discontinuous transition from free flow to synchronized flow induced by short range interaction between vehicles in a three phase traffic flow model abstract in this paper we incorporate a limitation on the interaction range between neighboring vehicles into the cellular automaton model proposed by gao and jiang et al k gao r jiang s x hu b h wang and q s wu phys rev e 76 2007 026105 which was established within the framework of kerner s three phase traffic theory and has been shown to be able to reproduce the three phase traffic flow this modification eliminates an unrealistic phenomenon found in the previous model where the velocity adaptation effect between neighboring vehicles can exist even if those vehicles are infinitely far away from each other therefore in the improved model we regulate that such interactions can only occur within a finite distance for simplicity we suppose a constant value to describe this distance in this paper as a result when compared to the previous model the improved model mainly simulates the following results which are believed to be an improvement 1 the improved model successfully reproduces the expected discontinuous transition from free flow to synchronized flow and the related moving synchronized flow pattern which are both absent in the original model but have been observed in real traffic 2 the improved model simulates the correlation functions time headway distributions and optimal velocity functions which are all more consistent with the empirical data than the previous model and most of the other models published before 3 together with the previous two models considering the velocity difference effect this model finally accomplishes a significative process of developing traffic flow models from the traditional fundamental diagram approach to the three phase traffic theory this process should be helpful for us to understand the traffic dynamics and mechanics further and deeper

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

phase transition and critical phenomenon in traffic flow model with velocity dependent sensitivity the traffic flow model with optimal velocity is extended to take into account the velocity dependent sensitivity the dependence of the jamming transition upon the sensitivity is investigated in the extended optimal velocity model the phase transition among the freely moving phase the coexisting phase and the homogeneous congested phase is studied by computer simulation order parameter s which is different from zero below the critical point is shown the phase diagrams are obtained for the sensitivity parameters depending upon the car velocity it is shown that the phase boundaries and the critical point depend largely upon the sensitivity parameters the scaling properties of the headway the car velocity and the jam s propagation velocity are found near the critical point it is shown that the scaling exponents are independent upon the velocity dependent sensitivity

time dependent ginzburg landau equation for the jamming transition in traffic flow abstract we present the thermodynamic theory describing the phase transition and critical phenomenon in traffic flow we derive the time dependent ginzburg landau tdgl equation through the modified korteweg de vries kdv equation from the car following model using the perturbation method we find the thermodynamic potential for the jamming transition it is shown that the coexisting and spinodal lines are obtained respectively from the first and second derivatives of the potential we prove that the jamming transition is the first order phase transition below the critical point and metastability exists between the coexisting and spinodal lines

approximate minimization of weighted tree automata abstract this paper studies the following approximate minimization problem given a minimal weighted tree automaton a with n states recognizing a weighted tree language f can we construct a smaller automaton a with n n states recognizing a language f that is a good approximation of f the corresponding problem for weighted automata on strings was recently studied by balle et al 16 15 where the authors introduced a new canonical form for weighted automata called singular value automata inspired by spectral methods and showed that truncating such canonical form yields a solution for the problem satisfying a certain approximation criteria in this paper we take a similar approach and show that in the tree case one can obtain an analogous canonical form that we call singular value tree automata and use it to study the approximate minimization problem for weighted tree automata we first establish the existence of this canonical form for weighted tree automata and then provide bounds on the quality of the resulting approximation method based on truncation we also study the problem of computing the canonical form given a minimal weighted tree automaton and show that in the tree case this task is considerably more complicated than in the string case in particular computing the canonical form reduces to solving a system of polynomial equations by further reducing this problem to the computation of generalized partition functions for weighted tree automata we propose and analyze two methods for computing the canonical form based on iterative methods fixed point iteration and newton s method our analysis of newton s method unveils a connection between iterative methods and sequences of sets of trees satisfying a certain technical condition that might be of independent interest

