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Mathematical Modeling in Physical Sciences
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Mathematical Modeling in Physical Sciences

A special issue of Mathematical and Computational Applications (ISSN 2297-8747). This special issue belongs to the section "Natural Sciences".

Deadline for manuscript submissions: closed (31 January 2019) | Viewed by 22057

Special Issue Editor

Prof. Dr. Hovik Matevossian

E-Mail Website
Guest Editor
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
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Special Issue Information

Dear Colleagues,

Please visit this site https://icmsquare.net/index.php for a detailed description of this Special Issue. The Special Issue will mainly consist of selected papers presented at the "7th International Conference on Mathematical Modeling in Physical Sciences". Papers considered to fit the scope of the journal and of sufficient quality, after evaluation by the reviewers, will be published free of charge.

The main topics of this Special Issue are:

  • Mathematical Physics and PDE
    Dynamical systems, including integrable systems; Equilibrium and non-equilibrium statistical mechanics, including interacting particle systems; PDE including fluid dynamics, wave equation, Boltzmann equation and material science; General relativity, Stochastic models and probabilistic methods including random matrices and stochastic PDE; Solvability, regularity, stability and other qualitative properties of linear and non-linear equations and systems; Spectral theory, scattering, inverse problems; Variational methods and calculus of variations; Algebraic methods, including operator algebras, representation theory and algebraic aspects of quantum field theory; Quantum field theory including gauge theories and conformal field theory; Geometry and topology in physics including string theory and quantum gravity
  • Applied Mathematics
    Fractional calculus, Numerical methods, ODE’s and PDE’s, Financial mathematics, Fuzzy logic, Efficient solvers, Nonlinear problems, Bifurcations, Stability, Chaos and Fractals
  • Mathematical Modeling in Applied Physics
    Semiconductor devices, Thin films, Superconductors, Organic molecules, Bioelectronics, Infrastructure design
  • Mathematical Modeling in Fundamental Physics
    High-energy physics, Particle physics, Nuclear physics, Atomic physics, Molecular physics, Gravitation, Cosmology, Astrophysics, Plasma physics, Electrodynamics, Fluid dynamics, Condensed-matter physics, Chemical physics, Chaos, Statistical physics
  • Scientific Computation
    Algorithms for scientific computation, Parallel algorithms and parallel computing, Grid computations, Mathematical programming, Heuristics, metaheuristics or simulation, Complex physical and technical systems, Experimental data processing, Distributed scientific computing
  • Complex Systems and Complex Networks
  • Geometric Integration in Physical Sciences and Engineering

Prof. Dr. Hovik Matevossian
Guest Editor

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Published Papers (7 papers)

