Foundations of Continuum Mechanics and Mathematical Physics

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (1 July 2023) | Viewed by 5084

Special Issue Editors


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International Research Center on Mathematics and Mechanics of Complex Systems, University of L’Aquila, Via Giovanni Gronchi 18, 67100 L’Aquila, Italy
Interests: continuum mechanics; porous media; piezo-electro-mechanical structures; nonlinear elasticity; second gradient materials; metamaterials; mechanics of living tissue; smart materials; composite materials; experimental mechanics; numerical mechanics
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Department of General Mathematics, Lomonosov Moscow State University, 11992 Moscow, Russia
Interests: quasi-classical asymtotics of ODE’s and PDE’s; resurgent analysis; functional analysis
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1. Federal Research Center "Computer Science and Control", Russian Academy of Sciences, Moscow, Russia
2. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
Interests: partial differential equations & mathematical physics; elasticity system; stokes system; biharmonic (polyharmonic) equation
Special Issues, Collections and Topics in MDPI journals

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Department of Theoretical Physics, Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
Interests: electrodynamics of imperfect solid; theory of gauge fields; gravity & astrophysics; computational physics; nonlinear science

Special Issue Information

Dear Colleagues,

The main topics of this Special Issue are:

  • Foundations of Continuum Mechanics: As is well known, the basic equations of continuum mechanics are obtained by imposing suitable invariance properties on Lagrangian functionals under suitable symmetry groups. Invariance under the Galilean symmetry group is involved in the equations of classical continuum mechanics. while invariance in the Lorentz group is involved in relativity;
  • Functional analysis: Analytical theory of linear differential equations; regular and irregular singularities;
  • Mathematical Physics and PDE: Asymptotics of ODEs and PDEs; mathematical physics and PDE including fluid dynamics, Helmhotz equation; solvability, regularity, stability, and other qualitative properties of linear and nonlinear equations and systems; scattering theory, inverse problems; variational methods and calculus of variations;
  • Foundation in Electromagnetic fields: wave propagandizing and media with defects.

Submit your paper and select the Journal “Symmetry” and the Special Issue “Foundations of Continuum Mechanics and Mathematical Physics” via: MDPI submission system. Our papers will be published on a rolling basis and we will be pleased to receive your submission once you have finished it.

Prof. Dr. Francesco dell’Isola
Prof. Maria Korovina
Prof. Dr. Hovik Matevossian
Prof. Dr. Nikolai E. Smirnov
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. Symmetry is an international peer-reviewed open access monthly 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 2400 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

  • Evolution equations for generalized continuum applications to homogenization and design of metamaterials
  • discrete and continuum mechanics, metamaterials and smart structures design, variational methods in mechanics, biomechanics, experimental mechanics
  • Quasi-classical asymptotics of ODEs and PDEs, resurgent analysis
  • Mathematical physics
  • PDE
  • fluid dynamics
  • applied mathematics
  • Electrodynamics, condensed matter, exactly solvable and integrable systems, high energy physics, general relativity and quantum cosmology, computational physics, differential geometry

Published Papers (4 papers)

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Editorial

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6 pages, 216 KiB  
Editorial
Foundations of Continuum Mechanics and Mathematical Physics—Editorial 2021–2023
by Francesco dell’Isola and Hovik A. Matevossian
Symmetry 2023, 15(9), 1643; https://doi.org/10.3390/sym15091643 - 25 Aug 2023
Viewed by 603
Abstract
It is well known that “Physics and Symmetry/Asymmetry” is a topical Section of Symmetry [...] Full article
(This article belongs to the Special Issue Foundations of Continuum Mechanics and Mathematical Physics)

