Frontiers in Physics | Mathematical Physics section | New and Recent Articles
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RSS Feed for Mathematical Physics section in the Frontiers in Physics journal | New and Recent Articlesen-usFrontiers Feed Generator,version:12020-01-26T22:56:17.519166+00:0060https://www.frontiersin.org/articles/10.3389/fphy.2019.00240
https://www.frontiersin.org/articles/10.3389/fphy.2019.00240
Jacobi Spectral Galerkin Method for Distributed-Order Fractional Rayleigh–Stokes Problem for a Generalized Second Grade Fluid2020-01-23T00:00:00ZRamy M. HafezMahmoud A. ZakyMohamed A. AbdelkawyDistributed-order fractional differential operators provide a powerful tool for mathematical modeling of multiscale multiphysics processes, where the differential orders are distributed over a range of values rather than being just a fixed fraction. In this work, we consider the Rayleigh-Stokes problem for a generalized second-grade fluid which involves the distributed-order fractional derivative in time. We develop a spectral Galerkin method for this model by employing Jacobi polynomials as temporal and spatial basis/test functions. The suggested approach is based on a novel distributed order fractional differentiation matrix for Jacobi polynomials. Numerical results for one- and two-dimensional examples are presented illustrating the performance of the algorithm. The results show that our scheme can achieve the spectral accuracy for the problem under consideration with smooth solution and allows a great flexibility to deal with multi-dimensional temporally-distributed order fractional Rayleigh-Stokes problems as the global behavior of the solution is taken into account.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00230
https://www.frontiersin.org/articles/10.3389/fphy.2019.00230
Approximate Simulations for the Non-linear Long-Short Wave Interaction System2020-01-23T00:00:00ZHaiyong QinMostafa M. A. KhaterRaghda A. M. AttiaDianchen LuThis research paper studies the semi-analytical and numerical solutions of the non-linear long-short wave interaction system. This represents an optical field that does not change through multiplication due to a sensitive balance being struck between linear and non-linear impacts in an elastic medium, defined as a medium that can adjust its shape as a consequence of deforming stress and return to its original form when the force is eliminated. In this medium, a wave is produced by vibrations that are a consequence of acoustic power, known as a sound wave or acoustic wave. The Adomian decomposition method and the cubic and septic B-spline methods are applied to the suggested system to obtain distinct types of solutions that are used to explain the novel physical properties of this system. These novel features are described by different types of figures that show more of the physical properties of this model. Also, the convergence between the obtained solutions is discussed through tables that show the values of absolute error between them.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00242
https://www.frontiersin.org/articles/10.3389/fphy.2019.00242
Lump-Type and Bell-Shaped Soliton Solutions of the Time-Dependent Coefficient Kadomtsev-Petviashvili Equation2020-01-21T00:00:00ZAliyu Isa AliyuYongjin LiLiu QiMustafa IncDumitru BaleanuAli S. AlshomraniIn this article, the lump-type solutions of the new integrable time-dependent coefficient (2+1)-dimensional Kadomtsev-Petviashvili equation are investigated by applying the Hirota bilinear technique and a suitable ansatz. The equation is applied in the modeling of propagation of small-amplitude surface waves in large channels or straits of slowly varying width, depth and non-vanishing vorticity. Applying the Bell's polynomials approach, we successfully acquire the bilinear form of the equation. We firstly find a general form of quadratic function solution of the bilinear form and then expand it as the sums of squares of linear functions satisfying some conditions. Most importantly, we acquire two lump-type and a bell-shaped soliton solutions of the equation. To our knowledge, the lump type solutions of the equation are reported for the first time in this paper. The physical interpretation of the results are discussed and represented graphically.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00214
https://www.frontiersin.org/articles/10.3389/fphy.2019.00214
Time-Dependent MHD Flow of Non-Newtonian Generalized Burgers' Fluid (GBF) Over a Suddenly Moved Plate With Generalized Darcy's Law2020-01-17T00:00:00ZAisha M. AlqahtaniIlyas KhanTime-dependent magnetohydrodynamic (MHD) motion of a generalized Burgers' fluid (GBF) is investigated in this article. GBF is a highly complicated non-Newtonian fluid and is of highest degree in the class of rate type fluids. GBF is taken electrically conducting by using the restriction of small magnetic Reynolds number. Darcy's law has been used here in its generalized form using the GBF constitutive relation; hence, the medium is made porous. The impulsive motion in the fluid is induced due to sudden jerk of the plate. Exact expressions for velocity as well as for shear stress fields are obtained using the Laplace transform method. The solutions for hydrodynamic fluid (absence of MHD) in a non-porous medium as well as those for a Newtonian fluid (NF) executing a similar motion are also recovered. Results are sketched in terms of several plots and discussed for embedded parameters. It is found that the Hartmann number and porosity of the medium have strong influence on the velocity and shear stress fields.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00220
