Applied Mathematics and Mechanics

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (30 April 2022) | Viewed by 9950

Special Issue Editors

Mathematical Sciences Department, Hellenic Army Academy, 16673 Vari, Greece
Interests: continuum mechanics; gradient elasticity; fractional calculus
Applied Mathematics and Physics applications, National Technical University of Athens, 14 Theatrou Str., Rafina 19009, Greece
Interests: finite elasticity; continuum mechanics; elastic stability theory; biomechanics; micromechanics; fractional analysis; experimental method of caustics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

As an Editorial Board Member of Axioms (Citescore: 2.6—Scopus), I would like to inform you about a Special Issue of our journal that concerns Applied Mathematics and Mechanics.

This Special Issue will accept high-quality papers that present original research results, and its purpose is to bring together mathematicians and engineers (mainly), as well as other scientists active in the field of mechanics.

The areas that will be covered are as follows: continuum mechanics, micromechanics, nanomechanics, fractional calculus and mechanics, biomechanics, among others.

Topics covered include but not limited to:
  • Continuum Mechanics
  • Micromechanics
  • Nanomechanics
  • Gradient Elasticity
  • Couple stress theory
  • Micropolar theory
  • Fractional Calculus and Mechanics
  • Fractional Calculus and Fractals
  • Random and Composite materials
  • Linear Elasticity
  • Non-Linear Elasticity
  • Crystalline Structure
  • Membranes
  • Plates
  • Shells
  • Biomechanics
  • Soil and rock mechanics

Dr. A. K. Lazopoulos
Prof. Dr. Konstantinos A. Lazopoulos
Guest Editors

Manuscript Submission Information

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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. Axioms 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

  • Applied Mathematics
  • Mechanics
  • Continuum mechanics
  • Micromechanics
  • Nanomechanics
  • Fractional Calculus and Mechanics
  • Biomechanics
  • Ballistics

Published Papers (6 papers)

