Related papers: The Godunov Method for a 2-Phase Model

This article describes methods for the deterministic simulation of the collisional Boltzmann equation. It presumes that the transport and collision parts of the equation are to be simulated separately in the time domain. Time stepping…

We consider a continuum of phase oscillators on the circle interacting through an impulsive instantaneous coupling. In contrast with previous studies on related pulse-coupled models, the stability results obtained in the continuum limit are…

The displacive structural phase transition in a two-dimensional model solid due to Benassi and co-workers [PRL 106, 256102 (2011)] is analyzed using Monte Carlo simulations and finite-size scaling. The model is shown to be a member of the…

In this paper, we focus on the different traffic flow models that exist in literature. Due to our frequently encountered confusion among traffic engineers and policy makers, this paper goes into more detail about transportation planning…

This paper investigates the position (state) distribution of the single step binomial (multi-nomial) process on a discrete state / time grid under the assumption that the velocity process rather than the state process is Markovian. In this…

We revisit the momentum independent many-body t-matrix approach for boson systems developed by Shi and Griffin~\cite{sg} and Bijlsma and Stoof~\cite{bs}. Despite its popularity, simplicity, and expected advantage of being its applicability…

This paper firstly show that a recent model (Tian et al., Transpn. Res. B 71, 138-157, 2015) is not able to well replicate the evolution concavity in traffic flow, i.e. the standard deviation of vehicles increases in a concave/linear way…

This paper presents a simple technique of multifractal traffic modeling. It proposes a method of fitting model to a given traffic trace. A comparison of simulation results obtained for an exemplary trace, multifractal model and Markov…

We give a rigorous proof of the fact that a phase transition discovered by Douglas and Kazakov in 1993 in the context of two-dimensional gauge theories occurs. This phase transition can be formulated in terms of the Brownian bridge on the…

In this paper we study a model for traffic flow on networks based on a hyperbolic system of conservation laws with discontinuous flux. Each equation describes the density evolution of vehicles having a common path along the network. In this…

By means of a novel variational approach and using dual maps techniques and general ideas of dynamical system theory we derive exact results about several models of transport flows, for which we also obtain a complete description of their…

We investigate a driven two-channel system where particles on different lanes mutually obstruct each others motion extending an earlier model by Popkov and Peschel [1]. This obstruction may occur in biological contexts due to steric…

Using the concept of self-decomposable subordinators introduced in Gardini et al. [11], we build a new bivariate Normal Inverse Gaussian process that can capture stochastic delays. In addition, we also develop a novel path simulation scheme…

A model for 1D traffic flow is developed, which is discrete in space and time. Like the cellular automaton model by Nagel and Schreckenberg [J. Phys. I France 2, 2221 (1992)], it is simple, fast, and can describe stop-and-go traffic. Due to…

Sampling all possible transition paths between two 3D states of a molecular system has various applications ranging from catalyst design to drug discovery. Current approaches to sample transition paths use Markov chain Monte Carlo and rely…

The focus of our work is to identify conditions for the presence of an isotropic-nematic phase transition in the context of a generic system with isotropic competing interactions. The comment 0709.4205 criticizes our results by showing that…

Recently, it has been claimed (O. V. Gendelman and A. V. Savin, Phys. Rev. Lett. {\bf 84}, 2381 (2000); A.V.Savin and O.V.Gendelman, arXiv: cond-mat/0204631 (2002)) that two nonlinear classical 1-d lattice models show transitions, at finite…

In this paper we propose a multiscale traffic model, based on the family of Generic Second Order Models, which integrates multiple trajectory data into the velocity function. This combination of a second order macroscopic model with…

Experimental results for congested pedestrian traffic are presented. For data analysis we apply a method providing measurements on an individual scale. The resulting velocity-density relation shows a coexistence of moving and stopping…

We present a review of nonequilibrium phase transitions in mass-transport models with kinetic processes like fragmentation, diffusion, aggregation, etc. These models have been used extensively to study a wide range of physical problems. We…