Frontiers in Physics | Mathematical and Statistical Physics section | New and Recent Articles
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RSS Feed for Mathematical and Statistical Physics section in the Frontiers in Physics journal | New and Recent Articlesen-usFrontiers Feed Generator,version:12021-02-27T10:36:30.3927123+00:0060https://www.frontiersin.org/articles/10.3389/fphy.2020.568554
https://www.frontiersin.org/articles/10.3389/fphy.2020.568554
Fractional-Order Investigation of Diffusion Equations via Analytical Approach2021-02-23T00:00:00ZHaobin LiuHassan KhanSaima MustafaLianming MouDumitru BaleanuThis research article is mainly concerned with the analytical solution of diffusion equations within a Caputo fractional-order derivative. The motivation and novelty behind the present work are the application of a sophisticated and straight forward procedure to solve diffusion equations containing a derivative of a fractional-order. The solutions of some illustrative examples are calculated to confirm the closed contact between the actual and the approximate solutions of the targeted problems. Through analysis it is shown that the proposed solution has a higher rate of convergence and provides a closed-form solution. The small number of calculations is the main advantage of the proposed method. Due to a comfortable and straight forward implementation, the suggested method can be utilized to nonlinear fractional-order problems in various applied science branches. It can be extended to solve other physical problems of fractional-order in multiple areas of applied sciences.]]>https://www.frontiersin.org/articles/10.3389/fphy.2021.599146
https://www.frontiersin.org/articles/10.3389/fphy.2021.599146
Instability of Double-Periodic Waves in the Nonlinear Schrödinger Equation2021-02-22T00:00:00ZDmitry E. PelinovskyIt is shown how to compute the instability rates for the double-periodic solutions to the cubic NLS (nonlinear Schrödinger) equation by using the Lax linear equations. The wave function modulus of the double-periodic solutions is periodic both in space and time coordinates; such solutions generalize the standing waves which have the time-independent and space-periodic wave function modulus. Similar to other waves in the NLS equation, the double-periodic solutions are spectrally unstable and this instability is related to the bands of the Lax spectrum outside the imaginary axis. A simple numerical method is used to compute the unstable spectrum and to compare the instability rates of the double-periodic solutions with those of the standing periodic waves.]]>https://www.frontiersin.org/articles/10.3389/fphy.2021.651127
https://www.frontiersin.org/articles/10.3389/fphy.2021.651127
Editorial: Towards a Local Realist View of the Quantum Phenomenon2021-02-19T00:00:00ZAna María CettoAlberto CasadoKarl HessAndrea Valdés-Hernándezhttps://www.frontiersin.org/articles/10.3389/fphy.2021.600564
https://www.frontiersin.org/articles/10.3389/fphy.2021.600564
Genetic Algorithm to Optimize the Design of High Temperature Protective Clothing Based on BP Neural Network2021-02-17T00:00:00ZFeng XuLing-Yu MoHong ChenJia-Ming ZhuFor the clothing design for high-temperature operation, the theory or method such as partial differential, nonlinear programming and finite difference method was first applied to construct the overall heat transfer model of “high temperature environment--clothing--air layer--skin” and draw the temperature distribution map. Secondly, according to the human body burn model, the optimal parameters of fabric thickness are obtained preliminarily. Finally, the weights and thresholds of BP neural network were optimized by genetic algorithm, and these optimized values were assigned to the optimized BP neural network, and the nonlinear thickness function was approximated and optimized with MATLAB.]]>https://www.frontiersin.org/articles/10.3389/fphy.2021.645324
https://www.frontiersin.org/articles/10.3389/fphy.2021.645324
Editorial: Contact Interactions in Quantum Mechanics–Theory, Mathematical Aspects and Applications2021-02-08T00:00:00ZManuel GadellaJosé Tadeu LunardiLuiz A. Manzonihttps://www.frontiersin.org/articles/10.3389/fphy.2020.599435
https://www.frontiersin.org/articles/10.3389/fphy.2020.599435
Local Emergence of Peregrine Solitons: Experiments and Theory2021-02-05T00:00:00ZAlexey TikanStéphane RandouxGennady ElAlexander TovbisFrancois CopiePierre SuretIt has been shown analytically that Peregrine solitons emerge locally from a universal mechanism in the so-called semiclassical limit of the one-dimensional focusing nonlinear Schrödinger equation. Experimentally, this limit corresponds to the strongly nonlinear regime where the dispersion is much weaker than nonlinearity at initial time. We review here evidences of this phenomenon obtained on different experimental platforms. In particular, the spontaneous emergence of coherent structures exhibiting locally the Peregrine soliton behavior has been demonstrated in optical fiber experiments involving either single pulse or partially coherent waves. We also review theoretical and numerical results showing the link between this phenomenon and the emergence of heavy-tailed statistics (rogue waves).]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.612318
