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Advances in Mathematical Physics
Hindawi Publishing Corporation
Advances in Mathematical Physics

Hindawi Publishing Corporation

1687-9120

Advances in Mathematical Physics/Journal Advances in Mathematical PhysicsSCI
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    Rational Solutions for the (2 + 1)-Dimensional Modified KdV-CBS Equation

    Yan LiTemuer ChaoluYuexing Bai
    12页
    查看更多>>摘要：In this paper, with the help of symbolic computation, three types of rational solutions for the (2 + 1)-dimensional modified KdV-Calogero-Bogoyavlenkskii-Schiff equation are derived. By means of the truncated Painlevé expansion, we show that the (2 + 1)-dimensional modified KdV-Calogero-Bogoyavlenkskii-Schiff equation can be written as a trilinear-linear equation, from which we get explicit representation for rational solutions of the (2 + 1)-dimensional modified KdV-Calogero-Bogoyavlenkskii- Schiff equation.
      原文链接:
    • NSTL
    • Hindawi Publishing Group

    Higher-Order Mode Electromagnetic Analysis of a Material Sample between Two Flanged Coaxial Probes for Broadband Modelling of Dielectric Measurement Setups

    Raúl V. Haro-BáezJuan CórcolesJorge A. Ruiz-CruzJosé R. Montejo-Garai...
    17页
    查看更多>>摘要：The characterization of the dielectric properties of amaterial requires ameasurement technique and its associated analysismethod. In this work, the configuration involving two coaxial probes with a material for dielectric measurement between them is analyzed with a mode-matching approach. To that effect, two models with different complexity and particularities are proposed. It will be shown how convergence is sped up for accurate results by using a proper choice of higher-order modes along with a combination of perfect electric wall and perfectmagnetic wall boundary conditions. It will also be shown how the frequency response is affected by the flange mounting size, which can be, rigorously and efficiently, taken into account with the same type of approach. This numerical study is validated through a wide range of simulations with reference values from another method, showing how the proposed approaches can be used for the broadband characterization of this well-known, but with a recent renewed interest from the research community, dielectric measurement setup.
      原文链接:
    • NSTL
    • Hindawi Publishing Group

    Deconstructing the Gel’fand–Yaglom Method and Vacuum Energy from a Theory Space

    Nahomi KanKiyoshi Shiraishi
    15页
    查看更多>>摘要：The discrete Gel’fand–Yaglom theorem was studied several years ago. In the present paper, we generalize the discrete Gel’fand–Yaglom method to obtain the determinants of mass matrices which appear in current works in particle physics, such as dimensional deconstruction and clockwork theory. Using the results, we show the expressions for vacuum energies in such various models.
      原文链接:
    • NSTL
    • Hindawi Publishing Group

    Fractional Hardy–Sobolev Inequalities with Magnetic Fields

    Min LiuFengli JiangZhenyu Guo
    5页
    查看更多>>摘要：A fractional Hardy–Sobolev inequality with a magnetic field is studied in the present paper. Under appropriate conditions, the achievement of the best constant of the fractional magnetic Hardy–Sobolev inequality is established.
      原文链接:
    • NSTL
    • Hindawi Publishing Group

    Krasnoselskii N-Tupled Fixed Point Theorem with Applications to Fractional Nonlinear Dynamical System

    Tamer Nabil
    9页
    查看更多>>摘要：In this paper, N-tupled fixed point theorems for two monotone nondecreasing mappings in complete normed linear space are established. The extension of Krasnoseskii fixed point theorem for a version of N-tupled fixed point is given. Our theoretical results are applied to prove the existence of a mild solution of the system of N-nonlinear fractional evolution equations. Finally, an example of a nonlinear fractional dynamical system is given to illustrate the results.
      原文链接:
    • NSTL
    • Hindawi Publishing Group

    Yukawa Potential Orbital Energy: Its Relation to Orbital Mean Motion as well to the Graviton Mediating the Interaction in Celestial Bodies

    Connor MartzSheldon Van MiddelkoopIoannis GkigkitzisIoannis Haranas...
    10页
    查看更多>>摘要：Research on gravitational theories involves several contemporary modified models that predict the existence of a non-Newtonian Yukawa-type correction to the classical gravitational potential. In this paper we consider a Yukawa potential and we calculate the time rate of change of the orbital energy as a function of the orbital mean motion for circular and elliptical orbits. In both cases we find that there is a logarithmic dependence of the orbital energy on the mean motion. Using that, we derive an expression for the mean motion as a function of the Yukawa orbital energy, as well as specific Yukawa potential parameters. Furthermore, various special cases are examined. Lastly, expressions for the Yukawa range A and coupling constant a are also derived. Finally, an expression for the mass of the graviton mgr mediating the interaction is calculated using the expression its Compton wavelength (i.e., the potential range A). Numerical estimates for the mass of the graviton mediating the interaction are finally obtained at various eccentricity values and in particular at the perihelion and aphelion points of Mercury's orbit around the sun.
      原文链接:
    • NSTL
    • Hindawi Publishing Group

