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Telegraph systems on networks and port-Hamiltonians. Ⅱ. Network realizability Netw. Heterog. Media (IF 1.0) Pub Date : 2021-12-24 Jacek Banasiak, Adam Błoch
Hyperbolic systems on networks often can be written as systems of first order equations on an interval, coupled by transmission conditions at the endpoints, also called port-Hamiltonians. However, general results for the latter have been difficult to interpret in the network language. The aim of this paper is to derive conditions under which a port-Hamiltonian with general linear Kirchhoff's boundary
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Well-posedness theory for nonlinear scalar conservation laws on networks Netw. Heterog. Media (IF 1.0) Pub Date : 2021-12-24 Markus Musch, Ulrik Skre Fjordholm, Nils Henrik Risebro
We consider nonlinear scalar conservation laws posed on a network. We define an entropy condition for scalar conservation laws on networks and establish $L^1$ stability, and thus uniqueness, for weak solutions satisfying the entropy condition. We apply standard finite volume methods and show stability and convergence to the unique entropy solution, thus establishing existence of a solution in the process
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Mean-field limit of collective dynamics with time-varying weights Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 Nastassia Pouradier Duteil
In this paper, we derive the mean-field limit of a collective dynamics model with time-varying weights, for weight dynamics that preserve the total mass of the system as well as indistinguishability of the agents. The limit equation is a transport equation with source, where the (non-local) transport term corresponds to the position dynamics, and the (non-local) source term comes from the weight redistribution
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Multiscale models of Covid-19 with mutations and variants Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 Nicola Bellomo,Diletta Burini,Nisrine Outada
This paper focuses on the multiscale modeling of the COVID-19 pandemic and presents further developments of the model [7] with the aim of showing how relaxations of the confinement rules can generate sequential waves. Subsequently, the dynamics of mutations into new variants can be modeled. Simulations are developed also to support the decision making of crisis managers.
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A study of computational and conceptual complexities of compartment and agent based models Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 Prateek Kunwar,Oleksandr Markovichenko,Monique Chyba,Yuriy Mileyko,Alice Koniges,Thomas Lee
The ongoing COVID-19 pandemic highlights the essential role of mathematical models in understanding the spread of the virus along with a quantifiable and science-based prediction of the impact of various mitigation measures. Numerous types of models have been employed with various levels of success. This leads to the question of what kind of a mathematical model is most appropriate for a given situation
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A measure model for the spread of viral infections with mutations Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 Xiaoqian Gong,Benedetto Piccoli
Genetic variations in the COVID-19 virus are one of the main causes of the COVID-19 pandemic outbreak in 2020 and 2021. In this article, we aim to introduce a new type of model, a system coupled with ordinary differential equations (ODEs) and measure differential equation (MDE), stemming from the classical SIR model for the variants distribution. Specifically, we model the evolution of susceptible
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Homogenization of stiff inclusions through network approximation Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 David Gérard-Varet,Alexandre Girodroux-Lavigne
We investigate the homogenization of inclusions of infinite conductivity, randomly stationary distributed inside a homogeneous conducting medium. A now classical result by Zhikov shows that, under a logarithmic moment bound on the minimal distance between the inclusions, an effective model with finite homogeneous conductivity exists. Relying on ideas from network approximation, we provide a relaxed
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Vaccination strategies through intra—compartmental dynamics Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 Rinaldo M. Colombo,Francesca Marcellini,Elena Rossi
We present a new epidemic model highlighting the roles of the immunization time and concurrent use of different vaccines in a vaccination campaign. To this aim, we introduce new intra-compartmental dynamics, a procedure that can be extended to various other situations, as detailed through specific case studies considered herein, where the dynamics within compartments are present and influence the whole
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Optimization of vaccination for COVID-19 in the midst of a pandemic Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 Qi Luo,Ryan Weightman,Sean T. McQuade,Mateo Díaz,Emmanuel Trélat,William Barbour,Dan Work,Samitha Samaranayake,Benedetto Piccoli
During the Covid-19 pandemic a key role is played by vaccination to combat the virus. There are many possible policies for prioritizing vaccines, and different criteria for optimization: minimize death, time to herd immunity, functioning of the health system. Using an age-structured population compartmental finite-dimensional optimal control model, our results suggest that the eldest to youngest vaccination
