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H(curl2)conforming quadrilateral spectral element method for quadcurl problems Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20211014
Lixiu Wang, Weikun Shan, Huiyuan Li, Zhimin ZhangIn this paper, we propose an H(curl2)conforming quadrilateral spectral element method to solve quadcurl problems. Starting with generalized Jacobi polynomials, we first introduce quasiorthogonal polynomial systems for vector fields over rectangles. H(curl2)conforming elements over arbitrary convex quadrilaterals are then constructed explicitly in a hierarchical pattern using the contravariant transform

Global solvability and asymptotic stabilization in a threedimensional Keller–Segel–Navier–Stokes system with indirect signal production Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20211013
Feng Dai, Bin LiuThis paper deals with the Keller–Segel–Navier–Stokes model with indirect signal production in a threedimensional (3D) bounded domain with smooth boundary. When the logistictype degradation here is weaker than the usual quadratic case, it is proved that for any sufficiently regular initial data, the associated noflux/noflux/noflux/Dirichlet problem possesses at least one globally defined solution

Control of COVID19 outbreak using an extended SEIR model Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20211008
Sean T. McQuade, Ryan Weightman, Nathaniel J. Merrill, Aayush Yadav, Emmanuel Trélat, Sarah R. Allred, Benedetto PiccoliThe outbreak of COVID19 resulted in high death tolls all over the world. The aim of this paper is to show how a simple SEIR model was used to make quick predictions for New Jersey in early March 2020 and call for action based on data from China and Italy. A more refined model, which accounts for social distancing, testing, contact tracing and quarantining, is then proposed to identify containment

Stability for the training of deep neural networks and other classifiers Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20211002
Leonid Berlyand, PierreEmmanuel Jabin, C. Alex SafstenWe examine the stability of lossminimizing training processes that are used for deep neural networks (DNN) and other classifiers. While a classifier is optimized during training through a socalled loss function, the performance of classifiers is usually evaluated by some measure of accuracy, such as the overall accuracy which quantifies the proportion of objects that are well classified. This leads

Modeling virus pandemics in a globally connected world a challenge towards a mathematics for living systems Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210930
N. Bellomo, F. Brezzi, M. A. J. ChaplainThis editorial paper presents the papers published in a special issue devoted to the modeling and simulation of mutating virus pandemics in a globally connected world. The presentation is proposed in three parts. First, motivations and objectives are presented according to the idea that mathematical models should go beyond deterministic population dynamics by considering the multiscale, heterogeneous

A datadriven epidemic model with social structure for understanding the COVID19 infection on a heavily affected Italian province Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210929
Mattia Zanella, Chiara Bardelli, Giacomo Dimarco, Silvia Deandrea, Pietro Perotti, Mara Azzi, Silvia Figini, Giuseppe ToscaniIn this work, using a detailed dataset furnished by National Health Authorities concerning the Province of Pavia (Lombardy, Italy), we propose to determine the essential features of the ongoing COVID19 pandemic in terms of contact dynamics. Our contribution is devoted to provide a possible planning of the needs of medical infrastructures in the Pavia Province and to suggest different scenarios about

Spectral analysis of dispersive shocks for quantum hydrodynamics with nonlinear viscosity Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210716
Corrado Lattanzio, Delyan ZhelyazovIn this paper, we investigate spectral stability of traveling wave solutions to 1D quantum hydrodynamics system with nonlinear viscosity in the (ρ,u), that is, density and velocity, variables. We derive a sufficient condition for the stability of the essential spectrum and we estimate the maximum modulus of eigenvalues with nonnegative real part. In addition, we present numerical computations of the

Darcy’s law as low Mach and homogenization limit of a compressible fluid in perforated domains Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210728
Richard M. Höfer, Karina Kowalczyk, Sebastian SchwarzacherWe consider the homogenization limit of the compressible barotropic Navier–Stokes equations in a threedimensional domain perforated by periodically distributed identical particles. We study the regime of particle sizes and distances such that the volume fraction of particles tends to zero but their resistance density tends to infinity. Assuming that the Mach number is decreasing with a certain rate

