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Mathematical modeling and dissipative structure for systems of magnetohydrodynamics with Hall effect Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220811
Shuichi Kawashima, Ryosuke Nakasato, Takayoshi OgawaThis paper is concerned with the mathematical modeling of electromagnetohydrodynamics and magnetohydrodynamics by taking account of the Hall effect. We discuss conservation laws, strict convexity of the negative entropy as a function of conserved quantities, and the associated energy form. Moreover, we investigate the dissipative structure and decay properties of the linearized systems as applications

A fast cardiac electromechanics model coupling the Eikonal and the nonlinear mechanics equations Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220725
Simone Stella, Francesco Regazzoni, Christian Vergara, Luca Dedé, Alfio QuarteroniWe present a new model of human cardiac electromechanics for the left ventricle where electrophysiology is described by a Reaction–Eikonal model and which enables an offline resolution of the reaction model, thus entailing a big saving of computational time. Subcellular dynamics is coupled with a model of tissue mechanics, which is in turn coupled with a Windkessel model for blood circulation. Our

Asymptotic analysis of deformation behavior in highcontrast fiberreinforced materials: Rigidity and anisotropy Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220722
Dominik Engl, Carolin Kreisbeck, Antonella RitortoWe identify the restricted class of attainable effective deformations in a model of reinforced composites with parallel, long, and fully rigid fibers embedded in an elastic body. In mathematical terms, we characterize the weak limits of sequences of Sobolev maps whose gradients on the fibers lie in the set of rotations. These limits are determined by an anisotropic constraint in the sense that they

Energy minimizing twinning with variable volume fraction, for two nonlinear elastic phases with a single rankone connection Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220712
Sergio Conti, Robert V. Kohn, Oleksandr MisiatsIn materials that undergo martensitic phase transformation, distinct elastic phases often form layered microstructures — a phenomenon known as twinning. In some settings the volume fractions of the phases vary macroscopically; this has been seen, in particular, in experiments involving the bending of a bar. We study a twodimensional (2D) model problem of this type, involving two geometrically nonlinear

On the formulation of sizestructured consumer resource models (with special attention for the principle of linearized stability) Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220707
Carles Barril, Àngel Calsina, Odo Diekmann, József Z. FarkasTo describe the dynamics of a sizestructured population and its unstructured resource, we formulate bookkeeping equations in two different ways. The first, called the PDE formulation, is rather standard. It employs a firstorder partial differential equation, with a nonlocal boundary condition, for the sizedensity of the consumer, coupled to an ordinary differential equation for the resource concentration

Virtual element method for the Helmholtz transmission eigenvalue problem of anisotropic media Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220630
Jian Meng, Liquan MeiIn this paper, we propose a conforming virtual element method for the Helmholtz transmission eigenvalue problem of anisotropic media. By using 𝕋coercivity theory, the spectral approximation theory of compact operator and the projection and interpolation error estimates, we prove the spectral convergence of the discrete scheme and the optimal a priori error estimates for the discrete eigenvalues and

Existence analysis and numerical approximation for a secondorder model of traffic with orderliness marker Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220630
Boris Andreianov, Abraham SyllaWe propose a toy model for selforganized road traffic taking into account the state of orderliness in drivers’ behavior. The model is reminiscent of the wide family of generalized secondorder models (GSOM) of road traffic. It can also be seen as a phasetransition model. The orderliness marker is evolved along vehicles’ trajectories and it influences the fundamental diagram of the traffic flow. The

Normalized solutions with positive energies for a coercive problem and application to the cubic–quintic nonlinear Schrödinger equation Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220625
Louis Jeanjean, ShengSen LuIn any dimension N ≥ 1, for given mass m > 0 and when the C1 energy functional I(u) := 1 2∫ℝN∣∇u∣2dx −∫ℝNF(u)dx is coercive on the mass constraint Sm := u ∈ H1(ℝN)∣∥u∥ L2(ℝN)2 = m, we are interested in searching for constrained critical points at positive energy levels. Under general conditions on F ∈ C1(ℝ, ℝ) and for suitable ranges of the mass, we manage to construct such critical points which appear

