on the hughes model for pedestrian flow the one dimensional case in this paper we investigate the mathematical theory of hughes model for the ow of pedestrians cf 17 consisting of a nonlinear conservation law for the density of pedestrians coupled with an eikonal equation for a potential modelling the common sense of the task we rst consider an approximation of the original model in which the eikonal equation is replaced by an elliptic approximation for such an approximated system we prove existence and uniqueness of entropy solutions in one space dimension in the sense of kru zkov 21 in which the boundary conditions are posed following the approach of bardos et al 7 we use bv estimates on the density and stability estimates on the potential in order to prove uniqueness furthermore we analyse the evolution of characteristics for the original hughes model in one space dimension and study the behaviour of simple solutions in order to reproduce interesting phenomena related to the formation of shocks and rarefaction waves the characteristic calculus is supported by numerical simulations

successive refinement with decoder cooperation and its channel coding duals we study cooperation in multiterminal source coding models involving successive refinement specifically we study the case of a single encoder and two decoders where the encoder provides a common description to both the decoders and a private description to only one of the decoders the decoders cooperate via cribbing i e the decoder with access only to the common description is allowed to observe in addition a deterministic function of the reconstruction symbols produced by the other we characterize the fundamental performance limits in the respective settings of noncausal strictly causal and causal cribbing we use a coding scheme referred to as forward encoding and block markov decoding which builds on one recently used by cuff and zhao for coordination via implicit communication finally we use the insight gained to introduce and solve some dual channel coding scenarios involving multiple access channels with cribbing

convergence of numerical approximations to non linear continuity equations with rough force fields we prove quantitative regularity estimates for the solutions to non linear continuity equations and their discretized numerical approximations on cartesian grids when advected by a rough force field this allows us to not only recover the known optimal regularity for linear transport equations but also to obtain the convergence of a wide range of numerical schemes our proof is based on novel commutator estimates quantifying and extending to the non linear case the classical commutator approach of the theory of renormalized solutions

compactness for nonlinear continuity equations abstract we prove compactness and hence existence for solutions to a class of nonlinear transport equations the corresponding models combine the features of linear transport equations and scalar conservation laws we introduce a new method which gives quantitative compactness estimates compatible with both frameworks

on the modelling of crowd dynamics by generalized kinetic models abstract we introduce a new approach for modelling the behavior of pedestrians which borrows techniques from the kinetic theory of rarefied gazes this approach is based on concepts from the kinetic theory for active particles in our modelling of crowd movements pedestrians are regarded as entities whose microscopic states include a geometric variable to denote position a mechanical variable to denote speed and a variable to describe the rate of development of individual strategies that influence the collective dynamics indeed the third variable is introduced to account for the ability of individuals to modify their dynamics according to specific objectives and strategies the equations eventually obtained are a set of nonlinear integro differential equations of vlasov or boltzmann type

geometric mesh fdm for self adjoint singular perturbation boundary value problems abstract a numerical method based on finite difference method with variable mesh is given for second order singularly perturbed self adjoint two point boundary value problems the original problem is reduced to its normal form and the reduced problem is solved by fdm taking variable mesh geometric mesh the maximum absolute errors max i y x i y i for different values of parameter number of points n and the mesh ratio r for three examples have been given in tables to support the efficiency of the method

probing capacity we consider the problem of optimal probing of states of a channel by transmitter and receiver for maximizing rate of reliable communication the channel is discrete memoryless dmc with i i d states the encoder takes probing actions dependent on the message it then uses the state information obtained from probing causally or noncausally to generate channel input symbols the decoder may also take channel probing actions as a function of the observed channel output and use the channel state information thus acquired along with the channel output to estimate the message we refer to the maximum achievable rate for reliable communication for such systems as the probing capacity we characterize this capacity when the encoder and decoder actions are cost constrained to motivate the problem we begin by characterizing the trade off between the capacity and fraction of channel states the encoder is allowed to observe while the decoder is aware of channel states in this setting of to observe or not to observe state at the encoder we compute certain numerical examples which exhibit a pleasing phenomenon where encoder can observe a relatively small fraction of states and yet communicate at maximum rate i e rate when observing states at encoder is not cost constrained

