An improved proximity force approximation for electrostatics

A quite straightforward approximation for the electrostatic interaction between two perfectly conducting surfaces suggests itself when the distance between them is much smaller than the characteristic lengths associated with their shapes. Indeed, in the so called “proximity force approximation” the electrostatic force is evaluated by first dividing each surface into a set of small flat patches, and then adding up the forces due two opposite pairs, the contributions of which are approximated as due to pairs of parallel planes. This approximation has been widely and successfully applied in different contexts, ranging from nuclear physics to Casimir effect calculations. We present here an improvement on this approximation, based on a derivative expansion for the electrostatic energy contained between the surfaces. The results obtained could be useful for discussing the geometric dependence of the electrostatic force, and also as a convenient benchmark for numerical analyses of the tip–sample electrostatic interaction in atomic force microscopes.     

An application of second order approximations for the Green's function

In a previous paper there was developed an approximation theory for the Green's functions which gives approximations consistent with the conservation laws of the Hamiltonian. We have chosen a concept of reduction which is different and which leads to other approximations for the particle-hole Green's function than the usual concept of reduction. The particle-hole Green's function is the function $$\langle \Psi _0 |\tau \{ a_1^ + (0)a_2 (0)a_3^ + (t)a_4 (t)\} |\Psi _0 \rangle $$ where ¦Ψ_o〉 is the real ground state and τ stands for the time ordered products of the operators. Now, in this paper we want to give an example of an application of this theory. We present a second order approximation since the first order approximation is the well known Random Phase Approximation.     

The force law for the dynamic two-body problem in the second post-Newtonian approximation of general relativity

We calculate the force between two well-separated bodies in a fully dynamic system of two extended bodies up to and including the second post-Newtonian approximation (PNA). We use the iteration procedure as formulated by Anderson and Decanio in a version whose divergences have been pushed to the third PNA. We show the following, (i) The force law assumes the Newtonian form if a second approximation in 1/(separation of the bodies) is made; (ii) the mass terms appearing in the force law are the (Tolman) masses of the individual bodies expanded up the second PNA; the interal masses equal the (passive and active) gravitational masses of the bodies in order considered; they are all constants of the motion; (iii) the self-fields of the bodies vanish in the second PNA; hence there is no Nordvedt effect in the second PNA; (iv) the compactness of the bodies, i.e., (gravitational radius)/(body size), does not appear in the force law; only the relation between mass and the matter variables is changed in the PNA as compared with the corresponding Newtonian result.     

A second order self-consistent IMEX method for radiation hydrodynamics

We present a second order self-consistent implicit/explicit (methods that use the combination of implicit and explicit discretizations are often referred to as IMEX (implicit/explicit) methods ,  and ) time integration technique for solving radiation hydrodynamics problems. The operators of the radiation hydrodynamics are splitted as such that the hydrodynamics equations are solved explicitly making use of the capability of well-understood explicit schemes. On the other hand, the radiation diffusion part is solved implicitly. The idea of the self-consistent IMEX method is to hybridize the implicit and explicit time discretizations in a nonlinearly consistent way to achieve second order time convergent calculations. In our self-consistent IMEX method, we solve the hydrodynamics equations inside the implicit block as part of the nonlinear function evaluation making use of the Jacobian-free Newton Krylov (JFNK) method ,  and . This is done to avoid order reductions in time convergence due to the operator splitting. We present results from several test calculations in order to validate the numerical order of our scheme. For each test, we have established second order time convergence.     

An efficient method for calculating the pair distribution functions of a ternary hard-sphere system in r space within the Percus-Yevick approximation

We present a direct method which allows an accurate and—at the same time—economical calculation of the pair distribution functions (PDFs) g_ij (r) of an additive ternary hard-sphere system within the Percus—Yevick approximation. The approach is based on the fact that for this approximation the Laplace transforms [?_ij (s)] of the PDFs are known analytically, so that the inversion of the ?_ij (s) into r space can be performed exactly. The expressions presented here allow the determination of the ?_ij (r) for r values up to 8R ₁, R ₁ being the diameter of the smallest species; this range in r space should be sufficient for applications in standard algorithms of liquid state theory, such as thermodynamic perturbation theories or integral-equation approaches.     

An efficient approximation for the vibro-acoustic response of a turbulent boundary layer excited panel

The aim of this study was to present a deterministic model for approximating the vibrations and the acoustic pressure radiated when a thin elastic plate is immersed in a low Mach number flow of fluid. As a prelude to this study, a classical random model based on a wavevector integration technique was used. In the case of a low Mach number turbulent flow, the numerical study showed that the subconvective region of the turbulent excitation power spectrum contributes significantly to the response of the panel. A deterministic approximate model was developed, based on this behaviour of the system.     

An improved decoupling approximation method for nonlinear granular composites

An improved decoupling approximation is proposed to estimate the spatial average of ∥E∥^β, where ∥E∥ denotes the magnitude of the local electric field E and β (β ≥ 3) is the nonlinear exponent. As an example, we recalculate the nonlinear susceptibilities of weakly nonlinear composites and find that our present results are very close to the simulation data.     

Pair approximation for polarization interaction: efficient method for Monte Carlo simulations of polarizable fluids

A new method is presented for the Monte Carlo simulations of polarizable models with induced dipole moments. This method updates induced dipole moments on all molecules when a single molecule is moved, without evaluating all pair interactions. Thus, depending on the number of molecules, it is 10–20 times faster than Monte Carlo simulations with full iteration. The efficiency makes it a powerful tool for the study of phase equilibria of polarizable models in grand canonical and Gibbs ensembles.     

