Related papers: Non-local time evolution equation with singular in…
In three space dimensions, we consider the compressible inviscid model describing the time evolution of two fluids sharing the same velocity and enjoying the algebraic pressure closure. By employing the technique of convex integration, we…
In the recent paper by Bernardini et al. [J. Comput. Phys. 232 (2013), 1-6] the discrepancy in the performance of finite difference and spectral models for simulations of flows with a preferential direction of propagation was studied. In a…
We propose a microscopic traffic model where the update velocity is determined by the deceleration capacity and response time. It is found that there is a class of collisions that cannot be distinguished by simply comparing the stop…
In this paper, we introduce a dynamical urban planning model. This leads us to study a system of nonlinear equations coupled through multi-marginal optimal transport problems. A simple case consists in solving two equations coupled through…
We present a detailed analysis of non-degenerate time-homogeneous It\^o-stochastic differential equations with low local regularity assumptions on the coefficients. In particular the drift coefficient may only satisfy a local integrability…
Balancing traffic flow by influencing drivers' route choices to alleviate congestion is becoming increasingly more appealing in urban traffic planning. Here, we introduce a discrete dynamical model comprising users who make their own…
We derive a local-time path-integral representation for a generic one-dimensional time-independent system. In particular, we show how to rephrase the matrix elements of the Bloch density matrix as a path integral over x-dependent local-time…
The initial boundary value problem for a class of scalar non autonomous conservation laws in one space dimension is proved to be well posed and stable with respect to variations in the flux. Targeting applications to traffic, the regularity…
Traffic on a circular road is described by dynamic programming equations associated to optimal control problems. By solving the equations analytically, we derive the relation between the average car density and the average car flow, known…
In this paper we present numerical models for electrodynamical flows with time-dependent electrical fields with transport of bubbles. Such models are applied in e-jet printing, e.g., additive manufacturing (AM), and convective cooling,…
We propose a model describing the traffic flow on a road with variable widths in this paper. The model, which is modified the Aw-Rascle model, is not conservative because of the source term. We obtain the elementary waves of the new traffic…
Traffic flow forecasting is a crucial task in transportation management and planning. The main challenges for traffic flow forecasting are that (1) as the length of prediction time increases, the accuracy of prediction will decrease; (2)…
We propose a new approximation-technique to deal with the exact macroscopic integro-differential evolution equations of statistical systems which self-consistently accounts for dissipative effects. Concentrating on one and two point…
We study traffic flow on roads with a localized periodic inhomogeneity such as traffic signals, using a stochastic car-following model. We find that in cases of congestion, traffic flow can be optimized by controlling the inhomogeneity's…
We consider an evolution equation generalising the viscous Burgers equation supplemented by an initial condition which is a homogeneous random field. We develop a non-linear framework enabling us to show the existence and regularity of…
Data-driven turbulence modeling is experiencing a surge in interest following algorithmic and hardware developments in the data sciences. We discuss an approach using the differentiable physics paradigm that combines known physics with…
This contribution summarizes and explains various principles from physics which are used for the simulation of traffic flows in large street networks, the modeling of destination, transport mode, and route choice, or the simulation of urban…
By means of microscopic simulations we show that non-instantaneous adaptation of the driving behaviour to the traffic situation together with the conventional measurement method of flow-density data can explain the observed…
Equation-free methods make possible an analysis of the evolution of a few coarse-grained or macroscopic quantities for a detailed and realistic model with a large number of fine-grained or microscopic variables, even though no equations are…
Accurate traffic flow forecasting is essential for the development of intelligent transportation systems (ITS), supporting tasks such as traffic signal optimization, congestion management, and route planning. Traditional models often fail…