What is life? A perspective of the mathematical kinetic theory of active particles Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210728
Nicola Bellomo, Diletta Burini, Giovanni Dosi, Livio Gibelli, Damian Knopoff, Nisrine Outada, Pietro Terna, Maria Enrica VirgillitoThe modeling of living systems composed of many interacting entities is treated in this paper with the aim of describing their collective behaviors. The mathematical approach is developed within the general framework of the kinetic theory of active particles. The presentation is in three parts. First, we derive the mathematical tools, subsequently, we show how the method can be applied to a number

Weak entropy solutions to a model in induction hardening, existence and weakstrong uniqueness Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210726
Dietmar Hömberg, Robert LasarzikIn this paper, we investigate a model describing induction hardening of steel. The related system consists of an energy balance, an ordinary differential equation (ODE) for the different phases of steel, and Maxwell’s equations in a potential formulation. The existence of weak entropy solutions is shown by a suitable regularization and discretization technique. Moreover, we prove the weakstrong uniqueness

Model predictive control with random batch methods for a guiding problem Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210726
Dongnam Ko, Enrique ZuazuaWe model, simulate and control the guiding problem for a herd of evaders under the action of repulsive drivers. The problem is formulated in an optimal control framework, where the drivers (controls) aim to guide the evaders (states) to a desired region of the Euclidean space. The numerical simulation of such models quickly becomes unfeasible for a large number of interacting agents, as the number

From particle swarm optimization to consensus based optimization: Stochastic modeling and meanfield limit Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210716
Sara Grassi, Lorenzo PareschiIn this paper, we consider a continuous description based on stochastic differential equations of the popular particle swarm optimization (PSO) process for solving global optimization problems and derive in the large particle limit the corresponding meanfield approximation based on Vlasov–Fokker–Plancktype equations. The disadvantage of memory effects induced by the need to store the local best position

The curl–curl conforming virtual element method for the quadcurl problem Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210728
Jikun Zhao, Bei ZhangIn this paper, we present the H(curl2)conforming virtual element (VE) method for the quadcurl problem in two dimensions. Based on the idea of de Rham complex, we first construct three families of H(curl2)conforming VEs, of which the simplest one has only one degree of freedom associated to each vertex and each edge in the lowestorder case, respectively. An exact discrete complex is established

Kinetic and macroscopic models for active particles exploring complex environments with an internal navigation control system Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210710
Luis Gómez Nava, Thierry Goudon, Fernando PeruaniA large number of biological systems — from bacteria to sheep — can be described as ensembles of selfpropelled agents (active particles) with a complex internal dynamic that controls the agent’s behavior: resting, moving slow, moving fast, feeding, etc. In this study, we assume that such a complex internal dynamic can be described by a Markov chain, which controls the moving direction, speed, and

On nonlinear problems of parabolic type with implicit constitutive equations involving flux Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210825
Miroslav Bulíček, Erika Maringová, Josef MálekWe study systems of nonlinear partial differential equations of parabolic type, in which the elliptic operator is replaced by the firstorder divergence operator acting on a flux function, which is related to the spatial gradient of the unknown through an additional implicit equation. This setting, broad enough in terms of applications, significantly expands the paradigm of nonlinear parabolic problems

Newtonian repulsion and radial confinement: Convergence toward steady state Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210617
Ruiwen Shu, Eitan TadmorWe investigate the large time behavior of multidimensional aggregation equations driven by Newtonian repulsion, and balanced by radial attraction and confinement. In case of Newton repulsion with radial confinement we quantify the algebraic convergence decay rate toward the unique steady state. To this end, we identify a oneparameter family of radial steady states, and prove dimensiondependent decay

Equilibrium analysis of an immersed rigid leaflet by the virtual element method Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210716
L. Beirão da Veiga, C. Canuto, R. H. Nochetto, G. VaccaWe study, both theoretically and numerically, the equilibrium of a hinged rigid leaflet with an attached rotational spring, immersed in a stationary incompressible fluid within a rigid channel. Through a careful investigation of the properties of the domain functional describing the angular momentum exerted by the fluid on the leaflet (which depends on both the leaflet angular position and its thickness)