modeling self consistent multi class dynamic traffic flow abstract in this study we present a systematic self consistent multiclass multilane traffic model derived from the vehicular boltzmann equation and the traffic dispersion model the multilane domain is considered as a two dimensional space and the interaction among vehicles in the domain is described by a dispersion model the reason we consider a multilane domain as a two dimensional space is that the driving behavior of road users may not be restricted by lanes especially motorcyclists the dispersion model which is a nonlinear poisson equation is derived from the car following theory and the equilibrium assumption under the concept that all kinds of users share the finite section the density is distributed on a road by the dispersion model in addition the dynamic evolution of the traffic flow is determined by the systematic gas kinetic model derived from the boltzmann equation multiplying boltzmann equation by the zeroth first and second order moment functions integrating both side of the equation and using chain rules we can derive continuity motion and variance equation respectively however the second order moment function which is the square of the individual velocity is employed by previous researches does not have physical meaning in traffic flow although the second order expansion results in the velocity variance equation additional terms may be generated the velocity variance equation we propose is derived from multiplying boltzmann equation by the individual velocity variance it modifies the previous model and presents a new gas kinetic traffic flow model by coupling the gas kinetic model and the dispersion model a self consistent system is presented

phase transition and critical phenomenon in the power law model of traffic abstract a power law model of traffic is proposed to extend the optimal velocity model of traffic the phase transition and critical phenomenon are investigated by computer simulation it is shown that the phase transition among the freely moving phase the coexisting phase and the homogeneous congested phase occurs below the critical point the dependence of the phase transition upon the power of model is derived from numerical simulation it is found that the headway the car velocity and the jam propagation velocity scale respectively as a c a a c a and a c a with and 2 where a is the sensitivity parameter and a c is its critical value the simulation results is compared with that obtained by the generalized traffic flow model the universality class of this model is definitely different from the generalized traffic flow model

holomorphic curves in surfaces of general type this note answers some questions on holomorphic curves and their distribution in an algebraic surface of positive index more specifically we exploit the existence of natural negatively curved pseudo finsler metrics on a surface s of general type whose chern numbers satisfy c 2 1 2c2 to show that a holomorphic map of a riemann surface to s whose image is not in any rational or elliptic curve must satisfy a distance decreasing property with respect to these metrics we show as a consequence that such a map extends over isolated punctures so assuming that the riemann surface is obtained from a compact one of genus q by removing a finite number of points then the map is actually algebraic and defines a compact holomorphic curve in s furthermore the degree of the curve with respect to a fixed polarization is shown to be bounded above by a multiple of q 1 irrespective of the map

defect relations for holomorphic maps between spaces of different dimensions there is now a rather rich theory of defect relations for holomorphic maps between spaces of equal dimension developed by nevanlinna stoll griffiths and many other people however for the case of maps between spaces of unequal dimension essentially there is only the theory developed by weyl weyl and ahlfors when the target space is the complex projective space and their theory is built on the projective linear structure of the projective space a partial list of references for these results is given at the end of this paper in this paper we derive a defect relation for holomorphic maps between spaces of different dimensions where the target space can be an arbitrary compact complex algebraic manifold since the special case of maps from c to a compact complex manifold of complex dimension two contains already the methods and techniques needed for the general case in order to avoid unnecessarily complicated notations and to make the arguments more easily understood we give complete details only for this special case and indicate the easy modifications needed for the general case besides the usual techniques in value distribution theory of using the poincar6 lelong formula the calculus lemma of estimating the integrand by its integral and the concavity of logarithm a new key point in our argument is to introduce a meromorphic connection so that the second fundamental form of a divisor with respect to the connection is zero more precisely for the case of a meromorphic map f from c to a compact kihler surface m to consider the defect for a nonsingular zero set of a holomorphic section s of a positive holomorphic line bundle l we introduce a meromorphic connection i v form with the following two properties i for some hermitian holomorphic line bundle f over m and some holomorphic section 0 of f

