bifurcation phenomena in the optimal velocity model for traffic flow in the optimal velocity model with a time lag we show that there appear multiple exact solutions in some ranges of car density describing a metastable uniform flow a metastable congested flow and an unstable congested flow this establishes the presence of subcritical hopf bifurcations our analytical results have implications for continuum traffic flow such as hysteresis phenomena associated with discontinuous transitions between uniform and congested flow

analysis of the backward euler langevin method for molecular dynamics this paper develops the theory of a recently introduced computational method for molecular dynamics the method in question uses the backward euler method to solve the classical langevin equations of a molecular system parameters are chosen to produce a cutoff frequency c which may be set equal to kt h to simulate quantum mechanical effects in the present paper an ensemble of identical hamiltonian systems modeled by the backward euler langevin method is considered an integral equation for the equilibrium phase space density is derived and an asymptotic analysis of that integral equation in the limit t 0 is performed the result of this asymptotic analysis is a second order partial differential equation for the equilibrium phase space density expressed as a function of the constants of the motion this equation is solved in two special cases a system of coupled harmonic oscillators and a diatomic molecule with a stiff bond

statistics of collapsing lattice animals we consider several lattice models of branched polymers in dilute solution in which the polymer molecule is modelled as a tree or animal in general the thermodynamic properties of the polymer are determined by monomer monomer and monomer solvent interactions we examine a two variable model which incorporates both types of interaction and discuss its relationship to other models which have previously been investigated in particular we discuss the collapse transition in these models

renormalized field theory of collapsing directed randomly branched polymers we present a dynamical field theory for directed randomly branched polymers and in particular their collapse transition we develop a phenomenological model in the form of a stochastic response functional that allows us to address several interesting problems such as the scaling behavior of the swollen phase and the collapse transition for the swollen phase we find that by choosing model parameters appropriately our stochastic functional reduces to the one describing the relaxation dynamics near the yang lee singularity edge this corroborates that the scaling behavior of swollen branched polymers is governed by the yang lee universality class as has been known for a long time the main focus of our paper lies on the collapse transition of directed branched polymers we show to arbitrary order in renormalized perturbation theory with ensuremath epsilon expansion that this transition belongs to the same universality class as directed percolation

an extended continuum traffic model with the consideration of the optimal velocity difference abstract in this letter we derived an extended continuum model from a car following model with consideration of the optimal velocity difference called the relative optimal velocity via employing the transformation relation from microscopic variables to macroscopic ones the stability condition of this continuum traffic model is obtained by performing linear stability analysis results show that the optimal velocity difference helps to improve the stability of traffic flow we make use of the upwind finite difference scheme for simulation the effects of the optimal velocity difference the relative optimal velocity and the velocity difference the optimal velocity on local clustering effect and instability are studied and compared each other respectively the spatiotemporal evolution patterns of traffic flow for the different initial density strength of the optimal velocity difference and the velocity difference are obtained their space time diagrams reveal the local clustering effect induced by the instability of traffic flow and generate the stop go traffic jams numerical simulation result indicates the unstable region is shrunken under the effect of the optimal velocity difference the relative optimal velocity and or the velocity difference the optimal velocity

two velocity difference model for a car following theory abstract in the light of the optimal velocity model a two velocity difference model for a car following theory is put forward considering navigation in modern traffic to our knowledge the model is an improvement over the previous ones theoretically because it considers more aspects in the car following process than others then we investigate the property of the model using linear and nonlinear analyses the korteweg de vries equation for short the kdv equation near the neutral stability line and the modified korteweg de vries equation for short the mkdv equation around the critical point are derived by applying the reductive perturbation method the traffic jam could be thus described by the kdv soliton and the kink anti kink soliton for the kdv equation and mkdv equation respectively numerical simulations are made to verify the model and good results are obtained with the new model

emd based refined composite multiscale entropy analysis of complex signals abstract multiscale entropy mse is an effective method to measure the complexity of signals from complex systems which has been applied to various fields successfully however mse may yield an inaccurate estimate of entropy and induce undefined entropy as the coarse graining procedure reduces the length of data considerably at large scales refined composite multiscale entropy rcmse is then developed to solve this problem however trends superimposed in signals may significantly affect the complexity measurement thus we introduce an empirical mode decomposition based rcmse called emd rcmse to first eliminate such effects of trends and then measure the complexity of signals it is validated from simulated signals and has good estimation in addition this method is also applied to study the complexity of traffic signals and we obtain some interesting results 1 traffic signals are more complex than the results showing from rcmse mse 2 weekday and weekend patterns different combination of trends greatly affect the results 3 complexity indices change with time at each day due to the degree of human activities

