Memory fragmentation in buddy methods for dynamic storage allocation

Summary Methods are presented for the estimation of bounds on the memory fragmentation in buddy methods of dynamic storage allocation. These bounds, when compared with the results of simulation studies, are found to be sufficiently precise to be of considerable practical utility.     

Dynamic programming and quantum mechanical motion

In this article we show that quantum dynamics is the most natural generalization of classical dynamics from the point of view of optimal control. Employing the techniques of dynamic programming, we derive the Schrödinger equation starting from the Lagrangian defined in terms of Nelson's forward and backward velocities. The generalization to the relativistic case is also analyzed and the Klein Gordon Equation is similarly derived.     

Angular momentum in molecular quantum mechanical integral evaluation

Solid-harmonic derivatives of quantum-mechanical integrals over Gaussian transforms of scalar, or radial, atomic basis functions create angular momentum about each center. Generalized Gaunt coefficients limit the amount of cross differentiation for multi-center integrals to ensure that cross differentiation does not affect the total angular momentum. The generalized Gaunt coefficients satisfy a number of other selection rules, which are exploited in a new computer code for computing forces in analytic density-functional theory based on robust and variational fitting of the Kohn-Sham potential. Two-center exponents are defined for four or more solid-harmonic differentiations of matrix elements. Those differentiations can either build up angular momentum about the centers or give forces on molecular potential-energy surfaces, thus generalized Gaunt coefficients of order greater than the number of centers are considered. These 4-j generalized Gaunt coefficients and two-center exponents are used to compute the first derivatives of all integrals involving all the Gaussian exponents on a triplet of centers at once. First all angular factors are contracted with the corresponding part of the linear-combination-of-atomic-orbitals density matrix. This intermediate quantity is then reused for the nuclear attraction integral and the integrals corresponding to each basis function in the analytic fit of the Kohn-Sham potential in the muffin-tin-like, but analytic, Slater-Roothaan method that allows molecules to dissociate into atoms having any desired energy, including the experimental electronic energy. The energy is stationary in all respects and all forces precisely agree with a previous code in tests on small molecules. During geometry optimization of an icosahedral C₇₂₀ fullerene computing these angular factors and transforming them via the 4-j generalized Gaunt coefficient takes more than sixty percent of the total computer time. These same angular factors could be used in identical fashion with Gaussian transforms of Slater-type and numerical radial atomic orbitals.     

Linearization methods in classical and quantum mechanics

The applicability and accuracy of linearization methods for initial-value problems in ordinary differential equations are verified on examples that include the nonlinear Duffing equation, the Lane-Emden equation, and scattering length calculations. Linearization methods provide piecewise linear ordinary differential equations which can be easily integrated, and provide accurate answers even for hypersingular potentials, for which perturbation methods diverge. It is shown that the accuracy of linearization methods can be substantially improved by employing variable steps which adjust themselves to the solution.     

量子力学系统的输出反馈控制

研究量子系统输出反馈控制问题建模以及控制律设计问题.首先讨论了量子力学VonNeumann测量原理与连续测量模型的一致性;然后在连续测量模型的基础上总结了已有量子反馈模型的结果,归纳出量子输出反馈控制系统模型;最后针对单比特振幅退相干抑制问题,利用线性直接输出反馈控制设计反馈控制律,指出利用最优控制的方法设计线性输出反馈控制的比例系数,可以得到较好的结果.     

Parallel methods for high-dimensional quantum dynamics

In this communication we propose new schemes for parallelizing the bend matrix-vector product required to compute spectra, cross-sections, etc. using iterative methods. The new schemes are compared to those already in the literature and results demonstrating the advantage of our best scheme are given for . We find that the best scheme parallelizes over a single quadrature index. This enables one to exploit the favorable scaling product basis matrix-vector products.     

量子系统中状态估计方法的综述

从广泛用于实验量子领域的典型状态估计方法,到基于系统论观点、可用于量子反馈控制的状态估计方法,详细综述了4种测量方式下的相应量子状态估计方法及其适用背景.通过其发展历程的叙述,从本质上阐述了估计的基本原理,从技术上对各种方法进行了相应的分析和比较.同时,对量子状态估计和经典状态估计进行了相应的比较,并对量子系统中的状态估计方法作了总结.     

基于李雅普诺夫量子系统控制方法的状态调控

从多方面对基于李雅普诺夫的量子系统控制方法进行了系统深入地研究, 包括该方法与最优控制的关系; 李雅普诺夫函数与性能指标之间的关系; 几种常用李雅普诺夫函数下的控制所能解决的问题, 适用范围和所存在的问题等. 在此基础上, 结合量子系统本身所具有的特点, 分别针对本征态, 叠加态和混合态的制备与调控目标, 总结出多种不同控制问题的改进方案. 对不同改进方案的设计思想, 所能解决的问题, 物理意义及其适用范围等进行剖析, 系统化了一套基于李雅普诺夫稳定性理论对量子系统进行状态调控的设计方法.     

