analysis of a novel lattice hydrodynamic model considering density integral and backward looking effect abstract by introducing the backward looking influence and the integration form of the density difference between the front and rear vehicles an improved lattice hydrodynamic model is proposed the linear stability condition is derived by linear stability analysis the results of the linear stability analysis demonstrate that the influence of backward looking and density difference between the front and rear vehicles play a positive part in improving the steadiness of the traffic flow system the nonlinear analysis testifies that the mkdv equation can describe the propagation feature of density wave the results of numerical simulation show that the steadiness of traffic flow can be amenable to improvement effectively by considering these two factors comprehensive analysis demonstrates that the effect of the backward looking and density difference is propitious to improve traffic stability and suppress traffic congestion

a new car following model with consideration of the velocity difference between the current speed and the historical speed of the leading car in this study a new car following model is proposed based on taking the effect of the leading vehicle s velocity difference between the current speed and the historical speed into account the model s linear stability condition is obtained via the linear stability theory the time dependent ginzburg landau tdgl equation and the modified korteweg de vries mkdv equation are deduced through the nonlinear analysis the kink antikink soliton can interpret the traffic jams near the critical point in addition the connection between the tdgl and the mkdv equations is also given numerical simulation shows that the new model can improve the stability of traffic flow which is consistent with the theoretical analysis correspondingly

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

analyticity of the density of states in the anderson model on the bethe lattice let h 1 2 v on l2 b whereb is the bethe lattice andv x xeb are i i d r v s with common probability distribution it is shown that for distributions sufficiently close to the cauchy distribution the density of states e is analytic in a strip about the real axis

stability analysis of a new lattice hydrodynamic model by considering lattice s self anticipative density effect abstract in this paper a new lattice hydrodynamic model with consideration of the density difference of a lattice s current density and its anticipative density is proposed the influence of lattice s self anticipative density on traffic stability is revealed through linear stability theory and it shows that lattice s self anticipative density can improve the stability of traffic flow to describe the phase transition of traffic flow the mkdv equation near the critical point is derived by using nonlinear analysis method the propagating behavior of density wave in the unstable region can be described by the kink antikink soliton of the mkdv equation numerical simulation validates the analytical results which shows that traffic jam can be suppressed efficiently by considering lattice s self anticipative density in the modified lattice hydrodynamic model

an extended macro traffic flow model accounting for the driver s bounded rationality and numerical tests abstract in this paper we propose a macro traffic flow model to explore the effects of the driver s bounded rationality on the evolutions of traffic waves which include shock and rarefaction waves and small perturbation and on the fuel consumption and emissions that include co hc and no x during the evolution process the numerical results illustrate that considering the driver s bounded rationality can prominently smooth the wavefront of the traffic waves and improve the stability of traffic flow which shows that the driver s bounded rationality has positive impacts on traffic flow but considering the driver s bounded rationality reduces the fuel consumption and emissions only at the upstream of the rarefaction wave while enhances the fuel consumption and emissions under other situations which shows that the driver s bounded rationality has positive impacts on the fuel consumption and emissions only at the upstream of the rarefaction wave while negative effects on the fuel consumption and emissions under other situations in addition the numerical results show that the driver s bounded rationality has little prominent impact on the total fuel consumption and emissions during the whole evolution of small perturbation

analysis of social optimum for staggered shifts in a single entry traffic corridor with no late arrivals abstract this paper investigates the traffic flow dynamics under the social optimum so principle in a single entry traffic corridor with staggered shifts from the analytical and numerical perspectives the lwr lighthill whitham and richards model and the greenshield s velocity density function are utilized to describe the dynamic properties of traffic flow the closed form so solution is analytically derived and some numerical examples are used to further testify the analytical solution the optimum proportion of the numbers of commuters with different desired arrival times is further discussed where the analytical and numerical results both indicate that the cumulative outflow curve under the so principle is piecewise smooth

simulating memory effects with discrete dynamical systems abstract we propose using discrete dynamical systems to model non markovian processes this implies a whole hierarchy of dynamical systems with dimensionality increasing proportional to the memory specific long range memory effects are investigated for a quadratic a cubic and a quartic map markovian processes transform the quadratic map into a normal form of the logistic equation the henon map corresponds to non markovian first generation memory effects higher memories imply new high dimensional systems non markovian processes imply new memory routes to chaos for the three polynomial maps discussed here it is possible to define critical memory lengths above which the systems essentially lose memory

