采用三层保护策略的强制进化随机游走算法同步综合换热网络

强制进化随机游走算法（RWCE）同步综合换热网络时,存在个体最优解的进化路径被接受差解打乱而不接受差解又很难跳出局部最优的问题.提出一种采用三层保护策略的RWCE算法,将种群中个体分为三层,底层采用基本RWCE进行优化,以保护个体的全局搜索能力;中层读取底层各个体的历史最优解,并采用带微调功能的RWCE进行优化,以保护各个体最优解的进化路径不被打乱;顶层所有个体以中层最优个体的解为初始点,采用带自动精细搜索功能的RWCE进行优化,以保证最优个体得到充分的搜索;最后将顶层搜索到的结果传递给底层对应个体.实例表明,算法在允许接受差解的同时保护了个体最优解的进化路径,并实现了全局搜索能力与局部搜索能力的兼顾.     

特解边界元法数值解三维Pennes方程及其应用

应用特解边界元法对非稳态的三维Pennes方程求解,将解分为一满足泊松方程的通解与一特解之和,通解按照边界元法求解,特解用分离变量法给出,与位置有关的部分采用截断多项式.逐时间段计算边界元的温度及热流值,然后计算域内点的值.并将该方法用于热疗温度场的数值实例计算.     

A new class of plane symmetric solution

A new class of static plane symmetric solution of Einstein field equation generated by a perfect fluid source is put forward. A special family of this new solution is investigated in detail. The constraints on the parameters by different energy conditions are studied. The classical stability of this solution is discussed. The junction conditions matching to Minkowski metric and Taub metric are analyzed respectively.     

Regular black holes in quadratic gravity

The first-order correction of the perturbative solution of the coupled equations of the quadratic gravity and nonlinear electrodynamics is constructed, with the zeroth-order solution coinciding with the ones given by Ayón-Beato and Garcí a and by Bronnikov. It is shown that a simple generalization of the Bronnikov's electromagnetic Lagrangian leads to the solution expressible in terms of the polylogarithm functions. The solution is parametrized by two integration constants and depends on two free parameters. By the boundary conditions the integration constants are related to the charge and total mass of the system as seen by a distant observer, whereas the free parameters are adjusted to make the resultant line element regular at the center. It is argued that various curvature invariants are also regular there that strongly suggests the regularity of the spacetime. Despite the complexity of the problem the obtained solution can be studied analytically. The location of the event horizon of the black hole, its asymptotics and temperature are calculated. Special emphasis is put on the extremal configuration.     

An Analytical Technique,Based on Natural Transform to Solve Fractional-Order Parabolic Equations

This research article is dedicated to solving fractional-order parabolic equations using an innovative analytical technique. The Adomian decomposition method is well supported by natural transform to establish closed form solutions for targeted problems. The procedure is simple, attractive and is preferred over other methods because it provides a closed form solution for the given problems. The solution graphs are plotted for both integer and fractional-order, which shows that the obtained results are in good contact with the exact solution of the problems. It is also observed that the solution of fractional-order problems are convergent to the solution of integer-order problem. In conclusion, the current technique is an accurate and straightforward approximate method that can be applied to solve other fractional-order partial differential equations.     

On the two-component Benard problem a numerical solution

A numerical solution for the two-component Bénard problem is presented, taking into account the contribution of thermal diffusion to the total density gradient. The results are compared with the approximate solution obtained by the variational technique of the local potential introduced some years ago by Glansdorff and Prigogine. The results calculated by the two methods are in agreement when the Soret coefficient is not too large. But when the gradients become important, the exact numerical solution presented here shows a small divergence from the variational method.The critical Rayleigh number is also compared with the one extrapolated from the analytical solution obtained for free boundary conditions.     

Three-dimensional MHD flow over a shrinking sheet: Analytical solution and stability analysis

The magnetohydrodynamic(MHD) steady and unsteady axisymmetric flows of a viscous fluid over a two-dimensional shrinking sheet are addressed. The mathematical analysis is carried out in the presence of a large magnetic field. The steady state problem results in a singular perturbation problem having an infinite domain singularity. The secular term appearing in the solution is removed and a two-term uniformly valid solution is derived using the Lindstedt–Poincaré technique. This asymptotic solution is validated by comparing it with the numerical solution. The solution for the unsteady problem is also presented analytically in the asymptotic limit of large magnetic field. The results of velocity profile and skin friction are shown graphically to explore the physical features of the flow field. The stability analysis of the unsteady flow is made to validate the asymptotic solution.     

