Symmetry in Nonequilibrium Statistical Mechanics and Dynamical Systems

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

Deadline for manuscript submissions: closed (30 November 2021) | Viewed by 13812

Special Issue Editor


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Department of Mathematics, EFrei Research Lab, Paris-Panthéon-Assas University, 30/32 Avenue de la République, 94800 Villejuif, France
Interests: mathematical modeling and analysis of complex systems; kinetic equations; numerical methods for PDE
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Special Issue Information

Dear Colleagues,

Recently, different mathematical frameworks coming from nonequilibrium statistical mechanics and dynamical systems theory have been proposed for the modeling of complex emerging phenomena occurring in nature and society. At the base of these phenomena, there is the role of the interactions among the different components composing the complex system. A preliminary phenomenological analysis is thus followed by the modeling of the interaction terms that are derived by the means of the definition of the interaction kernels and parameters on which some symmetry assumptions are made.

This Special Issue focuses on the development and application of the recent proposed mathematical frameworks. Specifically, the issue is referred, but is not limited, to physical, biological, economic, social, and engineering systems.

Please note that all of the submitted papers must be within the general scope of the Symmetry journal.

Prof. Carlo Bianca
Guest Editor

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

  • kinetic theory
  • chaos
  • lattice Boltzmann
  • fluctuations
  • agents
  • active matter
  • entropy
  • inverse problems
  • energy sources
  • delay

Published Papers (7 papers)

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Editorial

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3 pages, 164 KiB  
Editorial
Special Issue: Symmetry in Nonequilibrium Statistical Mechanics and Dynamical Systems
by Carlo Bianca
Symmetry 2022, 14(10), 1960; https://doi.org/10.3390/sym14101960 - 20 Sep 2022
Viewed by 813
Abstract
The recent developments in dynamical systems theory and non-equilibrium statistical mechanics have allowed the birth of new challenges and research perspectives. In particular, different frameworks have been proposed for the modeling of complex emerging phenomena occurring in nature and society. This editorial article [...] Read more.
The recent developments in dynamical systems theory and non-equilibrium statistical mechanics have allowed the birth of new challenges and research perspectives. In particular, different frameworks have been proposed for the modeling of complex emerging phenomena occurring in nature and society. This editorial article introduces the topic and the contributions of this Special Issue. This Special Issue focuses, on the one hand, on the development of new methods, frameworks and models coming from dynamical system theory and the equilibrium/non-equilibrium statistical mechanics and, on the other hand, opens problems related to the existing frameworks. The Special Issue also includes applications to physical, biological and engineering systems. Full article