geometrical arguments against the alexander orbach conjecture for lattice animals and diffusion limited aggregates geometrical arguments are given which suggest that the alexander orbach conjecture 1982 does not hold for lattice animals in d 2 and for the diffusion limited aggregates for large dimensions

metropolis monte carlo simulation of lattice animals we propose and study a metropolis monte carlo algorithm for the simulation of weighted lattice animals in in the canonical ensemble with a fixed number of edges we examine the implementation and performance of the algorithm data obtained by sampling uniformly weighted animals and animals weighted as critical percolation clusters are reported and analysed in particular we estimate autocorrelation times and dynamical exponents to study the efficiency of the algorithm and estimate the metric and branch exponents of lattice animals in two and three dimensions

two dimensional lattice vesicles and polygons we consider a lattice model of two dimensional vesicles in which the boundary of the vesicle is the perimeter of a self avoiding polygon embeddable in the square lattice with fixed boundary length m we incorporate an osmotic pressure difference by associating a fugacity with the area enclosed by the polygon we derive rigorous results concerning the behaviour of the associated free energy and the form of the phase diagram by deriving exact values ofthe numbers of polygons with m edges which enclose area n and analysing the resulting series we obtain the free energy the phase boundary and various scaling exponents and amplitudes numerically

practical criterion for delay estimation using random perturbations many systems contain an internal time delay which significantly influences their dynamical properties methods to estimate this delay from times series in the presence of dynamical noise are not systematically studied addressing this problem we demonstrate that it is sufficient to analyze the system s response to short correlated external disturbances or internal noise following this idea it is shown for linear and nonlinear systems as well as for periodic dynamics that the delay can be estimated by analyzing the correlation function this method covers the case of strong noise and multiple delays

linear stability and nonlinear analyses of traffic waves for the general nonlinear car following model with multi time delays abstract in this paper the general nonlinear car following model with multi time delays is investigated in order to describe the reactions of vehicle to driving behavior platoon stability and string stability criteria are obtained for the general nonlinear car following model burgers equation and korteweg de vries kdv equation and their solitary wave solutions are derived adopting the reductive perturbation method we investigate the properties of typical optimal velocity model using both analytic and numerical methods which estimates the impact of delays about the evolution of traffic congestion the numerical results show that time delays in sensing relative movement is more sensitive to the stability of traffic flow than time delays in sensing host motion

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

robotic reactions delay induced patterns in autonomous vehicle systems fundamental design principles are presented for vehicle systems governed by autonomous cruise control devices by analyzing the corresponding delay differential equations it is shown that for any car following model short wavelength oscillations can appear due to robotic reaction times and that there are tradeoffs between the time delay and the control gains the analytical findings are demonstrated on an optimal velocity model using numerical continuation and numerical simulation

stabilization effect of multiple drivers desired velocities in car following theory abstract in order to reveal the influence of driver s individual behavior on traffic flow more accurately a new car following model is proposed with consideration of multiple drives desired velocities the stability criterion of the new model is derived through linear stability theory and the results show that the current driver s desired velocity can stabilize traffic flow but the preceding driver s desired velocity can damage traffic stability through nonlinear analysis the traffic jamming transition characteristics near the critical point can be described by the kink antikink soliton of the mkdv equation numerical simulation confirms the analytical results which shows that the multiple drivers desired velocities play an important role in traffic evolution

multistability and stable asynchronous periodic oscillations in a multiple delayed neural system abstract we consider a network of three identical neurons with multiple discrete signal transmission delays the model for such a network is a system of nonlinear delay differential equations after some consideration of the absolute synchronization of the system and the global attractivity of the zero solution we present a detailed discussion about the boundaries of the stability region of the trivial solution this allows us to determine the possible codimension one bifurcations which occur in the system in particular we show the existence of standard hopf bifurcations giving rise to synchronized periodic solutions and of d 3 equivariant hopf bifurcations giving rise to three types of periodic solutions phase locked mirror reflecting and standing waves hopf hopf and hopf steady state bifurcations interactions are shown to exist and give rise to coexistence of stable synchronized and desynchronized solutions perturbation techniques coupled with the floquet theory are used to determine the stability of the phase locked oscillations

