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Physics, Volume 3, Issue 4 (December 2021) – 9 articles

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Article
Adaptive Synchronization of Fractional-Order Complex-Valued Chaotic Neural Networks with Time-Delay and Unknown Parameters
Physics 2021, 3(4), 924-939; https://0-doi-org.brum.beds.ac.uk/10.3390/physics3040058 - 12 Oct 2021
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Abstract
The purpose of this paper is to study and analyze the concept of fractional-order complex-valued chaotic networks with external bounded disturbances and uncertainties. The synchronization problem and parameter identification of fractional-order complex-valued chaotic neural networks (FOCVCNNs) with time-delay and unknown parameters are investigated. [...] Read more.
The purpose of this paper is to study and analyze the concept of fractional-order complex-valued chaotic networks with external bounded disturbances and uncertainties. The synchronization problem and parameter identification of fractional-order complex-valued chaotic neural networks (FOCVCNNs) with time-delay and unknown parameters are investigated. Synchronization between a driving FOCVCNN and a response FOCVCNN, as well as the identification of unknown parameters are implemented. Based on fractional complex-valued inequalities and stability theory of fractional-order chaotic complex-valued systems, the paper designs suitable adaptive controllers and complex update laws. Moreover, it scientifically estimates the uncertainties and external disturbances to establish the stability of controlled systems. The computer simulation results verify the correctness of the proposed method. Not only a new method for analyzing FOCVCNNs with time-delay and unknown complex parameters is provided, but also a sensitive decrease of the computational and analytical complexity. Full article
(This article belongs to the Special Issue Chaos in Electronics)
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Article
A Novel Feature of Valence Quark Distributions in Hadrons
Physics 2021, 3(4), 913-923; https://0-doi-org.brum.beds.ac.uk/10.3390/physics3040057 - 09 Oct 2021
Viewed by 181
Abstract
Examining the evolution of the maximum of valence quark distribution, qV, weighted by Bjorken x, h(x,t)xqV(x,t), it is observed that h(x,t) [...] Read more.
Examining the evolution of the maximum of valence quark distribution, qV, weighted by Bjorken x, h(x,t)xqV(x,t), it is observed that h(x,t) at the peak becomes a one-parameter function; h(xp,t)=Φ(xp(t)), where xp is the position of the peak, t=logQ2, and Q2 is the resolution scale. This observation is used to derive a new model-independent relation which connects the partial derivative of the valence parton distribution functions (PDFs) in xp to the quantum chromodynamics (QCD) evolution equation through the xp derivative of the logarithm of the function Φ(xp(t)). A numerical analysis of this relation using empirical PDFs results in an observation of the exponential form of the Φ(xp(t))=h(xp,t)=CeDxp(t) for leading to next-to-next leading order approximations of PDFs for the range of Q2, covering four orders in magnitude. The exponent, D, of the observed “height-position” correlation function converges with the increase in the order of approximation. This result holds for all the PDF sets considered. A similar relation is observed also for the pion valence quark distribution, indicating that the obtained relation may be universal for any non-singlet partonic distribution. The observed “height-position” correlation is used also to indicate that no finite number of exchanges can describe the analytic behavior of the valence quark distribution at the position of the peak at fixed Q2. Full article
(This article belongs to the Section High Energy Physics)
Article
Nonstandard Null Lagrangians and Gauge Functions for Newtonian Law of Inertia
Physics 2021, 3(4), 903-912; https://0-doi-org.brum.beds.ac.uk/10.3390/physics3040056 - 04 Oct 2021
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Abstract
New null Lagrangians and gauge functions are derived and they are called nonstandard because their forms are different than those previously found. The invariance of the action is used to make the Lagrangians and gauge functions exact. The first exact nonstandard null Lagrangian [...] Read more.
New null Lagrangians and gauge functions are derived and they are called nonstandard because their forms are different than those previously found. The invariance of the action is used to make the Lagrangians and gauge functions exact. The first exact nonstandard null Lagrangian and its gauge function for the law of inertia are obtained, and their physical implications are discussed. Full article
(This article belongs to the Section Classical Physics)
Article
Fluctuating Number of Energy Levels in Mixed-Type Lemon Billiards
Physics 2021, 3(4), 888-902; https://0-doi-org.brum.beds.ac.uk/10.3390/physics3040055 - 02 Oct 2021
Viewed by 320
Abstract
In this paper, the fluctuation properties of the number of energy levels (mode fluctuation) are studied in the mixed-type lemon billiards at high lying energies. The boundary of the lemon billiards is defined by the intersection of two circles of equal unit radius [...] Read more.
In this paper, the fluctuation properties of the number of energy levels (mode fluctuation) are studied in the mixed-type lemon billiards at high lying energies. The boundary of the lemon billiards is defined by the intersection of two circles of equal unit radius with the distance 2B between the centers, as introduced by Heller and Tomsovic. In this paper, the case of two billiards, defined by B=0.1953,0.083, is studied. It is shown that the fluctuation of the number of energy levels follows the Gaussian distribution quite accurately, even though the relative fraction of the chaotic part of the phase space is only 0.28 and 0.16, respectively. The theoretical description of spectral fluctuations in the Berry–Robnik picture is discussed. Also, the (golden mean) integrable rectangular billiard is studied and an almost Gaussian distribution is obtained, in contrast to theory expectations. However, the variance as a function of energy, E, behaves as E, in agreement with the theoretical prediction by Steiner. Full article
(This article belongs to the Special Issue Dedication to Professor Michael Tribelsky: 50 Years in Physics)
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Article
Measuring α-FPUT Cores and Tails
Physics 2021, 3(4), 879-887; https://0-doi-org.brum.beds.ac.uk/10.3390/physics3040054 - 30 Sep 2021
Viewed by 224
Abstract
Almost 70 years ago, the Fermi–Pasta–Ulam–Tsingou (FPUT) paradox was formulated in, observed in, and reported using normal modes of a nonlinear, one-dimensional, non-integrable string. Let us recap the paradox. One normal mode is excited, which drives three or four more normal modes in [...] Read more.