Investigation of implicit constitutive relations in which both the stress and strain appear linearly, adjacent to nonpenetrating cracks Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220623
Hiromichi Itou, Victor A. Kovtunenko, Kumbakonam R. RajagopalA novel class of implicit constitutive relations is studied, wherein the stress and the linearized strain appear linearly, that describe material response in elastic porous bodies like rocks, ceramics, concrete, cement, bones and metals. The constitutive relation is applied to a body with a crack subjected to nonpenetration conditions between the opposite crack faces. To treat wellposedness of a

Combined dynamics of magnetization and particle rotation of a suspended superparamagnetic particle in the presence of an orienting field: Semianalytical and numerical solution Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220621
Martin Kröger, Patrick IlgThe magnetization dynamics of suspended superparamagnetic particles is governed by internal Néel relaxation as well as Brownian diffusion of the whole particle. We here present semianalytical and numerical solutions of the kinetic equation, describing the combined rotation of particle orientation and magnetization. The solutions are based on an expansion of the joint probability density into a complete

Beltrami’s completeness for 𝕃p symmetric matrix fields Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220621
Aissa Aibeche, Chérif Amrouche, Bassem BahouliGeymonat extended Gurtin’s result on Beltrami’s completeness to L2case. The first objective of this paper is to generalize Geymonat’s result to Lpcase with tangential and normal boundary conditions. Maggiani et al. proposed an extension of Beltrami’stype decomposition for symmetric matrix fields in 𝕃sp(Ω) when Ω is simply connected domain and of class 𝒞∞. The second objective of this paper is

Existence and stability of symmetric and asymmetric patterns for the halfLaplacian Gierer–Meinhardt system in onedimensional domain Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220621
Markus de Medeiros, JunCheng Wei, Wen YangIn this paper, we study the existence and stability of multiple spikes pattern to the fractional Gierer–Meinhardt model with periodic boundary conditions and the fractional power s = 1 2. Specifically, we rigorously establish the existence of symmetric multiple spikes and asymmetric twospikes solutions by the classical Lyapunov–Schmidt reduction method. We also investigate the stability of the constructed

On the optimal control of propagation fronts Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220608
Alberto Bressan, Maria Teresa Chiri, Najmeh SalehiWe consider a controlled reaction–diffusion equation, motivated by a pest eradication problem. Our goal is to derive a simpler model, describing the controlled evolution of a contaminated set. In this direction, the first part of the paper studies the optimal control of 1dimensional traveling wave profiles. Using Stokes’ formula, explicit solutions are obtained, which in some cases require measurevalued

On a twospecies chemotaxis system with indirect signal production and general competition terms Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220604
Pan Zheng, Yuting Xiang, Jie XingThis paper deals with a twocompetingspecies chemotaxis system with indirect signal production ut=d1Δu−χ1∇⋅(u∇w)+f1(u,v),(x,t)∈Ω×(0,∞),vt=d2Δv−χ2∇⋅(v∇w)+f2(u,v),(x,t)∈Ω×(0,∞),wt=Δw−w+z,(x,t)∈Ω×(0,∞),zt=Δz−z+u+v,(x,t)∈Ω×(0,∞), under homogeneous Neumann boundary conditions in a smoothly bounded domain Ω⊂ℝn(n≥1), with the nonnegative initial data (u0,v0,w0,z0), where di>0 and χi>0, i=1,2. When f1(u,v)=μ1u(1−u−a1v)

Global generalized solutions for a twospecies chemotaxis system with tensorvalued sensitivity and logistic source Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220604
Qiang Wen, Bin LiuThis paper is devoted to investigating a twospecies chemotaxis system with tensorvalued sensitivity and logistic source. It is mainly concerned with the global existence of generalized solutions. More precisely, when the logistictype is weaker than the usual quadratic case, we prove, for any sufficiently smooth initial data, the associated noflux/noflux/noflux problem possesses at least one globally

Convergence analysis of the discrete consensusbased optimization algorithm with random batch interactions and heterogeneous noises Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220528
Dongnam Ko, SeungYeal Ha, Shi Jin, Doheon KimWe present stochastic consensus and convergence of the discrete consensusbased optimization (CBO) algorithm with random batch interactions and heterogeneous external noises. Despite the wide applications and successful performance in many practical simulations, the convergence of the discrete CBO algorithm was not rigorously investigated in such a generality. In this work, we introduce a generalized

