form when the initial headway is smaller than the safety distance otherwise they exhibit downward form comparison is made between the numerical and analytical results about the amplitude of kink antikink wave and the underlying mechanism is analyzed besides it is indicated that the maximal current of traffic flow increases with decreasing safety distance the numerical simulation shows a good agreement with the analytical results

r matrix and mickelsson algebras for orthosymplectic quantum groups let x1d524 be a complex orthogonal or symplectic lie algebra and x1d524 x1d524 the lie subalgebra of rank rk x1d524 rk x1d524 1 of the same type we give an explicit construction of generators of the mickelsson algebra zq x1d524 x1d524 in terms of chevalley generators via the r matrix of uq x1d524

jamming transition in pedestrian counter flow a lattice gas model with biased random walkers is presented to mimic the pedestrian counter flow in a channel under the open boundary condition of constant density there are two types of walkers without the back step the one is the random walker going to the right and the other is the random walker going to the left it is found that a dynamical jamming transition from the freely moving state at low density to the stopped state at high density occurs at the critical density the transition point is given by pc 0 45 0 01 not depending on the system size the transition point depends on the strength of drift and decreases with increasing drift also we present the extended model to take into account the traffic rule in which a pedestrian walks preferably on the right hand side of the channel

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

deterministic models for traffic jams abstract we study several deterministic one dimensional traffic models for integer positions and velocities we find the typical high and low density phases separated by a simple transition if positions and velocities are continuous variables the model shows self organized critically driven by the slowest car

compression of almost periodic data this paper presents the simple and double compression algorithms with error control for the compression of sets of data coming from almost periodic functions the compressed data are given as several chebyshev series with minimax properties the error control gives an estimation of the final error of the compression and it let the automatization of all the processes

parallel evaluation of chebyshev and trigonometric series abstract in this paper we introduce a general parallel algorithm for the evaluation of chebyshev and trigonometric series the algorithm is based on a recurrence property that allows the effective implementation on partial sums that can be calculated independently several examples carried out on a cray t3d are provided comparing the forsythe and clenshaw parallel algorithms

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

step algebras of quantum algebras of type a b and d we study the step algebras for the quantum algebras corresponding to the lie algebra pairs and

nonlinear analysis of a differential difference equation with next nearest neighbour interaction for traffic flow we analyse the newell whitham type car following model described by a differential difference equation with a generalized optimal velocity function which depends not only on the headway of each car but also on the headway of the immediately preceding one linear stability analysis shows that the model is stabilized for larger delay time by taking into account the headway of the immediately preceding car from the nonlinear analysis the propagating kink solution for traffic jams is obtained the fundamental diagram and the relation between the headway and the delay time are examined by numerical simulation we find that the result from the nonlinear analysis is in good agreement with that obtained from the numerical simulation

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

irregular uq sl 3 representations at roots of unity via gel fand weyl zetlin basis the gel fand weyl zetlin gwz description of the uq sl 3 irregular irreps at roots of unity is explicitly given those are irreps fixed by the same parameters as the unitary irreducible representations uirs of su 3 yet having dimensions smaller than their classical counterparts the reason being that to obtain an irregular irrep one has to make factorization of an additional submodule this description is made geometrically transparent by an arrangement of the standard su 3 gwz basis in a hexagonal pyramid which is valid for any q and seems new even for q 1 the pyramid has as a base the standard hexagon which gives the weight space of the uirs of su 3 in the plane of third component of isospin iz and hypercharge y while third dimension of this pyramid is related to the isospin i algebraically this arrangement is related to a one to one correspondence between the abstract gwz states and monomials in the algebra of raising generators uq g however those monomials are not in the standard poi

the theoretical analysis of the lattice hydrodynamic models for traffic flow theory abstract the lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model but also connected with the microscopic car following model closely the modified korteweg de vries mkdv equation related to the density wave in a congested traffic region has been derived near the critical point since nagatani first proposed it but the korteweg de vries kdv equation near the neutral stability line has not been studied which has been investigated in detail for the car following model we devote ourselves to obtaining the kdv equation from the original lattice hydrodynamic models and the kdv soliton solution to describe the traffic jam especially we obtain the general soliton solution of the kdv equation and the mkdv equation we review several lattice hydrodynamic models which were proposed recently we compare the modified models and carry out some analysis numerical simulations are conducted to demonstrate the nonlinear analysis results

phase diagram of a non signalized t shaped intersection abstract in this paper we investigated a non signalized t shaped intersection using the cellular automata model under the open boundary condition two different priority rules at intersection are introduced rule 1 rule 2 to eliminate the jam packed state phase diagram and its variation with the ratios of right and or left turning vehicles are investigated the space time and the density profiles are also studied the simulation results indicate that the system does not show the same performance under different priority rules where rule 1 resp rule 2 can be better than rule 2 resp rule 1 according to the ratios of turning vehicles