Scattering of plane waves by a wedge with different face impedances

The scattering process of plane waves by a wedge with different face impedances is examined in terms of the closed form series solution. A new boundary condition is derived using the solution of the reflection problem of plane waves by an impedance plane. The series solution is obtained for the wedge problem. The results are investigated numerically.     

Bcklund Transformations and Solutions of a Generalized Kadomtsev-Petviashvili Equation

In this paper,the bilinear form of a generalized Kadomtsev-Petviashvili equation is obtained by applying the binary Bell polynomials.The N-soliton solution and one periodic wave solution are presented by use of the Hirota direct method and the Riemann theta function,respectively.And then the asymptotic analysis demonstrates one periodic wave solution can be reduced to one soliton solution.In the end,the bilinear Bcklund transformations are derived.     

An elastodynamic solution of finite long orthotropic hollow cylinder under torsion impact

The paper presents an analytical method to solve the elastodynamic problem of a finite-length orthotropic hollow cylinder subjected to a torsion impact often occurring in engineering fields. The elastodynamic solution is composed of a quasi-static solution of homogeneous equation satisfied with the non-homogeneous boundary condition and a dynamic solution of non-homogeneous equation satisfied with homogeneous boundary condition. The quasi-static solution can be obtained by directly solving the quasi-static equation satisfied with the non-homogeneous boundary condition. The solution of a non-homogeneous dynamic equation is obtained by means of a finite Hankel transform to a radial variable r, Laplace transform to a time variable t and finite Fourier transform to an axial variable z. Thus, the elastodynamic solution of the finite length of an orthotropic hollow cylinder subjected to a torsion impact is obtained. On the other hand, a dynamic finite element for the same problem is also carried out by applying the ANSYS finite-element analysis system. Comparing the theoretical solution with finite-element solution, it can be found that two kinds of results obtained by making use of two different solving methods are suitably approached. Therefore, it is further concluded that the methods and computing processes of the theoretical solution are effective and accurate.     

Theoretical and numerical calculation of the acoustic radiation force acting on a circular rigid cylinder near a flat wall in a standing wave excitation in an ideal fluid

The acoustic radiation force acting on a cylinder near a flat wall in a standing wave is calculated by analytical methods and numerical simulations. An exact theoretical solution is presented as well as an approximate solution. The approximate solution is in algebraic form and quite easy to compute. The numerical simulation is based on FVM (Finite Volume Method) on unstructured triangular meshes. The exact theoretical, approximate and numerical solutions are compared with each other and good agreements are obtained. Furthermore, the effects of the flat wall are investigated in detail by the three methods.     

The Convergence Estimation of the Parallel Algorithm of the Linear Cauchy Problem Solution for Large Systems of First-Order Ordinary Differential Equations Using the Solution as Expansion over Orthogonal Polynomials

This paper is devoted to the algorithm of the linear Cauchy problem solution for large systems of first-order ordinary differential equations using parallel calculations. The proof of the convergence of the iteration process using the solution as expansion over orthogonal polynomials for the interval [0,1] is presented. The features of this algorithm are its simplicity, the opportunity to get a solution by parallel calculations, and also the possibility to get a solution for nonlinear problems by changing the operator using the solution from the iteration process.     

Detection of free radicals produced by a pulsed electrohydraulic discharge using electron spin resonance

The detection of free radicals such as hydroxyl radical and hydrogen radical for plasma in solution induced by a pulsed electrohydraulic discharge are successfully performed using electron spin resonance measurement. The plasma reactor is a barrier-type and consists of a stainless needle high-voltage (+35 to 65 kV) electrode partially immersed in the solution and a Pyrex glass solution container around which an aluminum film grounded electrode is wrapped. Streamers are induced in the solution. After adding iron (II) sulfate or radical trapping agent before the plasma application, the spectrum for radicals is clearly detected. A reactive dye solution is dramatically decolorized.     