https://www.frontiersin.org/articles/10.3389/fphy.2019.00220
Numerical Analysis of the Susceptible Exposed Infected Quarantined and Vaccinated (SEIQV) Reaction-Diffusion Epidemic Model2020-01-17T00:00:00ZNauman AhmedMehreen FatimaDumitru BaleanuKottakkaran Sooppy NisarIlyas KhanMuhammad RafiqMuhammad Aziz ur RehmanMuhammad Ozair AhmadIn this paper, two structure-preserving nonstandard finite difference (NSFD) operator splitting schemes are designed for the solution of reaction diffusion epidemic models. The proposed schemes preserve all the essential properties possessed by the continuous systems. These schemes are applied on a diffusive SEIQV epidemic model with a saturated incidence rate to validate the results. Furthermore, the stability of the continuous system is proved, and the bifurcation value is evaluated. A comparison is also made with the existing operator splitting numerical scheme. Simulations are also performed for numerical experiments.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00244
https://www.frontiersin.org/articles/10.3389/fphy.2019.00244
Fractional View Analysis of Third Order Kortewege-De Vries Equations, Using a New Analytical Technique2020-01-17T00:00:00ZRasool ShahUmar FarooqHassan KhanDumitru BaleanuPoom KumamMuhammad ArifIn the present article, fractional view of third order Kortewege-De Vries equations is presented by a sophisticated analytical technique called Mohand decomposition method. The Caputo fractional derivative operator is used to express fractional derivatives, containing in the targeted problems. Some numerical examples are presented to show the effectiveness of the method for both fractional and integer order problems. From the table, it is investigated that the proposed method has the same rate of convergence as compare to homotopy perturbation transform method. The solution graphs have confirmed the best agreement with the exact solutions of the problems and also revealed that if the sequence of fractional-orders is approaches to integer order, then the fractional order solutions of the problems are converge to an integer order solution. Moreover, the proposed method is straight forward and easy to implement and therefore can be used for other non-linear fractional-order partial differential equations.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00219
https://www.frontiersin.org/articles/10.3389/fphy.2019.00219
A Numerical Simulation for Darcy-Forchheimer Flow of Nanofluid by a Rotating Disk With Partial Slip Effects2020-01-15T00:00:00ZMalik Zaka UllahStefano Serra-CapizzanoDumitru BaleanuThis study examines Darcy-Forchheimer 3D nanoliquid flow caused by a rotating disk with heat generation/absorption. The impacts of Brownian motion and thermophoretic are considered. Velocity, concentration, and thermal slips at the surface of the rotating disk are considered. The change from the non-linear partial differential framework to the non-linear ordinary differential framework is accomplished by utilizing appropriate variables. A shooting technique is utilized to develop a numerical solution of the resulting framework. Graphs have been sketched to examine how the concentration and temperature fields are affected by several pertinent flow parameters. Skin friction and local Sherwood and Nusselt numbers are additionally plotted and analyzed. Furthermore, the concentration and temperature fields are enhanced for larger values of the thermophoresis parameter.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00229
https://www.frontiersin.org/articles/10.3389/fphy.2019.00229
Positivity Preserving Technique for the Solution of HIV/AIDS Reaction Diffusion Model With Time Delay2020-01-15T00:00:00ZMuhammad JawazNauman AhmedDumitru BaleanuMuhammad RafiqMuhammad Aziz-ur RehmanThis study is concerned with finding a numerical solution to the delay epidemic model with diffusion. This is not a simple task as variables involved in the model exhibit some important physical features. We have therefore designed an efficient numerical scheme that preserves the properties acquired by the given system. We also further develop Euler's technique for a delayed epidemic reaction–diffusion model. The proposed numerical technique is also compared with the forward Euler technique, and we observe that the forward Euler technique demonstrates the false behavior at certain step sizes. On the other hand, the proposed technique preserves the true behavior of the continuous system at all step sizes. Furthermore, the effect of the delay factor is discussed graphically by using the proposed technique.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00209
https://www.frontiersin.org/articles/10.3389/fphy.2019.00209