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A martingale formulation for stochastic compartmental susceptible-infected-recovered (SIR) models to analyze finite size effects in COVID-19 case studies Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 Xia Li,Chuntian Wang,Hao Li,Andrea L. Bertozzi
Deterministic compartmental models for infectious diseases give the mean behaviour of stochastic agent-based models. These models work well for counterfactual studies in which a fully mixed large-scale population is relevant. However, with finite size populations, chance variations may lead to significant departures from the mean. In real-life applications, finite size effects arise from the variance
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Nonlocal reaction traffic flow model with on-off ramps Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 Felisia Angela Chiarello,Harold Deivi Contreras,Luis Miguel Villada
We present a non-local version of a scalar balance law modeling traffic flow with on-ramps and off-ramps. The source term is used to describe the inflow and output flow over the on-ramp and off-ramps respectively. We approximate the problem using an upwind-type numerical scheme and we provide \begin{document}$ \mathbf{L^{\infty}} $\end{document} and \begin{document}$ \mathbf{BV} $\end{document} estimates
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An SIR–like kinetic model tracking individuals' viral load Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 Rossella Della Marca,Nadia Loy,Andrea Tosin
In classical epidemic models, a neglected aspect is the heterogeneity of disease transmission and progression linked to the viral load of each infected individual. Here, we investigate the interplay between the evolution of individuals' viral load and the epidemic dynamics from a theoretical point of view. We propose a stochastic particle model describing the infection transmission and the individual
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Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 Giulia Bertaglia,Liu Liu,Lorenzo Pareschi,Xueyu Zhu
Uncertainty in data is certainly one of the main problems in epidemiology, as shown by the recent COVID-19 pandemic. The need for efficient methods capable of quantifying uncertainty in the mathematical model is essential in order to produce realistic scenarios of the spread of infection. In this paper, we introduce a bi-fidelity approach to quantify uncertainty in spatially dependent epidemic models
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Stochastic two-scale convergence and Young measures Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 Martin Heida,Stefan Neukamm,Mario Varga
In this paper we compare the notion of stochastic two-scale convergence in the mean (by Bourgeat, Mikelić and Wright), the notion of stochastic unfolding (recently introduced by the authors), and the quenched notion of stochastic two-scale convergence (by Zhikov and Pyatnitskii). In particular, we introduce stochastic two-scale Young measures as a tool to compare mean and quenched limits. Moreover
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Emergence of synchronization in Kuramoto model with frustration under general network topology Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 Tingting Zhu
In this paper, we will study the emergent behavior of Kuramoto model with frustration on a general digraph containing a spanning tree. We provide a sufficient condition for the emergence of asymptotical synchronization if the initial data are confined in half circle. As lack of uniform coercivity in general digraph, we apply the node decomposition criteria in [25] to capture a clear hierarchical structure
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An atomistic derivation of von-Kármán plate theory Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 Julian Braun,Bernd Schmidt
We derive von-Kármán plate theory from three dimensional, purely atomistic models with classical particle interaction. This derivation is established as a \begin{document}$ \Gamma $\end{document}-limit when considering the limit where the interatomic distance \begin{document}$ \varepsilon $\end{document} as well as the thickness of the plate \begin{document}$ h $\end{document} tend to zero. In particular
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Input-output $ L^2 $-well-posedness, regularity and Lyapunov stability of string equations on networks Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 Dongyi Liu,Genqi Xu
We consider the general networks of elastic strings with Neumann boundary feedbacks and collocated observations in this paper. By selecting an appropriate multiplier, we show that this system is input-output \begin{document}$ L^2 $\end{document}-well-posed. Moreover, we verify its regularity by calculating the input-output transfer function of system. In the end, by choosing an appropriate multiplier
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Advanced mathematical methodologies to contrast COVID-19 pandemic Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 Monique Chyba,Rinaldo M. Colombo,Mauro Garavello,Benedetto Piccoli
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Mathematical analysis of a hybrid model: Impacts of individual behaviors on the spreading of an epidemic Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 Guillaume Cantin,Cristiana J. Silva,Arnaud Banos
