• Netw. Heterog. Media (IF 1.053) Pub Date : 2020-09-09
Julien Barré; Pierre Degond; Diane Peurichard; Ewelina Zatorska

Motivated by experiments on cell segregation, we present a two-species model of interacting particles, aiming at a quantitative description of this phenomenon. Under precise scaling hypothesis, we derive from the microscopic model a macroscopic one and we analyze it. In particular, we determine the range of parameters for which segregation is expected. We compare our analytical results and numerical

更新日期：2020-09-10
• Netw. Heterog. Media (IF 1.053) Pub Date : 2020-09-09
Nicola Bellomo; Sarah De Nigris; Damián Knopoff; Matteo Morini; Pietro Terna

This paper presents a development of the mathematical theory of swarms towards a systems approach to behavioral dynamics of social and economical systems. The modeling approach accounts for the ability of social entities are to develop a specific strategy which is heterogeneously distributed by interactions which are nonlinearly additive. A detailed application to the modeling of the dynamics of prices

更新日期：2020-09-10
• Netw. Heterog. Media (IF 1.053) Pub Date : 2020-09-09
José Antonio Carrillo; Yingping Peng; Aneta Wróblewska-Kamińska

We show how to obtain general nonlinear aggregation-diffusion models, including Keller-Segel type models with nonlinear diffusions, as relaxations from nonlocal compressible Euler-type hydrodynamic systems via the relative entropy method. We discuss the assumptions on the confinement and interaction potentials depending on the relative energy of the free energy functional allowing for this relaxation

更新日期：2020-09-10
• Netw. Heterog. Media (IF 1.053) Pub Date : 2020-09-09
Young-Pil Choi; Seok-Bae Yun

The global Cauchy problem for a local alignment model with a relaxational inter-particle interaction operator is considered. More precisely, we consider the global-in-time existence of weak solutions of BGK model with local velocity-alignment term when the initial data have finite mass, momentum, energy, and entropy. The analysis involves weak/strong compactness based on the velocity moments estimates

更新日期：2020-09-10
• Netw. Heterog. Media (IF 1.053) Pub Date : 2020-09-09
Michael Fischer; Gaspard Jankowiak; Marie-Therese Wolfram

Experiments with pedestrians revealed that the geometry of the domain, as well as the incentive of pedestrians to reach a target as fast as possible have a strong influence on the overall dynamics. In this paper, we propose and validate different mathematical models at the micro- and macroscopic levels to study the influence of both effects. We calibrate the models with experimental data and compare

更新日期：2020-09-10
• Netw. Heterog. Media (IF 1.053) Pub Date : 2020-09-09
Seung-Yeal Ha; Hansol Park; Yinglong Zhang

We study measurable stationary solutions for the kinetic Kuramoto-Sakaguchi (in short K-S) equation with frustration and their stability analysis. In the presence of frustration, the total phase is not a conserved quantity anymore, but it is time-varying. Thus, we can not expect the genuinely stationary solutions for the K-S equation. To overcome this lack of conserved quantity, we introduce new variables

更新日期：2020-09-10
• Netw. Heterog. Media (IF 1.053) Pub Date : 2020-09-09
Michael Herty; Lorenzo Pareschi; Giuseppe Visconti

We consider mean-field models for data–clustering problems starting from a generalization of the bounded confidence model for opinion dynamics. The microscopic model includes information on the position as well as on additional features of the particles in order to develop specific clustering effects. The corresponding mean–field limit is derived and properties of the model are investigated analytically

更新日期：2020-09-10
• Netw. Heterog. Media (IF 1.053) Pub Date : 2020-09-09
GuanLin Li; Sebastien Motsch; Dylan Weber

A generic feature of bounded confidence type models is the formation of clusters of agents. We propose and study a variant of bounded confidence dynamics with the goal of inducing unconditional convergence to a consensus. The defining feature of these dynamics which we name the No one left behind dynamics is the introduction of a local control on the agents which preserves the connectivity of the interaction