Negligibility of haptotaxis effect in a chemotaxis–haptotaxis model Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210628
HaiYang Jin, Tian XiangIn this work, we rigorously study chemotaxis effect versus haptotaxis effect on boundedness, blowup and asymptotical behavior of solutions for a chemotaxishaptotaxis model in 2D settings. It is wellknown that the corresponding Keller–Segel chemotaxisonly model possesses a striking feature of critical mass blowup phenomenon, namely, subcritical mass ensures boundedness, whereas, supercritical mass

Optimal control of cytotoxic and antiangiogenic therapies on prostate cancer growth Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210614
Pierluigi Colli, Hector Gomez, Guillermo Lorenzo, Gabriela Marinoschi, Alessandro Reali, Elisabetta RoccaProstate cancer can be lethal in advanced stages, for which chemotherapy may become the only viable therapeutic option. While there is no clear clinical management strategy fitting all patients, cytotoxic chemotherapy with docetaxel is currently regarded as the gold standard. However, tumors may regain activity after treatment conclusion and become resistant to docetaxel. This situation calls for new

Diffusioninduced blowup solutions for the shadow limit model of a singular Gierer–Meinhardt system Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210623
G. K. Duong, N. I. Kavallaris, H. ZaagIn this paper, we provide a thorough investigation of the blowing up behavior induced via diffusion of the solution of the following nonlocal problem: ∂tu=Δu−u+up∫ΩurdrγinΩ×(0,T),∂u∂ν=0onΓ=∂Ω×(0,T),u(0)=u0, where Ω is a bounded domain in ℝN with smooth boundary ∂Ω; such problem is derived as the shadow limit of a singular Gierer–Meinhardt system, Kavallaris and Suzuki [On the dynamics of a nonlocal

Collective dynamics in science and society Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210617
N. Bellomo, F. BrezziThis editorial paper presents the articles published in a special issue devoted to active particle methods applied to modeling, qualitative analysis, and simulation of the collective dynamics of large systems of interacting living entities in science and society. The modeling approach refers to the mathematical tools of behavioral swarms theory and to the kinetic theory of active particles. Applications

On a nonlocal Cahn–Hilliard model permitting sharp interfaces Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210705
Olena Burkovska, Max GunzburgerA nonlocal Cahn–Hilliard model with a nonsmooth potential of doublewell obstacle type that promotes sharp interfaces in the solution is presented. To capture longrange interactions between particles, a nonlocal Ginzburg–Landau energy functional is defined which recovers the classical (local) model as the extent of nonlocal interactions vanish. In contrast to the local Cahn–Hilliard problem that

Sharp discontinuous traveling waves in a hyperbolic Keller–Segel equation Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210413
Xiaoming Fu, Quentin Griette, Pierre MagalIn this work, we describe a hyperbolic model with cell–cell repulsion with a dynamics in the population of cells. More precisely, we consider a population of cells producing a field (which we call “pressure”) which induces a motion of the cells following the opposite of the gradient. The field indicates the local density of population and we assume that cells try to avoid crowded areas and prefer locally

Individualbased Markov model of virus diffusion: Comparison with COVID19 incubation period, serial interval and regional time series Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210417
Franco Flandoli, Eleonora La Fauci, Martina RivaA Markov chain individualbased model for virus diffusion is investigated. Both the virus growth within an individual and the complexity of the contagion within a population are taken into account. A careful work of parameter choice is performed. The model captures very well the statistical variability of quantities like the incubation period, the serial interval and the time series of infected people

New primal and dualmixed finite element methods for stable image registration with singular regularization Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210429
Nicolás Barnafi, Gabriel N. Gatica, Daniel E. Hurtado, Willian Miranda, Ricardo RuizBaierThis work introduces and analyzes new primal and dualmixed finite element methods for deformable image registration, in which the regularizer has a nontrivial kernel, and constructed under minimal assumptions of the registration model: Lipschitz continuity of the similarity measure and ellipticity of the regularizer on the orthogonal complement of its kernel. The aforementioned singularity of the

A cookbook for approximating Euclidean balls and for quadrature rules in finite element methods for nonlocal problems Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210619
Marta D’Elia, Max Gunzburger, Christian VollmannThe implementation of finite element methods (FEMs) for nonlocal models with a finite range of interaction poses challenges not faced in the partial differential equations (PDEs) setting. For example, one has to deal with weak forms involving double integrals which lead to discrete systems having higher assembly and solving costs due to possibly much lower sparsity compared to that of FEMs for PDEs