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

definable transductions and weighted logics for texts a text is a word together with an additional linear order on it we study quantitative models for texts i e text series which assign to texts elements of a semiring we introduce an algebraic notion of recognizability following reutenauer and bozapalidis as well as weighted automata for texts combining an automaton model of lodaya and weil with a model of esik and nemeth after that we show that both formalisms describe the text series definable in a certain fragment of weighted logics as introduced by droste and gastin in order to do so we study certain definable transductions and show that they are compatible with weighted logics

hyperbolicity of nodal hypersurfaces we show that a nodal hypersurface x in p3 of degree d with a sufficiently large number l of nodes l 8 3 d2 5 2 d is algebraically quasi hyperbolic i e x can only have finitely many rational and elliptic curves our results use the theory of symmetric differentials and algebraic foliations and give a very striking example of the jumping of the number of symmetric differentials in families

phase transition and scaling in the generalized traffic flow model the optimal velocity traffic model is generalized to the power law type of the optimal velocity the phase transition among the freely moving phase the coexisting phase and the homogeneous congested phase is investigated by computer simulation and the linear stability theory phase diagrams are obtained for various values of the power it is shown that the phase boundary and the critical point depend strongly upon the power the scaling behaviors of the headway the car velocity and the propagation velocity of jams are studied near the critical point it is found that the headway and the car velocity scale as ac a and ac a with n n 1 and the propagation velocity of jams scales as ac a with 2n n 1 where a is the sensitivity ac is its critical value and n is the power of the model

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

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

effective algebraic degeneracy we show that for every smooth projective hypersurface x n 1 of degree d and of arbitrary dimension n 2 if x is generic then there exists a proper algebraic subvariety y x such that every nonconstant entire holomorphic curve f x has image f which lies in y as soon as its degree satisfies the effective lower bound d geqslant 2 n 5

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

hyperbolicity of generic surfaces of high degree in projective 3 space the main goal of this work is to prove that a very generic surface of degree at least 21 in complex projective 3 dimensional space is hyperbolic in the sense of kobayashi this means that every entire holomorphic map f inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i x to the surface is constant in 1970 kobayashi conjectured more generally that a very generic hypersurface of sufficiently high degree in projective space is hyperbolic our technique follows the stream of ideas initiated by green and griffiths in 1979 which consists of considering jet differentials and their associated base loci however a key ingredient is the use of a different kind of jet bundle namely the semple jet bundles previously studied by the first named author the base locus calculation is achieved through a sequence of riemann roch formulas combined with a suitable generic vanishing theorem for order 2 jets our method covers the case of surfaces of general type with picard group inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i and 13 12 2 c 2 1 9 c 2 0 where 2 is the 2 jet threshold bounded below by 1 6 for surfaces in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i 3 the final conclusion is obtained by using recent results of mcquillan on holomorphic foliations

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

a remark on the codimension of the green griffiths locus of generic projective hypersurfaces of high degree we show that for every smooth generic projective hypersurface x in p n 1 there exists a proper subvariety y in x of codimension at least 2 such that for every non constant holomorphic map f c x one has f c is contained in y provided that the degree of x is greater than 2 n 5 in particular we obtain an affirmative confirmation of the kobayashi conjecture for threefolds in p 4

algebraic hyperbolicity of the very general quintic surface in p3 abstract we prove that a curve of degree dk on a very general surface of degree d 5 in p 3 has geometric genus at least d k d 5 k 2 1 this gives a substantial improvement on the celebrated genus bounds of geng xu as a corollary we deduce the algebraic hyperbolicity of a very general quintic surface in p 3 resolving a long standing conjecture of demailly this completely determines which very general hypersurfaces in p 3 are algebraically hyperbolic

improved fluid dynamic model for vehicular traffic the fluid dynamic traffic model of kerner and konh auser phys rev e 48 2335 1993 50 54 1994 is extended by an equation for the vehicles velocity variance it is able to describe the observed increase of velocity variance immediately before a traffic jam develops another modification takes into account the finite amount of space that each vehicle needs as a consequence the improved traffic model does not produce densities that exceed the maximum vehicle density or negative velocities like former models did