Quantitative observability for the Schrödinger and Heisenberg equations: An optimal transport approach Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220514
François Golse, Thierry PaulWe establish a quantitative observation inequality for the Schrödinger and the Heisenberg equations on Rd, uniform in the Planck constant ℏ∈[0,1]. The proof is based on the pseudometric introduced in F. Golse and T. Paul, The Schrödinger equation in the meanfield and semiclassical regime, Arch. Ration. Mech. Anal. 223 (2017) 57–94. This inequality involves only effective constants which are computed

Timefractional Moore–Gibson–Thompson equations Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220430
Barbara Kaltenbacher, Vanja NikolićIn this paper, we consider several timefractional generalizations of the Jordan–Moore–Gibson–Thompson (JMGT) equations in nonlinear acoustics as well as their linear Moore–Gibson–Thompson (MGT) versions. Following the procedure described in Jordan (2014), these timefractional acoustic equations are derived from four fractional versions of the Maxwell–Cattaneo law in Compte and Metzler (1997). Additionally

Approximation of surface diffusion flow: A secondorder variational Cahn–Hilliard model with degenerate mobilities Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220429
Elie Bretin, Simon Masnou, Arnaud Sengers, Garry TeriiThis paper addresses the approximation of surface diffusion flow using Cahn–Hilliardtype models. We introduce and analyze a new variational phase field model that associates the classical Cahn–Hilliard energy with two degenerate mobilities and guarantees a secondorder accuracy in the approximation of the sharp limit. We also introduce simple and efficient numerical schemes to approximate the solutions

Weak–strong uniqueness for energyreactiondiffusion systems Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220429
Katharina HopfWe establish weak–strong uniqueness and stability properties of renormalized solutions to a class of energyreactiondiffusion systems. The systems considered are motivated by thermodynamically consistent models, and their formal entropy structure allows us to use as a key tool a suitably adjusted relative entropy method. The weak–strong uniqueness principle holds for dissipative renormalized solutions

Chemotaxis and crossdiffusion models in complex environments: Models and analytic problems toward a multiscale vision Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220418
N. Bellomo, N. Outada, J. Soler, Y. Tao, M. WinklerThis paper proposes a review focused on exotic chemotaxis and crossdiffusion models in complex environments. The term exotic is used to denote the dynamics of models interacting with a timeevolving external system and, specifically, models derived with the aim of describing the dynamics of living systems. The presentation first, considers the derivation of phenomenological models of chemotaxis and

Micromagnetics of thin films in the presence of Dzyaloshinskii–Moriya interaction Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220418
Elisa Davoli, Giovanni Di Fratta, Dirk Praetorius, Michele RuggeriIn this paper, we study the thinfilm limit of the micromagnetic energy functional in the presence of bulk Dzyaloshinskii–Moriya interaction (DMI). Our analysis includes both a stationary Γconvergence result for the micromagnetic energy, as well as the identification of the asymptotic behavior of the associated Landau–Lifshitz–Gilbert equation. In particular, we prove that, in the limiting model,

Chemotaxis and crossdiffusion models in complex environments: Models and analytic problems toward a multiscale vision Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220418
N. Bellomo, N. Outada, J. Soler, Y. Tao, M. WinklerThis paper proposes a review focused on exotic chemotaxis and crossdiffusion models in complex environments. The term exotic is used to denote the dynamics of models interacting with a timeevolving external system and, specifically, models derived with the aim of describing the dynamics of living systems. The presentation first, considers the derivation of phenomenological models of chemotaxis and

Micromagnetics of thin films in the presence of Dzyaloshinskii–Moriya interaction Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220418
Elisa Davoli, Giovanni Di Fratta, Dirk Praetorius, Michele RuggeriIn this paper, we study the thinfilm limit of the micromagnetic energy functional in the presence of bulk Dzyaloshinskii–Moriya interaction (DMI). Our analysis includes both a stationary Γconvergence result for the micromagnetic energy, as well as the identification of the asymptotic behavior of the associated Landau–Lifshitz–Gilbert equation. In particular, we prove that, in the limiting model,

Elastoplastic evolution of single crystals driven by dislocation flow Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220412
Thomas Hudson, Filip RindlerThis work introduces a model for largestrain, geometrically nonlinear elastoplastic dynamics in single crystals. The key feature of our model is that the plastic dynamics are entirely driven by the movement of dislocations, that is, 1dimensional topological defects in the crystal lattice. It is well known that glide motion of dislocations is the dominant microscopic mechanism for plastic deformation