In this paper, we investigate the well-posedness and dynamics of a class of hybrid models, obtained by coupling a system of ordinary differential equations and an agent-based model. These hybrid models intend to integrate the microscopic dynamics of individual behaviors into the macroscopic evolution of various population dynamics models, and can be applied to a great number of complex problems arising
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Modelling and numerical study of the polyatomic bitemperature Euler system Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 Denise Aregba-Driollet,Stéphane Brull
This paper is devoted to the study of the bitemperature Euler system in a polyatomic setting. Physically, this model describes a mixture of one species of ions and one species of electrons in the quasi-neutral regime. We firstly derive the model starting from a kinetic polyatomic model and performing next a fluid limit. This kinetic model is shown to satisfy fundamental properties. Some exact solutions
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A periodic homogenization problem with defects rare at infinity Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 Rémi Goudey
We consider a homogenization problem for the diffusion equation \begin{document}$ -\operatorname{div}\left(a_{\varepsilon} \nabla u_{\varepsilon} \right) = f $\end{document} when the coefficient \begin{document}$ a_{\varepsilon} $\end{document} is a non-local perturbation of a periodic coefficient. The perturbation does not vanish but becomes rare at infinity in a sense made precise in the text. We
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Stability analysis of microscopic models for traffic flow with lane changing Netw. Heterog. Media (IF 1.0) Pub Date : 2022-01-01 Matteo Piu,Gabriella Puppo
This paper investigates the mathematical modeling and the stability of multi-lane traffic in the microscopic scale, studying a model based on two interaction terms. To do this we propose simple lane changing conditions and we study the stability of the steady states starting from the model in the one-lane case and extending the results to the generic multi-lane case with the careful design of the lane
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Asymptotic analysis of an elastic material reinforced with thin fractal strips Netw. Heterog. Media (IF 1.0) Pub Date : 2021-11-02 Mustapha El Jarroudi, Youness Filali, Aadil Lahrouz, Mustapha Er-Riani, Adel Settati
We study the asymptotic behavior of a three-dimensional elastic material reinforced with highly contrasted thin vertical strips constructed on horizontal iterated Sierpinski gasket curves. We use $ \Gamma $-convergence methods in order to study the asymptotic behavior of the composite as the thickness of the strips vanishes, their Lamé constants tend to infinity, and the sequence of the iterated curves
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An explicit finite volume algorithm for vanishing viscosity solutions on a network Netw. Heterog. Media (IF 1.0) Pub Date : 2021-09-06 John D. Towers
In [Andreianov, Coclite, Donadello, Discrete Contin. Dyn. Syst. A, 2017], a finite volume scheme was introduced for computing vanishing viscosity solutions on a single-junction network, and convergence to the vanishing viscosity solution was proven. This problem models $ m $ incoming and $ n $ outgoing roads that meet at a single junction. On each road the vehicle density evolves according to a scalar
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$ \Gamma $-convergence of quadratic functionals with non uniformly elliptic conductivity matrices Netw. Heterog. Media (IF 1.0) Pub Date : 2021-09-06 Lorenza D'Elia
We investigate the homogenization through $ \Gamma $-convergence for the $ L^2({\Omega}) $-weak topology of the conductivity functional with a zero-order term where the matrix-valued conductivity is assumed to be non strongly elliptic. Under proper assumptions, we show that the homogenized matrix $ A^\ast $ is provided by the classical homogenization formula. We also give algebraic conditions for two
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Irrigable measures for weighted irrigation plans Netw. Heterog. Media (IF 1.0) Pub Date : 2021-07-01 Qing Sun
A model of irrigation network, where lower branches must be thicker in order to support the weight of the higher ones, was recently introduced in [7]. This leads to a countable family of ODEs, describing the thickness of every branch, solved by backward induction. The present paper determines what kind of measures can be irrigated with a finite weighted cost. Indeed, the boundedness of the cost depends
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Reduction of a model for sodium exchanges in kidney nephron Netw. Heterog. Media (IF 1.0) Pub Date : 2021-07-09 Marta Marulli, Vuk Miliši$\grave{\rm{c}}$, Nicolas Vauchelet
This work deals with a mathematical analysis of sodium's transport in a tubular architecture of a kidney nephron. The nephron is modelled by two counter-current tubules. Ionic exchange occurs at the interface between the tubules and the epithelium and between the epithelium and the surrounding environment (interstitium). From a mathematical point of view, this model consists of a 5$ \times $5 semi-linear
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Qualitative properties of mathematical model for data flow Netw. Heterog. Media (IF 1.0) Pub Date : 2021-07-01 Cory D. Hauck, Michael Herty, Giuseppe Visconti
In this paper, properties of a recently proposed mathematical model for data flow in large-scale asynchronous computer systems are analyzed. In particular, the existence of special weak solutions based on propagating fronts is established. Qualitative properties of these solutions are investigated, both theoretically and numerically.
