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Related papers: Analysis of the generalised Aw-Rascle model

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We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…

Analysis of PDEs · Mathematics 2009-07-17 Joerg Kampen

This work presents a collapsed generalized Aw-Rascle-Zhang (CGARZ) model, which fits into a generic second order model (GSOM) framework. GSOMs augment the evolution of the traffic density by a second state variable characterizing a property…

Physics and Society · Physics 2017-02-14 Shimao Fan , Ye Sun , Benedetto Piccoli , Benjamin Seibold , Daniel B. Work

In this paper, a particle method is used to approximate the solutions of a "fluid-like" macroscopic traffic flow model for automated vehicles. It is shown that this method preserves certain differential inequalities that hold for the…

Numerical Analysis · Mathematics 2024-01-23 George Titakis , Iasson Karafyllis , Dionysis Theodosis , Ioannis Papamichail , Markos Papageorgiou

Analysis of the generalized Weierstrass-Enneper system includes the estimation of the degree of indeterminancy of the general analytic solution and the discussion of the boundary value problem. Several different procedures for constructing…

Analysis of PDEs · Mathematics 2015-06-26 Paul Bracken , Alfred M. Grundland

We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if…

Analysis of PDEs · Mathematics 2019-05-28 Brian P. Cupps , Jeff Morgan , Bao Quoc Tang

Under ray-optical light transport, the classical ray serves as a linear and local "point query" of light's behaviour. Linearity and locality are crucial to the formulation of sophisticated path tracing and sampling techniques, that enable…

Graphics · Computer Science 2024-01-09 Shlomi Steinberg , Ravi Ramamoorthi , Benedikt Bitterli , Eugene d'Eon , Ling-Qi Yan , Matt Pharr

We consider matrix-valued processes described as solutions to stochastic differential equations of very general form. We study the family of the empirical measure-valued processes constructed from the corresponding eigenvalues. We show that…

Probability · Mathematics 2019-01-10 Jacek Małecki , José Luis Pérez

This paper considers quadratic and super-quadratic reaction-diffusion systems for reversible chemistry, for which all species satisfy uniform-in-time $L^1$ a-priori estimates, for instance, as a consequence of suitable mass conservation…

Analysis of PDEs · Mathematics 2015-11-26 Klemens Fellner , Evangelos Latos , Takashi Suzuki

Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…

Dynamical Systems · Mathematics 2019-10-02 Théophile Caby , Davide Faranda , Giorgio Mantica , Sandro Vaienti , Pascal Yiou

A global-in-time existence theorem for classical solutions of the Vlasow-Darwin system is given under the assumption of smallness of the initial data. Furthermore it is shown that in case of spherical symmetry the system degenerates to the…

Mathematical Physics · Physics 2009-01-26 M. Seehafer

A general organizing principle is proposed that can be used to derive the equations of motion describing the near-equilibrium dynamics of causal and thermodynamically stable relativistic systems. The latter are found to display some new…

Nuclear Theory · Physics 2024-06-04 Lorenzo Gavassino , Marcelo M. Disconzi , Jorge Noronha

We consider infinite-dimensional parabolic rough evolution equations. Using regularizing properties of analytic semigroups we prove global-in-time existence of solutions and investigate random dynamical systems for such equations.

Probability · Mathematics 2019-04-08 Robert Hesse , Alexandra Neamtu

This paper investigates the well-posedness of contact discontinuity solutions and the vanishing pressure limit for the Aw-Rascle traffic flow model with general pressure functions. The well-posedness problem is formulated as a free boundary…

Analysis of PDEs · Mathematics 2025-06-10 Zijie Deng , Wenjian Peng , Tian-Yi Wang , Haoran Zhang

In this paper, the authors show the existence of global in time classical solutions to the 3D quasi-geostrophic system with Ekman pumping for any smooth initial value (possibly large). This system couples an inviscid transport equation in…

Analysis of PDEs · Mathematics 2018-01-17 Matthew D. Novack , Alexis F. Vasseur

This article deals with macroscopic traffic flow models on a road network. More precisely, we consider coupling conditions at junctions for the Aw-Rascle-Zhang second order model consisting of a hyperbolic system of two conservation laws.…

Numerical Analysis · Mathematics 2018-04-23 Oliver Kolb , Guillaume Costeseque , Paola Goatin , Simone Göttlich

Several classes of solutions of the generalized Weierstrass system, which induces constant mean curvature surfaces into four-dimensional Euclidean space are constructed. A gauge transformation allows us to simplify the system considered and…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 P. Bracken , A. M. Grundland

In this paper, we study the generalized Douglas-Rachford algorithm and its cyclic variants which include many projection-type methods such as the classical Douglas-Rachford algorithm and the alternating projection algorithm. Specifically,…

Optimization and Control · Mathematics 2020-04-14 Minh N. Dao , Hung M. Phan

This paper addresses the problem of traffic state estimation (TSE) in the presence of heterogeneous sensors which include both fixed and moving sensors. Traditional fixed sensors are expensive and cannot be installed throughout the highway.…

Systems and Control · Electrical Eng. & Systems 2024-07-04 Suyash C. Vishnoi , Sebastian A. Nugroho , Ahmad F. Taha , Christian G. Claudel

We introduce a formalism to deal with the microscopic modeling of vehicular traffic on a road network. Traffic on each road is uni-directional, and the dynamics of each vehicle is described by a Follow-the-Leader model. From a mathematical…

Physics and Society · Physics 2020-02-25 Rinaldo M. Colombo , Helge Holden , Francesca Marcellini

We generalize a recently introduced traffic model, where the statistical weights are associated with whole trajectories, to the case of two-way flow. An interaction between the two lanes is included which describes a slowing down when two…

Statistical Mechanics · Physics 2009-10-31 Vladislav Popkov , Ingo Peschel