A multiscale stochastic criminal behavior model and the convergence to a piecewisedeterministicMarkovprocess limit Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220408
Yiru Cai, Chuntian Wang, Yuan ZhangEver since the pioneering human–environment interaction model of criminal behavior [M. B. Short, M. R. DOrsogna, V. B. Pasour, G. E. Tita, P. J. Brantingham, A. L. Bertozzi and L. B. Chayes, A statistical model of criminal behavior, Math. Models Methods Appl. Sci. 18 (2008) 1249–1267] was published, many mathematical agentbased residential burglary models have been proposed. In order to reach an improved

Constrained overdamped Langevin dynamics for symmetric multimarginal optimal transportation Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220330
Aurélien Alfonsi, Rafaël Coyaud, Virginie EhrlacherThe Strictly Correlated Electrons (SCE) limit of the Levy–Lieb functional in Density Functional Theory (DFT) gives rise to a symmetric multimarginal optimal transport problem with Coulomb cost, where the number of marginal laws is equal to the number of electrons in the system, which can be very large in relevant applications. In this work, we design a numerical method, built upon constrained overdamped

Fast Diffusion leads to partial mass concentration in Keller–Segel type stationary solutions Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220310
J. A. Carrillo, M. G. Delgadino, R. L. Frank, M. LewinWe show that partial mass concentration can happen for stationary solutions of aggregation–diffusion equations with homogeneous attractive kernels in the fast diffusion range. More precisely, we prove that the free energy admits a radial global minimizer in the set of probability measures which may have part of its mass concentrated in a Dirac delta at a given point. In the case of the quartic interaction

On effects of the nonlinear signal production to the boundedness and finitetime blowup in a fluxlimited chemotaxis model Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220308
Xinyu Tu, Chunlai Mu, Pan ZhengWe study herein the initial–boundary value problem for the fluxlimited chemotaxis model with nonlinear signal production ut = ∇⋅ up∇u u2 + ∇u2 − χ∇⋅ uq∇v 1 + ∇v2 ,x ∈ Ω,t > 0,0 = Δv − μ(t) + uk, x ∈ Ω,t > 0, subject to noflux boundary conditions in a ball Ω = BR(0) ⊂ ℝn(n ≥ 1,R > 0), where χ > 0,k > 0,p ≥ 1,q ≥ 1, μ(t) := 1 Ω∫Ωuk(⋅,t)dx. For radially symmetric and positive initial data u0 ∈

Stochastic consensus dynamics for nonconvex optimization on the Stiefel manifold: Meanfield limit and convergence Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220226
SeungYeal Ha, Myeongju Kang, Dohyun Kim, Jeongho Kim, Insoon YangWe study a consensusbased method for minimizing a nonconvex function over the Stiefel manifold. The consensus dynamics consists of stochastic differential equations for interacting particle system, whose trajectory is guaranteed to stay on the Stiefel manifold. For the proposed model, we prove the meanfield limit of the stochastic system toward a nonlinear Fokker–Planck equation on the Stiefel manifold

Bloch wave spectral analysis in the class of generalized Hashin–Shtrikman microstructures Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220217
Loredana Bălilescu, Carlos Conca, Tuhin Ghosh, Jorge San Martín, Muthusamy VanninathanIn this paper, we use spectral methods to introduce Bloch waves for studying the homogenization process in the nonperiodic class of generalized Hashin–Shtrikman microstructures (see Ref. 35), which incorporates both translation and dilation with a family of scales, including one subclass of laminates. We establish the classical homogenization result by providing the spectral representation of the

Acoustic scattering by impedance screens/cracks with fractal boundary: Wellposedness analysis and boundary element approximation Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220207
J. Bannister, A. Gibbs, D. P. HewettWe study timeharmonic scattering in ℝn (n = 2, 3) by a planar screen (a “crack” in the context of linear elasticity), assumed to be a nonempty bounded relatively open subset Γ of the hyperplane Γ∞ = ℝn−1 ×{0}, on which impedance (Robin) boundary conditions are imposed. In contrast to previous studies, Γ can have arbitrarily rough (possibly fractal) boundary. To obtain wellposedness for such Γ we