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Rumor spreading dynamics with an online reservoir and its asymptotic stability Netw. Heterog. Media (IF 1.0) Pub Date : 2021-07-01 Sun-Ho Choi, Hyowon Seo
The spread of rumors is a phenomenon that has heavily impacted society for a long time. Recently, there has been a huge change in rumor dynamics, through the advent of the Internet. Today, online communication has become as common as using a phone. At present, getting information from the Internet does not require much effort or time. In this paper, the impact of the Internet on rumor spreading will
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Bi-Continuous semigroups for flows on infinite networks Netw. Heterog. Media (IF 1.0) Pub Date : 2021-07-01 Christian Budde, Marjeta Kramar Fijavž
We study transport processes on infinite metric graphs with non-constant velocities and matrix boundary conditions in the $ {\mathrm{L}}^{\infty} $-setting. We apply the theory of bi-continuous operator semigroups to obtain well-posedness of the problem under different assumptions on the velocities and for general stochastic matrices appearing in the boundary conditions.
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Well-posedness and approximate controllability of neutral network systems Netw. Heterog. Media (IF 1.0) Pub Date : 2021-07-01 Yassine El Gantouh, Said Hadd
In this paper, we study the concept of approximate controllability of retarded network systems of neutral type. On one hand, we reformulate such systems as free-delay boundary control systems on product spaces. On the other hand, we use the rich theory of infinite-dimensional linear systems to derive necessary and sufficient conditions for the approximate controllability. Moreover, we propose a rank
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Convex and quasiconvex functions in metric graphs Netw. Heterog. Media (IF 1.0) Pub Date : 2021-06-28 Leandro M. Del Pezzo, Nicolás Frevenza, Julio D. Rossi
We study convex and quasiconvex functions on a metric graph. Given a set of points in the metric graph, we consider the largest convex function below the prescribed datum. We characterize this largest convex function as the unique largest viscosity subsolution to a simple differential equation, $ u'' = 0 $ on the edges, plus nonlinear transmission conditions at the vertices. We also study the analogous
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Multiple patterns formation for an aggregation/diffusion predator-prey system Netw. Heterog. Media (IF 1.0) Pub Date : 2021-05-20 Simone Fagioli, Yahya Jaafra
We investigate existence of stationary solutions to an aggregation/diffusion system of PDEs, modelling a two species predator-prey interaction. In the model this interaction is described by non-local potentials that are mutually proportional by a negative constant $ -\alpha $, with $ \alpha>0 $. Each species is also subject to non-local self-attraction forces together with quadratic diffusion effects
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Vanishing viscosity for a \begin{document}$ 2\times 2 $\end{document} system modeling congested vehicular traffic Netw. Heterog. Media (IF 1.0) Pub Date : 2021-05-20 Giuseppe Maria Coclite, Nicola De Nitti, Mauro Garavello, Francesca Marcellini
We prove the convergence of the vanishing viscosity approximation for a class of $ 2\times2 $ systems of conservation laws, which includes a model of traffic flow in congested regimes. The structure of the system allows us to avoid the typical constraints on the total variation and the $ L^1 $ norm of the initial data. The key tool is the compensated compactness technique, introduced by Murat and Tartar
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Combined effects of homogenization and singular perturbations: A bloch wave approach Netw. Heterog. Media (IF 1.0) Pub Date : 2021-05-20 Vivek Tewary
In this work, we study Bloch wave homogenization of periodically heterogeneous media with fourth order singular perturbations. We recover different homogenization regimes depending on the relative strength of the singular perturbation and length scale of the periodic heterogeneity. The homogenized tensor is obtained in terms of the first Bloch eigenvalue. The higher Bloch modes do not contribute to
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Emergent behaviors of Lohe Hermitian sphere particles under time-delayed interactions Netw. Heterog. Media (IF 1.0) Pub Date : 2021-05-20 Seung-Yeal Ha, Gyuyoung Hwang, Hansol Park
We study emergent behaviors of the Lohe Hermitian sphere(LHS) model with a time-delay for a homogeneous and heterogeneous ensemble. The LHS model is a complex counterpart of the Lohe sphere(LS) aggregation model on the unit sphere in Euclidean space, and it describes the aggregation of particles on the unit Hermitian sphere in $ \mathbb C^d $ with $ d \geq 2 $. Recently it has been introduced by two
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Convergence rates for the homogenization of the Poisson problem in randomly perforated domains Netw. Heterog. Media (IF 1.0) Pub Date : 2021-04-19 Arianna Giunti
In this paper we provide converge rates for the homogenization of the Poisson problem with Dirichlet boundary conditions in a randomly perforated domain of $ \mathbb{R}^d $, $ d \geqslant 3 $. We assume that the holes that perforate the domain are spherical and are generated by a rescaled marked point process $ (\Phi, \mathcal{R}) $. The point process $ \Phi $ generating the centres of the holes is
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Influence of a slow moving vehicle on traffic: Well-posedness and approximation for a mildly nonlocal model Netw. Heterog. Media (IF 1.0) Pub Date : 2021-02-07 Abraham Sylla
In this paper, we propose a macroscopic model that describes the influence of a slow moving large vehicle on road traffic. The model consists of a scalar conservation law with a nonlocal constraint on the flux. The constraint level depends on the trajectory of the slower vehicle which is given by an ODE depending on the downstream traffic density. After proving well-posedness, we first build a finite
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Opinion fitness and convergence to consensus in homogeneous and heterogeneous populations Netw. Heterog. Media (IF 1.0) Pub Date : 2021-02-07 Mayte Pérez-Llanos, Juan Pablo Pinasco, Nicolas Saintier
In this work we study the formation of consensus in homogeneous and heterogeneous populations, and the effect of attractiveness or fitness of the opinions. We derive the corresponding kinetic equations, analyze the long time behavior of their solutions, and characterize the consensus opinion.