Analytical solution of equations describing slow axonal transport based on the stop-and-go hypothesis

This paper presents an analytical solution for slow axonal transport in an axon. The governing equations for slow axonal transport are based on the stop-and-go hypothesis which assumes that organelles alternate between short periods of rapid movement on microtubules (MTs), short on-track pauses, and prolonged off-track pauses, when they temporarily disengage from MTs. The model includes six kinetic states for organelles: two for off-track organelles (anterograde and retrograde), two for running organelles, and two for pausing organelles. An analytical solution is obtained for a steady-state situation. To obtain the analytical solution, the governing equations are uncoupled by using a perturbation method. The solution is validated by comparing it with a high-accuracy numerical solution. Results are presented for neurofilaments (NFs), which are characterized by small diffusivity, and for tubulin oligomers, which are characterized by large diffusivity. The difference in transport modes between these two types of organelles in a short axon is discussed. A comparison between zero-order and first-order approximations makes it possible to obtain a physical insight into the effects of organelle reversals (when organelles change the type of a molecular motor they are attached to, an anterograde versus retrograde motor).     

A hybrid discontinuous Galerkin method for computing the ground state solution of Bose–Einstein condensates

A numerical method for computing the ground state solution of Bose–Einstein condensates modeled by the Gross–Pitaevskii equation is presented. In this method, the three-dimensional computational domain is divided into hexahedral elements in which the solution is approximated by a sum of basis functions. Both polynomial and plane wave bases are considered for this purpose, and Lagrange multipliers are introduced to weakly enforce the interelement continuity of the solution. The ground state is computed by an iterative procedure for minimizing the energy. The performance results obtained for several numerical experiments demonstrate that the proposed method is more computationally efficient than similar solution approaches based on the standard higher-order finite element method.     

Solution to the MHD flow over a non-linear stretching sheet by homotopy perturbation method

In this study,by means of homotopy perturbation method(HPM) an approximate solution of the magnetohydrodynamic(MHD) boundary layer flow is obtained.The main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to solve.HPM produces analytical expressions for the solution to nonlinear differential equations.The obtained analytic solution is in the form of an infinite power series.In this work,the analytical solution obtained by using only two terms from HPM soluti...     

Electromagnetic wave scattering by a small impedance particle: Theory and modeling

Electromagnetic (EM) waves, scattered by a small impedance particle of arbitrary shape, embedded in a homogeneous medium, are calculated by a new analytic formula. The range of applicability and the accuracy of this formula are illustrated by numerical results. The formula was derived in (*) A.G.Ramm, Optics Communications, 284,(2011), 3872–3877. The accuracy of the new formula is estimated by a comparison with the Mie-type solution for an impedance sphere.The novelty of our paper is in the demonstration of the range of applicability of the new formula and its practical value, by the numerical results and their comparison with the exact solution for EM wave scattering by impedance spheres. The exact solution is obtained in the form of Mie-type series, and is new. Estimate of the error of this series, in which five terms are kept, shows that the relative error of this solution is less than 10^? 3 for the parameters' range considered. The numerical results obtained are of interest to a wide audience, and the novelty of the formula from (*) is in its applicability to wave scattering by small particles of arbitrary shapes, when Mie-type solution is not applicable.     

An interior solution for the gamma metric

Interior solutions for a static, axially symmetric family of solutions of Einstein's equations are described. The interior solutions correspond to spatially bound matter and are properly matched to an exterior vacuum solution. The family of solutions discussed include the Schwarzschild solution as a special case. A general method is exhibited for transforming any spherically symmetric interior solution to an interior for the other members of the family of solutions. The energy density remains positive for at least a finite range of the parameter that describes the family of solutions. Two solutions are explicitly exhibited. One is transformed from the constant density Schwarzschild interior solution and one from the Adler interior solution. The first solution would be expected to be unstable under adiabatic perturbations of the matter, the second would be expected to be stable.Supported in part by The National Science Foundation under Grant No. INT 782-5663.Supported in part by Consejo Nacional de Investigaciones Cientificas y Technologicas (CONICIT), Venezuela.     

Initial value problem of the Whitham equations for the Camassa-Holm equation

We study the Whitham equations for the Camassa-Holm equation. The equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested in the initial value problem of the Whitham equations. When the initial values are given by a step function, the Whitham solution is self-similar. When the initial values are given by a smooth function, the Whitham solution exists within a cusp in the x-t plane. On the boundary of the cusp, the Whitham solution matches the Burgers solution, which exists outside the cusp.     

On exact solutions of the Bogoyavlenskii equation

Exact solutions for the Bogoyavlenskii equation are studied by the travelling wave method and the singular manifold method. It is found that the linear superposition of the shock wave solution and the complex solitary wave solution for the physical field is still a solution of the equation of interest, except for a phase-shift. The dromion-like structures with elastic and nonelastic interactions are found.