An abstract infsup problem inspired by limit analysis in perfect plasticity and related applications Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210617
Stanislav Sysala, Jaroslav Haslinger, B. Daya Reddy, Sergey RepinThis paper is concerned with an abstract infsup problem generated by a bilinear Lagrangian and convex constraints. We study the conditions that guarantee no gap between the infsup and related supinf problems. The key assumption introduced in the paper generalizes the wellknown Babuška–Brezzi condition. It is based on an infsup condition defined for convex cones in function spaces. We also apply

Shape programming of a magnetic elastica Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210426
Riccardo Durastanti, Lorenzo Giacomelli, Giuseppe TomassettiWe consider a cantilever beam which possesses a possibly nonuniform permanent magnetization, and whose shape is controlled by an applied magnetic field. We model the beam as a plane elastic curve and we suppose that the magnetic field acts upon the beam by means of a distributed couple that pulls the magnetization towards its direction. Given a list of target shapes, we look for a design of the magnetization

Adaptive nonhierarchical Galerkin methods for parabolic problems with application to moving mesh and virtual element methods Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210417
Andrea Cangiani, Emmanuil H. Georgoulis, Oliver J. SuttonWe present a posteriori error estimates for inconsistent and nonhierarchical Galerkin methods for linear parabolic problems, allowing them to be used in conjunction with very general mesh modification for the first time. We treat schemes which are nonhierarchical in the sense that the spatial Galerkin spaces between timesteps may be completely unrelated from one another. The practical interest of

Efficient, secondorder in time, and energy stable scheme for a new hydrodynamically coupled three components volumeconserved Allen–Cahn phasefield model Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210413
Xiaofeng YangIn this paper, we establish a new hydrodynamically coupled phasefield model for three immiscible fluid components system. The model consists of the Navier–Stokes equations and three coupled nonlinear Allen–Cahn type equations, to which we add nonlocal type Lagrange multipliers to conserve the volume of each phase accurately. To solve the model, a linear and energy stable timemarching method is constructed

The stationary Boussinesq problem under singular forcing Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210422
Alejandro Allendes, Enrique Otárola, Abner J. SalgadoIn Lipschitz two and threedimensional domains, we study the existence for the socalled Boussinesq model of thermally driven convection under singular forcing. By singular we mean that the heat source is allowed to belong to H−1(ϖ,Ω), where ϖ is a weight in the Muckenhoupt class A2 that is regular near the boundary. We propose a finite element scheme and, under the assumption that the domain is convex

Geometric linearization of theories for incompressible elastic materials and applications Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210322
Martin Jesenko, Bernd SchmidtWe derive geometrically linearized theories for incompressible materials from nonlinear elasticity theory in the small displacement regime. Our nonlinear stored energy densities may vary on the same (small) length scale as the typical displacements. This allows for applications to multiwell energies as, e.g. encountered in martensitic phases of shape memory alloys and models for nematic elastomers

Computing oscillatory solutions of the Euler system via 𝒦convergence Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210313
Eduard Feireisl, Mária Lukáčová–Medvid’ová, Bangwei She, Yue WangWe develop a method to compute effectively the Young measures associated to sequences of numerical solutions of the compressible Euler system. Our approach is based on the concept of 𝒦convergence adapted to sequences of parameterized measures. The convergence is strong in space and time (a.e. pointwise or in certain Lq spaces) whereas the measures converge narrowly or in the Wasserstein distance

Transmission dynamics and quarantine control of COVID19 in cluster community: A new transmissionquarantine model with case study for diamond princess Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210409
Qingwu Gao, Jun Zhuang, Ting Wu, Houcai ShenCoronavirus Disease 2019 (COVID19) is a zoonotic illness which has spread rapidly and widely since December, 2019, and is identified as a global pandemic by the World Health Organization. The pandemic to date has been characterized by ongoing cluster community transmission. Quarantine intervention to prevent and control the transmission are expected to have a substantial impact on delaying the growth