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

gas kinetic theory and boltzmann equation of share price within an equilibrium market hypothesis and ad hoc strategy recent observations have indicated that the traditional equilibrium market hypothesis emh also known as efficient market hypothesis is unrealistic it is shown here that it is the analog of a boltzmann equation in physics thus having some bad properties of mean field approximations like a gaussian distribution of price fluctuations a kinetic theory for prices can be simply derived considering in a first approach that market actors have all identical relaxation times and solved within a chapman enskog like formalism in closing the set of equations i an equation of state with a pressure and ii the equilibrium isothermal equation for the price taken as the order parameter of a stock as a function of the volume of money available are obtained

vector fields on the total space of hypersurfaces in the projective space and hyperbolicity the results we obtain in this article concern the hyperbolicity of very generic hypersurfaces in the 3 dimensional projective space we show that the kobayashi conjecture is true in this setting as long as the degree of the hypersurface is greater than 18

varieties of recognizable tree series over fields we introduce varieties of recognizable s tree series k s vts for short over a field k and a ranked alphabet s our variety theorem establishes a bijective correspondence between these k s vtss and the varieties of finite dimensional k s algebras k s vfda for short a k s algebra is a k vector space equipped with multilinear s operations the link between k s vtss and k s vfdas is provided by the syntactic k s algebras of tree series the most immediate predecessors of this study are berstel s and reutenauer s 1982 2 work on tree series over fields reutenauer s 1980 27 theory of varieties of string series bozapalidis and his associates 1983 1989 1991 8 5 4 work on syntactic k s algebras steinby s 1979 1992 30 31 theory of varieties of tree languages and our previous work 2009 on series of general algebras and their syntactic k s algebras

existence of global invariant jet differentials on projective hypersurfaces of high degree let x subset mathbb p n 1 be a smooth complex projective hypersurface in this paper we show that if the degree of x is large enough then there exist global sections of the bundle of invariant jet differentials of order n on x vanishing on an ample divisor we also prove a logarithmic version effective in low dimension for the log pair mathbb p n d where d is a smooth irreducible divisor of high degree moreover these result are sharp i e one cannot have such jet differentials of order less than n

on the logarithmic kobayashi conjecture we study the hyperbolicity of the log variety pn x where x is a very general hypersurface of degree d 2n 1 which is the bound predicted by the kobayashi conjecture using a positivity result for the sheaf of twisted logarithmic vector fields which may be of independent interest we show that any log subvariety of pn x is of log general type give a new proof of the algebraic hyperbolicity of pn x and exclude the existence of maximal rank families of entire curves in the complement of the universal degree d hypersurface moreover we prove that as in the compact case the algebraic hyperbolicity of a log variety is a necessary condition for the metric one

effective constructors the formal series of trees french abstract in this paper we exhibit two different effective constructions of the syntactic algebra u s associated with a recognizable tree series s in order to make the first construction we only need a natural number n satisfying dim u s n the second way to obtain u s is by minimization of a given realization of s we finally describe effectively a minimal matrix representation of s

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

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

on the hyperbolicity of the complements of curves in algebraic surfaces the three component case the paper is a contribution to the conjecture of kobayashi that the complement of a generic curve in the projective plane is hyperbolic provided the degree is at least five previously the authors treated the cases of two quadrics and a line and three quadrics the main results are let c be the union of three curves in p 2 whose degrees are at least two one of which is at least three then for generic such configurations the complement of c is hyperbolic and hyperbolically embedded the same statement holds for complements of curves in generic hypersurfaces x of degree at least five and curves which are intersections of x with hypersurfaces of degree at least five furthermore results are shown for curves on surfaces with picard number one