1d quasiperiodic operators latent symmetries a large class of discrete quasiperiodic operators is shown to be decomposed into orbits ofsl 2 z action with equal densities of states moreover under some natural assumptions all nontrivial representatives of the mentioned action transform operators with pure point spectrum into those with absolutely continuous spectrum some applications of these results are presented

the dynamics of the henon map the purpose of this paper is to develop machinery which is suitable for a study of the long time behavior of systems such as the henon map with expansion combined with strong contraction our study is modeled on the treatment of the one dimensional system x 1 ax 2 and we study the perturbation of a from the value a 2 and b small a surprising number of complications arise when b 0 the computer simulations give some indication of the complicated structure of the attractor but it can safely be stated that the real difficulties do not show up the central aim of the paper is to introduce what we consider the relevant concepts and techniques needed to study mappings such as the henon one

dissecting shrimps results for some one dimensional physical models this paper describes how certain shrimp like clusters of stability organize themselves in the parameter space of dynamical systems clusters are composed of an infinite affine similar repetition of a basic elementary cell containing two primary noble points a head and a tail defining an axis of approximate symmetry knowledge of the axis and the skewness of the k periodic main cell of a k 2 cluster is enough to define the orientation of the whole cluster in space peculiarly simple directions along which shrimp like clusters align are formed by the locus of doubly degenerate saddle zero multipliers corresponding to the main shrimp head in addition we report a family of models having the boundaries of all isoperiodic domains of stability totally degenerate and describe different aspects of their mathematical arrangement and some of their consequences for example that shrimps are diffeomorphic copies of shrimps

combined effects of drivers disturbance risk preference heterogeneity and the nearest following vehicle headway on traffic flow instability analytical studies abstract driver s disturbance risk preference is defined as the driver s reaction degree to the disturbance which is a kind of the driver s attributes and can be expressed by the disturbance risk preference coefficient this paper proposes a new car following model and firstly attempts to analytically investigate the combined effects of drivers disturbance risk preference heterogeneity and the nearest following vehicle headway on traffic flow instability under some specific traffic scenarios solution of the model yields many insights including the following 1 when drivers disturbance risk preference increases from the following driver to the preceding driver traffic flow instability increases and the bigger the disturbance risk preference coefficient ratio of the preceding driver s coefficient to the following driver s coefficient the bigger the increasing effect and vice versa at this scenario the nearest following vehicle headway increases traffic flow instability 2 when drivers disturbance risk preference is homogeneous drivers disturbance risk preference and the nearest following vehicle headway have no effects on traffic flow instability 3 when drivers disturbance risk preference reduces from the following driver to the preceding driver for the general traffic situation traffic flow instability reduces and the smaller the disturbance risk preference coefficient ratio of the preceding driver s coefficient to the following driver s coefficient the bigger the reducing effect and vice versa at this scenario if the coefficient ratio reduces from the following to the preceding or is homogeneous the nearest following vehicle headway increases traffic flow instability otherwise the effects of the nearest following vehicle headway on traffic flow instability cannot be confirmed

nonlinear analysis of a new lattice hydrodynamic model with the consideration of honk effect on flux for two lane highway abstract influence of the honk on traffic flux is taken to construct a new lattice model for two lane freeway the linear stability analysis is applied to obtain the stability condition involving the honk effect on traffic flux in two lane system nonlinear analysis is implemented to get the mkdv equation for the phase transition of two lane lattice traffic flow numerical simulation is worked out to authenticate that the impact of honk on traffic flux strengthens the stability of traffic flow and suppresses the traffic congestion effectively under lane changing in two lane lattice traffic flow which is accordance with the analytic results

a novel lattice hydrodynamic model considering the optimal estimation of flux difference effect on two lane highway abstract the optimal estimation of flux difference effect is introduced to construct a new lattice hydrodynamic model for two lane highway through linear stability analysis it is found that the new consideration plays an important influence upon the stability of two lane traffic flow moreover the mkdv equation near the critical point is derived from nonlinear analysis which describes the propagation behavior of traffic jam in two lane traffic system simulation results show that the stability of two lane traffic system can be increased and the emergence of traffic jams are effectively relieved by the optimal estimation of flux difference effect which is in good agreement with theoretical analysis

