相关论文: Relaxation models for scalar traffic networks and …
We present a new asymptotic strategy for general micro-macro models which analyze complex viscoelastic fluids governed by coupled multiscale dynamics. In such models, the elastic stress appearing in the macroscopic continuum equation is…
We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase…
We consider time-dependent convection-diffusion problems with high P\'eclet number of order $\mathcal{O}(\varepsilon^{-1})$ in thin three-dimensional graph-like networks consisting of cylinders that are interconnected by small domains…
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…
We consider a linear transport equation on the edges of a network with time-varying coefficients. Using methods for non-autonomous abstract Cauchy problems, we obtain well-posedness of the problem and describe the asymptotic profile of the…
A new coupling rule for the Lighthill-Whitham-Richards model at merging junctions is introduced that imposes the preservation of the ratio between inflow from a given road to the total inflow into the junction. This rule is considered both…
While macroscopic models for single or multi-lane traffic flow are well established, these models are not applicable to the dynamics and characteristics of disordered traffic which is characterized by widely different types of vehicles and…
This paper investigates the asymptotic behavior of a hyperbolic relaxation system designed for homogeneous two-phase flows in the limit of vanishing relaxation time. The governing equations comprise conservation laws for mixture mass and…
Starting from microscopic interaction rules we derive kinetic models of Fokker--Planck type for vehicular traffic flow. The derivation is based on taking a suitable asymptotic limit of the corresponding Boltzmann model. As particular cases,…
Multi-lane totally asymmetric simple exclusion processes with interactions between the lanes have recently been investigated actively. This paper proposes a two-lane model with extended Langmuir kinetics on a periodic lattice. Both…
We consider the reflectionless transport of solitons in networks. The system is modeled in terms of the nonlinear Schr\"odinger equation on metric graphs, for which transparent boundary conditions at the branching points are imposed. This…
We investigate a scalar partial differential equation model for the formation of biological transportation networks. Starting from a discrete graph-based formulation on equilateral triangulations, we rigorously derive the corresponding…
We present a fluid-dynamic model for the simulation of urban traffic networks with road sections of different lengths and capacities. The model allows one to efficiently simulate the transitions between free and congested traffic, taking…
It is shown how a recent method to systematically extrapolate and resum the loop expansion for nonlinear sigma-models is related to solutions of the renormalization group equation. This relation is used to generalize the explicit equations…
We consider kinetic and related macroscopic equations on networks. A class of linear kinetic BGK models is considered, where the limit equation for small Knudsen numbers is given by the wave equation. Coupling conditions for the macroscopic…
We study the asymptotic behavior for asymmetric neuronal dynamics in a network of linear Hopfield neurons. The interaction between the neurons is modeled by random couplings which are centered i.i.d. random variables with finite moments of…
Complex networks are a successful framework to describe collective behaviour in many applications, but a notable gap remains in the current literature, that of proving asymptotic convergence in networks of piecewise-smooth systems. Indeed,…
We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semiconductor devices. First, we show the global well-posedness…
We consider singularly perturbed convection-diffusion equations on one-dimensional networks (metric graphs) as well as the transport problems arising in the vanishing diffusion limit. Suitable coupling condition at inner vertices are…
Earlier two of us (J.L. and L.P.) considered a matrix model for a two-level system interacting with a $n\times n$ reservoir and assuming that the interaction is modelled by a random matrix. We presented there a formula for the reduced…