Analysisaware defeaturing: Problem setting and a posteriori estimation Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220131
Annalisa Buffa, Ondine Chanon, Rafael VázquezDefeaturing consists in simplifying geometrical models by removing the geometrical features that are considered not relevant for a given simulation. Feature removal and simplification of computeraided design models enables faster simulations for engineering analysis problems, and simplifies the meshing problem that is otherwise often unfeasible. The effects of defeaturing on the analysis are then

On fully decoupled MSAV schemes for the Cahn–Hilliard–Navier–Stokes model of twophase incompressible flows Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220131
Xiaoli Li, Jie ShenWe construct first and secondorder time discretization schemes for the Cahn–Hilliard–Navier–Stokes system based on the multiple scalar auxiliary variables (MSAV) approach for gradient systems and (rotational) pressurecorrection for Navier–Stokes equations. These schemes are linear, fully decoupled, unconditionally energy stable, and only require solving a sequence of elliptic equations with constant

A discrete Weber inequality on threedimensional hybrid spaces with application to the HHO approximation of magnetostatics Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220119
Florent Chave, Daniele A. Di Pietro, Simon LemaireWe prove a discrete version of the first Weber inequality on threedimensional hybrid spaces spanned by vectors of polynomials attached to the elements and faces of a polyhedral mesh. We then introduce two Hybrid HighOrder methods for the approximation of the magnetostatics model, in both its (firstorder) field and (secondorder) vector potential formulations. These methods are applicable on general

Vorticitystabilized virtual elements for the Oseen equation Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220112
L. Beirão da Veiga, F. Dassi, G. VaccaIn this paper, we extend the divergencefree VEM of [L. Beirão da Veiga, C. Lovadina and G. Vacca, Virtual elements for the Navier–Stokes problem on polygonal meshes, SIAM J. Numer. Anal. 56 (2018) 1210–1242] to the Oseen problem, including a suitable stabilization procedure that guarantees robustness in the convectiondominated case without disrupting the divergencefree property. The stabilization

Towards a mathematical theory of behavioral human crowds Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220112
Nicola Bellomo, Livio Gibelli, Annalisa Quaini, Alessandro RealiThe first part of our paper presents a general survey on the modeling, analytic problems, and applications of the dynamics of human crowds, where the specific features of living systems are taken into account in the modeling approach. This critical analysis leads to the second part which is devoted to research perspectives on modeling, analytic problems, multiscale topics which are followed by hints

A C1 virtual element method for an elliptic distributed optimal control problem with pointwise state constraints Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220110
Susanne C. Brenner, LiYeng Sung, Zhiyu TanWe design and analyze a C1 virtual element method for an elliptic distributed optimal control problem with pointwise state constraints. Theoretical estimates and corroborating numerical results are presented.

Error estimates of local energy regularization for the logarithmic Schrödinger equation Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20220107
Weizhu Bao, Rémi Carles, Chunmei Su, Qinglin TangThe logarithmic nonlinearity has been used in many partial differential equations (PDEs) for modeling problems in various applications. Due to the singularity of the logarithmic function, it introduces tremendous difficulties in establishing mathematical theories, as well as in designing and analyzing numerical methods for PDEs with such nonlinearity. Here, we take the logarithmic Schrödinger equation

Repulsive chemotaxis and predator evasion in predator–prey models with diffusion and preytaxis Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211230
Purnedu Mishra, Dariusz WrzosekThe role of predator evasion mediated by chemical signaling is studied in a diffusive prey–predator model when preytaxis is taken into account (model A) or not (model B) with taxis strength coefficients χ and ξ, respectively. In the kinetic part of the models, it is assumed that the rate of prey consumption includes functional responses of Holling, Beddington–DeAngelis or Crowley–Martin. Existence

Populations facing a nonlinear environmental gradient: Steady states and pulsating fronts Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211228
Matthieu Alfaro, Gwenaël PeltierWe consider a population structured by a space variable and a phenotypical trait, submitted to dispersion, mutations, growth and nonlocal competition. This population is facing an environmental gradient: to survive at location x, an individual must have a trait close to some optimal trait yopt(x). Our main focus is to understand the effect of a nonlinear environmental gradient. We thus consider a nonlocal

