Zeitschrift fur Angewandte Mathematik und Physik最新文献

{"title":"Poroelasticity derived from the microstructure for intrinsically incompressible constituents.","authors":"R Penta, C Lonati, L Miller, A Marzocchi","doi":"10.1007/s00033-025-02651-2","DOIUrl":"10.1007/s00033-025-02651-2","url":null,"abstract":"<p><p>We provide a new derivation of the quasi-static equations of Biot's poroelasticity from the microstructure via the asymptotic (periodic) homogenisation method (AHM) by assuming intrinsic incompressibility of both an isotropic, linear elastic solid and a low Reynolds' number Newtonian fluid, in a small deformations regime. This is done by starting from a fluid-structure interaction (FSI) problem between the two phases at the pore scale, and by introducing both a solid and a fluid pressure, as both phases are equipped with an incompressibility constraint. Upscaling by the AHM then results in the expected Biot's equation at the macroscopic scale, with coefficients which are to be computed by solving non-standard periodic cell problems at the pore scale. These latter differ from the ones arising from classical derivations of poroelasticity via the AHM, which are typically obtained by assuming that the elastic phase is compressible, and are characterised by a saddle point structure which is inherited from the equations governing the original FSI problem. The proposed approach, which is new and cannot be derived as a particular case of existing formulations, means that the poroelastic governing equations for intrinsic incompressible phases are obtained without performing any \"a posteriori\" assumption on the macroscale coefficients, as these latter are typically employed based on physical arguments rather than following from a rigorous analysis of the properties of the pore scale cell problems. The advantages of the current formulation for incompressible solids are as follows. (a) The formulation is derived for two genuinely incompressible phases and in particular for an incompressible solid, which means that a reduced number of input parameters is required to compute the effective stiffness. In the case of pore scale isotropy, this means that only the shear modulus is to be provided. (b) The pore scale cell problems can be solved without approximating the pore scale elastic properties to that of an incompressible solid, i.e. in the case of isotropy, no additional errors are to be introduced by utilising approximate values of the Poisson's ratio (which in a compressible formulation can be close to, but not identical to, 0.5).</p>","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":"77 1","pages":"22"},"PeriodicalIF":1.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12717114/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145806427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Homogenised balance equations for nematic liquid crystal flow in elastic porous media.","authors":"Mohammed Alwady, Nigel J Mottram, Raimondo Penta","doi":"10.1007/s00033-025-02675-8","DOIUrl":"https://doi.org/10.1007/s00033-025-02675-8","url":null,"abstract":"<p><p>We derive a new mathematical model for the macroscopic behaviour of a linear elastic porous medium weakly interacting with an incompressible, slowly flowing, nematic liquid crystal under the one elastic constant approximation and a simplified hypothesis concerning the fluid viscosities for which the stress tensor remains dependent on the nematic director, which is the average fluid molecular orientation, but is symmetric. In this situation, the angular momentum equation, which governs the dynamics of the nematic director, decouples from the linear momentum equations of the fluid. As such, whilst the nematic anisotropy affects the flow profile, the fluid flow no longer affects the configuration of the nematic director. We assume that the typical pore dimension (the <i>microscale</i>) is significantly smaller than the average size of the whole domain (the <i>macroscale</i>), and exploit this sharp length-scale separation in our use of the asymptotic homogenisation technique to derive new macroscale governing equations by upscaling the fluid-structure interaction problem between the porous elastic structure and the nematic liquid crystal fluid phase. The resulting novel anisotropic macroscale viscoelastic model describes the overall system representing a nematic liquid crystal flowing through an elastic porous solid and could therefore be termed an <i>anisotropic poro-viscoelastic model</i>. This system of partial differential equations incorporates the nematic director, its spatial variations, and the underlying microstructure through coefficients that are computed by solving appropriate microscale cell problems. The homogenised constitutive relationships account for the roles of the nematic director field, the elastic response of the solid phase, and their interplay with the underlying microstructural configuration. We then focus on the particular case in which the role of the elastic porous structure is negligible. In this case, the fluid flow is no longer affected by the deformations of the porous medium and is solely driven by a volume load, which depends on macroscale spatial variations of the nematic director and its interplay with the underlying microscale geometry. The resulting theoretical framework opens up new modelling possibilities for a wide range of potential applications for nematic liquid crystals encapsulated in a complex porous network.</p>","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":"77 3","pages":"88"},"PeriodicalIF":1.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12923422/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147272613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the mathematical structure and numerical solution of discrete-continuous optimization problems in DDCM.","authors":"Cristian G Gebhardt, Senta Lange, Marc C Steinbach","doi":"10.1007/s00033-025-02536-4","DOIUrl":"https://doi.org/10.1007/s00033-025-02536-4","url":null,"abstract":"<p><p>In this work, we investigate data-driven elasticity problems defined on a closed interval of the real line that are spatially discretized by means of the finite element method. This one-dimensional setting allows us to gain a deeper understanding of the underlying <i>discrete-continuous quadratic optimization problems</i>. We provide an in-depth analysis of their structural properties and prove their global solvability. Based on this analysis, we propose a new structure-specific initialization for a solution strategy relying on an <i>alternating direction method</i>, and we prove that it is globally optimal in certain symmetric cases. Finally and to support our formal mathematical analysis, we also provide a series of examples that show the benefits of this kind of approach and briefly illustrate the challenges when dealing with real experimental data.</p>","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":"76 5","pages":"177"},"PeriodicalIF":1.