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

chaotic jam and phase transition in traffic flow with passing the lattice hydrodynamic model is presented to take into account the passing effect in one dimensional traffic flow when the passing constant gamma is small the conventional jamming transition occurs between the uniform traffic and kink density wave flows when passing constant gamma is larger than the critical value the jamming transitions occur from the uniform traffic flow through the chaotic density wave flow to the kink density wave flow with an increasing delay time the chaotic region increases with passing constant gamma the neutral stability line is derived from the linear stability analysis the neutral stability line coincides with the transition line between the uniform traffic and density wave flows the modified korteweg de vries equation describing the kink jam is derived for small values of gamma by use of a nonlinear analysis

random schrodinger operators arising from lattice gauge fields i existence and examples we consider new models of ergodic schrodinger operators whose existence relies on a cohomological theorem of feldman and moore in ergodic theory these operators generalize the harper operator which describes the case of a constant magnetic field an example is the case when the magnetic field is given by independent random variables attached to the lattice plaquettes a generalization of the feldman moore theorem by lind to non abelian groups also allows us to consider schrodinger operators obtained from non abelian lattice gauge fields the existence result extends to more general graphs like to operators on tilings and to higher dimensions we compute some moment expansions for the density of states for example for independent identically and uniformly distributed magnetic fields a model which has been studied at least since 1970 and whose existence can also be seen without involving the above mentioned existence theorem we show that the nth moment is the number of closed paths in the two dimensional lattice starting at the origin for which the winding number vanishes at each plaquette point this goes beyond the brinkman rice self retracing path approximation other examples are a higher dimensional example a one dimensional anderson model which can be treated in this framework as well as the hofstadter model with constant magnetic field where one averages over all possible magnetic fields we also reprove a result of jitomirskaya mandelshtam stating that the deterministic aharonov bohm model is a compact perturbation of the free laplacian

anderson localization for the almost mathieu equation ii point spectrum for lambda 2 we prove that for any 2 and a e the pure point spectrum of the almost mathieu operator h n n 1 n 1 cos 2 n n contains the essential closure hat sigma of the spectrum corresponding eigenfunctions decay exponentially the singular continuous component if it exists is concentrated on a set of zero measure which is nowhere dense in hat sigma

stability of incoherence in a population of coupled oscillators we analyze a mean field model of coupled oscillators with randomly distributed frequencies this system is known to exhibit a transition to collective oscillations for small coupling the system is incoherent with all the oscillators running at their natural frequencies but when the coupling exceeds a certain threshold the system spontaneously synchronizes we obtain the first rigorous stability results for this model by linearizing the fokker planck equation about the incoherent state an unexpected result is that the system has pathological stability properties the incoherent state is unstable above threshold butneutrally stable below threshold we also show that the system is singular in the sense that its stability properties are radically altered by infinitesimal noise

fractional equations of kicked systems and discrete maps starting from kicked equations of motion with derivatives of non integer orders we obtain fractional discrete maps these maps are generalizations of well known universal standard dissipative kicked damped rotator maps the main property of the suggested fractional maps is a long term memory the memory effects in the fractional discrete maps mean that their present state evolution depends on all past states with special forms of weights these forms are represented by combinations of power law functions

the backward looking effect in the lattice hydrodynamic model abstract the novel lattice hydrodynamic model is presented by incorporating the backward looking effect the stability condition for the the model is obtained using the linear stability theory the result shows that considering one following site in vehicle motion leads to the stabilization of the system compared with the original lattice hydrodynamic model and the cooperative driving lattice hydrodynamic model the korteweg de vries kdv for short equation near the neutral stability line is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by kdv soliton solution obtained from the kdv equation the simulation result is consistent with the nonlinear analysis

