Determination of the Robin coefficient in a nonlinear boundary condition for a steady‐state problem

In this paper, a constant heat transfer coefficient present in a nonlinear Robin‐type boundary condition associated with an elliptic equation is reconstructed uniquely from a single boundary energy measurement. Two types of such boundary energy measurement are considered, and solvability theorems for the solution of the resulting nonlinear inverse problems are provided. Further, one‐dimensional numerical results are presented and discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

A TAILORED FINITE POINT METHOD FOR THE HELMHOLTZ EQUATION WITH HIGH WAVE NUMBERS IN HETEROGENEOUS MEDIUM

In this paper, we propose a tailored-finite-point method for the numerical simulation of the Helmholtz equation with high wave numbers in heterogeneous medium. Our finite point method has been tailored to some particular properties of the problem, which allows us to obtain approximate solutions with the same behaviors as that of the exact solution very naturally. Especially, when the coefficients are piecewise constant, we can get the exact solution with only one point in each subdomain. Our finite-point method has uniformly convergent rate with respect to wave number k in L^2-norm.     

Calculation of the critical point for mixtures using mixture models based on Helmholtz energy equations of state

This paper mainly focuses on refrigerant mixtures with relatively simple critical behavior, and presents a practical and useful method for the critical point calculation for the mixtures using mixture models based on Helmholtz energy equations of state. The expression for critical point criterion suitable for this objective is derived first. Numerical manipulations to obtain a physically correct solution are described in detail. For four binary refrigerant mixtures of difluoromethane (R-32) + pentafluoroethane (R-125), R-125 + 1,1,1,2-tetrafluoroethane (R-134a), R-125 + 1,1,1-trifluoroethane (R-143a), and R-32 + propane (R-290), the critical temperatures and critical molar volumes are calculated applying the presented method. The calculation results are compared with experimental values, and the capabilities of the mixture models for the mixtures in the critical region are discussed.     

A new approach for modelling the damped Helmholtz oscillator:applications to plasma physics and electronic circuits

In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for undamped HE(integrable case)and approximate/semi-analytical solution to the damped HE(non-integrable case)are given for any arbitrary initial conditions.As a special case,the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is reported.In general,a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic function.In addition,the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in details.Also,we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge-Kutta fourth-order method,finite difference method,and homotopy perturbation method for the first-two approximations.Furthermore,the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be estimated.As real applications,the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model.     

The BEM for solving the nonhomogeneous Helmholtz equation with variable coefficients

Considering the fundamental solution of the Laplace equation as the weight function, we give the iterative format for solving the nonhomogeneous Helmholtz equation with variable coefficients. Furthermore, the iteration method of BEM for solving the equation mentioned above is obtained. The numerical example is given in this paper. Finally, the iteration method of BEM mentioned above is compared with the coupled method of BEM that was presented before then by authors.     

关于-RTlnK_c~■=Δ_rG_m~■(c~■)的讨论

在等温等压条件下,通过pB=cBRT关系转换,所得关系式证明了-RTlnK—cΟ=ΔrG—mΟ(c—Ο)。还分析推证出ΔrG—mΟ(c—Ο)和ΔrG—mΟ(p—Ο)、ΔrH—Οm(c—Ο)和ΔrHΟ—m(p—Ο)、ΔrSΟ—m(c—Ο)和ΔrSΟ—m(p—Ο)、ΔrUΟ—m(c—Ο)和ΔrHΟ—m(cΟ—)以及ΔrG—Οm(c—Ο)和ΔrA—mΟ(c—Ο)之间的几个关系式,进一步证实了-RTlnK—cΟ=ΔrGΟ—m(c—Ο)。     

ERROR ESTIMATION FOR NUMERICAL METHODS USING THE ULTRA WEAK VARIATIONAL FORMULATION IN MODEL OF NEAR FIELD SCATTERING PROBLEM

In this paper, we investigate the use of ultra weak variational formulation to solve a wave scattering problem in near field optics. In order to capture the sub-scale features of waves, we utilize evanescent wave functions together with plane wave functions to approximate the local properties of the field. We analyze the global convergence and give an error estimation of the method. Numerical examples are also presented to demonstrate the effectiveness of the strategy.     

Analysis of the convected Helmholtz equation with a uniform mean flow in a waveguide with complete radiation boundary conditions

In this paper, we propose complete radiation boundary conditions (CRBCs) for solutions of the convected Helmholtz equation with a uniform mean flow in a waveguide. We first study CRBCs for the Helmholtz equation in a waveguide. Noting that the convected Helmholtz equation is associated with the Helmholtz equation via the Prandtl–Glauert transformation, CRBCs for the convected Helmholtz equation is derived from CRBCs for the Helmholtz equation. We analyse well-posedness and convergence of approximate solutions satisfying CRBCs for the convected Helmholtz equation. In addition, simple numerical experiments will be presented to confirm the theoretical results.     

A Class of Operator Equations in Nonlinear Mechanics

A nonlinear evolution equation in Hilbert space is introduced and is shown to govern a broad class of problems of nonlinear solid mechanics. The simplest oscillations of this equation are described by a “generalized Liénard equation.”

AMS(MOS) Classification Nos: 73D35, 73F15, 58D25, 35L35, 34G20, 34C15.     

The Neumann problem and Helmholtz decomposition in convex domains

We show that the Neumann problem for Laplace's equation in a convex domain Ω with boundary data in Lp(∂Ω) is uniquely solvable for 1<p<∞. As a consequence, we obtain the Helmholtz decomposition of vector fields in Lp(Ω,Rd).