Almost 70 years ago, the Fermi–Pasta–Ulam–Tsingou (FPUT) paradox was formulated in, observed in, and reported using normal modes of a nonlinear, one-dimensional, non-integrable string. Let us recap the paradox. One normal mode is excited, which drives three or four more normal modes in the core. Then, that is it for quite a long time. So why are many normal modes staying weakly excited in the tail? Furthermore, how many? A quantitative, analytical answer to the latter question is given here using resonances and secular avalanches A comparison with the previous numerical data is made and extremely good agreement is found. Full article
(This article belongs to the Special Issue Dedication to Professor Michael Tribelsky: 50 Years in Physics)
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Review
From Asymptotic Series to Self-Similar Approximants
Physics 2021, 3(4), 829-878; https://0-doi-org.brum.beds.ac.uk/10.3390/physics3040053 - 27 Sep 2021
Viewed by 250
Abstract
The review presents the development of an approach of constructing approximate solutions to complicated physics problems, starting from asymptotic series, through optimized perturbation theory, to self-similar approximation theory. The close interrelation of underlying ideas of these theories is emphasized. Applications of the developed [...] Read more.
The review presents the development of an approach of constructing approximate solutions to complicated physics problems, starting from asymptotic series, through optimized perturbation theory, to self-similar approximation theory. The close interrelation of underlying ideas of these theories is emphasized. Applications of the developed approach are illustrated by typical examples demonstrating that it combines simplicity with good accuracy. Full article
(This article belongs to the Section Statistical Physics and Nonlinear Phenomena)
Article
Instability of Vertical Throughflows in Bidisperse Porous Media
Physics 2021, 3(4), 821-828; https://0-doi-org.brum.beds.ac.uk/10.3390/physics3040052 - 23 Sep 2021
Viewed by 253
Abstract
In this paper, the instability of a vertical fluid motion, or throughflow, is investigated in a horizontal bidisperse porous layer that is uniformly heated from below. By means of the order-1 Galerkin approximation method, the critical Darcy–Rayleigh number for the onset of steady [...] Read more.
In this paper, the instability of a vertical fluid motion, or throughflow, is investigated in a horizontal bidisperse porous layer that is uniformly heated from below. By means of the order-1 Galerkin approximation method, the critical Darcy–Rayleigh number for the onset of steady instability is determined in closed form. The coincidence between the linear instability threshold and the global nonlinear stability threshold, in the energy norm, is shown. Full article
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Article
Supervisor of the Universe
Physics 2021, 3(4), 814-820; https://0-doi-org.brum.beds.ac.uk/10.3390/physics3040051 - 23 Sep 2021
Viewed by 509
Abstract
In this paper, conformal invariant gravitation, based on Weyl geometry, is considered. In addition to the gravitational and matter action integrals, the interaction between the Weyl vector (entered in Weyl geometry) and the vector, representing the world line of the independent observer, are [...] Read more.
In this paper, conformal invariant gravitation, based on Weyl geometry, is considered. In addition to the gravitational and matter action integrals, the interaction between the Weyl vector (entered in Weyl geometry) and the vector, representing the world line of the independent observer, are introduced. It is shown that the very existence of such an interaction selects the exponentially growing scale factor solutions among the cosmological vacua. Full article
Article
Description of Nonlinear Vortical Flows of Incompressible Fluid in Terms of a Quasi-Potential
Physics 2021, 3(4), 799-813; https://0-doi-org.brum.beds.ac.uk/10.3390/physics3040050 - 22 Sep 2021
Viewed by 418
Abstract
As it was shown earlier, a wide class of nonlinear 3-dimensional (3D) fluid flows of incompressible viscous fluid can be described by only one scalar function dubbed the quasi-potential. This class of fluid flows is characterized by a three-component velocity field having a [...] Read more.
As it was shown earlier, a wide class of nonlinear 3-dimensional (3D) fluid flows of incompressible viscous fluid can be described by only one scalar function dubbed the quasi-potential. This class of fluid flows is characterized by a three-component velocity field having a two-component vorticity field. Both these fields may, in general, depend on all three spatial variables and time. In this paper, the governing equations for the quasi-potential are derived and simple illustrative examples of 3D flows in the Cartesian coordinates are presented. The generalisation of the developed approach to the fluid flows in the cylindrical and spherical coordinate frames represents a nontrivial problem that has not been solved yet. In this paper, this gap is filled and the concept of a quasi-potential to the cylindrical and spherical coordinate frames is further developed. A few illustrative examples are presented which can be of interest for practical applications. Full article
(This article belongs to the Special Issue Dedication to Professor Michael Tribelsky: 50 Years in Physics)
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