study on the interval integration effect of vehicle s self delayed velocity on traffic stability in micro traffic modeling abstract a new car following model is proposed in this paper to study the interval integration effect of vehicle s self delayed velocity information on traffic flow the stability condition of the new model is derived through linear analysis and the result shows that the traffic stability can be improved when a longer interval of vehicle s self delayed velocity information is taken into account also it is revealed that the traffic information in the time interval which is far from the present time is more positive in stabilizing traffic flow comparing to the traffic information in the time interval which is close to the present time through nonlinear analysis the mkdv equation is derived to describe the propagation properties of density wave in the unstable region finally the theoretical results are confirmed by numerical simulation

a new lattice model of traffic flow with the consideration of the traffic interruption probability abstract in this paper we present a new lattice model which involves the effects of traffic interruption probability to describe the traffic flow on single lane freeways the stability condition of the new model is obtained by the linear stability analysis and the modified korteweg de vries kdv equation is derived through nonlinear analysis thus the space will be divided into three regions stable metastable and unstable the simulation results also show that the traffic interruption probability could stabilize traffic flow

on the origin of integrability in matrix models the matrix integrals involved in 2d lattice gravity are studied at finiten the integrable systems that arise in the continuum theory are shown to result directly from the formulation of the matrix integrals in terms of orthogonal polynomials the partition function proves to be a tau function of the toda lattice hierarchy the associated linear problem is equivalent to finding the polynomial basis which diagonalizes the partition function the cases of one hermitian matrix one unitary matrix and hermitian matrix chains all fall within the toda framework

cellular automaton for migration in ecosystem application of traffic model to a predator prey system in most cases physicists have studied the migration of biospecies by the use of random walk in the present article we apply cellular automaton of traffic model for simplicity we deal with an ecosystem contains a prey and predator and use one dimensional lattice with two layers preys stay on the first layer but predators uni directionally move on the second layer the spatial and temporal evolution is numerically explored it is shown that the migration has the important effect on populations of both prey and predator without migration the phase transition between a prey phase and coexisting phase occurs in contrast the phase transition disappears by migration this is because predator can survive due to migration we find another phase transition for spatial distribution in one phase prey and predator form a stripe pattern of condensation and rarefaction while in the other phase they uniformly distribute the self organized stripe may be similar to the migration patterns in real ecosystems

a lattice hydrodynamic model based on delayed feedback control considering the effect of flow rate difference abstract in this paper a lattice hydrodynamic model is derived considering not only the effect of flow rate difference but also the delayed feedback control signal which including more comprehensive information the control method is used to analyze the stability of the model furthermore the critical condition for the linear steady traffic flow is deduced and the numerical simulation is carried out to investigate the advantage of the proposed model with and without the effect of flow rate difference and the control signal the results are consistent with the theoretical analysis correspondingly

social optimum for evening commute in a single entry traffic corridor with no early departures abstract in this paper we investigate the evening commute behaviors on the social optimum so state in a single entry traffic corridor with no early departures differing from the previous studies on evening commute the dynamic properties of traffic flow are analyzed with the lwr lighthill whitham richards model the properties of optimum cumulative inflow curve with general desired departure time distribution curve are deduced and then the analytic solutions for common desired departure time in so are obtained three numerical examples are carried out to capture the characteristics of evening commuting behaviors under different values of time the analytic and numerical results both indicate that the rarefaction wave originating from the first entry point influences the whole or part of the outflow curve no shock wave exists through the commuting process in addition the cost curves show that the trip cost increases and the departure delay cost decreases with departure time whereas the travel time cost first increases then decreases with departure time under the so principle