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12325500/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144800951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamical anomalous transport of molecules subject to inhomogeneous body forces.","authors":"A Girelli, G Giantesio, A Musesti, R Penta","doi":"10.1007/s00033-025-02614-7","DOIUrl":"10.1007/s00033-025-02614-7","url":null,"abstract":"<p><p>This work explores diffusion with scale-dependent coefficients, starting from a general advection-diffusion framework from a theoretical standpoint, and then focusing numerically on a purely diffusive regime. Advection-diffusion processes are central to modeling transport phenomena in natural and engineered systems. However, classical models often fail to capture the complexities of systems with spatial and temporal variability. In this work, we present a multiscale advection-diffusion model that incorporates time-dependent diffusion coefficients and spatially inhomogeneous, multiscale body forces. Using the asymptotic homogenization technique, we derive a macroscopic equation that reflects the evolution of transport properties across multiple scales, accounting for both spatial and temporal variations. A key contribution of this study is the formulation of new cell problems associated with the dual time-dependence of the diffusion coefficient and the multiscale forces, which lead to the introduction of additional source terms. Furthermore, we incorporate a novel source term arising from the nonzero divergence of the advective velocity field, which modifies the effective macroscopic advection velocity to capture source and sink effects at the microscale. We apply this model to describe water molecule diffusion in packed erythrocytes, a system exhibiting dual time scales, and by showing how our approach captures the temporal evolution of transport under dynamic diffusion.</p>","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":"76 6","pages":"249"},"PeriodicalIF":1.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12665631/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145662673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Characterization of the spectra of rotating truncated gas planets and inertia-gravity modes.","authors":"Maarten V de Hoop, Sean Holman","doi":"10.1007/s00033-025-02629-0","DOIUrl":"10.1007/s00033-025-02629-0","url":null,"abstract":"<p><p>We study the essential spectrum, which corresponds to inertia-gravity modes, of the system of equations governing a rotating and self-gravitating gas planet. With certain boundary conditions, we rigorously and precisely characterize the essential spectrum and show how it splits from the portion of the spectrum corresponding to the acoustic modes. The fundamental mathematical tools in our analysis are a generalization of the Helmholtz decomposition and the Lopantinskii conditions.</p>","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":"76 6","pages":"253"},"PeriodicalIF":1.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12665629/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145662642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Viscoelasticity and accretive phase-change at finite strains.","authors":"Andrea Chiesa, Ulisse Stefanelli","doi":"10.1007/s00033-025-02434-9","DOIUrl":"10.1007/s00033-025-02434-9","url":null,"abstract":"<p><p>We investigate the evolution of a two-phase viscoelastic material at finite strains. The phase evolution is assumed to be irreversible: One phase accretes in time in its normal direction, at the expense of the other. Mechanical response depends on the phase. At the same time, growth is influenced by the mechanical state at the boundary of the accreting phase, making the model fully coupled. This setting is inspired by the early stage development of solid tumors, as well as by the swelling of polymer gels. We formulate the evolution problem by coupling the balance of momenta in weak form and the growth dynamics in the viscosity sense. Both a diffused- and a sharp-interface variant of the model are proved to admit solutions and the sharp-interface limit is investigated.</p>","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":"76 2","pages":"53"},"PeriodicalIF":1.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11782464/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143082327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Shear-induced wrinkling in accelerating thin elastic discs","authors":"Ciprian D. Coman","doi":"10.1007/s00033-023-02131-5","DOIUrl":"https://doi.org/10.1007/s00033-023-02131-5","url":null,"abstract":"Abstract The wrinkling instabilities produced by in-plane angular accelerations in a rotating disc are discussed here in a particular limit of relevance to very thin plates. By coupling the classical linear elasticity solution for this configuration with the Föppl–von Kármán plate buckling equation, a fourth-order boundary-value problem with variable coefficients is obtained. The singular-perturbation character of the resulting problem arises from a combination of factors encompassing both the pre-stress (due to the spinning motion) and the geometry of the annular domain. With the help of a simplified multiple-scale perturbation method in conjunction with matched asymptotics, we succeed in capturing the dependence of the critical (wrinkling) acceleration on the instantaneous speed of the disc as well as other physical parameters. We show that the asymptotic predictions compare well with the results of direct numerical simulations of the original bifurcation problem. The limitations of the formulae obtained are also considered, and some practical suggestions for improving their accuracy are suggested.","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":" 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135240992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global dynamics in a chemotaxis system involving nonlinear indirect signal secretion and logistic source","authors":"Chang-Jian Wang, Pengyan Wang, Xincai Zhu","doi":"10.1007/s00033-023-02126-2","DOIUrl":"https://doi.org/10.1007/s00033-023-02126-2","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":" 26","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135241003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sign-changing solutions to critical Schrödinger equation with Hartree-type nonlinearity","authors":"Cui Zhang, Fuyi Li","doi":"10.1007/s00033-023-02133-3","DOIUrl":"https://doi.org/10.1007/s00033-023-02133-3","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":" 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135241708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Poisson structure and action–angle variables for the Hirota equation","authors":"Yu Zhang, Shou-Fu Tian","doi":"10.1007/s00033-023-02129-z","DOIUrl":"https://doi.org/10.1007/s00033-023-02129-z","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135635333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}