Effective coefficients of quasi-steady Maxwell’s equations with multiscale isotropic random conductivity

The effective coefficients in the quasi-steady Maxwell’s equations are calculated for a multiscale isotropic medium by using a subgrid modeling approach. The conductivity is mathematically represented by a Kolmogorov multiplicative continuous cascade with a lognormal probability distribution. The scale of the solution domain is assumed to be large as compared with the scale of heterogeneities of the medium. The theoretical results obtained in the paper are compared with the results of a direct 3D numerical simulation and the results of the conventional perturbation theory.     

Spin-1/2 Maxwell Fields

Requiring covariance of Maxwell's equations without a priori imposing charge invariance allows for both spin-1 and spin-1/2 transformations of the complete Maxwell field and current. The spin-1/2 case yields new transformation rules, with new invariants, for all traditional Maxwell field and source quantities. The accompanying spin-1/2 representations of the Lorentz group employ the Minkowski metric, and consequently the primary spin-1/2 Maxwell invariants are also spin-1 invariants; for example, ²–A ², E ²–B ²+2i EB–(₀ +A)². The associated Maxwell Lagrangian density is also the same for both spin-1 and spin-1/2 fields. However, in the spin-1/2 case, standard field and source quantities are complex and both charge and gauge invariance are lost. Requiring the potentials to satisfy the Klein–Gordon equation equates the Maxwell and field-potential equations with two Dirac equations of the Klein–Gordon mass, and thus one complex Klein–Gordon Maxwell field describes either two real vector fields or two Dirac fields, all of the same mass.     

Doubly Periodic Wave Solutions of Jaulent-Miodek Equations Using Variational Iteration Method Combined with Jacobian-function Method

One of the advantages of the variational iteration method is the free choice of initial guess. In this paper we use the basic idea of the Jacobian-function method to construct a generalized trial function with some unknown parameters. The Jaulent-Miodek equations are used to illustrate effectiveness and convenience of this method, some new explicit exact travelling wave solutions have been obtained, which include bell-type soliton solution, kink-type soliton solutions, solitary wave solutions, and doubly periodic wave solutions.     

The time dependent Ginzburg-Landau equation in fractal space-time

We use the hydrodynamic formulation of Scale Relativity Theory to analyze the TDGL equation. As a result, London equations come naturally from the system, when equating to zero the real velocity, the imaginary one turns real, the superconducting fluid act as a subquantum medium energy accumulator, the vector potential, the real and the imaginary velocity are all written in terms of the elliptic function. When solving the resulted system by means of WKBJ method, we get tunneling and quantization. In other words, scale transformation laws produce, on the motion equation of particles governed by the TDGL equation, under some peculiar assumptions, effects which are analogous to those of a “macroscopic quantum mechanics”.     

Pressure-driven transient flows of Newtonian fluids through microtubes with slip boundary

Recent advances in microscale experiments and molecular simulations confirm that slip of fluid on solid surface occurs at small scale, and thus the traditional no-slip boundary condition in fluid mechanics cannot be applied to flow in micrometer and nanometer scale tubes and channels. On the other hand, there is an urgent need to understand fluid flow in micrometer scale due to the emergence of biochemical lab-on-the-chip system and micro-electromechanical system fabrication technologies. In this paper, we study the pressure driven transient flow of an incompressible Newtonian fluid in microtubes with a Navier slip boundary condition. An exact solution is derived and is shown to include some existing known results as special cases. Through analysis of the derived solution, it is found that the influences of boundary slip on the flow behaviour are qualitatively different for different types of pressure fields driving the flow. For pressure fields with a constant pressure gradient, the boundary slip does not alter the interior material deformation and stress field; while, for pressure fields with a wave form pressure gradient, the boundary slip causes the change of interior material deformation and consequently the velocity profile and stress field. We also derive asymptotic expressions for the exact solution through which a parameter is identified to dominate the behaviour of the flow driven by the wave form pressure gradient, and an explicit formulae for the critical slip parameter leading to the maximum transient flow rate is established.     

Fractal differential equations and fractal-time dynamical systems

Differential equations and maps are the most frequently studied examples of dynamical systems and may be considered as continuous and discrete time-evolution processes respectively. The processes in which time evolution takes place on Cantor-like fractal subsets of the real line may be termed as fractal-time dynamical systems. Formulation of these systems requires an appropriate framework. A new calculus calledF ^α-calculus, is a natural calculus on subsetsF⊂ R of dimension α,0 < α ≤ 1. It involves integral and derivative of order α, calledF ^α-integral andF ^α-derivative respectively. TheF ^α-integral is suitable for integrating functions with fractal support of dimension α, while theF ^α-derivative enables us to differentiate functions like the Cantor staircase. The functions like the Cantor staircase function occur naturally as solutions ofF ^α-differential equations. Hence the latter can be used to model fractal-time processes or sublinear dynamical systems. We discuss construction and solutions of some fractal differential equations of the form

Comments on the mean spherical approximation for hard-core and soft potentials and an application to the one-component plasma

The thermodynamic properties of the mean spherical (MSA), Percus-Yevick (PY), and hypernetted-chain (HNC) approximations are derived by a simple and unified approach by considering the RPA free-energy functionalF and employing an Ewald-type identity. It is demonstrated that with decreasing relative contribution of the hard-core insertion to the thermodynamic functions, the MSA changes its nature from PY-like to HNC-like, withF changing its role from excess pressure to excess free energy, respectively. It is found that the condition of continuity of the MSA pair functions is equivalent to a stationarity condition forF and leads to thermodynamic consistency between the virial and energy equations of state for the (thus defined) soft-MSA (SMSA), withF playing the role of the excess free energy. It is shown that the PY-compressibility and virial equations of state forD-dimensional hard spheres may be simply obtained one from the other without knowing any details of the solution of the model. Using this relation we find an indication that the PY approximation for hard spheres becomes less accurate with increasing dimensionality. A general variational formulation is presented for the application of the MSA for soft potentials, and results for the one-component plasma are discussed and extended.On sabbatical leave from the Nuclear Research Center-Negev, P.O. Box 9001, Beer Sheva, Israel.     

sine-Gordon型方程的无穷序列新精确解

为了获得sine-Gordon型方程的无穷序列精确解,给出三角函数型辅助方程和双曲函数型辅助方程及其Bäcklund变换和解的非线性叠加公式,借助符号计算系统Mathematica,构造了sine-Gordon方程、mKdV-sine-Gordon方程、(n+1)维双sine-Gordon方程和sinh-Gordon方程的无穷序列新精确解.其中包括无穷序列三角函数解、无穷序列双曲函数解、无穷序列Jacobi椭圆函数解和无穷序列复合型解. 关键词： sine-Gordon型方程 解的非线性叠加公式 辅助方程 无穷序列精确解     

THE BOUNDARY ELEMENT METHOD (BEM) FOR WAVE EQUATION

The formula of BEM suited to solve the problems of wave propagation in boundlessmedium is obtained from numerical treatment of Kirchhoff integral equation.Afer quotingthe coefficients of refraction and reflection of wave at surface or interface,the expression ofBEM which is suitable for the problems of wave propagation in multi-isotropic mediums isalso given.     

TREANOR算法有病态吗?

文在计算“HL-1”两台电机并车过程时,、用了Treanor方法,且指出算法有病态现象。我们的分析是Treanor算法不存在病态现象,实际计算也表明Treanor算法可正确地描述并车过程。 描述两台双Y30°电机并车同步过程的微分方程为