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  • Modelling pattern formation through differential repulsion
    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
  • Swarms dynamics approach to behavioral economy: Theoretical tools and price sequences
    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
  • Relative entropy method for the relaxation limit of hydrodynamic models
    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
  • A BGK kinetic model with local velocity alignment forces
    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
  • Micro- and macroscopic modeling of crowding and pushing in corridors
    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
  • Nonlinear stability of stationary solutions to the Kuramoto-Sakaguchi equation with frustration
    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
  • Mean field models for large data–clustering problems
    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
  • Bounded confidence dynamics and graph control: Enforcing consensus
    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
  • Kinetic modelling of multiple interactions in socio-economic systems
    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
  • Synchronization of a Kuramoto-like model for power grids with frustration
    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
  • Convexity and starshapedness of feasible sets in stationary flow networks
    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
  • Vanishing viscosity on a star-shaped graph under general transmission conditions at the node
    Netw. Heterog. Media (IF 1.053) Pub Date : 
    Giuseppe Maria Coclite; Carlotta Donadello

    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
  • Homogenization of multivalued monotone operators with variable growth exponent
    Netw. Heterog. Media (IF 1.053) Pub Date : 2020-05-19
    Svetlana Pastukhova; Valeria Chiadò Piat

    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
  • Deep neural network approach to forward-inverse problems
    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
  • Comparative study of macroscopic traffic flow models at road junctions
    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
  • A new mixed finite element method for the n-dimensional Boussinesq problem with temperature-dependent viscosity
    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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