Computational and Physical Examination About the Aspects of Fluid Flow Between Two Coaxially Rotated Disks by Capitalizing Non-fourier Heat Flux Theory: Finite Difference Approach2020-01-09T00:00:00ZSardar BilalAsifa TassaddiqA. H. MajeedKottakkaran Sooppy NisarFarhad AliM. Y. MalikThis pagination is executed to exemplify flow features exhibited by viscous fluid between two coaxially rotated disks. Thermal analysis is performed by using Cattaneo-Christov heat flux theory. Porosity aspects are also taken into account. Mathematically structured non-linear PDEs are transmuted into non-linear ODEs by employing Karman transformations. Afterward, solution is heeded by applying implicit finite difference scheme renowned as Keller box method. Interpretation of flow controlling parameters on axial, tangential, and radial components of velocity, thermal distribution is exhibited. Assurance of computed data is done by managing comparison for skin friction coefficients at walls of disks. From the attained outcomes, it is addressed that the magnitude of axial and radial velocities diminishes at lower disk contrary to upper disk for intensifying magnitude of Reynolds number. Increment in tangential component of velocity is also demonstrated for uplifts values of Reynolds number. It is also concluded that thermal field decrements for increasing of Pr and thermal relaxation parameter. It is worthy to mention that shear drag coefficient at wall of lower disk decreases conversely to the wall shear coefficient magnitude at wall of upper disk.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00202
https://www.frontiersin.org/articles/10.3389/fphy.2019.00202
New Solutions of Gardner's Equation Using Two Analytical Methods2019-12-06T00:00:00ZBehzad GhanbariDumitru BaleanuThis article introduces and applies new methods to determine the exact solutions of partial differential equations that will increase our understanding of the capabilities of applied models in real-world problems. With these new solutions, we can achieve remarkable advances in science and technology. This is the basic idea in this article. To accurately describe this, some exact solutions to the Gardner's equation are obtained with the help of two new analytical methods including the generalized exponential rational function method and a Jacobi elliptical solution finder method. A set of new exact solutions containing four parameters is reported. The results obtained in this paper are new solutions to this equation that have not been introduced in previous literature. Another advantage of these methods is the determination of the varied solutions involving various classes of functions, such as exponential, trigonometric, and elliptic Jacobian. The three-dimensional diagrams of some of these solutions are plotted with specific values for their existing parameters. By examining these graphs, the behavior of the solution to this equation will be revealed. Mathematica software was used to perform the computations and simulations. The suggested techniques can be used in other real-world models in science and engineering.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00193
https://www.frontiersin.org/articles/10.3389/fphy.2019.00193
Fractional Approach for Equation Describing the Water Transport in Unsaturated Porous Media With Mittag-Leffler Kernel2019-12-04T00:00:00ZD. G. PrakashaP. VeereshaJagdev SinghIn this paper, we find the solution for a fractional Richards equation describing the water transport in unsaturated porous media using the q-homotopy analysis transform method (q-HATM). The proposed technique is to use graceful amalgamations of the Laplace transform technique with the q-homotopy analysis scheme as well as the fractional derivative that is defined with the Atangana-Baleanu (AB) operator. The fixed point hypothesis is considered in order to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. In order to validate and illustrate the efficiency of the future technique, we analyze the projected model in terms of fractional order. Meanwhile, the physical behavior of the q-HATM solutions are captured in terms of plots for diverse fractional order and the numerical simulation is also demonstrated. The achieved results illuminate that the future algorithm is easy to implement, highly methodical, effective, and very accurate in its analysis of the behavior of non-linear differential equations of fractional order that arise in the connected areas of science and engineering.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00196
https://www.frontiersin.org/articles/10.3389/fphy.2019.00196