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

the rank of a formal tree power series we prove that a tree series s t k k a field is recognizable iff dim vs iff dim fs where vs resp fs is the subspace if kp resp kt generated by the vectors t 1 s p s t t t p and where t is the set of all trees over and p is the free monoid of all pruned trees over we finally give a myhill like criterion for tree recognizability

recognizable formal power series on trees trees are a very basic object in computer science they intervene in nearly a ly domain and they are studied for their own or used to represent conveniently a given situation there are at least three directions where investigations on trees themselves are motivated and this for different reasons first the notion of tree is the basis of algebraic semantics nivat 19 rosen 2 2 etc in this context the study of special languages of trees i e forests their classification and their behaviour under various types of transformations are of great importance arnold fl dauchet 8 j l ilin 1161 mongy 18 by essence work in this area is an extension of the algebraic theory of languages trees and ianguages are in fact directly related via the derivation trees of an algebraic grammar thatcher 25 a second topic heavily related to trees concerns dzra structures trees mainly binary trees and its variants constitute one of the most widely known data structures see e g hlnuth 15 the analysis of the worst cale expected or average running time t ehzvgrr nfi certain algorithms requires sometimes long and delicate computations flajolet lo kemp 14 flajolet and steyaert 12 finally trees occupy a distinguished place in the enumeration of graphs and maps both because of the simplicity of their structure and for the relationship between their el lcodings and aigebraic languages the nature of the enumerating series and especially the question whether they are algebraic or not is one of the central problems in this domain cori 7 chottin 4 we propose here a theory of formal power series on trees and present some of their basic properties together with various examples of applications which as we hope will show the interest of its development within the framework we just sketched a formal power series on trees is a function which gssociates a number to esch tree thus we could also have called them tree functions ii in analogy with the term word function used by several authors paz and salomaa zo cobham 5 as an equivalent denomination for formal power series on words the main goal of a formal power series is to count or to represent the result of some computation on

holomorphic flexibility properties of complex manifolds we obtain results on approximation of holomorphic maps by algebraic maps the jet transversality theorem for holomorphic and algebraic maps between certain classes of manifolds and the homotopy principle for holomorphic submersions of stein manifolds to certain algebraic manifolds

theoretical foundation of macroscopic traffic models abstract on the basis of the elementary laws of individual driver behavior concerning the acceleration and interaction of vehicles a gas kinetic traffic model is constructed this yields theoretical relations for the fundamental diagram and the equilibrium variance density relation but above all it allows the derivation of macroscopic traffic equations these build a hierarchy of non closed equations which can be closed by different zeroth order approximations in this way one obtains the traffic equations of lighthill and whitham or those of phillips alternatively one can derive euler like traffic equations which are proposed here since they include additional dynamical equations for the velocity variance the new variance equation is able to describe the empirically observed increase of variance directly before a traffic jam develops

traffic flow models considering an internal degree of freedom we solve numerically the integrodifferential equation for the equilibrium case of paveri fontana s boltzmann like traffic equation beside space and actual velocity paveri fontana used an additional phase space variable the desired velocity to distinguish between the various driver characters we refine his kinetic equation by introducing a modified cross section in order to incorporate finite vehicle length we then calculate from the equilibrium solution the mean velocity density relation and investigate its dependence on the imposed desired velocity distribution a further modification is made by modeling the interaction as an imperfect showing down process we find that the velocity cumulants of the stationary homogeneous solution essentially only depend on the first two cumulants but not on the exact shape of the imposed desired velocity distribution the equilibrium solution can therefore be approximated by a bivariate gaussian distribution which is in agreement with empirical velocity distributions from the improved kinetic equation we then derive a macroscopic model by neglecting third and higher order cumulants the equilibrium solution of the macroscopic model is compared with the cumulants of the kinetic equilibrium solution and shows good agreement thus justifying the closure assumption

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

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