Modeling and simulating the spatial spread of an epidemic through multiscale kinetic transport equations Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210429
Walter Boscheri, Giacomo Dimarco, Lorenzo PareschiIn this paper, we propose a novel spacedependent multiscale model for the spread of infectious diseases in a twodimensional spatial context on realistic geographical scenarios. The model couples a system of kinetic transport equations describing a population of commuters moving on a large scale (extraurban) with a system of diffusion equations characterizing the noncommuting population acting over

Uniformintime error estimate of the random batch method for the Cucker–Smale model Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210429
SeungYeal Ha, Shi Jin, Doheon Kim, Dongnam KoWe present a uniformintime (and in particle numbers as well) error estimate for the random batch method (RBM) [S. Jin, L. Li and J.G. Liu, Random batch methods (RBM) for interacting particle systems, J. Comput. Phys.400 (2020) 108877] to the Cucker–Smale (CS) model. The uniformintime error estimates of the RBM have been obtained for various interacting particle systems, when corresponding flow

Hydrodynamic limit of a coupled Cucker–Smale system with strong and weak internal variable relaxation Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210429
Jeongho Kim, David Poyato, Juan SolerIn this paper, we present the hydrodynamic limit of a multiscale system describing the dynamics of two populations of agents with alignment interactions and the effect of an internal variable. It consists of a kinetic equation coupled with an Eulertype equation inspired by the thermomechanical Cucker–Smale (TCS) model. We propose a novel drag force for the fluidparticle interaction reminiscent of

Generalized solutions to boundedconfidence models Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210422
Benedetto Piccoli, Francesco RossiBoundedconfidence models in social dynamics describe multiagent systems, where each individual interacts only locally with others. Several models are written as systems of ordinary differential equations (ODEs) with discontinuous righthand side: this is a direct consequence of restricting interactions to a bounded region with nonvanishing strength at the boundary. Various works in the literature

A kinetic theory approach for 2D crowd dynamics with emotional contagion Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210417
Daewa Kim, Kaylie O’Connell, William Ott, Annalisa QuainiIn this paper, we present a computational modeling approach for the dynamics of human crowds, where the spreading of an emotion (specifically fear) has an influence on the pedestrians’ behavior. Our approach is based on the methods of the kinetic theory of active particles. The model allows us to weight between two competing behaviors depending on fear level: the search for less congested areas and

Disease contagion models coupled to crowd motion and meshfree simulation Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210409
Parveena Shamim Abdul Salam, Wolfgang Bock, Axel Klar, Sudarshan TiwariModeling and simulation of disease spreading in pedestrian crowds have recently become a topic of increasing relevance. In this paper, we consider the influence of the crowd motion in a complex dynamical environment on the course of infection of the pedestrians. To model the pedestrian dynamics, we consider a kinetic equation for multigroup pedestrian flow based on a social force model coupled with

Global solvability and asymptotic behavior in a twospecies chemotaxis system with Lotka–Volterra competitive kinetics Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210409
Guoqiang Ren, Bin LiuIn this work, we consider the twospecies chemotaxis system with Lotka–Volterra competitive kinetics in a bounded domain with smooth boundary. We construct weak solutions and prove that they become smooth after some waiting time. In addition, the asymptotic behavior of the solutions is studied. Our results generalize some wellknown results in the literature.

Final size and convergence rate for an epidemic in heterogeneous populations Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210409
Luis Almeida, PierreAlexandre Bliman, Grégoire Nadin, Benoît Perthame, Nicolas VaucheletWe formulate a general SEIR epidemic model in a heterogeneous population characterized by some trait in a discrete or continuous subset of a space ℝd. The incubation and recovery rates governing the evolution of each homogeneous subpopulation depend upon this trait, and no restriction is assumed on the contact matrix that defines the probability for an individual of a given trait to be infected by

Statistical solutions of the incompressible Euler equations Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210216
S. Lanthaler, S. Mishra, C. ParésPulidoWe propose and study the framework of dissipative statistical solutions for the incompressible Euler equations. Statistical solutions are timeparameterized probability measures on the space of squareintegrable functions, whose timeevolution is determined from the underlying Euler equations. We prove partial wellposedness results for dissipative statistical solutions and propose a Monte Carlo type

