understanding interarrival and interdeparture time statistics from interactions in queuing systems abstract we discuss the statistics of long queues in which the interdeparture time statistics is dominated by spatial interactions among the elements in a queue rather than the arrival or exit processes based on a fokker planck approach it is possible to calculate the stationary distance distribution among the elements in a queue as a function of their interaction potential the results relate to the ones known from random matrix theory together with the velocity distribution one can determine the time gap distribution as well this yields an analytical approach to the interdeparture and interarrival time distributions of queuing systems with spatially interacting elements while these distributions are usually determined from empirical data or from theoretical assumptions about the arrival or exit process we offer here an alternative interpretation of interdeparture time distributions as an effect of interactions in a queue this is relevant for the understanding of traffic and production systems and for the optimization of the statistical behavior of some queuing systems

on the positivity of the effective action in a theory of random surfaces it is shown that the functional s eta frac 1 24 pi int left frac 1 2 left nabla eta right 2 2 eta right d mu 0 defined onc functions on the two dimensional sphere satisfies the inequalitys 0 if is subject to the constraint int e eta 1 d mu 0 0 the minimums 0 is attained at the solutions of the euler lagrange equations the proof is based on a sharper version of moser trudinger s inequality due to aubin which holds under the additional constraint int e eta xd mu 0 0 this condition can always be satisfied by exploiting the invariance ofs under the conformal transformations ofs2 the result is relevant for a recently proposed formulation of a theory of random surfaces

modeling highway traffic headway distributions using superstatistics we study traffic clearance distributions i e the instantaneous gap between successive vehicles and time headway distributions by applying the beck and cohen superstatistics we model the transition from free phase to congested phase with the increase of vehicle density as a transition from the poisson statistics to that of the random matrix theory we derive an analytic expression for the spacing distributions that interpolates from the poisson distribution and wigner s surmise and apply it to the distributions of the net distance and time gaps among the succeeding cars at different densities of traffic flow the obtained distribution fits the experimental results for single vehicle data of the dutch freeway a9 and the german freeway a5

a finite element based level set method for fluid elastic solid interaction with surface tension summary a numerical method for simulating fluid elastic solid interaction with surface tension is presented a level set method is used to capture the interface between the solid bodies and the incompressible surrounding fluid within an eulerian approach the mixed velocity pressure variational formulation is established for the global coupled mechanical problem and discretized using a continuous linear approximation in both velocity and pressure three ways are investigated to reduce the spurious oscillations of the pressure that appear at the fluid solid interface first two stabilized finite element methods are used the mini element and the algebraic subgrid method second the surface integral corresponding to the surface tension term is treated either by the continuum surface force technique or by a surface local reconstruction algorithm finally besides the direct evaluation method proposed by bruchon et al an alternative method is proposed to avoid the explicit computation of the surface curvature which may be a source of difficulty these different issues are addressed through various numerical examples such as the two incompressible fluid flow the elastic inclusion embedded into a newtonian fluid or the study of a granular packing copyright 2012 john wiley sons ltd

scalar curvatures on sn soit m n g une variete de riemann compacte de dimension n 3 et r x une fonction lisse sur m n on etudie si r x peut etre la courbure scalaire d une metrique g qui est conforme point par point a la metrique originale g

pedestrian headways reflection of territorial social forces abstract the aim of the article is to give a more detailed insight into territorial social forces acting between pedestrians by means of headway distribution and spectral rigidity probabilistic distribution of time headways between consecutive pedestrians is studied theoretically and experimentally several original experiments empirical observations are presented and compared to data obtained from previously published experiments the study is restricted to an unidirectional one lane motion where overtaking is forbidden the main stress is put on natural choices of mutual interaction represented by logarithmic and hyperbolic potentials leading to gamma and generalized inverse gaussian distribution respectively we show that the time headway distribution does not sufficiently reflect the differences between such distributions the tools related to spectral rigidity and compressibility are chosen instead so as to predict the territorial social forces more accurately surprisingly pedestrian flow seems to show a higher level of synchronization lower compressibility than vehicular flow

headways in traffic flow remarks from a physical perspective traffic flow can be understood as a realization of a broad class of one dimensional physical systems where a hard core repulsive interaction competes with a longer ranged attraction between the particles it can be shown rigorously that the statistical properties of such systems in thermal equilibrium are well described by a family of distributions that stems from the random matrix theory analyzing the traffic data from different sources we show that traffic on real roads belongs to that class of random matrix distributions also various traffic simulation models show a similar behavior it is demonstrated in such a way that the headway distribution of a highway traffic that serves usually as a paradigm of systems driven far from equilibrium is reasonably well described by a distribution originating from equilibrium statistical physics

the scalar curvature flow on s n perturbation theorem revisited for the problem of finding a geometry on s n for n 3 with a prescribed scalar curvature there is a well known result which is called the perturbation theorem it is due to chang and yang duke math j 64 27 69 1991 their key assumption is that the candidate f for the prescribed scalar curvature is sufficiently near the scalar curvature of the standard metric in the sup norm it is important to know how large that difference in sup norm can possibly be here we consider prescribing scalar curvature problem using the scalar curvature flow

conformal deformation of metrics on s 2 soit d un domaine lisse de s 2 et k une fonction lisse definie sur d alors pour que le probleme aux limites de neumann u k exp 2u 1 sur d u n 0 sur d ait une solution u on a a quand aire d max x d k x 0