Research

Jump to: Editorial

19 pages, 1767 KiB  
Article
An Efficient Mechanism to Solve Fractional Differential Equations Using Fractional Decomposition Method
by Mahmoud S. Alrawashdeh, Seba A. Migdady and Ioannis K. Argyros
Symmetry 2021, 13(6), 984; https://doi.org/10.3390/sym13060984 - 01 Jun 2021
Cited by 2 | Viewed by 1846
Abstract
We present some new results that deal with the fractional decomposition method (FDM). This method is suitable to handle fractional calculus applications. We also explore exact and approximate solutions to fractional differential equations. The Caputo derivative is used because it allows traditional initial [...] Read more.
We present some new results that deal with the fractional decomposition method (FDM). This method is suitable to handle fractional calculus applications. We also explore exact and approximate solutions to fractional differential equations. The Caputo derivative is used because it allows traditional initial and boundary conditions to be included in the formulation of the problem. This is of great significance for large-scale problems. The study outlines the significant features of the FDM. The relation between the natural transform and Laplace transform is a symmetrical one. Our work can be considered as an alternative to existing techniques, and will have wide applications in science and engineering fields. Full article
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17 pages, 3005 KiB  
Article
Lyapunov Functions and Lipschitz Stability for Riemann–Liouville Non-Instantaneous Impulsive Fractional Differential Equations
by Ravi Agarwal, Snezhana Hristova and Donal O’Regan
Symmetry 2021, 13(4), 730; https://doi.org/10.3390/sym13040730 - 20 Apr 2021
Cited by 4 | Viewed by 1795
Abstract
In this paper a system of nonlinear Riemann–Liouville fractional differential equations with non-instantaneous impulses is studied. We consider a Riemann–Liouville fractional derivative with a changeable lower limit at each stop point of the action of the impulses. In this case the solution has [...] Read more.
In this paper a system of nonlinear Riemann–Liouville fractional differential equations with non-instantaneous impulses is studied. We consider a Riemann–Liouville fractional derivative with a changeable lower limit at each stop point of the action of the impulses. In this case the solution has a singularity at the initial time and any stop time point of the impulses. This leads to an appropriate definition of both the initial condition and the non-instantaneous impulsive conditions. A generalization of the classical Lipschitz stability is defined and studied for the given system. Two types of derivatives of the applied Lyapunov functions among the Riemann–Liouville fractional differential equations with non-instantaneous impulses are applied. Several sufficient conditions for the defined stability are obtained. Some comparison results are obtained. Several examples illustrate the theoretical results. Full article
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10 pages, 276 KiB  
Article
Qualitative Properties of Solutions of Second-Order Neutral Differential Equations
by Omar Bazighifan, Marianna Ruggieri, Shyam Sundar Santra and Andrea Scapellato
Symmetry 2020, 12(9), 1520; https://doi.org/10.3390/sym12091520 - 15 Sep 2020
Cited by 35 | Viewed by 2038
Abstract
In this work, we consider a type of second-order functional differential equations and establish qualitative properties of their solutions. These new results complement and improve a number of results reported in the literature. Finally, we provide an example that illustrates our results. Full article
7 pages, 257 KiB  
Article
Mathematical Modeling of Autoimmune Diseases
by Mikhail Kolev
Symmetry 2020, 12(9), 1457; https://doi.org/10.3390/sym12091457 - 04 Sep 2020
Cited by 8 | Viewed by 2417
Abstract
The human organism is a very complex system. To be in good health, its components must function properly. One of the most important systems of an organism is the immune system. It protects the body from the harmful effects of various external and [...] Read more.
The human organism is a very complex system. To be in good health, its components must function properly. One of the most important systems of an organism is the immune system. It protects the body from the harmful effects of various external and internal agents. Sometimes, however, the immune system starts attacking its own healthy cells, tissues and organs. Then autoimmune diseases arise. They are widespread in recent decades. There is evidence that often autoimmune responses occur due to viral infections. In this paper, a new mathematical model of a general autoimmune disease is proposed. It describes the interactions between viral particles and host cells. The model is formulated by using integro-differential equations of Boltzmann type. This approach is typical for the nonequilibrium statistical mechanics. A preliminary qualitative and quantitative analysis of the model is presented. Full article
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14 pages, 325 KiB  
Article
Necessary and Sufficient Conditions for Time Reversal Symmetry in Presence of Magnetic Fields
by Davide Carbone and Lamberto Rondoni
Symmetry 2020, 12(8), 1336; https://doi.org/10.3390/sym12081336 - 10 Aug 2020
Cited by 9 | Viewed by 2684
Abstract
Time reversal invariance (TRI) of particles systems has many consequences, among which the celebrated Onsager reciprocal relations, a milestone in Statistical Mechanics dating back to 1931. Because for a long time it was believed that (TRI) dos not hold in presence of a [...] Read more.
Time reversal invariance (TRI) of particles systems has many consequences, among which the celebrated Onsager reciprocal relations, a milestone in Statistical Mechanics dating back to 1931. Because for a long time it was believed that (TRI) dos not hold in presence of a magnetic field, a modification of such relations was proposed by Casimir in 1945. Only in the last decade, the strict traditional notion of reversibility that led to Casimir’s work has been questioned. It was then found that other symmetries can be used, which allow the Onsager reciprocal relations to hold without modification. In this paper we advance this investigation for classical Hamiltonian systems, substantially increasing the number of symmetries that yield TRI in presence of a magnetic field. We first deduce the most general form of a generalized time reversal operation on the phase space of such a system; secondly, we express sufficient conditions on the magnetic field which ensure TRI. Finally, we examine common examples from statistical mechanics and molecular dynamics. Our main result is that TRI holds in a much wider generality than previously believed, partially explaining why no experimental violation of Onsager relations has so far been reported. Full article
19 pages, 330 KiB  
Article
On the Cauchy Problem of Vectorial Thermostatted Kinetic Frameworks
by Carlo Bianca, Bruno Carbonaro and Marco Menale
Symmetry 2020, 12(4), 517; https://doi.org/10.3390/sym12040517 - 02 Apr 2020
Cited by 10 | Viewed by 1364
Abstract
This paper is devoted to the derivation and mathematical analysis of new thermostatted kinetic theory frameworks for the modeling of nonequilibrium complex systems composed by particles whose microscopic state includes a vectorial state variable. The mathematical analysis refers to the global existence and [...] Read more.
This paper is devoted to the derivation and mathematical analysis of new thermostatted kinetic theory frameworks for the modeling of nonequilibrium complex systems composed by particles whose microscopic state includes a vectorial state variable. The mathematical analysis refers to the global existence and uniqueness of the solution of the related Cauchy problem. Specifically, the paper is divided in two parts. In the first part the thermostatted framework with a continuous vectorial variable is proposed and analyzed. The framework consists of a system of partial integro-differential equations with quadratic type nonlinearities. In the second part the thermostatted framework with a discrete vectorial variable is investigated. Real world applications, such as social systems and crowd dynamics, and future research directions are outlined in the paper. Full article
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