Research

Jump to: Editorial

13 pages, 2665 KiB  
Article
Conductive Heat Transfer in Materials under Intense Heat Flows
by Gregory Fedotenkov, Lev Rabinskiy and Sergey Lurie
Symmetry 2022, 14(9), 1950; https://doi.org/10.3390/sym14091950 - 19 Sep 2022
Cited by 15 | Viewed by 1418
Abstract
The paper presents the solution of the spatial transient problem of the impact of a moving heat flux source induced by the laser radiation on the surface of a half-space using the superposition principle and the method of transient functions. The hyperbolic equation [...] Read more.
The paper presents the solution of the spatial transient problem of the impact of a moving heat flux source induced by the laser radiation on the surface of a half-space using the superposition principle and the method of transient functions. The hyperbolic equation of transient thermal conductivity accounting for the relaxation time is used to model the laser heating process. It is assumed that the heat flux is distributed symmetrically with respect to the center of the heating spot. The combined numerical and analytical algorithm has been developed and implemented, which allows one to determine the temperature distribution both on the surface and on the depth of the half-space. In this case, the principle of superposition is used with the use of a special symmetric Gaussian distribution to describe the model of a source of high-intensity heat flux. The use of such a symmetric distribution made it possible to calculate the integrals over the spatial variables analytically. The results of the work could be used to estimate the contribution of the conductive component in the overall heat transfer of materials exposed to intense heat flows (laser surface treatment, laser additive technologies, streamlining and heating of materials by high-enthalpy gases, etc.). Full article
(This article belongs to the Special Issue Foundations of Continuum Mechanics and Mathematical Physics)
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16 pages, 294 KiB  
Article
Six-Dimensional Manifold with Symmetric Signature in a Unified Theory of Gravity and Electromagnetism
by Nikolay Popov and Ivan Matveev
Symmetry 2022, 14(6), 1163; https://doi.org/10.3390/sym14061163 - 05 Jun 2022
Cited by 6 | Viewed by 1144
Abstract
A six dimensional manifold of symmetric signature (3,3) is proposed as a space structure for building combined theory of gravity and electromagnetism. Special metric tensor is proposed, yielding the space which combines the properties of Riemann, Weyl and Finsler [...] Read more.
A six dimensional manifold of symmetric signature (3,3) is proposed as a space structure for building combined theory of gravity and electromagnetism. Special metric tensor is proposed, yielding the space which combines the properties of Riemann, Weyl and Finsler spaces. Geodesic line equations are constructed where coefficients can be divided into depending on the metric tensor (relating to the gravitational interaction) and depending on the vector field (relating to the electromagnetic interaction). If there is no gravity, the geodesics turn into the equations of charge motion in the electromagnetic field. Furthermore, symmetric six-dimensional electrodynamics can be reduced to traditional four-dimensional Maxwell system, where two additional time dimensions are compactified. A purely geometrical interpretation of the concept of electromagnetic field and point electric charge is proposed. Full article
(This article belongs to the Special Issue Foundations of Continuum Mechanics and Mathematical Physics)
11 pages, 2853 KiB  
Article
Analytical Model of Heating an Isotropic Half-Space by a Moving Laser Source with a Gaussian Distribution
by Alexander Orekhov, Lev Rabinskiy and Gregory Fedotenkov
Symmetry 2022, 14(4), 650; https://doi.org/10.3390/sym14040650 - 23 Mar 2022
Cited by 18 | Viewed by 1979
Abstract
This study presents the solution of the transient spatial problem of the impact of a moving source of heat flux induced by laser radiation on the surface of a half-space using the superposition principle and the method of transient functions. The solution is [...] Read more.
This study presents the solution of the transient spatial problem of the impact of a moving source of heat flux induced by laser radiation on the surface of a half-space using the superposition principle and the method of transient functions. The solution is based on the Green’s function method, according to which the influence function of a surface-concentrated heat source is found at the first stage. The influence function has axial symmetry and the problem of finding the influence function is axisymmetric. To find the Green’s function, Laplace and Fourier integral transforms are used. The novelty of the obtained analytical solution is that the heat transfer at the free surface of the half-space is taken into account. The Green’s function that was obtained is used to construct an analytical solution to the moving heat-source problem in the integral form. The kernel of the advising integral operator is the constructed Green’s function. The Gaussian distribution is used to calculate integrals on spatial variables analytically. Gaussian law models the distribution of heat flux in the laser beam. As a result, the corresponding integrals on the spatial variables can be calculated analytically. A convenient formula that allows one to study the non-stationary temperature distribution when the heat source moves along arbitrary trajectories is obtained. A numerical, analytical algorithm has been developed and implemented that allows one to determine temperature distribution both on the surface and on the depth of a half-space. For verification purposes, the results were compared with the solution obtained using FEM. Full article
(This article belongs to the Special Issue Foundations of Continuum Mechanics and Mathematical Physics)
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