https://www.frontiersin.org/articles/10.3389/fphy.2020.612318
Waves that Appear From Nowhere: Complex Rogue Wave Structures and Their Elementary Particles2021-01-15T00:00:00ZNail AkhmedievThe nonlinear Schrödinger equation has wide range of applications in physics with spatial scales that vary from microns to kilometres. Consequently, its solutions are also universal and can be applied to water waves, optics, plasma and Bose-Einstein condensate. The most remarkable solution presently known as the Peregrine solution describes waves that appear from nowhere. This solution describes unique events localized both in time and in space. Following the language of mariners they are called “rogue waves”. As thorough mathematical analysis shows, these waves have properties that differ them from any other nonlinear waves known before. Peregrine waves can serve as ‘elementary particles’ in more complex structures that are also exact solutions of the nonlinear Schrödinger equation. These structures lead to specific patterns with various degrees of symmetry. Some of them resemble “atomic like structures”. The number of particles in these structures is not arbitrary but satisfies strict rules. Similar structures may be observed in systems described by other equations of mathematical physics: Hirota equation, Davey-Stewartson equations, Sasa-Satsuma equation, generalized Landau-Lifshitz equation, complex KdV equation and even the coupled Higgs field equations describing nucleons interacting with neutral scalar mesons. This means that the ideas of rogue waves enter nearly all areas of physics including the field of elementary particles.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.600960
https://www.frontiersin.org/articles/10.3389/fphy.2020.600960
Resistance Distances in Linear Polyacene Graphs2021-01-12T00:00:00ZDayong WangYujun YangThe resistance distance between any two vertices of a connected graph is defined as the net effective resistance between them in the electrical network constructed from the graph by replacing each edge with a unit resistor. In this article, using electric network approach and combinatorial approach, we derive exact expression for resistance distances between any two vertices of polyacene graphs.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.584294
https://www.frontiersin.org/articles/10.3389/fphy.2020.584294
Analyzing the Motion of Symmetric Tops Without Recurring to Analytical Mechanics2020-12-23T00:00:00ZZsolt I. LázárAntal JakovácPéter HantzCharacterizing the dynamics of heavy symmetric tops is essential in several fields of theoretical and applied physics. Accordingly, a series of approaches have been developed to describe their motion. In this paper, we present a derivation based on elementary geometric considerations carried out in the laboratory frame. Our framework enabled the simple derivation of the equation of motion for small nutations. The introduced formalism is also employed to determine the alteration of the dynamics of heavy, symmetric, spinning tops in a rotating force field, that is compared to the precession characteristics of a quantum magnetic dipole in rotating magnetic field.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.588415
https://www.frontiersin.org/articles/10.3389/fphy.2020.588415
Innsbruck Teleportation Experiment in the Wigner Formalism: A Realistic Description Based on the Role of the Zero-Point Field2020-12-11T00:00:00ZAlberto CasadoSantiago GuerraJosé PlácidoIn this article, an undulatory description of the Innsbruck teleportation experiment is given, grounded in the role of the zero-point field (ZPF). The Wigner approach in the Heisenberg picture is used, so that the quadruple correlations of the field, along with the subtraction of the zero-point intensity at the detectors, are shown to be the essential ingredients that replace entanglement and collapse. This study contrasts sharply with the standard particle-like analysis and offers the possibility of understanding the hidden mechanism of teleportation, relying on vacuum amplitudes as hidden variables.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.609926
https://www.frontiersin.org/articles/10.3389/fphy.2020.609926
Spreading Kinetics of Herschel-Bulkley Fluids Over Solid Substrates2020-12-11T00:00:00ZJie ZhangHai GuJianhua SunBin LiJie JiangWeiwei WuThe spreading kinetics of Herschel-Bulkley fluids on horizontal solid substrates were theoretically studied. The equations of film thickness were derived in both gravitational and capillary regimes. The dynamic contact angle for the capillary regime was also derived. Finally, a limiting result for the case of τ_{0} = 0 was obtained, which was compared with the known solution for validation. The results show that the yield behavior of the fluids had a significant impact on the spreading kinetics in both cases. Only when stress was larger than the yield stress, would substantial flow occur. The spreading zone was divided into two parts by the yield surface: sheared zone and yield zone, which was completely different from common Newtonian fluids or power-law fluids. The thickness of the yield zone mainly depended on yield stress and pressure gradient along the z-direction. According to the final evolution, both the film thickness and dynamic contact angle were affected not only by the power-law index but also by the yield behavior.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.608894