modeling and application analysis of car following model with predictive headway variation abstract this work proposes an improved microscopic model by taking the predictive driving behavior of the preceding car into account firstly we use the linear method to investigate performance of the proposed model deduce the critical linear stability conditions and obtain a neutral curve accounting for stability of the new model then using the nonlinear analysis technique we derive the equations of burgers the korteweg de vries kdv and the modified kdv mkdv respectively to describe the triangular shock wave soliton density wave and the kink antikink density wave finally numerical experiments unfold from two aspects one for verifying the theoretical analysis results and another for testing the impact of predictive driving behavior of the preceding car on traffic stability simulation results show that the new model can stabilize traffic flow compared with the fvd model and confirm that the existence of three kinds of density waves in different phase diagram regions

bifurcation analysis of a class of car following traffic models abstract we consider a follow the leader traffic model describing the dynamics of n cars on a circular road where each car driver chooses his acceleration according to a certain law the model is represented by a nonlinear system of ode s this model is known to have a solution with constant velocities and headways which in a certain parameter regime is stable varying the density of the cars we prove that the loss of stability is generally due to a hopf bifurcation also we investigate numerically the global bifurcation diagram for periodic solutions and obtain a complete picture of the dynamics of general optimal velocity models finally some analytical results on the stability of solutions in the case of non equal drivers are given

bifurcation analysis of a speed gradient continuum traffic flow model abstract a bifurcation analysis approach is presented based on the macroscopic traffic flow model this method can be used to describe and predict the nonlinear traffic phenomena on the highway from a system global stability perspective based on a recently proposed speed gradient continuum traffic flow model the types and stabilities of the equilibrium solutions are discussed and the existence of hopf bifurcation and saddle node bifurcation is proved then various bifurcations such as hopf bifurcation saddle node bifurcation limit point bifurcation of cycles cusp bifurcation and bogdanov takens bifurcation are found and the traffic flow behaviors at some of them are analyzed when the hopf bifurcation is selected as the starting point of density temporal evolution it may help to explain the stop and go traffic phenomena

analysis of optimal velocity model with explicit delay we analyze the optimal velocity model ovm with explicit delay the properties of congestion and the delay time of car motion are investigated by analytical and numerical methods it is shown that the small explicit delay time has almost no effects in the case of the large explicit delay time a new phase of congestion pattern of ovm seems to appear

an improved inertia model to reproduce car following instability abstract in order to better study dynamic traffic experiment and modeling are two common methods through experiments some interesting phenomena and conclusions can be found in the experiment of jiang et al 2014 the standard deviations of speeds of cars show a concave tendency the amplitudes of car accelerations become larger along the car platoon however the simulation results by the inertia model and 2d inertia model cannot be consistent with the experimental ones quantitatively to this end we put forward an improved 2d inertial model in which different mechanisms of acceleration and deceleration are considered as a result both the speed standard deviation and acceleration tendency in simulation can match to the experimental ones moreover the fundamental relationship between flow rate density and speed has been analyzed there are different traffic dynamics at the high density from homogeneous mega jam initial configuration

bifurcations and multiple traffic jams in a car following model with reaction time delay we investigate an optimal velocity car following model for n cars on a circular singlelane road where reaction time delay of drivers is taken into account the stability of the uniform ow equilibrium is studied analytically while bifurcating periodic solutions for difierent wave numbers are investigated with numerical continuation techniques this reveals that the periodic solution with the smallest wave number may be stable and all other periodic solutions are unstable as n is increased periodic solutions develop stop and go fronts that correspond to rapid deceleration and acceleration between regions of uniformly owing and stagnant tra c in terms of the positions of all cars on the ring these fronts are associated with tra c jams all tra c jams form a tra c pattern that evolves under time due to slow motion of the fronts the tra c pattern corresponding to the stable periodic motion of cars is the only stable one however we flnd that other periodic orbits may be unstable only so weakly that they give rise to transient tra c jams that may persist for long times eventually such tra c jams either merge with one another or disperse until the stable tra c pattern is reached