A virtual finite element method for twodimensional Maxwell interface problems with a background unfitted mesh Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211224
Shuhao Cao, Long Chen, Ruchi GuoA virtual element method (VEM) with the firstorder optimal convergence order is developed for solving twodimensional Maxwell interface problems on a special class of polygonal meshes that are cut by the interface from a background unfitted mesh. A novel virtual space is introduced on a virtual triangulation of the polygonal mesh satisfying a maximum angle condition, which shares exactly the same

An Lp spacesbased mixed virtual element method for the twodimensional Navier–Stokes equations Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211224
Gabriel N. Gatica, Filánder A. SequeiraIn this paper we extend the utilization of the Banach spacesbased formulations, usually employed for solving diverse nonlinear problems in continuum mechanics via primal and mixed finite element methods, to the virtual element method (VEM) framework and its respective applications. More precisely, we propose and analyze an Lp spacesbased mixed virtual element method for a pseudostressvelocity formulation

Global weak solutions and absorbing sets in a chemotaxisNavier–Stokes system with prescribed signal concentration on the boundary Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211224
Tobias Black, Michael WinklerAn initialboundary value problem for a coupled chemotaxisNavier–Stokes model with porous medium type diffusion is considered. Previous related literature has provided profound knowledge in cases when the system is augmented with noflux/noflux/noslip boundary conditions for the density of cells, the chemical concentration and the fluid velocity field, respectively; in particular, available qualitative

On the stochastic singular Cucker–Smale model: Wellposedness, collisionavoidance and flocking Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211223
Qiao Huang, Xiongtao ZhangWe study the Cucker–Smale (CS) flocking systems involving both singularity and noise. We first show the local strong wellposedness for the stochastic singular CS systems before the first collision time, which is a welldefined stopping time. Then, for communication with higher order singularity at origin (corresponding to α ≥ 1 in the case of ψ(r) = r−α), we establish the global wellposedness by

Recent results and perspectives for virtual element methods Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211220
L. Beirao da Veiga, N. Bellomo, F. Brezzi, L. D. MariniThis editorial paper is devoted to present the papers published in a special issue focused on recent views, applications, and results of virtual element methods (VEM). A critical analysis of the overall contents of the issue is proposed, thus leading to a forward look to research perspectives.

A robust VEMbased approach for flow simulations in porofractured media Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211220
Stefano Berrone, Andrea Borio, Alessandro D’Auria, Stefano Scialò, Fabio ViciniIn this paper, a Virtual Element Method (VEM)based approach is proposed for the simulation of flow in fractured porous media. The method is based on a robust meshing strategy, capable of producing conforming polyhedral meshes of intricate geometries and relies on the robustness of the VEM in handling distorted and elongated elements. Numerical tests in challenging configurations are presented and

Hybridization of the virtual element method for linear elasticity problems Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211220
Franco Dassi, Carlo Lovadina, Michele VisinoniIn this paper, we extend the hybridization procedure proposed in [D. N. Arnold and F. Brezzi, Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates, ESAIM Math. Model. Numer. Anal.19 (1985) 7–32] to the Virtual Element Method for linear elasticity problems based on the Hellinger–Reissner principle. To illustrate such a technique, we focus on a specific 2D

Recent results and perspectives for virtual element methods Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211220
L. Beirão da Veiga, N. Bellomo, F. Brezzi, L. D. MariniThis editorial paper is devoted to present the papers published in a special issue focused on recent views, applications, and results of virtual element methods (VEM). A critical analysis of the overall contents of the issue is proposed, thus leading to a forward look to research perspectives.

A robust VEMbased approach for flow simulations in porofractured media Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211220
Stefano Berrone, Andrea Borio, Alessandro D’Auria, Stefano Scialò, Fabio ViciniIn this paper, a Virtual Element Method (VEM)based approach is proposed for the simulation of flow in fractured porous media. The method is based on a robust meshing strategy, capable of producing conforming polyhedral meshes of intricate geometries and relies on the robustness of the VEM in handling distorted and elongated elements. Numerical tests in challenging configurations are presented and

Hybridization of the virtual element method for linear elasticity problems Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211220
Franco Dassi, Carlo Lovadina, Michele VisinoniIn this paper, we extend the hybridization procedure proposed in [D. N. Arnold and F. Brezzi, Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates, ESAIM Math. Model. Numer. Anal. 19 (1985) 7–32] to the Virtual Element Method for linear elasticity problems based on the Hellinger–Reissner principle. To illustrate such a technique, we focus on a specific

