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Mathematics
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Multiscale Mathematical Modeling
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Multiscale Mathematical Modeling

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 31 May 2024 | Viewed by 2275

Special Issue Editors

Prof. Dr. Julius Kaplunov

E-Mail Website
Guest Editor
School of Computer Science and Mathematics, Keele University, Keele ST5 5BG, UK
Interests: continuum mechanics; wave propagation; asymptotic methods
Prof. Dr. Igor Andrianov

E-Mail Website
Guest Editor
Chair and Institute of General Mechanics, RWTH Aachen University, Eilfschornsteinstraße 18, D-52062 Aachen, Germany
Interests: asymptotology; nonlinear dynamics; composite materials; thin-walled structures
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The open access journal Mathematics (latest Impact Factor of 2.4, Q1), indexed in Scopus and Web of Science, is pleased to announce a new Special Issue titled "Multiscale Mathematical Modeling".

Given the depth of your expertise in this field, we would like to cordially invite you to contribute an article to the Special Issue. 

Making predictions from a finer-scale theory of a large-scale behavior  to create a fine-scale theory is a key goal of modern natural sciences and is of particular importance for numerous engineering applications. The problems of multiscale modeling are often of an interdisciplinary nature. The recent major progress in this area is due to the development of advanced computational and experimental methodologies, along with establishing powerful mathematical frameworks operating with multiple lengths and time scales. The latter is the focus of the current Special Issue, which is expected to address the state of the art of the subject and is oriented to a broad scientific and engineering community.

Specific topics of this Issue include but are not limited to the modeling of highly heterogeneous media and structures at different length and time scales; robust algorithms for solving multiscale problems; micro, macro, meso, and hierarchical models; multiscale analysis using machine learning techniques; and matching of discrete lattice structures and continua.

Prof. Dr. Julius Kaplunov
Prof. Dr. Igor Andrianov
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • multiscale modeling
  • heterogeneous media and structures
  • micro, macro, meso, and hierarchical models
  • asymptotic methods
  • averaging and homogenization
  • matching of discrete lattice structures and continua

Published Papers (4 papers)