the discrete memoryless multiple access channel with partially cooperating encoders corresp we introduce the communication situation in which the encoders of a multiple access channel are partially cooperating these encoders are connected by communication links with finite capacities which permit both encoders to communicate with each other first we give a general definition of such a communication process conference then by proving a converse and giving an achievability proof we establish the capacity region of the multiple access channel with partially cooperating encoders it turns out that the optimal conference is very simple

convergence of a difference scheme for conservation laws with a discontinuous flux convergence is established for a scalar finite difference scheme based on the godunov or engquist osher eo flux for scalar conservation laws having a flux that is spatially dependent through a possibly discontinuous coefficient other works in this direction have established convergence for methods employing the solution of 2 2 riemann problems the algorithm discussed here uses only scalar riemann solvers satisfaction of a set of kruzkov type entropy inequalities is established for the limit solution from which geometric entropy conditions follow assuming a piecewise constant coefficient it is shown that these conditions imply l1 contractiveness for piecewise c1 solutions thus extending a well known theorem

a system of convection diffusion equations with small diffusion coefficient arising in semiconductor physics abstract we consider a system of two convection diffusion equations with a small diffusion parameter in one space dimension subject to dirichlet boundary conditions the system governs the evolution of the flow of electrons and holes in semiconductor devices on the dielectrical relaxation time scale the equations are coupled by nonlinear nonlocal electric field driven convection terms we prove the convergence in suitable topologies of the solutions of the diffusion convection problem to the unique solution of the convective limit problem subject to inflow boundary conditions as the diffusion coefficient tends to zero

jamming transition in two dimensional pedestrian traffic abstract jamming transitions of pedestrian traffic are investigated under the periodic boundary condition on the square lattice by the use of the lattice gas model of biased random walkers without the back step the two cases are presented the one with two types of walkers and the other with four types of walkers in the two types of walkers the first is the random walker going to the right and the second is the random walker going up in the four types of walkers the first second third and fourth are respectively the random walkers going to the right left up and down it is found that the dynamical jamming transitions occur at the critical densities the transition points do not depend on the system size for large system but depend strongly on the strength of drift the jamming transitions are compared with that obtained by the cellular automaton model of car traffic

existence results for hughes model for pedestrian flows in this paper we prove two global existence results for hughes model for pedestrian flows under assumptions that ensure that the traces of the solutions along the turning curve are zero for any positive times

a hierarchy of heuristic based models of crowd dynamics we derive a hierarchy of kinetic and macroscopic models from a noisy variant of the heuristic behavioral individual based model of ngai et al disaster med public health prep 3 191 195 2009 where pedestrians are supposed to have constant speeds this ibm supposes that pedestrians seek the best compromise between navigation towards their target and collisions avoidance we first propose a kinetic model for the probability distribution function of pedestrians then we derive fluid models and propose three different closure relations the first two closures assume that the velocity distribution function is either a dirac delta or a von mises fisher distribution respectively the third closure results from a hydrodynamic limit associated to a local thermodynamical equilibrium we develop an analogy between this equilibrium and nash equilibria in a game theoretic framework in each case we discuss the features of the models and their suitability for practical use

real time coding with limited lookahead a real time coding system with lookahead consists of a memoryless source a memoryless channel an encoder which encodes the source symbols sequentially with knowledge of future source symbols up to a fixed finite lookahead d with or without feedback of the past channel output symbols and a decoder which sequentially constructs the source symbols using the channel output the objective is to minimize the expected per symbol distortion for a fixed finite lookahead d 1 we invoke the theory of controlled markov chains to obtain an average cost optimality equation acoe the solution of which denoted by d d is the minimum expected per symbol distortion with increasing d d d bridges the gap between causal encoding d 0 where symbol by symbol encoding decoding is optimal and the infinite lookahead case d where shannon theoretic arguments show that separation is optimal we extend the analysis to a system with finite state decoders with or without noise free feedback for a bernoulli source and binary symmetric channel under hamming loss we compute the optimal distortion for various source and channel parameters and thus obtain computable bounds on d d we also identify regions of source and channel parameters where symbol by symbol encoding decoding is suboptimal finally we demonstrate the wide applicability of our approach by applying it in additional coding scenarios such as the case where the sequential decoder can take cost constrained actions affecting the quality or availability of side information about the source