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Research

17 pages, 342 KiB  
Article
On Determination of Wave Velocities through the Eigenvalues of Material Objects
by Mikhail U. Nikabadze, Sergey A. Lurie, Hovik A. Matevossian and Armine R. Ulukhanyan
Math. Comput. Appl. 2019, 24(2), 39; https://doi.org/10.3390/mca24020039 - 11 Apr 2019
Cited by 2 | Viewed by 2563
Abstract
The statement of the eigenvalue problem for a tensor–block matrix of any order and of any
even rank is formulated. It is known that the eigenvalues of the tensor and the tensor–block matrix
are invariant quantities. Therefore, in this work, our goal is [...] Read more.
The statement of the eigenvalue problem for a tensor–block matrix of any order and of any
even rank is formulated. It is known that the eigenvalues of the tensor and the tensor–block matrix
are invariant quantities. Therefore, in this work, our goal is to find the expression for the velocities of
wave propagation of some medias through the eigenvalues of the material objects. In particular, we
consider the classical and micropolar materials with the different anisotropy symbols and for them
we determine the expressions for the velocities of wave propagation through the eigenvalues of the
material objects. Full article
(This article belongs to the Special Issue Mathematical Modeling in Physical Sciences)
19 pages, 343 KiB  
Article
Some Applications of Eigenvalue Problems for Tensor and Tensor–Block Matrices for Mathematical Modeling of Micropolar Thin Bodies
by Mikhail Nikabadze and Armine Ulukhanyan
Math. Comput. Appl. 2019, 24(1), 33; https://doi.org/10.3390/mca24010033 - 22 Mar 2019
Cited by 5 | Viewed by 3243
Abstract
The statement of the eigenvalue problem for a tensor–block matrix (TBM) of any order and of any even rank is formulated, and also some of its special cases are considered. In particular, using the canonical presentation of the TBM of the tensor of [...] Read more.
The statement of the eigenvalue problem for a tensor–block matrix (TBM) of any order and of any even rank is formulated, and also some of its special cases are considered. In particular, using the canonical presentation of the TBM of the tensor of elastic modules of the micropolar theory, in the canonical form the specific deformation energy and the constitutive relations are written. With the help of the introduced TBM operator, the equations of motion of a micropolar arbitrarily anisotropic medium are written, and also the boundary conditions are written down by means of the introduced TBM operator of the stress and the couple stress vectors. The formulations of initial-boundary value problems in these terms for an arbitrary anisotropic medium are given. The questions on the decomposition of initial-boundary value problems of elasticity and thin body theory for some anisotropic media are considered. In particular, the initial-boundary problems of the micropolar (classical) theory of elasticity are presented with the help of the introduced TBM operators (tensors–operators). In the case of an isotropic micropolar elastic medium (isotropic and transversely isotropic classical media), the TBM operator (tensors–operators) of cofactors to TBM operators (tensors–tensors) of the initial-boundary value problems are constructed that allow decomposing initial-boundary value problems. We also find the determinant and the tensor of cofactors to the sum of six tensors used for decomposition of initial-boundary value problems. From three-dimensional decomposed initial-boundary value problems, the corresponding decomposed initial-boundary value problems for the theories of thin bodies are obtained. Full article
(This article belongs to the Special Issue Mathematical Modeling in Physical Sciences)
14 pages, 2503 KiB  
Article
Thermoelastic Diffusion Multicomponent Half-Space under the Effect of Surface and Bulk Unsteady Perturbations
by Sergey A. Davydov, Andrei V. Zemskov and Elena R. Akhmetova
Math. Comput. Appl. 2019, 24(1), 26; https://doi.org/10.3390/mca24010026 - 19 Feb 2019
Cited by 7 | Viewed by 3426
Abstract
This article presents an algorithm for solving the unsteady problem of one-dimensional coupled thermoelastic diffusion perturbations propagation in a multicomponent isotropic half-space, as a result of surface and bulk external effects. One-dimensional physico-mechanical processes, in a continuum, have been described by a local-equilibrium [...] Read more.
This article presents an algorithm for solving the unsteady problem of one-dimensional coupled thermoelastic diffusion perturbations propagation in a multicomponent isotropic half-space, as a result of surface and bulk external effects. One-dimensional physico-mechanical processes, in a continuum, have been described by a local-equilibrium model, which included the coupled linear equations of an elastic medium motion, heat transfer, and mass transfer. The unknown functions of displacement, temperature, and concentration increments were sought in the integral form, which was a convolution of the surface and bulk Green’s functions and external effects functions. The Laplace transform on time and the Fourier sine and cosine transforms on the coordinate were used to find the Green’s functions. The obtained Green’s functions was analyzed. Test calculations were performed on the examples of some technological processes. Full article
(This article belongs to the Special Issue Mathematical Modeling in Physical Sciences)
