Numerical treatment of a parabolic boundary-value control problem

The purpose of this paper is to present a method to compute optimal controls for a class of one-dimensional heat-diffusion processes. The approach used is in the spirit of the Ritz method and approximates the given problem with simpler tasks which are solved by means of algorithms based on the principles of semi-infinite programming. General convergence properties of the procedures are shown. Some illustrative numerical examples are also given.This research was supported by NSF Grant No. GK-31833 and by The Swedish Institute of Applied Mathematics, Stockholm, Sweden.     

Boundary element numerical method for the electric field generated by oblique multi-needle electrodes

According to the electric potential of oblique multi-needle electrodes (OMNE) in biological tissue, the discrete equations based on the indetermination linear current density were established by the boundary element integral equations (BEIE). The non-uniform distribution of the current flowing from multi-needle electrodes to conductive biological tissues was imaged by solving a set of linear equations. Then, the electric field and potential generated by OMNE in biological tissues at any point may be determined through the boundary element method (BEM). The time of program running and stability of computing method are examined by an example. It demonstrates that the algorithm possesses a quick speed and the steady computed results. It means that this method has an important referenced significance for computing the field and the potential generated by OMNE in bio-tissue, which is a fast, effective and accurate computing method. Supported by the Natural Science Foundation of Beijing (Grant No. 1083011), the National Natural Science Foundation of China (Grant No. 10705049), and the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality     

Wavelet Transformation and Wigner-Husimi Distribution Function

We find that the optical wavelet transformation can be used to study the Husimi distribution function in phase space theory of quantum optics. We prove that the Husimi distribution function of a quantum state |ψ〉 is just the modulus square of the wavelet transform of with ψ(x) being the mother wavelet up to a Gaussian function. Thus a convenient approach for calculating various Husimi distribution functions of miscellaneous quantum states is presented.     

Extended structures and new infinite-dimensional hidden symmetries for the Einstein–Maxwell-dilaton-axion theory with multiple vector fields

A so-called extended elliptical-complex (EEC) function method is proposed and used to further study the Einstein–Maxwell-dilaton-axion theory with p vector fields (EMDA-p theory, for brevity) for . An Ernst-like matrix EEC potential is introduced and the motion equations of the stationary axisymmetric EMDA-p theory are written as a so-called Hauser–Ernst-like self-dual relation for the EEC matrix potential. In particular, for the EMDA-2 theory, two Hauser–Ernst-type EEC linear systems are established and based on their solutions some new parametrized symmetry transformations are explicitly constructed. These hidden symmetries are verified to constitute an infinite-dimensional Lie algebra, which is the semidirect product of the Kac–Moody algebra and Virasoro algebra (without centre charges). These results show that the studied EMDA-p theories possess very rich symmetry structures and the EEC function method is necessary and effective.     

Delay of terminal current in systems with abruptly changed Hamiltonian

The current response for the parameter change of a mesoscopic system is a practical issue for future's circuit design. Nowadays most considered cases are various types of bias modulation, while the effect of change of conductor Hamiltonian is seldom addressed. In this paper, we investigate the response of ballistic transport induced by a sudden change of the conductor Hamiltonian. We formulize the terminal current in language of non-equilibrium Green's function. Our method is applied to one-dimensional tight-binding chains and we find that the terminal current has a delay to the Hamiltonian change. The amount of delay is not determined by the velocity of incident electrons in the bias window, but depends on the tight-binding hopping energy γ. The delay of current response at the detecting point away from where the Hamiltonian changes is $C{\gamma }^{?1}$, where C is a constant independent of the system.     

