压缩感知理论在矩量法中的应用

矩阵填充与线性方程组求解是矩量法中最耗计算资源的环节.为提高计算效率,提出了一种基于压缩感知理论的矩量法的改进方法.通过引入稀疏变换矩阵实现对待求响应的稀疏表示,从而可在压缩感知理论框架下构造欠定方程,并优化求解.数值仿真实验结果表明:该方法不仅可以减小矩阵填充计算量,还可以有效提高解的求解效率.     

复式格子上无规行走问题的一种处理方法

本文中通过引入格子无规行走的结构因子矩阵,推广了生成函数技术,提出一种可以处理具有复杂元胞结构的格子无规行走问题的理论方法。为说明这一方法的有效性以及如何运用这一方法,本文求解了一维无限二聚化链上的无规行走问题。 关键词：     

长周期光纤光栅透射谱计算方法的比较与分析

长周期光纤光栅透射谱的求解方法有多种,本文以耦合模理论为基础,对常用的积分法、公式法、传输矩阵法求解长周期光纤光栅的透射谱进行比较与分析,指出这三种求解方法各自的特点和适用条件.积分法可在较宽波长范围内直接得到多个模式透射谱的精确解,但求解过程繁琐,运算量大;公式法虽然在表述和计算上较为方便,但只能在较小波长范围内直接求解单个模式的透射谱;传输矩阵法求解过程简便、准确度高、计算量相对较小,特别适合计算一些非均匀光纤光栅的透射谱.该研究为选择一种精确度高且理论和计算都较简单的计算长周期光纤光栅透射谱的方法提供理论依据.     

长周期光纤光栅透射谱计算方法的比较与分析

长周期光纤光栅透射谱的求解方法有多种,本文以耦合模理论为基础,对常用的积分法、公式法、传输矩阵法求解长周期光纤光栅的透射谱进行比较与分析,指出这三种求解方法各自的特点和适用条件.积分法可在较宽波长范围内直接得到多个模式透射谱的精确解,但求解过程繁琐,运算量大;公式法虽然在表述和计算上较为方便,但只能在较小波长范围内直接求解单个模式的透射谱;传输矩阵法求解过程简便、准确度高、计算量相对较小,特别适合计算一些非均匀光纤光栅的透射谱.该研究为选择一种精确度高且理论和计算都较简单的计算长周期光纤光栅透射谱的方法提供理论依据.     

一种欠驱动两级柔性自平衡机器人的建模及其最优控制

文章以一种欠驱动两级柔性自平衡机器人这一被控对象的控制问题作为出发点,详细阐述了其数学建模方法,讨论了其最优控制策略,并针对设计过程中出现的LQ加权矩阵Q的选取难题给出了一种解析解和证明,同时运用这一结论计算出了实际问题的加权矩阵Q,从而求得最优的状态反馈矩阵K;仿真结果表明,这样一种加权矩阵Q的求解方法是有效的,并能够在较为复杂的实际问题中获得应用。     

水平变化波导中一种声场计算方法的数值实现

全局矩阵方法计算水平变化环境中的声场具有稳定性好、速度快、精度高等优点,在数值实现中如何快速、准确的求解大规模矩阵是该方法的一个关键问题。本文针对全局矩阵的特点,分别利用两种矩阵求解器,PARDISO和LAPACK,求解该问题。经过比较和讨论,得出结论:LAPACK对于全局矩阵的求解更有优势,求解速度快,而且可求解问题规模相对较大。使用不同的数值实现方法计算了楔形波导的传播损失(ASA标准问题),与解析解比较,证明全局矩阵方法计算精度很高。     

基于成像矩阵的物数据求解方法

提出了一种利用成像矩阵求解物数据的方法。通过对物、像矩阵的一维化处理,构建了二维成像矩阵,将物矩阵卷积点扩散函数矩阵得到像矩阵的卷积运算关系转变为物向量乘以成像矩阵进而得到像向量的乘积运算关系。最后将像向量乘以成像逆矩阵便可求解物向量,实现了从光学系统像数据中对物数据的精确求解,且计算误差为10-12量级。     

中子输运方程源项反演的瑞利商迭代算法

中子输运方程源项反演问题中,有效倍增因子的求解经过球谐函数展开和差分离散后,转化为求解大型矩阵的特征值问题.针对矩阵的特点,利用Gerschgorin圆盘定理,给出反幂法迭代初值的选取方法,并进行相应的扰动分析.针对有效倍增因子是矩阵最大特征值的特点,采用瑞利商迭代算法进行求解.理论和算例表明,该方法不需选取特定初值,达到三阶收敛速度.     