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9 pages, 264 KiB  
Article
On the Mixed Dirichlet–Steklov-Type and Steklov-Type Biharmonic Problems in Weighted Spaces
by Hovik Matevossian
Math. Comput. Appl. 2019, 24(1), 25; https://doi.org/10.3390/mca24010025 - 18 Feb 2019
Cited by 7 | Viewed by 2707
Abstract
We studied the properties of generalized solutions in unbounded domains and the asymptotic behavior of solutions of elliptic boundary value problems at infinity. Moreover, we studied the unique solvability of the mixed Dirichlet–Steklov-type and Steklov-type biharmonic problems in the exterior of a compact [...] Read more.
We studied the properties of generalized solutions in unbounded domains and the asymptotic behavior of solutions of elliptic boundary value problems at infinity. Moreover, we studied the unique solvability of the mixed Dirichlet–Steklov-type and Steklov-type biharmonic problems in the exterior of a compact set under the assumption that generalized solutions of these problems has a bounded Dirichlet integral with weight | x | a. Depending on the value of the parameter a, we obtained uniqueness (non-uniqueness) theorems of these problems or present exact formulas for the dimension of the space of solutions. Full article
(This article belongs to the Special Issue Mathematical Modeling in Physical Sciences)
14 pages, 1370 KiB  
Article
An Elastodiffusive Orthotropic Euler–Bernoulli Beam Considering Diffusion Flux Relaxation
by Dmitry Tarlakovskii and Andrei Zemskov
Math. Comput. Appl. 2019, 24(1), 23; https://doi.org/10.3390/mca24010023 - 6 Feb 2019
Cited by 5 | Viewed by 2790
Abstract
This article considers an unsteady elastic diffusion model of Euler–Bernoulli beam oscillations in the presence of diffusion flux relaxation. We used the model of coupled elastic diffusion for a homogeneous orthotropic multicomponent continuum to formulate the problem. A model of unsteady bending for [...] Read more.
This article considers an unsteady elastic diffusion model of Euler–Bernoulli beam oscillations in the presence of diffusion flux relaxation. We used the model of coupled elastic diffusion for a homogeneous orthotropic multicomponent continuum to formulate the problem. A model of unsteady bending for the elastic diffusive Euler–Bernoulli beam was obtained using Hamilton’s variational principle. The Laplace transform on time and the Fourier series expansion by the spatial coordinate were used to solve the obtained problem. Full article
(This article belongs to the Special Issue Mathematical Modeling in Physical Sciences)
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11 pages, 298 KiB  
Article
On a Problem Arising in Application of the Re-Quantization Method to Construct Asymptotics of Solutions to Linear Differential Equations with Holomorphic Coefficients at Infinity
by Maria Korovina, Ilya Smirnov and Vladimir Smirnov
Math. Comput. Appl. 2019, 24(1), 16; https://doi.org/10.3390/mca24010016 - 28 Jan 2019
Cited by 3 | Viewed by 2851
Abstract
The re-quantization method—one of the resurgent analysis methods of current importance—is developed in this study. It is widely used in the analytical theory of linear differential equations. With the help of the re-quantization method, the problem of constructing the asymptotics of the inverse [...] Read more.
The re-quantization method—one of the resurgent analysis methods of current importance—is developed in this study. It is widely used in the analytical theory of linear differential equations. With the help of the re-quantization method, the problem of constructing the asymptotics of the inverse Laplace–Borel transform is solved for a particular type of functions with holomorphic coefficients that exponentially grow at zero. Two examples of constructing the uniform asymptotics at infinity for the second- and forth-order differential equations with the help of the re-quantization method and the result obtained in this study are considered. Full article
(This article belongs to the Special Issue Mathematical Modeling in Physical Sciences)
7 pages, 934 KiB  
Article
On the Moving Trajectory of a Ball in a Viscous Liquid between Two Concentric Rigid Spheres
by Sergey Gladkov and Sophie Bogdanova
Math. Comput. Appl. 2018, 23(4), 77; https://doi.org/10.3390/mca23040077 - 4 Dec 2018
Viewed by 2676
Abstract
In the paper, the dynamic motion of a point ball with a mass of m , sliding in a viscous liquid between two concentric spheres under the influence of gravity and viscous and dry resistance, is investigated. In addition, it is considered that [...] Read more.
In the paper, the dynamic motion of a point ball with a mass of m , sliding in a viscous liquid between two concentric spheres under the influence of gravity and viscous and dry resistance, is investigated. In addition, it is considered that the ball starts its motion from some arbitrary point M 0 = M ( θ 0 , φ 0 ) . A system of nonlinear differential equations in a spheroidal coordinate system is obtained for the angular variables θ and φ to account for all the forces acting on the ball. The dependence of the reaction force on the angular variables is found, and the solution of the resulting system of equations is numerically analyzed. The projections of the trajectories on the plane x − y ,   y − z ,   x − z are found. Full article
(This article belongs to the Special Issue Mathematical Modeling in Physical Sciences)
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