Particle Interactions Mediated by Dynamical Networks: Assessment of Macroscopic Descriptions

We provide a numerical study of the macroscopic model of Barré et al. (Multiscale Model Simul, 2017, to appear) derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodeling process is very fast, the macroscopic model takes the form of a single aggregation–diffusion equation for the density of particles. The theoretical study of the macroscopic model gives precise criteria for the phase transitions of the steady states, and in the one-dimensional case, we show numerically that the stationary solutions of the microscopic model undergo the same phase transitions and bifurcation types as the macroscopic model. In the two-dimensional case, we show that the numerical simulations of the macroscopic model are in excellent agreement with the predicted theoretical values. This study provides a partial validation of the formal derivation of the macroscopic model from a microscopic formulation and shows that the former is a consistent approximation of an underlying particle dynamics, making it a powerful tool for the modeling of dynamical networks at a large scale.     

Balanced vehicular traffic at a bottleneck

The balanced vehicular traffic model is a macroscopic model for vehicular traffic flow. We use this model to study the traffic dynamics at highway bottlenecks either caused by the restriction of the number of lanes or by on-ramps or off-ramps. The coupling conditions for the Riemann problem of the system are applied in order to treat the interface between different road sections consistently. Our numerical simulations show the appearance of synchronized flow at highway bottlenecks.     

Short-time dynamics in the presence of wave–particles interactions: A perturbative approach

The self-consistent interaction between a beam of charged particles and a wave is considered, within a Vlasov picture. The model is discussed with reference to the case of a Free Electron Laser. Starting with a spatially bunched water-bag distribution, we derive, via perturbative methods, closed analytical expressions for the time evolution of the main macroscopic observables. Predictions of the theory are shown to agree with direct numerical simulations.     

Modeling of the effective viscoelastic material behavior of textile reinforced composites using a multi-scale approach

The increasing importance of constructive lightweight in modern engineering science involves the use of advanced materials like textile reinforced composites. In order to reduce development costs, efficient numerical simulations are needed to model the macroscopic behavior of the final product. Focussing on long term phenomena, which are important when parts made of composites with rate-dependent material behavior are assembled by bolted or screwed joints, a two-step homogenization procedure is used to obtain an effective homogeneous equivalent material at the macroscopic scale. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of a micro–macro acceleration method with minimum relative entropy moment matching

We analyse convergence of a micro–macro acceleration method for the simulation of stochastic differential equations with time-scale separation. The method alternates short bursts of path simulations with the extrapolation of macroscopic state variables forward in time. After extrapolation, a new microscopic state is constructed, consistent with the extrapolated macroscopic state, that minimises the perturbation caused by the extrapolation in a relative entropy sense. We study local errors and numerical stability of the method to prove its convergence to the full microscopic dynamics when the extrapolation time step tends to zero and the number of macroscopic state variables tends to infinity.     

Dynamical properties of a stochastic predator-prey model with functional response

A stochastic prey-predator model with functional response is investigated in this paper. A complete threshold analysis of coexistence and extinction is obtained. Moreover, we point out that the stochastic predator-prey model undergoes a stochastic Hopf bifurcation from the viewpoint of numerical simulations. Some numerical simulations are carried out to support our results.     

Simulating vehicular traffic in a network using dynamic routing

We present a new numerical code which solves the Lighthill – Whitham model, the classic macroscopic model for vehicular traffic flow, in a network with multi-destinations. We use a high-resolution shock-capturing scheme with approximate Riemann solver to solve the partial differential equations of the Lighthill – Whitham theory. These schemes are very efficient, robust and moreover well adapted to simulations of traffic flows. We develop a theory of dynamic routing including a procedure for traffic flow assignment at junctions which reproduces the correct propagation of irregularities and ensures at the same time conservation of the number of vehicles.     

Efficient and accurate numerical modeling of a micro–macro nonlinear optics model for intense and short laser pulses

In this work we are interested in the fast simulation of ultrashort and intense laser pulses propagating in macroscopic nonlinear media. In this goal, we consider the numerical micro–macro Maxwell–Schrödinger-Plasma model originally presented by Lorin et al. [9], [10]. Although this model is, in theory, applicable to large domains, due to its computational complexity, only short distances of propagation could be considered (less than 1 mm so far, see [9]). In the present paper, we explore some simple, but fast and accurate techniques allowing to reduce the computational complexity by a large factor (up to 60) and then to consider larger domains. This reduction is naturally essential to make this model relevant to study realistic laser–matter interactions at a macroscopic scale. Numerical simulations are proposed to illustrate the chosen approach.     

Generalized distortional hardening in a thermomechanically coupled framework

In many metals like aluminum the evolution of the microstructure leads to an evolution of the macroscopic yield surface. Clearly, isotropic and kinematic hardening models cannot capture this effect realistically. For that purpose, a new generalized distortional hardening model is proposed. This novel approach belongs to the class of so-called generalized standard materials and is thermodynamically consistent. Although the approach is relatively simple, it shows several advantages like yield surface convexity and yield limit saturation. This novel model is embedded into a thermomechanically coupled finite strain framework. Several numerical simulations show the predictive capabilities. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Thermo‐Mechanical Formulation Describing the Frictional Behavior of Rubber

In this paper mechanical and thermal phenomena during the sliding motion of a rubber block on a rough surface are investigated. The presented formulation describes the frictional behavior of rubber on a macroscopic scale. Thus, it is not necessary to consider the roughness of the surface explicitly. Only macroscopic characteristics of the involved solids are required for the contact formulation. For the purpose of parameter identification and model verification, experiments have been carried out. The results from numerical simulations by means of the Finite Element Method (FEM) agree well with the experimental results.