    A Continuum Approach to the Nonlinear In-Plane Galloping of Shallow Flexible Cables

    M. FerrettiD. ZulliA. Luongo
    12页
    查看更多>>摘要：The aeroelastic stability of horizontal, suspended, shallow, iced cables is studied via a continuum model. Both external and internal damping, consistent with the Rayleigh model, are taken into account. The quasi-static theory of the aerodynamic forces is applied. An in-plane nonlinear model of galloping is formulated, displaying the importance of internal damping, both on the critical velocity and on the limit-cycle amplitude. A perturbation procedure is developed for nonlinear analysis in nonresonant conditions (monomodal galloping). The modification of the galloping mode due to quadratic nonlinearities is studied, and its real or complex character is discussed.
      原文链接:
    • NSTL
    • Hindawi Publishing Group

    Solution to the Problem of a Mass Traveling on a Taut String via Integral Equation

    M. FerrettiA. Luongo
    9页
    查看更多>>摘要：The problem of a massive taut string, traveled by a heavy point mass, moving with an assigned law, is formulated in a linear context. Displacements are assumed to be transverse, and the dynamic tension is neglected. The equations governing the moving boundary problem are derived via a variational principle, in which the geometric compatibility between the point mass and the string is enforced via a Lagrange multiplier, having the meaning of transverse reactive force. The equations are rearranged in the form of a unique Volterra integral equation in the reactive force, which is solved numerically. A classical Galerkin solution is implemented for comparison. Numerical results throw light on the physics of the phenomenon and confirm the effectiveness of the algorithm.
      原文链接:
    • NSTL
    • Hindawi Publishing Group

    Analysis and Optimization of a Cyclone Integrated with a Cartridge Filter in a Hazardous Materials Collection Truck

    Shuwen ZhouYu Wang
    12页
    查看更多>>摘要：In order to meet the filtration separation of hazardous materials on hazardous materials collection truck, the most popular separation devices, such as the cyclone separator and the filter cartridge, are combined to form a new filtration device in this study. The advantages of the two devices are utilized to achieve effective separation of solid particles and prevent secondary pollution. Among the various structural influence factors of filtration equipment, four structural parameters that affect the separation performance significantly are selected as optimization variables. The response surface methodology was used to design the simulation experiment. Using fluid mechanics analysis software, multiple sets of parameters were simulated. Then, the simulation data was used to establish a mathematical model of separation efficiency, and structural optimization analysis was performed based on the mathematical model. Finally, the results show that the inner exhaust pipe diameter and the cone height have more influence on the efficiency of the cyclone separation structure. The interaction between the diameter and insertion depth of the inner exhaust pipe is also obvious. Among the four optimization variables, there is an optimum value for the inner exhaust pipe insertion depth, and the effect of the other three factors on the separation efficiency is monotonic. In the case of a total separation efficiency of 99.9% and after optimizing the combined model within a reasonable interval, 81.25% of the l-μm particles can be removed by the cyclone separation part, and only 18.75% are removed by the filter cartridge.
      原文链接:
    • NSTL
    • Hindawi Publishing Group

    Application of the Complex Variable Function Method to SH-Wave Scattering Around a Circular Nanoinclusion

    Hongmei Wu
    8页
    查看更多>>摘要：This paper focuses on analyzing SH-wave scattering around a circular nanoinclusion using the complex variable function method. The surface elasticity theory is employed in the analysis to account for the interface effect at the nanoscale. Considering the interface effect, the boundary condition is given, and the infinite algebraic equations are established to solve the unknown coefficients of the scattered and refracted wave solutions. The analytic solutions of the stress field are obtained by using the orthogonality of trigonometric function. Finally, the dynamic stress concentration factor and the radial stress of a circular nanoinclusion are analyzed with some numerical results. The numerical results show that the interface effect weakens the dynamic stress concentration but enhances the radial stress around the nanoinclusion; further, we prove that the analytic solutions are correct.
      原文链接:
    • NSTL
    • Hindawi Publishing Group