Optimal control computation for linear time-lag systems with linear terminal constraints

A computational scheme using the technique of control parameterization is developed for solving a class of optimal control problems involving linear hereditary systems with bounded control region and linear terminal constraints. Several examples have been solved to illustrate the efficiency of the technique.The authors wish to thank Dr. B. D. Craven for pointing out an error in an earlier version of this paper.From January 1985, Associate Professor, Department of Industrial and Systems Engineering, National University of Singapore, Kent Ridge, Singapore.     

Polynomial-based non-uniform interpolatory subdivision with features control

Starting from a well-known construction of polynomial-based interpolatory 4-point schemes, in this paper we present an original affine combination of quadratic polynomial samples that leads to a non-uniform 4-point scheme with edge parameters. This blending-type formulation is then further generalized to provide a powerful subdivision algorithm that combines the fairing curve of a non-uniform refinement with the advantages of a shape-controlled interpolation method and an arbitrary point insertion rule. The result is a non-uniform interpolatory 4-point scheme that is unique in combining a number of distinctive properties. In fact it generates visually-pleasing limit curves where special features ranging from cusps and flat edges to point/edge tension effects may be included without creating undesired undulations. Moreover such a scheme is capable of inserting new points at any positions of existing intervals, so that the most convenient parameter values may be chosen as well as the intervals for insertion.Such a fully flexible curve scheme is a fundamental step towards the construction of high-quality interpolatory subdivision surfaces with features control.     

A molecular mechanics force field for lignin

A CHARMM molecular mechanics force field for lignin is derived. Parameterization is based on reproducing quantum mechanical data of model compounds. Partial atomic charges are derived using the RESP electrostatic potential fitting method supplemented by the examination of methoxybenzene:water interactions. Dihedral parameters are optimized by fitting to critical rotational potentials and bonded parameters are obtained by optimizing vibrational frequencies and normal modes. Finally, the force field is validated by performing a molecular dynamics simulation of a crystal of a lignin fragment molecule and comparing simulation-derived structural features with experimental results. Together with the existing force field for polysaccharides, this lignin force field will enable full simulations of lignocellulose.     

The Generalized Parameterization Procedure for Semiempirical MO Method and Calculation of ionization Potentials for the Fourth-Period Element Molecules

This study presents a set of the generalized parameters from a unique resource for the elements which are from the first-period to the fourth-period (H to Xe). In addition, these series of parameters are used to examine forty-five compounds consisting of the fourth-period elements and the second-period transition metal elements. Herein, the major calculation theory applied is the s-p-d INDO MO method. To verify the reliability of the molecular calculations, similar calculations of the STO-3G and STO-3G* ab inito methods, along with the semiempirical PM3 and AM1 methods are also compared. Results in this study demonstrate that the s-p-d INDO MO computed with the generalized parameter is the best available method.     

A biomolecular force field based on the free enthalpy of hydration and solvation: the GROMOS force-field parameter sets 53A5 and 53A6

Successive parameterizations of the GROMOS force field have been used successfully to simulate biomolecular systems over a long period of time. The continuing expansion of computational power with time makes it possible to compute ever more properties for an increasing variety of molecular systems with greater precision. This has led to recurrent parameterizations of the GROMOS force field all aimed at achieving better agreement with experimental data. Here we report the results of the latest, extensive reparameterization of the GROMOS force field. In contrast to the parameterization of other biomolecular force fields, this parameterization of the GROMOS force field is based primarily on reproducing the free enthalpies of hydration and apolar solvation for a range of compounds. This approach was chosen because the relative free enthalpy of solvation between polar and apolar environments is a key property in many biomolecular processes of interest, such as protein folding, biomolecular association, membrane formation, and transport over membranes. The newest parameter sets, 53A5 and 53A6, were optimized by first fitting to reproduce the thermodynamic properties of pure liquids of a range of small polar molecules and the solvation free enthalpies of amino acid analogs in cyclohexane (53A5). The partial charges were then adjusted to reproduce the hydration free enthalpies in water (53A6). Both parameter sets are fully documented, and the differences between these and previous parameter sets are discussed.     

Deriving effective mesoscale potentials from atomistic simulations

We demonstrate how an iterative method for potential inversion from distribution functions developed for simple liquid systems can be generalized to polymer systems. It uses the differences in the potentials of mean force between the distribution functions generated from a guessed potential and the true distribution functions to improve the effective potential successively. The optimization algorithm is very powerful: convergence is reached for every trial function in few iterations. As an extensive test case we coarse-grained an atomistic all-atom model of polyisoprene (PI) using a 13:1 reduction of the degrees of freedom. This procedure was performed for PI solutions as well as for a PI melt. Comparisons of the obtained force fields are drawn. They prove that it is not possible to use a single force field for different concentration regimes.     