three methods for estimating a range of vehicular interactions abstract we present three different approaches how to estimate the number of preceding cars influencing a decision making procedure of a given driver moving in saturated traffic flows the first method is based on correlation analysis the second one evaluates quantitatively deviations from the main assumption in the convolution theorem for probability and the third one operates with advanced instruments of the theory of counting processes statistical rigidity we demonstrate that universally accepted premise on short ranged traffic interactions may not be correct all methods introduced have revealed that minimum number of actively followed vehicles is two it supports an actual idea that vehicular interactions are in fact middle ranged furthermore consistency between the estimations used is surprisingly credible in all cases we have found that the interaction range the number of actively followed vehicles drops with traffic density whereas drivers moving in congested regimes with lower density around 30 vehicles per kilometer react on four or five neighbors drivers moving in high density flows respond to two predecessors only

conformal metrics on the unit ball with prescribed mean curvature this paper focuses on the study of the prescribed mean curvature problem on the unit ball if the difference between the mean curvature candidate f and mean curvature of the standard metric in the supremum norm is sufficiently small then the existence of positive solutions of conformal mean curvature equation has been known the purpose of the paper is to investigate quantitatively how large that difference can be by using a flow method

extremals of determinants of laplacians on etudie le determinant associe au laplacien en fonction de la metrique sur une surface donnee et en particulier ses valeurs extremes quand la metrique est bien restreinte

the concentrated solutions on the nonhomogeneous scalar curvature problem abstract we consider the following scalar curvature equation u 1 e k x u 2 1 in r n if k x is nonhomogeneous at the critical points we give the precise description on the concentrated solutions which contains the necessary and existence on the two peak solutions here we generalize the results of cao noussair yan in 6 to the nonhomogeneous case

extremal metrics of zeta function determinants on 4 manifolds in conformal geometry the sobolev inequality at a critical exponent has received much attention in particular the determination of the best constants has played a crucial role in the yamabe problem in dimension two the analogous problem deals with the moser trudinger inequality on a compact riemann surface m2 there exists a constant c c m so that f e47w2 c m if f ivw12 1 and f w 0 the connection of this inequality with geometry comes through the zeta functional determinant of the laplacian as defined by ray singer for a riemannian metric g let 0 a1 a2 be the spectrum

spectral rigidity of vehicular streams random matrix theory approach using a method originally developed for the random matrix theory we derive an approximate mathematical formula for the number variance n l describing the rigidity of particle ensembles with a power law repulsion the resulting relation is compared with the relevant statistics of the single vehicle data measured on the dutch freeway a9 the detected value of the inverse temperature which can be identified as a coefficient of the mental strain of the car drivers is then discussed in detail with the relation to the traffic density and flow j

scalar curvature functions in a conformal class of metrics and conformal transformations on etudie le probleme de prescrire la courbure scalaire dans une classe conforme pour l action du groupe conforme on montre l universalite des conditions d integrabilite dues a j l kazdan et f w warner

the adaptive verlet method we discuss the integration of autonomous hamiltonian systems via dynamical rescaling of the vector field reparameterization of time appropriate rescalings e g based on normalization of the vector field or on minimum particle separation in an n body problem do not alter the time reversal symmetry of the flow and it is desirable to maintain this symmetry under discretization for standard form mechanical systems without rescaling this can be achieved by using the explicit leapfrog verlet method we show that explicit time reversible integration of the reparameterized equations is also possible if the parameterization depends on positions or velocities only for general rescalings a scalar nonlinear equation must be solved at each step but only one force evaluation is needed the new method also conserves the angular momentum for an n body problem the use of reversible schemes together with a step control based on normalization of the vector field arclength reparameterization is demonstrated in several numerical experiments including a double pendulum the kepler problem and a three body problem

a perturbation method for spinorial yamabe type equations on s m and its application for m ge 2 we prove the existence of non trivial solutions for a certain kind of nonlinear dirac equations with critical sobolev nonlinearities on s m via a perturbative variational method for the special case m 2 this establishes the existence of a conformal immersion s 2 rightarrow mathbb r 3 with prescribed mean curvature h which is close to a positive constant under an index counting condition on h

compactness results in conformal deformations of riemannian metrics on manifolds with boundaries this paper is devoted to the study of a problem arising from a geometric context namely the conformal deformation of a riemannian metric to a scalar flat one having constant mean curvature on the boundary by means of blow up analysis techniques and the positive mass theorem we show that on locally conformally flat manifolds with umbilic boundary all metrics stay in a compact set with respect to the c2 norm and the total leray schauder degree of all solutions is equal to 1 then we deduce from this compactness result the existence of at least one solution to our problem

theoretical predictions for vehicular headways and their clusters this paper presents a derivation of analytical predictions for steady state distributions of netto time gaps among clusters of vehicles moving inside a traffic stream using the thermodynamic socio physical traffic model with short ranged repulsion between particles originally introduced in krbalek and helbing 2004 physica a 333 370 we first derive the time clearance distribution in the model and confront it with relation to the theoretical criteria for the acceptability of analytical clearance distributions consecutively the approximating statistical distributions for the so called time multi clearances are calculated by means of the theory of functional convolutions moreover all the theoretical surmises used during the above mentioned calculations are evaluated by the statistical analysis of traffic data the mathematical predictions acquired in this paper are thoroughly compared with relevant empirical quantities and discussed in the context of traffic theory