Nonlinear optimal control as quantum mechanical eigenvalue problems

A novel approach for approximating the nonlinear optimal feedback control of a system with a terminal cost is proposed. To lessen the difficulty due to nonlinearity, we try to treat the system in a framework of linear theories. For this, we assume a quantum mechanical linear wave associated with the system. Since the control system is constrained by state equations, we handle the system according to quantum mechanics of constrained dynamics. A Hamiltonian is represented as a linear operator acting on a function that describes behavior of waves. Subsequently, nonlinear feedback is calculated without any time integration in the backward direction. Using eigenvalues and eigenfunctions of the linear Hamiltonian operator, an optimal feedback law is given as a combination of analytic functions of time and state variables. We take as an example a system described by two scalar variables for state and control input. Simulation studies on the system by the eigenvalue analysis show that the proposed method reduces calculation time to nearly a tenth that of a numerical calculation of a Hamilton-Jacobi equation by a finite difference method.     

Lyapunov control methods of closed quantum systems

According to special geometric or physical meanings, the paper summarizes three Lyapunov functions in controlling closed quantum systems and their controller designing processes. Specially, for the average value-based method, the paper gives the generalized condition of the largest invariant set in the original reference and develops the construction method of the imaginary mechanical quantity; for the error-based method, this paper gives its strict mathematical proof train of thought on the asymptotic stability and the corresponding physical meaning. Also, we study the relations among the three Lyapunov functions and give a unified form of these Lyapunov functions. Finally, we compare the control effects of three Lyapunov methods by doing some simulation experiments.     

Predicted phototoxicities of carbon nano-material by quantum mechanical calculations

The purpose of this research was to develop a predictive model for the phototoxicity potential of carbon nanomaterials (fullerenols and single-walled carbon nanotubes). This model is based on the quantum mechanical (ab initio) calculations on these carbon-based materials and comparison of the triplet excited states of these materials to published work relating phototoxicity of polynuclear aromatic hydrocarbons (PAH) to their predictive triplet excited state energy. A successful outcome will add another tool to the arsenal of predictive methods for the U.S. EPA program offices as they assess the toxicity of compounds in use or coming into commerce.The basis of this research was obtaining the best quantum mechanical structure of the carbon nanomaterial and was fundamental in determining the triplet excited state energy. The triplet excited state, in turn, is associated with the phototoxicity of the material.This project relies heavily on the interaction of the predictive results (physical chemistry) and the experimental results obtained by biologists and toxicologists. The results of the experiments (toxicity testing) will help refine the predictive model, while the predictions will alert the scientists to red flag compounds. It is hoped that a guidance document for the U.S. EPA will be forthcoming to help determine the toxicity of compounds. This can be a screening tool that would rely on further testing for those compounds found by these predictions to be a phototoxic danger to health and the environment.     

发光纳米材料和量子点化学传感及其机理

介绍了荧光和磷光纳米材料的种类,如无机半导体量子点,金属离子掺杂的半导体量子点,金属纳米粒子或纳米簇,硅点,碳点和石墨烯点等。接着阐述了这些纳米材料的光致发光的光物理机制和猝灭或增强的一般性原理。最后简要综述了量子点或纳米材料发光的猝灭或增强现象在化学传感中的应用和具体的响应机理。     

Combined quantum mechanical and molecular mechanical reaction pathway calculation for aromatic hydroxylation by p-hydroxybenzoate-3-hydroxylase

The reaction pathway for the aromatic 3-hydroxylation of p-hydroxybenzoate by the reactive C4a-hydroperoxyflavin cofactor intermediate in p-hydroxybenzoate hydroxylase (PHBH) has been investigated by a combined quantum mechanical and molecular mechanical (QM/MM) method. A structural model for the C4a-hydroperoxyflavin intermediate in the PHBH reaction cycle was built on the basis of the crystal structure coordinates of the enzyme-substrate complex. A reaction pathway for the subsequent hydroxylation step was calculated by imposing a reaction coordinate that involves cleavage of the peroxide oxygen-oxygen bond and formation of the carbon-oxygen bond between the C3 atom of the substrate and the distal oxygen of the peroxide moiety of the cofactor. The geometric changes and the Mulliken charge distributions along the calculated reaction pathway are in line with an electrophilic aromatic substitution type of mechanism. The energy barrier of the calculated reaction is considerably lower when the substrate hydroxyl moiety is deprotonated, in comparison with the barrier found with a protonated hydroxyl moiety. This effect of the protonation state of the substrate on the calculated energy barrier supports experimental observations that deprotonation is required for hydroxylation of the substrate. A notable event in the calculated reaction pathway is a lengthening of the peroxide oxygen-oxygen bond at an intermediate stage. Further analysis of the reaction pathway indicates that this oxygen-oxygen bond elongation is accompanied by an increase in electrophilic reactivity on the distal oxygen of the peroxide moiety, which may assist the C-O bond formation in the reaction of the C4a-hydroperoxyflavin intermediate with the substrate. Analysis of the effect of individual active site residues on the reaction reveals a specific transition state stabilization by the backbone carbonyl moiety of Pro293. The crystal water 717 appears to drive the hydroxylation step through a stabilizing hydrogen bond interaction to the proximal oxygen of the C4a-hydroperoxyflavin intermediate, which increases in strength as the hydroperoxyflavin cofactor converts to the anionic (deprotonated) hydroxyflavin.     