A bonding evolution theory study on the catalytic Noyori hydrogenation reaction

ABSTRACT

The electronic rearrangements involved in Noyori hydrogenation reactions with double bonds (ethene and formaldehyde) are analysed using the bonding evolution theory. The study and analysis of the changes on the electron localisation function topology along a given reaction path reveals fluxes of electron density, allowing to unambiguously identify the main chemical events happening along the chemical reactions. This analysis shows that the first hydrogen transfer (with hydride character) occurs before the transition state (TS), while the second hydrogen transfer (with proton character) takes places after having reached the TS. The lower energy barrier found for formaldehyde over ethene is explained by two reasons. First, the hydride transfer is favoured for the C?=?O bond over C?=?C due to the electrophilic character of the carbon atom. Second, a negatively charged CH₃–X (X?=?CH₂, O) hidden intermediate is formed in the proximities of the TS region. The oxygen atom is able to stabilise this negatively charged species more effectively than the CH₂ group due to its higher electronegativity and the presence of V(O) lone pairs. The obtained analysis explains and rationalises catalyst chemoselectivity (C?=?O vs. C?=?C). Finally, a curly arrow representation diagram accounting for the electronic rearrangements is proposed on the basis of BET results.     

磁流体力学湍流的一些规律

本文从处理湍流场的普遍方法──“任一物理量都可分解成平均值与涨落值之和”出发，利用量纲估计和磁流体力学湍流近似对磁流体力学基本方程进行讨论，得出有关磁流体力学湍流场的一些结论．这些结论对研究目前阶段的磁流体力学湍流理论是很有用的。     

流体的塔阱状态方程及其对迁移性质的推算

流体的塔阱状态方程及其对迁移性质的推算曾向东，严家（哈尔滨工业大学能源科学与工程学院哈尔滨１５０００６）牛文科，韩立中（哈尔滨船舶锅炉涡轮机研究所哈尔滨）关键词势能模型，配分函数，状态方程，平衡性质，迁移性质１流体的塔阱状态方程Ｐｒｉｇｏｇｉｎｅ认为...     

Implementation of an algorithm for detecting patterns in defocused scenes using binary joint transform correlation

An original method to detect images in defocused scenes by means of a binary joint transform correlation is presented. Defocused images are described in frequency domain as the product between the Fourier transform of the in-focus scene by the optical transfer function of the imaging lens. This function, which presents positive and negative values, introduces sign errors in the joint power spectrum. The goal of this study is to detect the sign of the optical transfer function starting from the defocused image by means of a digital algorithm. Information provided by the algorithm allows to compensate the sign errors in the binary joint power spectrum and to obtain invariant correlations with respect to defocusing. Theoretical analysis and digital experiments to test the procedure are provided.     

Solution of Time-Dependent Diffusion Equations with Variable Coefficients Using Multiwavelets

A new numerical algorithm is developed for the solution of time-dependent differential equations of diffusion type. It allows for an accurate and efficient treatment of multidimensional problems with variable coefficients, nonlinearities, and general boundary conditions. For space discretization we use the multiwavelet bases introduced by Alpert (1993,SIAM J. Math. Anal.24, 246–262), and then applied to the representation of differential operators and functions of operators presented by Alpert, Beylkin, and Vozovoi (Representation of operators in the multiwavelet basis, in preparation). An important advantage of multiwavelet basis functions is the fact that they are supported only on non-overlapping subdomains. Thus multiwavelet bases are attractive for solving problems in finite (non periodic) domains. Boundary conditions are imposed with a penalty technique of Hesthaven and Gottlieb (1996,SIAM J. Sci. Comput., 579–612) which can be used to impose rather general boundary conditions. The penalty approach was extended to a procedure for ensuring the continuity of the solution and its first derivative across interior boundaries between neighboring subdomains while time stepping the solution of a time dependent problem. This penalty procedure on the interfaces allows for a simplification and sparsification of the representation of differential operators by discarding the elements responsible for interactions between neighboring subdomains. Consequently the matrices representing the differential operators (on the finest scale) have block-diagonal structure. For a fixed order of multiwavelets (i.e., a fixed number of vanishing moments) the computational complexity of the present algorithm is proportional to the number of subdomains. The time discretization method of Beylkin, Keiser, and Vozovoi (1998, PAM Report 347) is used in view of its favorable stability properties. Numerical results are presented for evolution equations with variable coefficients in one and two dimensions.