nonlocal systems of balance laws in several space dimensions with applications to laser technology for a class of systems of nonlinear and nonlocal balance laws in several space dimensions we prove the local in time existence of solutions and their continuous dependence on the initial datum the choice of this class is motivated by a new model devoted to the description of a metal plate being cut by a laser beam using realistic parameters solutions to this model obtained through numerical integrations meet qualitative properties of real cuts moreover the class of equations considered comprises a model describing the dynamics of solid particles along a conveyor belt

stability of conservation laws with discontinuous coefficients we prove l1 contractivity of weak solutions to a conservation law with a flux function that may depend discontinuously on the space variable furthermore we show that the l1 difference between solutions to conservation laws with different flux functions is bounded by the total variation with respect to the space variable of the difference between the flux functions

global solution to the cauchy problem for discrete velocity models of vehicular traffic abstract this paper offers the proof of the existence for large times of the cauchy problem for a class of vehicular traffic models with discrete velocities derived from the mathematical tools of the kinetic theory for active particles this approach has the ability to capture some basic aspects concerning the complexity of the systems under consideration through an appropriate modeling via stochastic games of the interactions at the microscopic scale the proof is related to specific aspects of the real system and hopefully can contribute towards improving the modeling approach

the wave front tracking algorithm for hughes model of pedestrian motion we code the wave front tracking algorithm for hughes model of pedestrian motion with generalized running cost this model displays a nonclassical dynamic at the splitting point between the two directions of motion the wave front tracking scheme provides us with reference solutions for testing numerically the convergence of classical finite volume schemes which do not treat explicitly the dynamics at the turning point

information embedding on actions the problem of optimal actuation for channel and source coding was recently formulated and solved in a number of relevant scenarios in this class of models actions are taken at encoders or decoders either to acquire side information in an efficient way or to control or probe effectively the channel state in this paper the problem of embedding information on the actions is studied for both the source and the channel coding setups in both cases a decoder is present that observes only a function of the actions taken by an encoder or a decoder of an action dependent point to point link for the source coding model this decoder wishes to reconstruct a lossy version of the source being transmitted over the point to point link while for the channel coding problem the decoder wishes to retrieve a portion of the message conveyed over the link for the problem of source coding with actions taken at the decoder a single letter characterization of the set of all achievable tuples of rate distortions at the two decoders and action cost is derived under the assumption that the mentioned decoder observes a function of the actions noncausally strictly causally or causally a special case of the problem in which the actions are taken by the encoder is also solved a single letter characterization of the achievable capacity cost region is then obtained for the channel coding setup with actions examples are provided that shed light into the effect of information embedding on the actions for the action dependent source and channel coding problems

a conservation law with point source and discontinuous flux function modelling continuous sedimentation continuous sedimentation of solid particles in a liquid takes place in a clarifier thickener unit which has one feed inlet and two outlets the aim of the paper is to formulate and analyse a dynamic model for this process under idealized physical conditions the conservation of mass yields the scalar conservation law frac partial u x t partial t frac partial partial x f u x t x s t delta x where delta is the dirac measure s is a source and f is a flux function which is discontinuous at three points in the one dimensional space coordinate x under certain regularity assumptions a procedure for constructing a solution locally in time is presented the nonlinear phenomena are complicated and so is the general construction of a solution the problem of nonuniqueness due to the discontinuities of f u cdot is handled by a generalized entropy condition an advantage of this approach is that the a priori boundary conditions at the discontinuities

a fifth order accurate geometric mesh finite difference method for general nonlinear two point boundary value problems second order boundary value problems are treated using fifth order accurate geometric mesh finite difference approximations the method uses evaluation at two off steps three neighbouring knots and it reduces to simple five terms recurrence relations the formal convergence analysis and error estimate reveals that the truncation errors of the new discretizations are fifth order accurate some physical problems are solved to demonstrate efficiency and reliability of the proposed numerical method the root mean square errors for different values of mesh ratio parameter have been given in tables to support the utility of the method

boundary conditions for nonlinear hyperbolic systems of conservation laws we propose two formulations of the boundary conditions for nonlinear hyperbolic systems of conservation laws a first approach is based on the vanishing viscosity method and a second one is related to the riemann problem the equivalence between these two conditions is studied the latter formulation is extended to treat numerically physically relevant boundary conditions monodimensional experiments are presented