On the optimality of the rocksalt structure among lattices with charge distributions Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210224
Laurent Bétermin, Markus Faulhuber, Hans KnüpferThe goal of this paper is to investigate the optimality of the ddimensional rocksalt structure, i.e. the cubic lattice V1/dℤd of volume V with an alternation of charges ±1 at lattice points, among periodic distributions of charges and lattice structures. We assume that the charges are interacting through two types of radially symmetric interaction potentials, according to their signs. We first restrict

Quantifying the hydrodynamic limit of Vlasovtype equations with alignment and nonlocal forces Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210224
José A. Carrillo, YoungPil Choi, Jinwook JungIn this paper, we quantify the asymptotic limit of collective behavior kinetic equations arising in mathematical biology modeled by Vlasovtype equations with nonlocal interaction forces and alignment. More precisely, we investigate the hydrodynamic limit of a kinetic Cucker–Smale flocking model with confinement, nonlocal interaction, and local alignment forces, linear damping and diffusion in velocity

Linear instability of Zpinch in plasma: Inviscid case Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210226
Dongfen Bian, Yan Guo, Ian TiceThe zpinch is a classical steady state for the MHD model, where a confined plasma fluid is separated by vacuum, in the presence of a magnetic field which is generated by a prescribed current along the z direction. We develop a variational framework to study its stability in the absence of viscosity effect, and demonstrate for the first time that such a zpinch is always unstable. Moreover, we discover

Asymptotic profile of a twodimensional Chemotaxis–Navier–Stokes system with singular sensitivity and logistic source Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210306
Peter Y. H. Pang, Yifu Wang, Jingxue YinThis paper is concerned with a spatially twodimensional version of a chemotaxis system with logistic cell proliferation and death, for a singular tactic response of standard logarithmic type, and with interaction with a surrounding incompressible fluid through transport and buoyancy. Systems of this form are of significant relevance to the understanding of chemotaxisfluid interaction, but the rigorous

Remarks on Poincaré and interpolation estimates for Truncated Hierarchical Bsplines Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210301
Annalisa Buffa, Carlotta GiannelliThis paper should be considered as an addendum to [A. Buffa and C. Giannelli, Adaptive isogeometric methods with hierarchical splines: Error estimator and convergence, Math. Models Methods Appl. Sci.26 (2016) 1–25] and [A. Buffa and C. Giannelli, Adaptive isogeometric methods with hierarchical splines: Optimality and convergence rates, Math. Models Methods Appl. Sci.27 (2017) 2781–2802] where Poincaré

Lagrange multiplier approach to unilateral indentation problems: Wellposedness and application to linearized viscoelasticity with noninvertible constitutive response Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210226
Hiromichi Itou, Victor A. Kovtunenko, Kumbakonam R. RajagopalThe Boussinesq problem describing indentation of a rigid punch of arbitrary shape into a deformable solid body is studied within the context of a linear viscoelastic model. Due to the presence of a nonlocal integral constraint prescribing the total contact force, the unilateral indentation problem is formulated in the general form as a quasivariational inequality with unknown indentation depth, and

A ternary Cahn–Hilliard–Navier–Stokes model for twophase flow with precipitation and dissolution Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20201217
Christian Rohde, Lars von WolffWe consider the incompressible flow of two immiscible fluids in the presence of a solid phase that undergoes changes in time due to precipitation and dissolution effects. Based on a seminal sharp interface model a phasefield approach is suggested that couples the Navier–Stokes equations and the solid’s ion concentration transport equation with the Cahn–Hilliard evolution for the phase fields. The

A dimensionreduction model for brittle fractures on thin shells with mesh adaptivity Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20201222
Stefano Almi, Sandro Belz, Stefano Micheletti, Simona PerottoIn this paper, we derive a new 2D brittle fracture model for thin shells via dimension reduction, where the admissible displacements are only normal to the shell surface. The main steps include to endow the shell with a small thickness, to express the threedimensional energy in terms of the variational model of brittle fracture in linear elasticity, and to study the Γlimit of the functional as the

The onephase fractional Stefan problem Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20201228
Félix del Teso, Jørgen Endal, Juan Luis VázquezWe study the existence and properties of solutions and free boundaries of the onephase Stefan problem with fractional diffusion posed in ℝN. In terms of the enthalpy h(x,t), the evolution equation reads ∂th+(−Δ)sΦ(h)=0, while the temperature is defined as u:=Φ(h):=max{h−L,0} for some constant L>0 called the latent heat, and (−Δ)s stands for the fractional Laplacian with exponent s∈(0,1). We prove