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Coupling techniques for nonlinear hyperbolic equations. Ⅱ. resonant interfaces with internal structure Netw. Heterog. Media (IF 1.0) Pub Date : 2021-02-07 Benjamin Boutin, Frédéric Coquel, Philippe G. LeFloch
In the first part of this series, an augmented PDE system was introduced in order to couple two nonlinear hyperbolic equations together. This formulation allowed the authors, based on Dafermos's self-similar viscosity method, to establish the existence of self-similar solutions to the coupled Riemann problem. We continue here this analysis in the restricted case of one-dimensional scalar equations
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An inverse problem for quantum trees with observations at interior vertices Netw. Heterog. Media (IF 1.0) Pub Date : 2021-03-12 Sergei Avdonin, Julian Edward
In this paper we consider a non-standard dynamical inverse problem for the wave equation on a metric tree graph. We assume that positive masses may be attached to the internal vertices of the graph. Another specific feature of our investigation is that we use only one boundary actuator and one boundary sensor, all other observations being internal. Using the Dirichlet-to-Neumann map (acting from one
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Properties of the LWR model with time delay Netw. Heterog. Media (IF 1.0) Pub Date : 2020-12-08 Simone Göttlich, Elisa Iacomini, Thomas Jung
In this article, we investigate theoretical and numerical properties of the first-order Lighthill-Whitham-Richards (LWR) traffic flow model with time delay. Since standard results from the literature are not directly applicable to the delayed model, we mainly focus on the numerical analysis of the proposed finite difference discretization. The simulation results also show that the delay model is able
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Pointwise long time behavior for the mixed damped nonlinear wave equation in \begin{document}$ \mathbb{R}^n_+ $\end{document} Netw. Heterog. Media (IF 1.0) Pub Date : 2020-12-08 Linglong Du, Min Yang
In this paper, we investigate the long time behavior of the solution for the nonlinear wave equation with frictional and visco-elastic damping terms in $ \mathbb{R}^n_+ $. It is shown that for the long time, the frictional damped effect is dominated. The Green's functions for the linear initial boundary value problem can be described in terms of the fundamental solutions for the full space problem
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A two-dimensional multi-class traffic flow model Netw. Heterog. Media (IF 1.0) Pub Date : 2020-12-08 Caterina Balzotti, Simone Göttlich
The aim of this work is to introduce a two-dimensional macroscopic traffic model for multiple populations of vehicles. Starting from the paper [21], where a two-dimensional model for a single class of vehicles is proposed, we extend the dynamics to a multi-class model leading to a coupled system of conservation laws in two space dimensions. Besides the study of the Riemann problems we also present
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A new model for the emergence of blood capillary networks Netw. Heterog. Media (IF 1.0) Pub Date : 2020-12-21 Pedro Aceves-Sanchez, Benjamin Aymard, Diane Peurichard, Pol Kennel, Anne Lorsignol, Franck Plouraboué, Louis Casteilla, Pierre Degond
We propose a new model for the emergence of blood capillary networks. We assimilate the tissue and extra cellular matrix as a porous medium, using Darcy's law for describing both blood and interstitial fluid flows. Oxygen obeys a convection-diffusion-reaction equation describing advection by the blood, diffusion and consumption by the tissue. Discrete agents named capillary elements and modelling groups
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Periodic consensus in network systems with general distributed processing delays Netw. Heterog. Media (IF 1.0) Pub Date : 2020-12-21 Yicheng Liu, Yipeng Chen, Jun Wu, Xiao Wang
How to understand the dynamical consensus patterns in network systems is of particular significance in both theories and applications. In this paper, we are interested in investigating the influences of distributed processing delay on the consensus patterns in a network model. As new observations, we show that the desired network model undergoes both weak consensus and periodic consensus behaviors
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Existence results and stability analysis for a nonlinear fractional boundary value problem on a circular ring with an attached edge : A study of fractional calculus on metric graph Netw. Heterog. Media (IF 1.0) Pub Date : 2021-01-18 Vaibhav Mehandiratta, Mani Mehra, Günter Leugering