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

nonlinear analysis of the optimal velocity difference model with reaction time delay abstract we investigate the effect of reaction time delay of drivers upon traffic flow analytically and numerically we extend the optimal velocity difference model by taking reaction time delay of drivers into account the stability condition is obtained the burgers korteweg de vries kdv and modified korteweg de vries mkdv equations are derived in the stable metastable and unstable regions the results show that the increase of reaction time delay of drivers leads to the unrealistic traffic phenomena and unstable traffic flow by adjusting the coefficient of the velocity and optimal velocity difference the unrealistic traffic phenomena and unstable traffic flow can disappear

analysis of a continuous car following model for a bus route existence stability and bifurcations of synchronous motions abstract this paper studies the synchronous motions motions for which each of the buses moves with a constant velocity of a car following model for a circular bus route different types of synchronous motion are identified and their local stability is studied using root locus methods the bifurcations of synchronous motions are described and simulation results are given

potts model formulation of branched polymers in a solvent a potts model formulation of the statistics of branched polymers or lattice animals in a solvent is given the migdal kadanoff renormalisation group is employed to study the critical behaviour or fractal dimension of the branched polymer four different critical behaviours are found corresponding to random animal collapse or theta point percolation and compact cluster the theta point behaviour is described by a tricritical point while percolation corresponds to a higher order critical point where the effect of the solvent on the branched polymer is the same as the screening effect of the other clusters in percolation

lattice animal contact models of a collapsing branched polymer the authors consider two lattice animal models for the collapse of dilute branched polymers in a good solvent in both cases the collapse is driven by a near neighbour contact fugacity the two models differing in the way molecular weights are assessed either by the site content or the bond content of the animal they describe some rigorous results including bounds for the temperature dependence of their reduced limiting free energies on a d dimensional hypercubic lattice and compare these results with numerical estimates derived from exact enumeration data from the specific heat they estimate the collapse temperature of both models on a variety of lattices in addition they estimate the cross over exponent phi and find that for both models phi 0 60 or 0 03 d 2 and phi 0 82 or 0 02 d 3

phase diagram of branched polymer collapse the phase diagram of the collapse of a two dimensional infinite branched polymer interacting with the solvent and with itself through contact interactions is studied from the q ensuremath rightarrow 1 limit of an extension of the q state potts model exact solution on the bethe lattice and migdal kadanoff renormalization group calculations shows that there is a line of ensuremath theta transitions from the extended to a single compact phase the ensuremath theta line governed by three different fixed points consists of two lines of extended compact transitions which are in different universality classes and meet in a multicritical point on the other hand directed branched polymers are shown to be completely determined by the strongly embedded case and there is a single ensuremath theta transition which is in the directed percolation universality class textcopyright 1996 the american physical society

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

asymmetric optimal velocity car following model abstract taking the asymmetric characteristic of the velocity differences of vehicles into account we present an asymmetric optimal velocity model for a car following theory the asymmetry between the acceleration and the deceleration is represented by the exponential function with an asymmetrical factor which agrees with the published experiment this model avoids the disadvantage of the unrealistically high acceleration appearing in previous models when the velocity difference becomes large this model is simple and only has two independent parameters the linear stability condition is derived and the phase transition of the traffic flow appears beyond the critical density the strength of interaction between clusters is shown to increase with the asymmetry factor in our model

continuation of bifurcations in periodic delay differential equations using characteristic matrices in this paper we describe a method for continuing periodic solution bifurcations in periodic delay differential equations first the notion of characteristic matrices of periodic orbits is introduced and equivalence with the monodromy operator is demonstrated an alternative formulation of the characteristic matrix is given which can be computed efficiently defining systems of bifurcations are constructed in a standard way including the characteristic matrix and its derivatives for following bifurcation curves in two parameters the pseudo arclength method is used combined with newton iteration two test examples an interrupted machining model and a traffic model with driver reaction time conclude the paper the algorithm has been implemented in the software tool pdde cont

collapse of two dimensional linear polymers we study the collapse transition of a two dimensional very long polymer the model we consider is a lattice model where the chain is represented by a self avoiding walk with nearest neighbor attraction by using the transfer matrix technique we calculate exactly the thermal and geometrical properties of the polymer on strips of finite width we then use finite size scaling to determine the values of the tricritical point exponentsv1 0 55 0 01vu 1 15 0 15 1 v1 1 80 0 05 we compare these results to the other values already proposed in the literature

derivation of continuum traffic flow models from microscopic follow the leader models in this paper we establish a connection between a microscopic follow the leader model based on ordinary differential equations and a semidiscretization of a macroscopic continuum model based on a c