近尾迹流动的数值模拟

通过数值求解可压缩Navier-Stokes方程的方法来模拟近尾迹的分离流动。Navier-Stokes方程^[1]是利用中所给出的方法进行差分逼近的。这一方法兼备显式格式和隐式格式的优点。这是一隐式格式,因而可放松稳定性对时间步长的限制。这一格式又具有显式格式的简单性,差分方程的解可显式表达出来。求解过程中避免了通常隐式格式所要求的大量数值矩阵求逆和大量的矩阵运算。文中对不同的马赫数M_∞和雷诺数Re进行了计算。数值实验表明,本文所采用的方法是模拟底部分离流动的一个简单而有效的方法,可用来计算高马赫数和高雷诺数的分离流动。     

用矩阵方法设计变焦镜头

传统上，在设计变焦距镜头时都要利用高斯光学求解变焦距的各组元焦距、组间隔。与传统方法不同的是，该文利用矩阵光学理论，建立变焦距镜头的光线传输矩阵，并以此矩阵建立非线性方程组，然后用数学软件对其求解，得到各组元的焦距、组间隔等参数。最后以设计一个普通的摄像物镜为例，演示了矩阵光学在设计变焦距镜头中的应用。     

Mixed-system brain dynamics: Neural memory as a macroscopic ordered state

The paper reviews the current situation regarding a new theory of brain dynamics put forward by the authors in an earlier publication. Motivation for the theory is discussed in terms of two issues: the long-standing problem of accounting for the stability and nonlocal properties of memory, and the experimental and theoretical evidence against the classical theory of brain action. It is shown that the new theory provides an explanation and a conceptually unifying framework for phenomena of brain action that resist classical explanation. Further independent experiments provide strong additional support for the theory. The fact that this theory incorporates quantum mechanisms in an essential way is considered to be of wide scientific interest in view of the unique status of the brain in relation to the physical, biological, and mental orders in nature.     

An application of cell theory to molecular models of n-alkane solids

Solid phase properties for hard sphere chain molecular models of n-alkanes are calculated using the cell theory, and a numerical method for implementation of cell theory for chain molecules is described. Good agreement with Monte Carlo simulations for solid phase properties is obtained from the theory. By using cell theory for the solid phase and an equation of state for the fluid phase, solid-phase equilibrium can be calculated. The predictions are in quite good agreement with Monte Carlo simulation results. Cell theory is used to assess the impact of an approximate treatment used in earlier work for the effect of the temperature dependence of the molecular flexibility upon the solid phase properties of a hard chain model with a realistic torsional potential.     

Stabilizer Notation for Spekkens’ Toy Theory

Spekkens has introduced a toy theory (Spekkens in Phys. Rev. A 75(3):032110, 2007) in order to argue for an epistemic view of quantum states. I describe a notation for the theory (excluding certain joint measurements) which makes its similarities and differences with the quantum mechanics of stabilizer states clear. Given an application of the qubit stabilizer formalism, it is often entirely straightforward to construct an analogous application of the notation to the toy theory. This assists calculations within the toy theory, for example of the number of possible states and transformations, and enables superpositions to be defined for composite systems.     

Can stochastic physics be a complete theory of nature?

The prospects for a complete stochastic theory of microscopic phenomena are considered. The two traditional schools of stochastic physics, the diffusion process school and the zero-point electromagnetic field school, are reviewed. A completely relativistic theory, stochastic field theory, is proposed as an extension of the ideas of these two schools. Within the context of stochastic field theory we present the following new results: an elementary stochastization scheme which produces the zero-point electromagnetic field; a physical interpretation of the mathematical methods developed by Lukosz for calculating zero-point energies; a calculation of the first-order Lamb shift which generalizes that of Welton; a new setting for a finite-temperature theory; and comments on the bag model for quark confinement.Research financed in part by Colciencias.     

