High-dimensional model representations generated from low order terms--lp-RS-HDMR

High-dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for improving the efficiency of deducing high dimensional input-output system behavior. RS-HDMR is a particular form of HDMR based on random sampling (RS) of the input variables. The component functions in an HDMR expansion are optimal choices tailored to the n-variate function f(x) being represented over the desired domain of the n-dimensional vector x. The high-order terms (usually larger than second order, or equivalently beyond cooperativity between pairs of variables) in the expansion are often negligible. When it is necessary to go beyond the first and the second order RS-HDMR, this article introduces a modified low-order term product (lp)-RS-HDMR method to approximately represent the high-order RS-HDMR component functions as products of low-order functions. Using this method the high-order truncated RS-HDMR expansions may be constructed without directly computing the original high-order terms. The mathematical foundations of lp-RS-HDMR are presented along with an illustration of its utility in an atmospheric chemical kinetics model.     

Non-iterative optimal design of quantum controls

A non-iterative means for quantum control design is introduced with the aim of offering practical designs that can later be fine-tuned with laboratory closed-loop techniques. The procedure recognizes that Hamiltonians for realistic system control applications are rarely known accurately. The algorithm takes advantage of this fact by allowing for managed deviations in the equations of motion, thus removing the standard Lagrange multiplier. Suitable time-dependent cost functional weights are introduced that eliminate the traditional final time matching condition, thereby producing non-iterative design equations as an initial value problem. Removal of the final time condition also eliminates the demand that the target state be reached at any artificially imposed time. Tests on a simple molecular system indicate that the algorithm leads to well-behaved designs and that the weight functions are adequately estimated by order of magnitude analysis. Received 30 June 2000 and Received in final form 22 November 2000     

Acousto-optical shaping of ultraviolet femtosecond pulses

This work demonstrates a simple method for ultraviolet (UV) acousto-optical pulse shaping of both spectral amplitude and phase. A fused-silica acousto-optical modulator is used to ensure high transmission and a high damage threshold at 400-nm center wavelength. The technique eliminates complications associated with the parametric transfer of the spectral phase of near-infrared pulses through a nonlinear process out to UV wavelengths, by separating the frequency doubling and shaping processes. Three illustrative applications of phase control are presented: the compensation of material dispersion, the generation of multiple pulse trains, and the generation of arbitrarily shaped pulse trains. Self-diffraction frequency-resolved optical gating is used to characterize the success of the technique.     

Quantum control implemented as combinatorial optimization

Optimal control theory provides a general means for designing controls to manipulate quantum phenomena. Traditional implementation requires solving coupled nonlinear equations to obtain the optimal control solution, whereas this work introduces a combinatorial quantum control (CQC) algorithm to avoid this complexity. The CQC technique uses a predetermined toolkit of small time step propagators in conjunction with combinatorial optimization to identify a proper sequence for the toolkit members. Results indicate that the CQC technique exhibits invariance of search effort to the number of system states and very favorable scaling upon comparison to a standard gradient algorithm, taking into consideration that CQC is easily parallelizable. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

脉冲控制量子系统的哈密顿量约化

探索了脉冲控制的含近简并能级的有限维量子系统的哈密顿量的约化．由一个非简并基态能级和几个近简并激发态能级组成的量子系统被一个短脉冲控制,目标是控制所有激发态的布居数之和．考虑了两个可以看成等价二能级系统的例子,当脉冲强度比较弱时,得到了原始系统和约化系统的简单关系;当脉冲强度比较强时,对于只含一个频率的脉冲,一阶近似的关系也是存在的．     

Exploring the top and bottom of the quantum control landscape

A controlled quantum system possesses a search landscape defined by the target physical objective as a function of the controls. This paper focuses on the landscape for the transition probability P(i → f) between the states of a finite level quantum system. Traditionally, the controls are applied fields; here, we extend the notion of control to also include the Hamiltonian structure, in the form of time independent matrix elements. Level sets of controls that produce the same transition probability value are shown to exist at the bottom P(i → f)=0.0 and top P(i → f)=1.0 of the landscape with the field and/or Hamiltonian structure as controls. We present an algorithm to continuously explore these level sets starting from an initial point residing at either extreme value of P(i → f). The technique can also identify control solutions that exhibit the desirable properties of (a) robustness at the top and (b) the ability to rapidly rise towards an optimal control from the bottom. Numerical simulations are presented to illustrate the varied control behavior at the top and bottom of the landscape for several simple model systems.     

Evolution of reactions on surfaces exhibiting defect structures

This paper considers the time and spatial dependent behavior of an active surface exposed to two reactants which may diffuse on the surface, desorb, and also react. The surface is assumed to contain defect structures corresponding to either inherent lattice faults or foreign material on the surface. A number of case studies are examined corresponding to different assumptions about the desorption and kinetic characteristics of the defect sites. The surface concentration profiles are examined to gain physical insight into the competing surface processes. The net effect of surface defects on chemical production rates was examined by integrating the local production rate over a test region on the surface. Of special interest was the study of the poisoning effect of the product species on the diffusion and reaction of the reactants. The reaction-diffusion equations of the models were solved by the alternating direction collocation technique which shows promise for providing an efficient numerical procedure capable of handling practical large scale problems.     

Sensitivity analysis in chemical kinetics: Recent developments and computational comparisons

The advantages and disadvantages of various methods of parametric sensitivity analysis in chemical kinetic modeling are discussed. Particular attention is given to estimates of computational labor for realistic problems, and quantitative comparisons are made utilizing a 52-reaction, 11-species CO oxidation mechanism. The authors′ CHEMSEN/AIM program compares favorably to other techniques in many circumstances, and provides the additional convenience of accepting input information in familiar chemical notation. This paper also reviews recent developments in theory of sensitivity analysis, relevant to chemical kinetic modeling.     

The scaling approach to multicenter molecular integrals with Slater-type orbitals

A scaling approach to multicenter molecular integrals with Slater-type orbitals (STOs) is presented. The result is significant in that it shows (1) the existence of a simple relationship between multicenter integrals and (2) an implied computational savings. Operation count estimates indicate that the significant savings would occur for a system having large numbers of STOs on each atom.