discrete magnetic laplacian we consider a 2 dimensional discrete operator which we call the discrete magnetic laplacian dml it is an analogue of the magnetic schrodinger operator it follows from well known arguments that dml has the same spectrum as a subset inr as the almost mathieu operator am they also have the same integrated density of states ids which is known to be continuous we show that dml is an element in a ii1 factor and its ids can be expressed through the trace in the ii1 factor it follows that dml never has anyl2 eigenfunctions i e has no point spectrum then we formulate a natural algebraic conjecture which implies that the spectrum of dml hence the spectrum of am is a cantor set

a remark on schrodinger operators on aperiodic tilings we prove that for a large class of schrodinger operators on aperiodic tilings the spectrum and the integrated density of states are the same for all tilings in the local isomorphism class i e for all tilings in the orbit closure of one of the tilings this generalizes the argument in earlier work from discrete strictly ergodic operators onl2 d to operators on thel2 spaces of sets of vertices of strictly ergodic tilings

effect of optimal estimation of flux difference information on the lattice traffic flow model abstract in this paper a new lattice model is proposed by considering the optimal estimation of flux difference information the effect of this new consideration upon the stability of traffic flow is examined through linear stability analysis furthermore a modified korteweg de vries mkdv equation near the critical point is constructed and solved by means of nonlinear analysis method and thus the propagation behavior of traffic jam can be described by the kink antikink soliton solution of the mkdv equation numerical simulation is carried out under periodical condition with results in good agreement with theoretical analysis therefore it is verified that the new consideration can enhance the stability of traffic systems and suppress the emergence of traffic jams effectively

the influence of continuous historical velocity difference information on micro cooperative driving stability abstract in this paper a new micro cooperative driving car following model is proposed to investigate the effect of continuous historical velocity difference information on traffic stability the linear stability criterion of the new model is derived with linear stability theory and the results show that the unstable region in the headway sensitivity space will be shrunk by taking the continuous historical velocity difference information into account through nonlinear analysis the mkdv equation is derived to describe the traffic evolution behavior of the new model near the critical point via numerical simulations the theoretical analysis results are verified and the results indicate that the continuous historical velocity difference information can enhance the stability of traffic flow in the micro cooperative driving process

analyticity of the density of states and replica method for random schrodinger operators on a lattice we analyze the density of states and some aspects of the replica method for anderson s tight binding model on a lattice of arbitrary dimension with diagonal disorder we give heuristic arguments for the conjectures that the classical value of the exponent of the localization length is 1 2 and that the upper critical dimension d c loc is bounded by 4 d c loc 6

differential equations with fractional derivative and universal map with memory discrete maps with long term memory are obtained from nonlinear differential equations with riemann liouville and caputo fractional derivatives these maps are generalizations of the well known universal map the memory means that their present state is determined by all past states with special forms of weights to obtain discrete maps from fractional differential equations we use the equivalence of the cauchy type problems and to the nonlinear volterra integral equations of the second kind general forms of the universal maps with memory which take into account general initial conditions for the cases of the riemann liouville and caputo fractional derivative are suggested

analysis of the spectrum of a particle on a triangular lattice with two magnetic fluxes by algebraic and numerical methods the authors consider an electron on a triangular lattice with two magnetic fluxes using a c algebra formalism a perturbation theory around rational fluxes is developed this semiclassical type of analysis leads to the wilkinson rammal formula for the energy eigenvalues the analytic result is verified numerically with high accuracy up to second order crossing of eigenvalues near band edges is shown analytically as well as numerically

jamming transitions and the effect of interruption probability in a lattice traffic flow model with passing abstract a new lattice hydrodynamic model is proposed by considering the interruption probability effect on traffic flow with passing and analyzed both theoretically and numerically from linear and non linear stability analysis the effect of interruption probability on the phase diagram is investigated and the condition of existence for kink antikink soliton solution of mkdv equation is derived the stable region is enhanced with interruption probability and the jamming transition occurs from uniform flow to kink flow through chaotic flow for higher and intermediate values of non interruption effect of passing it is also observed that there exists conventional jamming transition between uniform flow and kink flow for lower values of non interruption effect of passing numerical simulations are carried out and found in accordance with the theoretical findings which confirm that the effect of interruption probability plays an important role in stabilizing traffic flow when passing is allowed