The fractional quantum Hall effect: Chern-Simons mapping,duality, Luttinger liquids and the instanton vacuum

We derive, from first principles, the complete Luttinger liquid theory of abelian quantum Hall edge states. This theory includes disorder and Coulomb interactions as well as the coupling to external electromagnetic fields. We introduce a theory of spatially separated edge modes, find an enlarged dual symmetry and obtain a complete classification of quasiparticle operators and tunneling exponents. The chiral anomaly on the edge is used to obtain unambiguously the Hall conductance. In resolving the problem of counter-flowing edge modes, we find that the long range Coulomb interactions play a fundamental role. In order to set up a theory for arbitrary ν we use the idea of a two-dimensional network of percolating edge modes. We derive an effective, single mode Luttinger liquid theory for tunneling processes into the edge which yields a continuous tunneling exponent 1/ν. The network approach is also used to re-derive the instanton vacuum theory for plateau transitions.     

Time-dependent density functional theory of classical fluids

We establish a rigorous time-dependent density functional theory of classical fluids for a wide class of microscopic dynamics. We obtain a stationary action principle for the density. We further introduce an exact practical scheme, to obtain hydrodynamical effects in density evolution, that is analogous to the Kohn-Sham theory of quantum systems. Finally, we show how the current theory recovers existing phenomenological theories in an adiabatic limit.     

Systematic low-energy effective theory for magnons and charge carriers in an antiferromagnet

By electron or hole doping quantum antiferromagnets may turn into high-temperature superconductors. The low-energy dynamics of antiferromagnets are governed by their Nambu–Goldstone bosons—the magnons—and are described by an effective field theory analogous to chiral perturbation theory for the pions in strong interaction physics. In analogy to baryon chiral perturbation theory—the effective theory for pions and nucleons—we construct a systematic low-energy effective theory for magnons and electrons or holes in an antiferromagnet. The effective theory is universal and makes model-independent predictions for the entire class of antiferromagnetic cuprates. We present a detailed analysis of the symmetries of the Hubbard model and discuss how these symmetries manifest themselves in the effective theory. A complete set of linearly independent leading contributions to the effective action is constructed. The coupling to external electromagnetic fields is also investigated.     

Memory function for dressed particles

This paper is concerned with the calculation of the memory function and derivation of a kinetic equation for one-body phase space correlation functions. The theory uses a one-body additive projection operator and a division of the Liouville operator with an unperturbed part that describes dressed particles. Binary collisions are neglected, for the theory aims at describing the screening and backflow effects of a type contained in the plasma kinetic theory of Balescu and Lenard. We obtain an explicit kinetic equation which is an improvement of these theories for the plasma case, and involves the exact equilibrium pair and triplet distributions. The equation also describes systems with strong short-range forces and shows how the screening effects occur in this case as well. The unifying function is the direct correlation function. The theory is meant to provide understanding for a more complete theory of fluids where a proper account is given of close collisions.Work supported by National Science Foundation, Grant No. GH 35691.     

Kochen-Specker Theorem as a Precondition for Quantum Computing

We study the relation between the Kochen-Specker theorem (the KS theorem) and quantum computing. The KS theorem rules out a realistic theory of the KS type. We consider the realistic theory of the KS type that the results of measurements are either +1 or ?1. We discuss an inconsistency between the realistic theory of the KS type and the controllability of quantum computing. We have to give up the controllability if we accept the realistic theory of the KS type. We discuss an inconsistency between the realistic theory of the KS type and the observability of quantum computing. We discuss the inconsistency by using the double-slit experiment as the most basic experiment in quantum mechanics. This experiment can be for an easy detector to a Pauli observable. We cannot accept the realistic theory of the KS type to simulate the double-slit experiment in a significant specific case. The realistic theory of the KS type can not depicture quantum detector. In short, we have to give up both the observability and the controllability if we accept the realistic theory of the KS type. Therefore, the KS theorem is a precondition for quantum computing, i.e., the realistic theory of the KS type should be ruled out.