第二玻恩近似理论研究激光辅助e-Ar散射

在电子入射方向平行于激光场的极化方向这种特殊的散射模式下，应用第二玻恩近似(SBA)理论，分别利用含有极化势的静电屏蔽势和单纯的静电屏蔽势这两种原子势模型对激光场中电子-氩原子散射进行了研究，并与低频近似和实验数据进行了比较.结果表明，第二玻恩近似理论给出的结果与实验符合较好.另外，极化势在激光辅助电子-原子散射中起着重要作用. 关键词： 极化势 第二玻恩近似 微分截面 激光场     

基于光斑二阶矩的阵列光束倾斜相差自适应控制方法

针对阵列光束相干合成中存在的倾斜相差大的问题,提出了基于合成光束远场光斑二阶矩的阵列光束倾斜相差自适应控制方法。以合成光束远场光斑二阶矩作为评价函数,理论上模拟了采用随机并行梯度下降算法实现7路光束的倾斜闭环控制过程。实验上搭建了7路光纤激光相干合成系统,利用自适应光纤准直器对倾斜相差进行校正。以合成光束远场光斑的二阶矩作为评价函数,采用随机并行梯度下降算法,实现了7路光束的倾斜的闭环控制,合成光束模拟远场光斑的桶中功率由0.05 V提升至1.95 V。实验中将倾斜扰动的增益系数变为与二阶矩相关的函数,实现了自适应变增益系数的倾斜闭环,在一定程度上提升了倾斜控制的带宽。从理论上和实验上验证了基于光斑二阶矩的倾斜相差自适应控制方法在光束合成及合成孔径探测领域应用的可行性。     

On the calculation of second order properties: An equation of motion approach

In the light of the equation of motion method a general expression for polarisability calculation has been derived. From this general expression, different approximation methods can be deduced for different choices of ground state and excitation manifold. Among these the coupled Hartree-Fock theory is the most extensively used one for polarisability calculations. It has also been shown that this theory has a simple relationship with random phase approximation.     

An efficient numerical method for time-dependent NLTE radiation transfer

We present a numerical method for performing coupled time-dependent radiation transfer and atomic rate equation calculations. The method incorporates the desirable features of time-dependent, non-local thermodynamic equilibrium (NLTE) radiation transfer calculations. It has the advantage that it allows existing time-dependent calculations to be adapted to model time dependent effects. The approximations which are used are discussed.Calculations have been performed for a highly ionised silicon plasma with a single optically thick line. The line is taken to have a top-hat profile which is independent of position. Although the model is simple, it serves to illustrate some important features of time-dependent calculations.     

An efficient method for solving highly anisotropic elliptic equations

Solving elliptic PDEs in more than one dimension can be a computationally expensive task. For some applications characterized by a high degree of anisotropy in the coefficients of the elliptic operator, such that the term with the highest derivative in one direction is much larger than the terms in the remaining directions, the discretized elliptic operator often has a very large condition number – taking the solution even further out of reach using traditional methods. This paper will demonstrate a solution method for such ill-behaved problems. The high condition number of the D-dimensional discretized elliptic operator will be exploited to split the problem into a series of well-behaved one and (D − 1)-dimensional elliptic problems. This solution technique can be used alone on sufficiently coarse grids, or in conjunction with standard iterative methods, such as Conjugate Gradient, to substantially reduce the number of iterations needed to solve the problem to a specified accuracy. The solution is formulated analytically for a generic anisotropic problem using arbitrary coordinates, hopefully bringing this method into the scope of a wide variety of applications.     

An efficient shooting method for fiber amplifiers and lasers

A simple shooting method is proposed for the design of distributed multi-pumped Raman fiber amplifiers (RFAs) and Yb-doped double-clad fiber lasers (DCFLs). Using the proposed method a distributed RFA with 10 pump sources and 1700 mW total input pump power is simulated and high-power Yb-doped DCFL rate equations are solved numerically. The numerical simulation results show that the proposed method has good convergence in the condition of increasing numbers and power of input pump sources.     

An efficient Jacobian scaling method for time-domain optical mammography

<正>Time-domain diffuse optical tomography can efficiently reconstruct optical parameters which can be further applied in diagnosing early breast cancer.Nevertheless,the performances of reconstructed imaging are badly influenced by different Jacobian magnitudes of absorption coefficient and reduced scattering coefficient.With the introudction of a relative data type based on generalized pulse spectrum technique, an efficient Jacobian scaling method is proposed.The interrelated simulated validation is also revealed for the enhancing performances.     

An efficient surrogate-based method for computing rare failure probability

In this paper, we present an efficient numerical method for evaluating rare failure probability. The method is based on a recently developed surrogate-based method from Li and Xiu [J. Li, D. Xiu, Evaluation of failure probability via surrogate models, J. Comput. Phys. 229 (2010) 8966–8980] for failure probability computation. The method by Li and Xiu is of hybrid nature, in the sense that samples of both the surrogate model and the true physical model are used, and its efficiency gain relies on using only very few samples of the true model. Here we extend the capability of the method to rare probability computation by using the idea of importance sampling (IS). In particular, we employ cross-entropy (CE) method, which is an effective method to determine the biasing distribution in IS. We demonstrate that, by combining with the CE method, a surrogate-based IS algorithm can be constructed and is highly efficient for rare failure probability computation—it incurs much reduced simulation efforts compared to the traditional CE-IS method. In many cases, the new method is capable of capturing failure probability as small as 10⁻¹² ∼ 10⁻⁶ with only several hundreds samples.