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

on a functional differential equation arising from a traffic flow model we provide a derivation in the context of a traffic flow model as well as both analytical and numerical studies of the functional differential equation z s alpha 2 z s beta z s z s z s here alpha and beta are positive parameters and we are in particular investigating the existence and properties of nonconstant traveling wave type solutions

collapse transition of randomly branched polymers renormalized field theory we present a minimal dynamical model for randomly branched isotropic polymers and we study this model in the framework of renormalized field theory for the swollen phase we show that our model provides a route to understand the well established dimensional reduction results from a different angle for the collapse transition we uncover a hidden becchi rouet stora supersymmetry signaling the sole relevance of tree configurations we correct the long standing one loop results for the critical exponents and we push these results on to two loop order for the collapse transition we find a runaway of the renormalization group flow which lends credence to the possibility that this transition is a fluctuation induced first order transition our dynamical model allows us to calculate for the first time the fractal dimension of the shortest path on randomly branched polymers in the swollen phase as well as at the collapse transition and related fractal dimensions

an optimal velocity estimation ove model based on non empirical formula abstract in many research of optimal velocity model the optimal velocity is estimated by empirical formulas there are several aspects of this approach that need to be improved on the one hand the physical significance of such empirical formulas is not clear enough on the other hand the empirical formula of macro results is not detailed enough at the micro level in this paper we derived an equation to estimate the optimal velocity from two basic assumptions based on this equation the optimal velocity estimation ove model was established to verify the rationality of ove model we conducted two single file pedestrian experiments from the results of experiments we find that pedestrians pursue a consistent velocity and a comfortable distance between pedestrians in single file movement and the comfortable distance is proportional to the square of the steady velocity these conclusions provide support for our assumptions in addition we simulated the experiments with the ovm model and a traditional ov model by comparison the ovm model can reproduce macro results very well further the ovm model has a better performance than traditional ov model in micro level in view of the clear physical meanings our ovm model has an important significance in studying the influencing factors of pedestrian movement

bifurcation analysis of traffic flow through an improved car following model considering the time delayed velocity difference abstract in this paper a new car following model with consideration of time delayed velocity difference is proposed to investigate the effect of time delayed velocity on traffic flow via bifurcation analysis based on this model the linear stability analysis is carried out and the corresponding stability condition is obtained then the hopf bifurcation analysis is performed in term of theoretical analysis and numerical simulation the result shows that there exist hopf bifurcation critical points and the position of the critical points is found to be located on the boundary of the instability region finally the influence of the delay time and sensitivity of velocity difference on hopf bifurcation is discussed respectively

can classical equations simulate quantum mechanical behavior a molecular dynamics investigation of a diatomic molecule with a morse potential in a recent paper we presented a new computational method for molecular dynamics which uses the backward euler scheme to solve the classical langevin dynamics equations parameters for the simulation include a target temperature t a time step t and a cutoff frequency c we showed for a harmonic oscillator system that the cutoff frequency can be set as c kt h in order to mimic quantum mechanical behavior we now continue this investigation for a nonlinear case a diatomic molecule governed by a morse bond potential since approximate quantum mechanical energy levels are explicitly known for this model a comparison of energies can be made with molecular dynamics results by performing dynamics runs for a wide range of temperatures and calculating mean energies we find a very good agreement between these energies and quantum mechanical predictions vibrational excitation begins at temperatures around 800 k and for higher temperatures both energy curves molecular dynamics and quantum mechanics approach the classical prediction of 7 2kt energy per molecule future investigations will focus on more general nonlinear potential functions employed in force fields of nucleic acids and proteins

on pattern formation in a class of traffic models abstract we consider a simple microscopic follow the leader model of n identical cars on a circular road in the classical setting a car is not allowed to reach its leader if it happens at a particular time t e we propose to extend the model beyond this time t e the idea is to define a physically reasonable leader for each car mathematically the resulting model is a kind of filippov system the objective is to study a long time behavior of the model in case n 3 we observed several invariant patterns which apparently exhibit spatial temporal symmetries we managed to classify and identify two kinds of rotating waves the classification exploits symbolic dynamical notions

an improved car following model considering the immediately ahead car s velocity difference abstract the field car following data at a signalized intersection of jinan in china are collected for data mining an improved car following model considering the immediately ahead car s velocity difference on a single lane road was proposed calibrated and verified based on full velocity difference model the results of some numerical simulations indicate that the immediately ahead car s velocity difference has significant effects on the following car s motion that the improved car following model fits the measured data well and can qualitatively describe the impacts of the immediately ahead car s velocity difference on traffic flow and that modeling the car following behavior considering the immediately ahead car s velocity difference can improve the stability of the simulated traffic flow