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Research

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9 pages, 1519 KiB  
Article
Computation of the Deuteron Mass and Force Unification via the Rotating Lepton Model
Axioms 2022, 11(11), 657; https://doi.org/10.3390/axioms11110657 - 20 Nov 2022
Cited by 2 | Viewed by 1720
Abstract
The rotating lepton model (RLM), which is a 2D Bohr-type model of three gravitating rotating neutrinos, combining Newton’s gravitational law, special relativity, and the de Broglie equation of quantum mechanics, and which has already been used to model successfully quarks and the strong [...] Read more.
The rotating lepton model (RLM), which is a 2D Bohr-type model of three gravitating rotating neutrinos, combining Newton’s gravitational law, special relativity, and the de Broglie equation of quantum mechanics, and which has already been used to model successfully quarks and the strong force in several hadrons, has been extended to 3D and to six rotating neutrinos located at the vertices of a normal triangular octahedron in order to compute the Lorentz factors, gamma, of the six neutrinos and, thus, to compute the total energy and mass of the deuteron, which is the lightest nucleus. The computation includes no adjustable parameters, and the computed deuteron mass agrees within 0.05% with the experimental mass value. This very good agreement suggests that, similarly to the strong force in hadrons, the nuclear force in nuclei can also be modeled as relativistic gravity. This implies that, via the combination of special relativity and quantum mechanics, the Newtonian gravity gets unified with the strong force, including the residual strong force. Full article
(This article belongs to the Special Issue Applied Mathematics and Mechanics)
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9 pages, 1022 KiB  
Article
Exploring the Limits of Euler–Bernoulli Theory in Micromechanics
Axioms 2022, 11(3), 142; https://doi.org/10.3390/axioms11030142 - 19 Mar 2022
Cited by 2 | Viewed by 1838
Abstract
In this study, the limits of the Euler–Bernoulli theory in micromechanics are explored. Raman spectroscopy, which is extremely accurate and reliable, is employed to study the bending of a microbeam of a length of 191 μm. It is found that at the micro-scale, [...] Read more.
In this study, the limits of the Euler–Bernoulli theory in micromechanics are explored. Raman spectroscopy, which is extremely accurate and reliable, is employed to study the bending of a microbeam of a length of 191 μm. It is found that at the micro-scale, the Euler–Bernoulli theory remains an exact and consistent tool, and, possibly, other elasticity theories (such as micropolar theory, gradient elasticity theory, and couple stress theory) are not always required to study this phenomenon. More specifically, good correlation was achieved between the theoretical and experimental results, the former acquired via the theoretical equations and the latter obtained with the use of atomic force microscopy and Raman spectroscopy. The exact predicted strain of an atomic force microscope microbeam under bending, by Euler–Bernoulli equations is confirmed by Raman spectroscopy. Full article
(This article belongs to the Special Issue Applied Mathematics and Mechanics)
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21 pages, 5379 KiB  
Article
On Λ-Fractional Analysis and Mechanics
Axioms 2022, 11(3), 85; https://doi.org/10.3390/axioms11030085 - 22 Feb 2022
Cited by 3 | Viewed by 1060
Abstract
Λ-Fractional analysis was introduced to fill up the mathematical gap exhibited in fractional calculus, where the various fractional derivatives fail to fulfill the prerequisites demanded by differential topology. Nevertheless, the various advantages exhibited by the fractional derivatives, and especially their non-local character, attracted [...] Read more.
Λ-Fractional analysis was introduced to fill up the mathematical gap exhibited in fractional calculus, where the various fractional derivatives fail to fulfill the prerequisites demanded by differential topology. Nevertheless, the various advantages exhibited by the fractional derivatives, and especially their non-local character, attracted the interest of physicists, although the majority of them try to avoid it. The introduced Λ-fractional analysis can generate fractional geometry since the Λ-fractional derivatives generate differentials. The Λ-fractional analysis is introduced to mechanics to formulate non-local response problems with the demanded mathematical accuracy. Further, fractional peridynamic problems with horizon are suggested. Full article
(This article belongs to the Special Issue Applied Mathematics and Mechanics)
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13 pages, 566 KiB  
Article
Fractional Derivatives and Projectile Motion
Axioms 2021, 10(4), 297; https://doi.org/10.3390/axioms10040297 - 08 Nov 2021
Cited by 2 | Viewed by 1354
Abstract
Projectile motion is studied using fractional calculus. Specifically, a newly defined fractional derivative (the Leibniz L-derivative) and its successor (Λ-fractional derivative) are used to describe the motion of the projectile. Experimental data were analyzed in this study, and conclusions were made. The results [...] Read more.
Projectile motion is studied using fractional calculus. Specifically, a newly defined fractional derivative (the Leibniz L-derivative) and its successor (Λ-fractional derivative) are used to describe the motion of the projectile. Experimental data were analyzed in this study, and conclusions were made. The results of well-established fractional derivatives were also compared with those of L-derivative and Λ-fractional derivative, showing the many advantages of these new derivatives. Full article
(This article belongs to the Special Issue Applied Mathematics and Mechanics)
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8 pages, 982 KiB  
Article
Analysis of Novel Oscillations of Quantized Mechanical Energy in Mass-Accreting Nano-Oscillator Systems
Axioms 2021, 10(3), 153; https://doi.org/10.3390/axioms10030153 - 10 Jul 2021
Viewed by 1525
Abstract
Quantum characteristics of a mass-accreting oscillator are investigated using the invariant operator theory, which is a rigorous mathematical tool for unfolding quantum theory for time-dependent Hamiltonian systems. In particular, the quantum energy of the system is analyzed in detail and compared to the [...] Read more.
Quantum characteristics of a mass-accreting oscillator are investigated using the invariant operator theory, which is a rigorous mathematical tool for unfolding quantum theory for time-dependent Hamiltonian systems. In particular, the quantum energy of the system is analyzed in detail and compared to the classical one. We focus on two particular cases; one is a linearly mass-accreting oscillator and the other is an exponentially mass-accreting one. It is confirmed that the quantum energy is in agreement with the classical one in the limit 0. We showed that not only the classical but also the quantum energy oscillates with time. It is carefully analyzed why the energy oscillates with time, and a reasonable explanation for that outcome is given. Full article
(This article belongs to the Special Issue Applied Mathematics and Mechanics)
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Review

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32 pages, 680 KiB  
Review
Survey of Eight Modern Methods of Hamiltonian Mechanics
Axioms 2021, 10(4), 293; https://doi.org/10.3390/axioms10040293 - 04 Nov 2021
Cited by 4 | Viewed by 1305
Abstract
Here we describe eight new methods, arisen in the last 60 years, to study solutions of a Hamiltonian system with n degrees of freedom. The first six of them are intended for systems with small parameters or without them. The methods allow to [...] Read more.
Here we describe eight new methods, arisen in the last 60 years, to study solutions of a Hamiltonian system with n degrees of freedom. The first six of them are intended for systems with small parameters or without them. The methods allow to find families of periodic solutions and families of invariant n-dimensional tori by means of analytic computation near a stationary solution, near a periodic solution and near an invariant torus, using the corresponding normal form of a Hamiltonian. Then we can continue the founded families by means of numerical computation. In a Hamiltonian system without parameters, only periodic solutions and invariant n-dimensional tori form one-parameter families. The last two methods are intended for systems with not small parameters, which do not depend on time. They allow computing sets of parameters, which guarantee the stability of some solutions for linear (method seven) and nonlinear (method eight) systems. We do not consider chaotic behaviors, but only regular ones. Full article
(This article belongs to the Special Issue Applied Mathematics and Mechanics)
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