A New Feature of the Fractional Euler–Lagrange Equations for a Coupled Oscillator Using a Nonsingular Operator Approach2019-11-26T00:00:00ZAmin JajarmiDumitru BaleanuSamaneh Sadat SajjadiJihad H. AsadIn this new work, the free motion of a coupled oscillator is investigated. First, a fully description of the system under study is formulated by considering its classical Lagrangian, and as a result, the classical Euler–Lagrange equations of motion are constructed. After this point, we extend the classical Lagrangian in fractional sense, and thus, the fractional Euler–Lagrange equations of motion are derived. In this new formulation, we consider a recently introduced fractional operator with Mittag–Leffler non-singular kernel. We also present an efficient numerical method for solving the latter equations in a proper manner. Due to this new powerful technique, we are able to obtain remarkable physical thinks; indeed, we indicate that the complex behavior of many physical systems is realistically demonstrated via the fractional calculus modeling. Finally, we report our numerical findings to verify the theoretical analysis.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00189
https://www.frontiersin.org/articles/10.3389/fphy.2019.00189
Bio-Heat Models Revisited: Concepts, Derivations, Nondimensalization and Fractionalization Approaches2019-11-21T00:00:00ZJordan HristovThe heat transfer in living tissues is an evergreen problem in mathematical modeling with great practical importance starting from the Pennes equation postulation. This study focuses on concept in model building, the correct scaling of the bio-heat equation (one-dimensional) by appropriate choice of time and length scales, and consequently order of magnitude analysis of effects, as well as fractionalization approaches. Fractionalization by different constitutive approaches, leading to application of different fractional differential operators, modeling the finite speed of the heat wave, is one of the principle problems discussed in the study. The correct choice of the damping (relaxation) function of the heat flux is of primarily importance in the formulation of the bio-heat equation with memory. Moreover, this affects the consequent scaling, order of magnitude analysis and solutions.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00197
https://www.frontiersin.org/articles/10.3389/fphy.2019.00197
Complex and Real Optical Soliton Properties of the Paraxial Non-linear Schrödinger Equation in Kerr Media With M-Fractional2019-11-21T00:00:00ZWei GaoHajar F. IsmaelSizar A. MohammedHaci Mehmet BaskonusHasan BulutIn this paper, we use the modified exponential function method in terms of K^{f(x)} instead of e^{f(x)}and the extended sinh-Gordon method to find some new family solution of the M-fractional paraxial non-linear Schrödinger equation. The novel complex and real optical soliton solutions are plotted in 2-D, 3-D with a contour plot. Moreover, the dark exact solutions, singular soliton solutions, kink-type soliton solution, and periodic dark-singular soliton solutions for M-fractional paraxial non-linear Schrödinger equation are constructed. We guarantee that all solutions are new and verified the main equation of the M-fractional paraxial wave equation. For existence, the constraint condition is also added.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00186
https://www.frontiersin.org/articles/10.3389/fphy.2019.00186
Magnetohydrodynamic Free Stream and Heat Transfer of Nanofluid Flow Over an Exponentially Radiating Stretching Sheet With Variable Fluid Properties2019-11-15T00:00:00ZMuhammad IrfanMuhammad Asif FarooqTousif IqraThis article deals with the nanofluid flow and heat transfer of the MHD free stream over an exponentially radiating stretching sheet accompanied by constant and variable fluid characteristics together. The underlying governing partial differential equations (PDEs) have been translated into nonlinear ordinary differential equations (ODEs) by incorporating adequate similarity transformations. By using the shooting method and the MATLAB built-in solver bvp4c, the corresponding ODEs are effectively solved. The impact on the skin friction coefficient (quantifying resistance), the local Nusselt number (heat transfer rate) and the local Sherwood number (mass transfer rate) on the surface due to the flow field variables has been computed against various parameters i.e., magnetic parameter M, Prandtl number Pr_{o}, Lewis number Le, thermophoresis parameter Nt, Brownian motion parameter Nb, velocity parameter λ, radiation parameter Rd and thermal conductivity parameter ϵ. Graphs are also plotted to study the impact of distinct parameters on velocity, temperature and concentration profiles. It has been noted by raising the values of ϵ, the heat transfer rate reduces for variable fluid properties. On the other hand, raising Pr_{o} increases the heat transfer rate.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00164
https://www.frontiersin.org/articles/10.3389/fphy.2019.00164
Numerical Simulation of Magnetohydrodynamic Nanofluids Under the Influence of Shape Factor and Thermal Transport in a Porous Media Using CVFEM2019-11-06T00:00:00ZZahir ShahHouman BabazadehPoom KumamAhmad ShafeePhatiphat ThounthongIn this article, the migration of nanomaterials through a permeable domain was modeled numerically. Aluminum oxide was dispersed into testing fluid which was selected water in the current paper. Utilizing Darcy LAW for a porous medium helps us to find simpler form of equations. Influences of shape factor and radiation on the thermal conduct of nanoparticles within a porous region were scrutinized. Nanomaterial within such region is applied under the Lorentz force. CVFEM approach for simulation goals has been applied. This approach provides the advantages of two common CFD methods. Impacts of radiation, magnetic, buoyancy parameters on the treatment of nanomaterials were demonstrated. Outcomes showed that greater amounts of shape factor cause stronger convection. Reverse relationships exist between the Hartmann number and temperature gradient.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00175