global bifurcation investigation of an optimal velocity traffic model with driver reaction time we investigate an optimal velocity model which includes the reflex time of drivers after an analytical study of the stability and local bifurcations of the steady state solution we apply numerical continuation techniques to investigate the global behavior of the system specifically we find branches of oscillating solutions connecting hopf bifurcation points which may be super or subcritical depending on parameters this analysis reveals several regions of multistability

stochastic master equation approach to aggregation in freeway traffic in analogy to the usual aggregation phenomena such as the formation of liquid droplets in a supersaturated vapor the nucleation growth and condensation of car clusters are considered in a one lane freeway traffic flow model the clustering behavior known as congestion in an initially homogeneous traffic stream is described by a master equation the construction of the stochastic equation is given as well as its relationship to other dynamical models numerical experiments in heavy traffic with well explained transition probabilities show the transition from the initial free particle situation free jet of vehicles to the final congested cluster state where one big aggregate of cars is formed the results are presented analytically in dependence of the stable cluster size from car concentration and numerically as stochastic trajectories

a new car following model with the consideration of anticipation optimal velocity abstract in this paper a new anticipation optimal velocity model aovm is proposed by considering anticipation effect on the basis of the full velocity difference model fvdm for car following theory on single lane the linear stability condition is derived from linear stability analysis starting and braking process is investigated for the car motion under a traffic signal which shows that the results accord with empirical traffic values especially aovm can avoid the disadvantage of the unrealistically high deceleration appearing in fvdm furthermore numerical simulation shows that aovm might avoid the disadvantage of negative velocity and headway that occur at small sensitivity coefficients in the fvdm since the anticipation effect is taken into account in aovm which means that collision disappears with the consideration of an appropriate anticipation parameter

improved stability bound for steady state flow in a car following model of road traffic on a circular route this note revisits a car following model of road traffic on a circular route that was studied in recent literature and improves a stability result for steady state flows that was obtained in this literature it will be shown through a counter example that the stability bound obtained in the literature only gives a sufficient condition for stability which only becomes necessary when the number of cars on the route tends to infinity we will further present a result that gives a necessary and sufficient condition for stability

on directed interacting animals and directed percolation we study the phase diagram of fully directed lattice animals with nearest neighbour interactions on the square lattice this model comprises several interesting ensembles directed site and bond trees bond animals strongly embeddable animals as special cases and its collapse transition is equivalent to a directed bond percolation threshold precise estimates for the animal size exponents in the different phases and for the critical fugacities of these special ensembles are obtained from a phenomenological renormalization group analysis of the correlation lengths for strips of width up to n 17 the crossover region in the vicinity of the collapse transition is analysed in detail and the crossover exponent is determined directly from the singular part of the free energy we show using scaling arguments and an exact relation due to dhar that is equal to the fisher exponent governing the size distribution of large directed percolation clusters

soliton mass and discrete coupling constants in the quantized sine gordon model the soliton mass in the quantized sine gordon model over the whole range of the coupling constant g2 from 0 to 8 pi is evaluated by means of the gaussian effective potential method the analytical expression with numerical results is presented the authors find that the coupling constant g can only take discrete values a new kind of soliton linking g phi 0 to g phi pi emerges at a set of special coupling constants g

adsorption of branched polymers at surfaces exact results for d 3 exploiting the supersymmetric connection between the statistics of branched polymers and the problem of the yang lee edge singularity the authors study universal properties of the adsorption transition of diluted branched polymers in a three dimensional solution at a hard wall they calculate various scaling functions for the crossover between the non adsorbed and adsorbed state exactly in particular the crossover exponent is found to be phi 1 2

statistics of collapsed lattice animals rigorous results and monte carlo simulations in this paper a two dimensional model of collapsed lattice animals with nearest neighbour contact interactions is introduced and the limiting free energy for the model is proved to exist we also establish that the partition function for collapsed lattice animals is related to the reliability polynomial for the m m grid graph and to the generating function for spanning forests on the m m grid graph from these relationships and using results about directed animals we are able to obtain rigorous upper and lower bounds on the free energy for collapsed lattice animals in addition we present monte carlo evidence that the heat capacity associated with this model remains bounded in the thermodynamic limit in fact we do not find any evidence for a second order phase transition for collapsed lattice animals