Q-fit: a probabilistic method for docking molecular fragments by sampling low energy conformational space

A new method is presented that docks molecular fragments to a rigid protein receptor. It uses a probabilistic procedure based on statistical thermodynamic principles to place ligand atom triplets at the lowest energy sites. The probabilistic method ranks receptor binding modes so that the lowest energy ones are sampled first. This allows constraints to be introduced to limit the depth of the search leading to a computationally efficient method of sampling low energy conformational space. This is combined with energy minimization of the initial fragment placement to arrive at a low energy conformation for the molecular fragment. Two different search methods are tested involving (i) geometric hashing and (ii) pose clustering methods. Ten molecular fragments were docked that have commonly been used to test docking methods. The success rate was 8/10 and 10/10 for generating a close solution ranked first using the two different sampling procedures. In general, all five of the top ranked solutions reproduce the observed binding mode, which increases confidence in the predictions. A set of ten molecular fragments that have previously been identified as problematic were docked. Success was achieved in 3/10 and 4/10 using the two different methods. Again there is a high level of agreement between the two methods and again in the successful cases the top ranked solutions are correct whilst in the case of the failures none are. The geometric hashing and pose clustering methods are fast averaging 13 and 11 s per placement respectively using conservative parameters. The results are very encouraging and will facilitate the process of finding novel small molecule lead compounds by virtual screening of chemical databases.     

半干旱草原下垫面动量和感热总体输送系数参数化关系研究

本文利用锡林郭勒草原2008年春季近地层涡旋相关系统和铁塔的风、 温平均梯度观测资料, 分析了总体输送系数随梯度Richardson数的变化特征, 建立了动量总体输送系数随大气稳定度、近地层风速以及感热总体输送系数随大气稳定度和近地层气温的关系. 中性条件下, 半干旱草原植被下垫面动量总体输送系数与近地层大气动力状态之间存在明显的相互作用, 总体输送系数与近地面层风速之间满足二次曲线拟合关系; 风速较小时, 大气动力特征对地表粗糙度长度的改变不是很明显, 动量总体输送系数随气流增强而增大; 而当风速较大时, 强风速会使植被高度发生改变, 动量总体输送系数随气流增强而减小. 另外, 感热总体输送系数与近地层气温之间也存在二次曲线关系. 动量总体输送系数与近地层风速之间的关系、感热总体输送系数与近地层气温之间关系的建立为总体输送系数参数化提供了重要途径, 同时该方案避免了对动力学粗糙度长度和热力学粗糙度长度的求解. 关键词： 总体输送系数 参数化 湍流通量 相似性函数     

MATCH: an atom-typing toolset for molecular mechanics force fields

We introduce a toolset of program libraries collectively titled multipurpose atom-typer for CHARMM (MATCH) for the automated assignment of atom types and force field parameters for molecular mechanics simulation of organic molecules. The toolset includes utilities for the conversion of multiple chemical structure file formats into a molecular graph. A general chemical pattern-matching engine using this graph has been implemented whereby assignment of molecular mechanics atom types, charges, and force field parameters are achieved by comparison against a customizable list of chemical fragments. While initially designed to complement the CHARMM simulation package and force fields by generating the necessary input topology and atom-type data files, MATCH can be expanded to any force field and program, and has core functionality that makes it extendable to other applications such as fragment-based property prediction. In this work, we demonstrate the accurate construction of atomic parameters of molecules within each force field included in CHARMM36 through exhaustive cross validation studies illustrating that bond charge increment rules derived from one force field can be transferred to another. In addition, using leave-one-out substitution it is shown that it is also possible to substitute missing intra and intermolecular parameters with ones included in a force field to complete the parameterization of novel molecules. Finally, to demonstrate the robustness of MATCH and the coverage of chemical space offered by the recent CHARMM general force field (Vanommeslaeghe, et al., J Comput Chem 2010, 31, 671), one million molecules from the PubChem database of small molecules are typed, parameterized, and minimized.     

An automated approach for the parameterization of accurate intermolecular force‐fields: Pyridine as a case study

An automated protocol is proposed and validated, which integrates accurate quantum mechanical calculations with classical numerical simulations. Intermolecular force fields, (FF) suitable for molecular dynamics (MD) and Monte Carlo simulations, are parameterized through a novel iterative approach, fully based on quantum mechanical data, which has been automated and coded into the PICKY software, here presented. The whole procedure is tested and validated for pyridine, whose bulk phase, described through MD simulations performed with the specifically parameterized FF, is characterized by computing several of its thermodynamic, structural, and transport properties, comparing them with their experimental counterparts. © 2011 Wiley Periodicals, Inc.