https://www.frontiersin.org/articles/10.3389/fphy.2019.00175
Self-Adjoint Extension Approach for Singular Hamiltonians in (2 + 1) Dimensions2019-11-06T00:00:00ZVinicius SalemRamon F. CostaEdilberto O. SilvaFabiano M. AndradeIn this work, we review two methods used to approach singular Hamiltonians in (2 + 1) dimensions. Both methods are based on the self-adjoint extension approach. It is very common to find singular Hamiltonians in quantum mechanics, especially in quantum systems in the presence of topological defects, which are usually modeled by point interactions. In general, it is possible to apply some kind of regularization procedure, as the vanishing of the wave function at the location of the singularity, ensuring that the wave function is square-integrable and then can be associated with a physical state. However, a study based on the self-adjoint extension approach can lead to more general boundary conditions that still gives acceptable physical states. We exemplify the methods by exploring the bound and scattering scenarios of a spin 1/2 charged particle with an anomalous magnetic moment in the Aharonov-Bohm potential in the conical space.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00171
https://www.frontiersin.org/articles/10.3389/fphy.2019.00171
Study of the Couple Stress Convective Micropolar Fluid Flow in a Hall MHD Generator System2019-11-05T00:00:00ZZahir ShahPoom KumamAbdullah DawarEbraheem O. AlzahraniPhatiphat ThounthongThe steady non-isothermal convective heat transfer in magnetohydrodynamic micropolar fluid flow over a non-linear extending wall is examined. The fluid flow is treated with strong magnetic field. The influence of magnetic field, Hall current, and couple stress are mainly focused in this work. The fluid flow problem is solved analytically. The impact of developing dimensionless parameters on primary, secondary, and angular velocity components and temperature profile are determined through graphs. The primary velocity component has reduced throughout the flow study. The greater magnetic parameter, Hall parameter and couple stress parameter have increased the secondary velocity component while the local Grashof number has reduced the secondary velocity component. The greater magnetic parameter and Hall parameter have reduced the angular velocity component. The greater magnetic parameter has increased the temperature profile while the Hall parameter and local Grashof number have decreased the temperature profile. The impact of developing dimensionless parameters on skin friction coefficient and local Nusselt number are determined through Tables.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00167
https://www.frontiersin.org/articles/10.3389/fphy.2019.00167
Point-Particle Catalysis2019-11-05T00:00:00ZPeter HaymanCliff P. BurgessWe use the point-particle effective field theory (PPEFT) framework to describe particle-conversion mediated by a flavor-changing coupling to a point-particle. We do this for a toy model of two non-relativistic scalars coupled to the same point-particle, on which there is a flavor-violating coupling. It is found that the point-particle couplings all must be renormalized with respect to a radial cut-off near the origin, and it is an invariant of the flow of the flavor-changing coupling that is directly related to particle-changing cross-sections. At the same time, we find an interesting dependence of those cross-sections on the ratio k_{out}/k_{in} of the outgoing and incoming momenta, which can lead to a 1/k_{in} enhancement in certain regimes. We further connect this model to the case of a single-particle non-self-adjoint (absorptive) PPEFT, as well as to a PPEFT of a single particle coupled to a two-state nucleus. These results could be relevant for future calculations of any more complicated reactions, such as nucleus-induced electron-muon conversions, monopole catalysis of baryon number violation, as well as nuclear transfer reactions.]]>https://www.frontiersin.org/articles/10.3389/fphy.2019.00168
https://www.frontiersin.org/articles/10.3389/fphy.2019.00168
Fuzzy Type RK4 Solutions to Fuzzy Hybrid Retarded Delay Differential Equations2019-10-25T00:00:00ZPrasantha Bharathi DhandapaniDumitru BaleanuJayakumar ThippanVinoth SivakumarThis paper constructs the numerical solution of particular type of differential equations called fuzzy hybrid retarded delay-differential equations using the method of Runge-Kutta for fourth order. The concept of fuzzy number, hybrid-differential equations, and delay-differential equations binds together to form our equations. An example following the algorithm is presented to understand the Concept of fuzzy hybrid retarded delay-differential equations and its accuracy is discussed in terms of decimal places for easy understanding of laymen.]]>