stability and rupture of bifurcation bridges in semiconductor lasers subject to optical feedback the bifurcation diagram of a single mode semiconductor laser subject to a delayed optical feedback is examined by using numerical continuation methods for this we show how to cope with the special symmetry properties of the equations as the feedback strength is increased branches of modes and antimodes appear and we have found that pairs of modes and antimodes are connected by closed branches of periodic solutions bifurcation bridges such connections seem generically present as new pairs of modes and antimodes appear we subsequently investigate the behavior of the first connection as a function of the linewidth enhancement factor and the feedback phase our results extend and confirm existing results and hypotheses reported in the literature for large values of the linewidth enhancement factor alpha 5 6 bridges break through homoclinic orbits changing the feedback phase unfolds the bifurcation diagram of the modes and antimodes allowing different types of connections between modes

a traffic flow model with overtaking as a filippov system abstract we investigate microscopic models of road traffic in particular we consider a car following model for a single line traffic flow of n identical cars on a circular road the classical differentiable model breaks down at the time instant when two cars collide however the natural action of a driver would be to overtake a slower car in our previous work we proposed a model which simulates the overtaking we observed a large variety of oscillatory solutions oscillatory patterns of the model in the present contribution we formulate our model as a particular filippov system i e odes with discontinuous right hand sides hence we can identify our problem with a well defined solution class we define oscillatory patterns as invariant objects of this filippov system

non universality in the collapse of two dimensional branched polymers in this paper we study the complete phase diagram of a model of interacting branched polymers the model we consider is a lattice animal one where the collapse transition can be driven both by a contact fugacity between two occupied nearest neighbours and by a fugacity related to each occupied edge using a potts model formulation of the problem we conjecture the existence of two different universality classes for the theta transitions with thermal exponents nu and phi equal to 1 2 2 3 and 8 15 8 15 separated by a higher order percolation point we also present convincing numerical evidence for these exponent values using a transfer matrix approach we discuss the possibility of a collapse collapse transition and we predict the behaviour of our model when an adsorbing surface is included

collapse transitions in animals and vesicles we discuss the relationship between the solvent model of collapse in strongly and weakly embeddable lattice animals and a model recently introduced by vanderzande 1993 and by stella et al 1992 we show that there are important qualitative differences in the behaviour predicted by these two models in the compact regime

consensus problems with distributed delays with application to traffic flow models this paper focuses on consensus problems for a class of linear systems with distributed delay that are encountered in modeling traffic flow dynamics in the application problems the distributed delay whose kernel is a gamma distribution with a gap represents the human drivers behavior in the average the aim of the paper is to give a characterization of the regions in the corresponding delay parameter space where a consensus is reached for all initial conditions the structure and properties of the system are fully exploited which leads to explicit and computationally tractable expressions as a by product a stability theory for distributed delay systems with a gamma distribution kernel is developed also explicit expressions for the consensus function al of time delay systems with constant and distributed delays that solve a consensus problem are provided several illustrative examples complete the presentation

assimilating eulerian and lagrangian data in traffic flow models abstract data assimilation of traffic flow remains a challenging problem one difficulty is that data come from different sources ranging from stationary sensors and camera data to gps and cell phone data from moving cars sensors and cameras give information about traffic density while gps data provide information about the positions and velocities of individual cars previous methods for assimilating lagrangian data collected from individual cars relied on specific properties of the underlying computational model or its reformulation in lagrangian coordinates these approaches make it hard to assimilate both eulerian density and lagrangian positional data simultaneously in this paper we propose an alternative approach that allows us to assimilate both eulerian and lagrangian data we show that the proposed algorithm is accurate and works well in different traffic scenarios and regardless of whether ensemble kalman or particle filters are used we also show that the algorithm is capable of estimating parameters and assimilating real traffic observations and synthetic observations obtained from microscopic models

subcritical hopf bifurcations in a car following model with reaction time delay a nonlinear car following model of highway traffic is considered which includes the reaction time delay of drivers linear stability analysis shows that the uniform flow equilibrium of the system loses its stability via hopf bifurcations and thus oscillations can appear the stability and amplitudes of the oscillations are determined with the help of normal form calculations of the hopf bifurcation that also handles the essential translational symmetry of the system we show that the subcritical case of the hopf bifurcation occurs robustly which indicates the possibility of bistability we also show how these oscillations lead to spatial wave formation as can be observed in real world traffic flows