In this paper, we study a nonlinear fractional boundary value problem on a particular metric graph, namely, a circular ring with an attached edge. First, we prove existence and uniqueness of solutions using the Banach contraction principle and Krasnoselskii's fixed point theorem. Further, we investigate different kinds of Ulam-type stability for the proposed problem. Finally, an example is given in
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A multiclass Lighthill-Whitham-Richards traffic model with a discontinuous velocity function Netw. Heterog. Media (IF 1.0) Pub Date : 2021-01-18 Raimund Bürger, Christophe Chalons, Rafael Ordoñez, Luis Miguel Villada
The well-known Lighthill-Whitham-Richards (LWR) kinematic model of traffic flow models the evolution of the local density of cars by a nonlinear scalar conservation law. The transition between free and congested flow regimes can be described by a flux or velocity function that has a discontinuity at a determined density. A numerical scheme to handle the resulting LWR model with discontinuous velocity
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Efficient numerical methods for gas network modeling and simulation Netw. Heterog. Media (IF 1.0) Pub Date : 2020-08-26 Yue Qiu, Sara Grundel, Martin Stoll, Peter Benner
We study the modeling and simulation of gas pipeline networks, with a focus on fast numerical methods for the simulation of transient dynamics. The obtained mathematical model of the underlying network is represented by a system of nonlinear differential algebraic equations (DAEs). With our modeling approach, we reduce the number of algebraic constraints, which correspond to the $ (2,2) $ block in
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The selection problem for some first-order stationary Mean-field games Netw. Heterog. Media (IF 1.0) Pub Date : 2020-08-26 Diogo A. Gomes, Hiroyoshi Mitake, Kengo Terai
Here, we study the existence and the convergence of solutions for the vanishing discount MFG problem with a quadratic Hamiltonian. We give conditions under which the discounted problem has a unique classical solution and prove convergence of the vanishing-discount limit to a unique solution up to constants. Then, we establish refined asymptotics for the limit. When those conditions do not hold, the
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A 2-dimensional shape optimization problem for tree branches Netw. Heterog. Media (IF 1.0) Pub Date : 2020-10-30 Alberto Bressan, Sondre Tesdal Galtung
The paper is concerned with a shape optimization problem, where the functional to be maximized describes the total sunlight collected by a distribution of tree leaves, minus the cost for transporting water and nutrient from the base of trunk to all the leaves. In a 2-dimensional setting, the solution is proved to be unique and explicitly determined.
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Modelling pattern formation through differential repulsion Netw. Heterog. Media (IF 1.0) 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
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Swarms dynamics approach to behavioral economy: Theoretical tools and price sequences Netw. Heterog. Media (IF 1.0) 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
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Relative entropy method for the relaxation limit of hydrodynamic models Netw. Heterog. Media (IF 1.0) 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
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A BGK kinetic model with local velocity alignment forces Netw. Heterog. Media (IF 1.0) 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
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Micro- and macroscopic modeling of crowding and pushing in corridors Netw. Heterog. Media (IF 1.0) 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
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Nonlinear stability of stationary solutions to the Kuramoto-Sakaguchi equation with frustration Netw. Heterog. Media (IF 1.0) 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
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Mean field models for large data–clustering problems Netw. Heterog. Media (IF 1.0) 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
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Bounded confidence dynamics and graph control: Enforcing consensus Netw. Heterog. Media (IF 1.0) 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
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Kinetic modelling of multiple interactions in socio-economic systems Netw. Heterog. Media (IF 1.0) 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