Study of quantum correlation swapping with relative entropy methods

To generate long-distance shared quantum correlations (QCs) for information processing in future quantum networks, recently we proposed the concept of QC repeater and its kernel technique named QC swapping. Besides, we extensively studied the QC swapping between two simple QC resources (i.e., a pair of Werner states) with four different methods to quantify QCs (Xie et al. in Quantum Inf Process 14:653–679, 2015). In this paper, we continue to treat the same issue by employing other three different methods associated with relative entropies, i.e., the MPSVW method (Modi et al. in Phys Rev Lett 104:080501, 2010), the Zhang method (arXiv:1011.4333 [quant-ph]) and the RS method (Rulli and Sarandy in Phys Rev A 84:042109, 2011). We first derive analytic expressions of all QCs which occur during the swapping process and then reveal their properties about monotonicity and threshold. Importantly, we find that a long-distance shared QC can be generated from two short-distance ones via QC swapping indeed. In addition, we simply compare our present results with our previous ones.     

Selective control of the observables in the ensemble of quantum mechanical molecular systems

A new approach to synthesize algorithms for selective control of the observables in quantum mechanical systems in the presence of additional constraints during the whole period of control is proposed. Analytic results of achieving the goal of control under some additional assumptions were obtained. It was demonstrated that the error in achieving the goal of control is proportionate to the error in prescribing the initial state of system and the error in realizing the control action. Numerical results for the problem of selective control for energy of hydrogen molecules (H₂) with different isotopes are represented. The proposed algorithms are easy to design.     

Modeling catalytic mechanism of nitrile hydratase by semi-empirical quantum mechanical calculation

Nitrile hydratase (NHase) is an important industrial enzyme capable of converting nitriles to corresponding amides. Utilizing the method of semi-empirical quantum mechanical (QM) calculation by TRITON, the bioconversion process of acrylonitrile to acrylamide catalyzed by NHase was successfully performed on a computer. Crystal structure of a Co-type NHase from Pseudonocardia thermophila JCM 3095 (PDB code 1IRE) was selected as the target for acrylonitrile autodock. In silico calculations were performed on the NHase-acrylonitrile complex to simulate the enzyme catalysis mechanism by quantitatively comparing energy changes of each reaction pathway. Simulation results showed that active site activation is the first step of NHase catalysis, in which the Co2+ coordinated to a water molecule forms a Co-OH complex mediated by the oxidized alpha-CEA113. Then the oxygen atom in the Co-OH attacks the C atom in the -CN triple bond of acrylonitrile, forming a precursor of acrylamide. Consequently, proton rearrangement happens transforming the precursor into the final product of acrylamide, under the assistance of the hydrogen atom in the -OH group of alpha-SER112. Gibbs energy changes of three steps corresponding to the active center activation, nucleophilic attack and proton rearrangement are around -31, 23 and -12 kcal/mol, respectively.     

Asynchronous Schwarz methods applied to constrained mechanical structures in grid environment

This paper deals with the parallel solution of the stationary obstacle problem with convection–diffusion operator. The obstacle problem can be formulated by various ways and in the present study it is formulated like a multivalued problem. Another formulation by complementary problem is also considered. Appropriate discretization schemes are considered for the numerical solution on decentralised memory machines by using parallel synchronous and asynchronous Schwarz alternating algorithms. The considered discretization schemes ensure the convergence of the parallel synchronous or asynchronous Schwarz alternating methods on one hand for the solution of the multivalued problem and on the other hand for the solution of the complementary problem. Finally the implementation of the algorithms is described and the results of parallel simulations are presented.     

Construction of quantum states with special properties by projection methods

Quantum Information Processing - The Goldreich–Levin algorithm was originally proposed for a cryptographic purpose and then applied to learning. The algorithm is to find some larger Walsh...