https://www.frontiersin.org/articles/10.3389/fphy.2020.608894
Ghost Interaction of Breathers2020-12-07T00:00:00ZGang XuAndrey GelashAmin ChabchoubVladimir ZakharovBertrand KiblerMutual interaction of localized nonlinear waves, e.g., solitons and modulation instability patterns, is a fascinating and intensively-studied topic of nonlinear science. Here we report the observation of a novel type of breather interaction in telecommunication optical fibers, in which two identical breathers propagate with opposite group velocities. Under controlled conditions, neither amplification nor annihilation occurs at the collision point and most interestingly, the respective envelope amplitude, resulting from the interaction, almost equals another envelope maximum of either oscillating and counterpropagating breather. This ghost-like breather interaction dynamics is fully described by an N-breather solution of the nonlinear Schrödinger equation.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.596886
https://www.frontiersin.org/articles/10.3389/fphy.2020.596886
Peregrine Solitons of the Higher-Order, Inhomogeneous, Coupled, Discrete, and Nonlocal Nonlinear Schrödinger Equations2020-12-03T00:00:00ZT. UthayakumarL. Al SakkafU. Al KhawajaThis study reviews the Peregrine solitons appearing under the framework of a class of nonlinear Schrödinger equations describing the diverse nonlinear systems. The historical perspectives include the various analytical techniques developed for constructing the Peregrine soliton solutions, followed by the derivation of the general breather solution of the fundamental nonlinear Schrödinger equation through Darboux transformation. Subsequently, we collect all forms of nonlinear Schrödinger equations, involving systematically the effects of higher-order nonlinearity, inhomogeneity, external potentials, coupling, discontinuity, nonlocality, higher dimensionality, and nonlinear saturation in which Peregrine soliton solutions have been reported.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.602229
https://www.frontiersin.org/articles/10.3389/fphy.2020.602229
Breather Structures and Peregrine Solitons in a Polarized Space Dusty Plasma2020-11-26T00:00:00ZKuldeep SinghN. S. SainiIn this theoretical investigation, we have examined the combined effects of nonthermally revamped polarization force on modulational instability MI of dust acoustic waves DAWs and evolution of different kinds of dust acoustic (DA) breathers in a dusty plasma consisting of negatively charged dust as fluid, Maxwellian electrons, and ions obeying Cairns’ nonthermal distribution. The nonthermality of ions has considerably altered the strength of polarization force. By employing the multiple-scale perturbation technique, the nonlinear Schrödinger equation NLSE is derived to study modulational MI instability of dust acoustic waves DAWs. It is noticed that influence of the polarization force makes the wave number domain narrow where MI sets in. The rational solutions of nonlinear Schrödinger equation illustrate the evolution of DA breathers, namely, Akhmediev breather, Kuznetsov–Ma breather, and Peregrine solitons (rogue waves). Further, the formation of super rogue waves due to nonlinear superposition of DA triplets rogue waves is also discussed. It is analyzed that combined effects of variation in the polarization force and nonthermality of ions have a comprehensive influence on the evolution of different kinds of DA breathers. It is remarked that outcome of present theoretical investigation may provide physical insight into understanding the role of nonlinear phenomena for the generation of various types of DA breathers in experiments and different regions of space (e.g., the planetary spoke and cometary tails).]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.00250
https://www.frontiersin.org/articles/10.3389/fphy.2020.00250
Entropy Optimization of Third-Grade Nanofluid Slip Flow Embedded in a Porous Sheet With Zero Mass Flux and a Non-Fourier Heat Flux Model2020-11-24T00:00:00ZK. LoganathanG. MuhiuddinA. M. AlanaziFehaid S. AlshammariBader M. AlqurashiS. RajanThe prime objective of this article is to explore the entropy analysis of third-order nanofluid fluid slip flow caused by a stretchable sheet implanted in a porous plate along with thermal radiation, convective surface boundary, non-Fourier heat flux applications, and nanoparticle concentration on zero mass flux conditions. The governing physical systems are modified into non-linear ordinary systems with the aid of similarity variables, and the outcomes are solved by a homotopy analysis scheme. The impression of certain governing flow parameters on the nanoparticle concentration, temperature, and velocity is illustrated through graphs, while the alteration of many valuable engineering parameters viz. the Nusselt number and Sherwood number are depicted in graphs. Entropy generation with various parameters is obtained and discussed in detail. The estimation of entropy generation using the Bejan number find robust application in power engineering and aeronautical propulsion to forecast the smartness of entire system.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.580554