更新日期：2020-09-10
• Netw. Heterog. Media (IF 1.053) Pub Date : 2020-09-09
Giuseppe Toscani; Andrea Tosin; Mattia Zanella

Unlike the classical kinetic theory of rarefied gases, where microscopic interactions among gas molecules are described as binary collisions, the modelling of socio-economic phenomena in a multi-agent system naturally requires to consider, in various situations, multiple interactions among the individuals. In this paper, we collect and discuss some examples related to economic and gambling activities

更新日期：2020-09-10
• Netw. Heterog. Media (IF 1.053) Pub Date : 2020-09-09
Xiaoxue Zhao; Zhuchun Li

We discuss the complete synchronization for a Kuramoto-like model for power grids with frustration. For identical oscillators without frustration, it will converge to complete phase and frequency synchronization exponentially fast if the initial phases are distributed in a half circle. For nonidentical oscillators with frustration, we present a framework leading to complete frequency synchronization

更新日期：2020-09-10
• Netw. Heterog. Media (IF 1.053) Pub Date :
Martin Gugat; Rüdiger Schultz; Michael Schuster

In this paper, we consider a stationary model for the flow through a network. The flow is determined by the values at the boundary nodes of the network. We call these values the loads of the network. In the applications, the feasible loads must satisfy some box constraints. We analyze the structure of the set of feasible loads. Our analysis is motivated by gas pipeline flows, where the box constraints

更新日期：2020-07-20
• Netw. Heterog. Media (IF 1.053) Pub Date :

In this paper we consider a family of scalar conservation laws defined on an oriented star shaped graph and we study their vanishing viscosity approximations subject to general matching conditions at the node. In particular, we prove the existence of converging subsequence and we show that the limit is a weak solution of the original problem.

更新日期：2020-07-20
• Netw. Heterog. Media (IF 1.053) Pub Date : 2020-05-19

We consider the Dirichlet problem for an elliptic multivalued maximal monotone operator ${\mathcal A}_\varepsilon$ satisfying growth estimates of power type with a variable exponent. This exponent $p_\varepsilon(x)$ and also the symbol of the operator ${\mathcal A}_\varepsilon$ oscillate with a small period $\varepsilon$ with respect to the space variable $x$. We prove a homogenization result

更新日期：2020-07-20
• Netw. Heterog. Media (IF 1.053) Pub Date : 2020-04-30
Hyeontae Jo; Hwijae Son; Hyung Ju Hwang; Eun Heui Kim

In this paper, we construct approximated solutions of Differential Equations (DEs) using the Deep Neural Network (DNN). Furthermore, we present an architecture that includes the process of finding model parameters through experimental data, the inverse problem. That is, we provide a unified framework of DNN architecture that approximates an analytic solution and its model parameters simultaneously

更新日期：2020-04-30
• Netw. Heterog. Media (IF 1.053) Pub Date : 2020-04-30
Paola Goatin; Elena Rossi

We qualitatively compare the solutions of a multilane model with those produced by the classical Lighthill-Whitham-Richards equation with suitable coupling conditions at simple road junctions. The numerical simulations are based on the Godunov and upwind schemes. Several tests illustrate the models' behaviour in different realistic situations.

更新日期：2020-04-30
• Netw. Heterog. Media (IF 1.053) Pub Date : 2020-04-10
Javier A. Almonacid; Gabriel N. Gatica; Ricardo Oyarzúa; Ricardo Ruiz-Baier

In this paper we propose a new mixed-primal formulation for heat-driven flows with temperature-dependent viscosity modeled by the stationary Boussinesq equations. We analyze the well-posedness of the governing equations in this mathematical structure, for which we employ the Banach fixed-point theorem and the generalized theory of saddle-point problems. The motivation is to overcome a drawback in a

更新日期：2020-04-10
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