A review on arbitrarily regular conforming virtual element methods for second and higherorder elliptic partial differential equations Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211215
Paola F. Antonietti, Gianmarco Manzini, Simone Scacchi, Marco VeraniThe virtual element method is well suited to the formulation of arbitrarily regular Galerkin approximations of elliptic partial differential equations of order 2p1, for any integer p1 ≥ 1. In fact, the virtual element paradigm provides a very effective design framework for conforming, finite dimensional subspaces of Hp2(Ω), Ω being the computational domain and p2 ≥ p1 another suitable integer number

A multilayer network model of the coevolution of the spread of a disease and competing opinions Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211211
Kaiyan Peng, Zheng Lu, Vanessa Lin, Michael R. Lindstrom, Christian Parkinson, Chuntian Wang, Andrea L. Bertozzi, Mason A. PorterDuring the COVID19 pandemic, conflicting opinions on physical distancing swept across social media, affecting both human behavior and the spread of COVID19. Inspired by such phenomena, we construct a twolayer multiplex network for the coupled spread of a disease and conflicting opinions. We model each process as a contagion. On one layer, we consider the concurrent evolution of two opinions — p

Linearized von Kármán theory for incompressible magnetoelastic plates Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211124
Marco BrescianiWe study the asymptotic behavior, in the sense of Γconvergence, of a thin incompressible magnetoelastic plate, as its thickness goes to zero. We focus on the linearized von Kármán regime. The model features a mixed Eulerian–Lagrangian formulation, as magnetizations are defined on the deformed configuration.

A meanfield approach to selfinteracting networks, convergence and regularity Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211124
Rémi Catellier, Yves D’Angelo, Cristiano RicciThe propagation of chaos property for a system of interacting particles, describing the spatial evolution of a network of interacting filaments is studied. The creation of a network of mycelium is analyzed as representative case, and the generality of the modeling choices are discussed. Convergence of the empirical density for the particle system to its meanfield limit is proved, and a result of regularity

A parabolic local problem with exponential decay of the resonance error for numerical homogenization Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211115
Assyr Abdulle, Doghonay Arjmand, Edoardo PaganoniThis paper aims at an accurate and efficient computation of effective quantities, e.g. the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a micro–macrocoupling, where the macromodel describes the coarse scale behavior, and the micromodel is solved only locally to upscale the effective

On some smooth symmetric transonic flows with nonzero angular velocity and vorticity Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211030
Shangkun Weng, Zhouping Xin, Hongwei YuanThis paper concerns the structural stability of smooth cylindrically symmetric transonic flows in a concentric cylinder. Both cylindrical and axisymmetric perturbations are considered. The governing system here is of mixed elliptic–hyperbolic and changes type and the suitable formulation of boundary conditions at the boundaries is of great importance. First, we establish the existence and uniqueness

Thermodynamically consistent modeling for complex fluids and mathematical analysis Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211029
Yukihito Suzuki, Masashi Ohnawa, Naofumi Mori, Shuichi KawashimaThe goal of this paper is to derive governing equations for complex fluids in a thermodynamically consistent way so that the conservation of energy and the increase of entropy is guaranteed. The model is a system of firstorder partial differential equations on density, velocity, energy (or equivalently temperature), and conformation tensor. A barotropic model is also derived. In the onedimensional

Parameter identification for nonlocal phase field models for tumor growth via optimal control and asymptotic analysis Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211029
Elisabetta Rocca, Luca Scarpa, Andrea SignoriIn this paper, we introduce the problem of parameter identification for a coupled nonlocal Cahn–Hilliardreactiondiffusion PDE system stemming from a recently introduced tumor growth model. The inverse problem of identifying relevant parameters is studied here by relying on techniques from optimal control theory of PDE systems. The parameters to be identified play the role of controls, and a suitable

A probust polygonal discontinuous Galerkin method with minus one stabilization Math. Models Methods Appl. Sci. (IF 3.803) Pub Date : 20211029
Silvia Bertoluzza, Ilaria Perugia, Daniele PradaIn this paper, we introduce a new stabilization for discontinuous Galerkin methods for the Poisson problem on polygonal meshes, which induces optimal convergence rates in the polynomial approximation degree p. The stabilization is obtained by penalizing, in each mesh element K, a residual in the norm of the dual of H1(K). This negative norm is algebraically realized via the introduction of new auxiliary