https://www.frontiersin.org/articles/10.3389/fphy.2020.580554
The Maximum Principle for Variable-Order Fractional Diffusion Equations and the Estimates of Higher Variable-Order Fractional Derivatives2020-11-24T00:00:00ZGuangming XueFuning LinGuangwang SuIn this paper, the maximum principle of variable-order fractional diffusion equations and the estimates of fractional derivatives with higher variable order are investigated. Firstly, we deduce the fractional derivative of a function of higher variable order at an arbitrary point. We also give an estimate of the error. Some important inequalities for fractional derivatives of variable order at arbitrary points and extreme points are presented. Then, the maximum principles of Riesz-Caputo fractional differential equations in terms of the multi-term space-time variable order are proved. Finally, under the initial-boundary value conditions, it is verified via the proposed principle that the solutions are unique, and their continuous dependance holds.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.591995
https://www.frontiersin.org/articles/10.3389/fphy.2020.591995
Review on the Stability of the Peregrine and Related Breathers2020-11-24T00:00:00ZMiguel A. AlejoLuca FanelliClaudio MuñozIn this note, we review stability properties in energy spaces of three important nonlinear Schrödinger breathers: Peregrine, Kuznetsov-Ma, and Akhmediev. More precisely, we show that these breathers are unstable according to a standard definition of stability. Suitable Lyapunov functionals are described, as well as their underlying spectral properties. As an immediate consequence of the first variation of these functionals, we also present the corresponding nonlinear ODEs fulfilled by these nonlinear Schrödinger breathers. The notion of global stability for each breather mentioned above is finally discussed. Some open questions are also briefly mentioned.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.00280
https://www.frontiersin.org/articles/10.3389/fphy.2020.00280
A Correlation Between Solutions of Uncertain Fractional Forward Difference Equations and Their Paths2020-11-23T00:00:00ZHari Mohan SrivastavaPshtiwan Othman MohammedWe consider the comparison theorems for the fractional forward h-difference equations in the context of discrete fractional calculus. Moreover, we consider the existence and uniqueness theorem for the uncertain fractional forward h-difference equations. After that the relations between the solutions for the uncertain fractional forward h-difference equations with symmetrical uncertain variables and their α-paths are established and verified using the comparison theorems and existence and uniqueness theorem. Finally, two examples are provided to illustrate the relationship between the solutions.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.596950
https://www.frontiersin.org/articles/10.3389/fphy.2020.596950
Peregrine Solitons on a Periodic Background in the Vector Cubic-Quintic Nonlinear Schrödinger Equation2020-11-17T00:00:00ZYanlin YeLili BuWanwan WangShihua ChenFabio BaronioDumitru MihalacheWe present exact explicit Peregrine soliton solutions based on a periodic-wave background caused by the interference in the vector cubic-quintic nonlinear Schrödinger equation involving the self-steepening effect. It is shown that such periodic Peregrine soliton solutions can be expressed as a linear superposition of two fundamental Peregrine solitons of different continuous-wave backgrounds. Because of the self-steepening effect, some interesting Peregrine soliton dynamics such as ultrastrong amplitude enhancement and rogue wave coexistence are still present when they are built on a periodic background. We numerically confirm the stability of these analytical solutions against non-integrable perturbations, i.e., when the coefficient relation that enables the integrability of the vector model is slightly lifted. We also demonstrate the interaction of two Peregrine solitons on the same periodic background under some specific parameter conditions. We expect that these results may shed more light on our understanding of the realistic rogue wave behaviors occurring in either the fiber-optic telecommunication links or the crossing seas.]]>https://www.frontiersin.org/articles/10.3389/fphy.2020.00357
https://www.frontiersin.org/articles/10.3389/fphy.2020.00357
Certain Concepts of Vague Graphs With Applications to Medical Diagnosis2020-11-11T00:00:00ZZehui ShaoSaeed KosariMuhammad ShoaibHossein RashmanlouThe purpose of this research study is to present and explore the key properties of some new operations on vague graphs, including rejection, maximal product, symmetric difference, and residue product. This article introduces the notions of degree of a vertex and total degree of a vertex in a vague graph. As well, this study outlines the specific conditions required for obtaining the degrees of vertices in vague graphs under the operations of maximal product, symmetric difference, and rejection. The article also discusses applications of vague sets in medical diagnosis.]]>