DG approach to large bending plate deformations with isometry constraint Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210106
Andrea Bonito, Ricardo H. Nochetto, Dimitrios NtogkasWe propose a new discontinuous Galerkin (dG) method for a geometrically nonlinear Kirchhoff plate model for large isometric bending deformations. The minimization problem is nonconvex due to the isometry constraint. We present a practical discrete gradient flow that decreases the energy and computes discrete minimizers that satisfy a prescribed discrete isometry defect. We prove Γconvergence of the

Modeling glioma invasion with anisotropy and hypoxiatriggered motility enhancement: From subcellular dynamics to macroscopic PDEs with multiple taxis Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20201228
Gregor Corbin, Axel Klar, Christina Surulescu, Christian Engwer, Michael Wenske, Juanjo Nieto, Juan SolerWe deduce a model for glioma invasion that accounts for the dynamics of brain tissue being actively degraded by tumor cells via excessive acidity production, but also according to the local orientation of tissue fibers. Our approach has a multiscale character: we start with a microscopic description of single cell dynamics including biochemical and/or biophysical effects of the tumor microenvironment

Global regularity for a 1D Euleralignment system with misalignment Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210216
Qianyun Miao, Changhui Tan, Liutang XueWe study onedimensional Eulerian dynamics with nonlocal alignment interactions, featuring strong shortrange alignment, and longrange misalignment. Compared with the wellstudied Euleralignment system, the presence of the misalignment brings different behaviors of the solutions, including the possible creation of vacuum at infinite time, which destabilizes the solutions. We show that with a strongly

Convergence of knowledge in a stochastic cultural evolution model with population structure, social learning and credibility biases Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20201207
Sylvain Billiard, Maxime Derex, Ludovic Maisonneuve, Thomas ReyUnderstanding how knowledge emerges and propagates within groups is crucial to explain the evolution of human populations. In this work, we introduce a mathematically oriented model that draws on individualbased approaches, inhomogeneous Markov chains and learning algorithms, such as those introduced in [F. Cucker and S. Smale, On the mathematical foundations of learning, Bull. Amer. Math. Soc. 39

Consensusbased optimization on hypersurfaces: Wellposedness and meanfield limit Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210118
Massimo Fornasier, Hui Huang, Lorenzo Pareschi, Philippe SünnenWe introduce a new stochastic differential model for global optimization of nonconvex functions on compact hypersurfaces. The model is inspired by the stochastic Kuramoto–Vicsek system and belongs to the class of ConsensusBased Optimization methods. In fact, particles move on the hypersurface driven by a drift towards an instantaneous consensus point, computed as a convex combination of the particle

Point defects in tight binding models for insulators Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20210106
Christoph Ortner, Jack ThomasWe consider atomistic geometry relaxation in the context of linear tight binding models for point defects. A limiting model as Fermitemperature is sent to zero is formulated, and an exponential rate of convergence for the nuclei configuration is established. We also formulate the thermodynamic limit model at zero Fermitemperature, extending the results of [H. Chen, J. Lu and C. Ortner, Thermodynamic

An adaptive edge element approximation of a quasilinear H(curl)elliptic problem Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20201210
Yifeng Xu, Irwin Yousept, Jun ZouAn adaptive edge element method is designed to approximate a quasilinear H(curl)elliptic problem in magnetism, based on a residualtype a posteriori error estimator and general marking strategies. The error estimator is shown to be both reliable and efficient, and its resulting sequence of adaptively generated solutions converges strongly to the exact solution of the original quasilinear system. Numerical

Linear instability of Zpinch in plasma: Viscous case Math. Models Methods Appl. Sci. (IF 3.817) Pub Date : 20201205
Dongfen Bian, Yan Guo, Ian TiceThe zpinch is a classical steady state for the MHD model, where a confined plasma fluid is separated by vacuum, in the presence of a magnetic field which is generated by a prescribed current along the zdirection. We develop a scaled variational framework to study its stability in the presence of viscosity effect, and demonstrate that any such zpinch is always unstable. We also establish the existence