stability of the car following model on two lanes in the case of two lane traffic vehicle drivers always worry about the lane changing actions from neighbor lane this paper studies the stability of a car following model on two lanes which incorporates the lateral effects in traffic the stability condition of the model is obtained by using the linear stability theory the modified korteweg de vries equation is constructed and solved and three types of traffic flows in the headway sensitivity space stable metastable and unstable are classified both analytical and simulation results show that the anxiousness about lane changing from neighbor lane indeed has influence upon people s driving behavior and the consideration of lateral effects could stabilize the traffic flows on both lanes

phase diagram and critical behaviour of homopolymers with steric frustration the effect of steric frustration on the collapse of a linear homopolymer is investigated depending on the temperature and the strength of the frustration we find that three different phases exist swollen compact and branched we study the phase diagram and the critical behaviour of the system through exact enumerations and monte carlo simulations in addition we present an analytical argument which determines qualitatively the phase boundaries despite the similarity between our model and one previously introduced in the literature there is a discrepancy on the value of a critical exponent

time series forecasting using a system of ordinary differential equations this paper presents a hybrid evolutionary method for identifying a system of ordinary differential equations odes to predict the small time scale traffic measurements data we used the tree structure based evolutionary algorithm to evolve the architecture and a particle swarm optimization pso algorithm to fine tune the parameters of the additive tree models for the system of ordinary differential equations we also illustrate some experimental comparisons with genetic programming gene expression programming and a feedforward neural network optimized using pso algorithm experimental results reveal that the proposed method is feasible and efficient for forecasting the small scale traffic measurements data

ordinary differential equations of molecular dynamics abstract the ordinary differential equations of newtonian dynamics are used in atomic simulations with the method of molecular dynamics the basic issues are surveyed and standard algorithms are described several algorithmic variants are discussed some advanced ideas relating to parallel computation are considered

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

density waves in a traffic flow model with reaction time delay abstract density waves are investigated analytically and numerically in the optimal velocity model with reaction time delay of drivers the stability condition of this model is obtained by using the linear stability theory the results show that the decrease of reaction time delay of drivers leads to the stabilization of traffic flow the burgers korteweg de vries kdv and modified korteweg de vries mkdv equations are derived to describe the density waves in the stable metastable and unstable regions respectively the triangular shock waves soliton waves and kink antikink waves appearing respectively in the three distinct regions are derived to describe the traffic jams the numerical simulations are given

simulations of lattice animals and trees the scaling behaviour of randomly branched polymers in a good solvent is studied in two to nine dimensions using as microscopic models lattice animals and lattice trees on simple hypercubic lattices as a stochastic sampling method we use a biased sequential sampling algorithm with re sampling similar to the pruned enriched rosenbluth method perm used extensively for linear polymers essentially we start simulating percolation clusters either site or bond re weigh them according to the animal tree ensemble and prune or branch the further growth according to a heuristic fitness function in contrast to previous applications of perm this fitness function is not the weight with which the actual configuration would contribute to the partition sum but is closely related to it we obtain high statistics of animals with up to several thousand sites in all dimension 2 d 9 in addition to the partition sum number of different animals we estimate gyration radii and numbers of perimeter sites in all dimensions we verify the parisi sourlas prediction and we verify all exactly known critical exponents in dimensions 2 3 4 and 8 in addition we present the hitherto most precise estimates for growth constants in d 3 for clusters with one site attached to an attractive surface we verify for d 3 the superuniversality of the cross over exponent at the adsorption transition predicted by janssen and lyssy but not for d 2 there we find 0 480 4 instead of the conjectured 1 2 finally we discuss the collapse of animals and trees arguing that our present version of the algorithm is also efficient for some of the models studied in this context but showing that it is not very efficient for the classical model for collapsing animals

comment on analysis of optimal velocity model with explicit delay the effect of including an explicit delay time due to driver reaction on the optimal velocity model is studied for a platoon of vehicles to avoid collisions many vehicle simulations demonstrate that delay times must be well below the critical delay time determined by a linear analysis for the response of a single vehicle safe platoons require rather small delay times substantially smaller than typical reaction times of drivers the present results do not support the conclusion of bando et al m bando k hasebe k nakanishi and a nakayama phys rev e 58 5429 1998 that explicit delay plays no essential role