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Research

21 pages, 397 KiB  
Article
Norm-Resolvent Convergence for Neumann Laplacians on Manifold Thinning to Graphs
by Kirill D. Cherednichenko, Yulia Yu. Ershova and Alexander V. Kiselev
Mathematics 2024, 12(8), 1161; https://doi.org/10.3390/math12081161 - 12 Apr 2024
Viewed by 247
Abstract
Norm-resolvent convergence with an order-sharp error estimate is established for Neumann Laplacians on thin domains in Rd, d≥2, converging to metric graphs in the limit of vanishing thickness parameter in the “resonant” case. The vertex matching conditions [...] Read more.
Norm-resolvent convergence with an order-sharp error estimate is established for Neumann Laplacians on thin domains in Rd, d≥2, converging to metric graphs in the limit of vanishing thickness parameter in the “resonant” case. The vertex matching conditions of the limiting quantum graph are revealed as being closely related to those of the δ′ type. Full article
(This article belongs to the Special Issue Multiscale Mathematical Modeling)
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14 pages, 7271 KiB  
Article
Utilization of a Genetic Algorithm to Identify Optimal Geometric Shapes for a Seismic Protective Barrier
by Vladimir Bratov, Andrey Murachev and Sergey V. Kuznetsov
Mathematics 2024, 12(3), 492; https://doi.org/10.3390/math12030492 - 04 Feb 2024
Viewed by 537
Abstract
The utilization of seismic barriers for protection against the hazardous impact of natural or technogenic waves is an extremely promising emerging technology to secure buildings, structures and entire areas against earthquake-generated seismic waves, high-speed-transport-induced vibrations, etc. The current research is targeted at studying [...] Read more.
The utilization of seismic barriers for protection against the hazardous impact of natural or technogenic waves is an extremely promising emerging technology to secure buildings, structures and entire areas against earthquake-generated seismic waves, high-speed-transport-induced vibrations, etc. The current research is targeted at studying the effect of seismic-barrier shape on the reduction of seismic-wave magnitudes within the protected region. The analytical solution of Lamb’s problem was used to verify the adopted numerical approach. It was demonstrated that the addition of complementary geometric features to a simple barrier shape provides the possibility of significantly increasing the resulting seismic protection. A simple genetic algorithm was employed to evaluate the nontrivial but extremely effective geometry of the seismic barrier. The developed approach can be used in various problems requiring optimization of non-parameterizable geometric shapes. The applicability of genetic algorithms and other generative algorithms to discover optimal (or close to optimal) geometric configurations for the essentially multiscale problems of the interaction of mechanical waves with inclusions is discussed. Full article
(This article belongs to the Special Issue Multiscale Mathematical Modeling)
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25 pages, 1406 KiB  
Article
A General Case of a Line Contact Lubricated by a Non-Newtonian Giesekus Fluid
by Ilya I. Kudish and Sergei S. Volkov
Mathematics 2023, 11(22), 4679; https://doi.org/10.3390/math11224679 - 17 Nov 2023
Viewed by 498
Abstract
A steady plane hydrodynamic problem of lubrication of a lightly loaded contact of two parallel cylinders lubricated by a non-Newtonian fluid with Giesekus rheology is considered. The advantage of this non-Newtonian rheology is its ability to properly describe the real behavior of formulated [...] Read more.
A steady plane hydrodynamic problem of lubrication of a lightly loaded contact of two parallel cylinders lubricated by a non-Newtonian fluid with Giesekus rheology is considered. The advantage of this non-Newtonian rheology is its ability to properly describe the real behavior of formulated lubricants at high and low shear stresses. The problem is solved by using a modification of the regular perturbation method with respect to the small parameter α, characterizing the degree to which the polymeric molecules of the additive to the lubricant follow the streamlines of the lubricant flow. It is assumed that the lubricant relaxation time and the value of α are of the order of the magnitude of the ratio of the characteristic gap between the contact surfaces and the contact length. The obtained analytical solution of the problem is analyzed numerically for the dependencies of the problem characteristics such as contact pressure, fluid flux, lubrication film thickness, friction force, energy loss in the lubricated contact, etc., on the problem input parameters. Full article
(This article belongs to the Special Issue Multiscale Mathematical Modeling)
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11 pages, 425 KiB  
Article
Degenerated Boundary Layers and Long-Wave Low-Frequency Motion in High-Contrast Elastic Laminates
by Lenser A. Aghalovyan, Lusine G. Ghulghazaryan, Julius Kaplunov and Danila Prikazchikov
Mathematics 2023, 11(18), 3905; https://doi.org/10.3390/math11183905 - 14 Sep 2023
Viewed by 577
Abstract
The effect of high contrast on the multiscale behaviour of elastic laminates is studied. Mathematical modelling in this area is of significant interest for a variety of modern applications, including but not limited to advanced sandwich structures and photovoltaic panels. As an example, [...] Read more.
The effect of high contrast on the multiscale behaviour of elastic laminates is studied. Mathematical modelling in this area is of significant interest for a variety of modern applications, including but not limited to advanced sandwich structures and photovoltaic panels. As an example, the antiplane shear of a symmetric, three-layered plate is considered. The problem parameters expressing relative thickness, stiffness and density are assumed to be independent. The high contrast may generally support extra length and time scales corresponding to degenerated boundary layers and propagating long-wave low-frequency vibration modes. The main focus is on the relation between these two phenomena. The developed multiparametric approach demonstrates that those do not always appear simultaneously. The associated explicit estimates on contrast parameters are established. In addition, the recent asymptotic extension of the classical Saint-Venant’s principle is adapted for calculating the contribution of the degenerate boundary layer or long-wave low-frequency propagation mode. The peculiarity of the limiting absorption principle in application to layered media is also addressed. Full article
(This article belongs to the Special Issue Multiscale Mathematical Modeling)
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