Some software aspects of DAE simulation & optimization software

Considerable numerical software has been written for simulation and optimization of dynamical systems. From the beginning of their development, differential algebraic equations (DAEs) have often been proposed as a way to make modeling easier. The modeler need only write down equations relating the variables in the model. However, much DAE software requires at least as much user numerical and mathematical expertise as explicit methods. An important aspect of our research has been working toward helping the idea of DAEs achieve its promise in modeling and simulation by both pushing the software to handle more general problems and to also allow for less user expertise. Some recent examples are presented where this research impacts on software and their underlying algorithms. Space necessitates we assume the reader has a rough idea of what a DAE is. The examples are implicit Scicos, and optimization of DAE models. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solving the nonlinear least square problem: Application of a general method

An algorithm for solving the general nonlinear least-square problem is developed. An estimate for the Hessian matrix is constructed as the sum of two matrices. The first matrix is the usual first-order estimate used by the Gauss method, while the second matrix is generated recursively using a rank-one formula. Test results indicate that the method is superior to the standard Gauss method and compares favorably with other methods, especially for problems with nonzero residuals at the solution.This work was supported by the US Air Force under Contract No. F04701-73-C-0074.The author expresses his appreciation to Dr. H. E. Pickett and Dr. J. L. Searcy for their continuing support in the theoretical and practical development of the algorithm. The recursive method for generating the estimate of the Hessian matrix was developed jointly with Drs. Pickett and Searcy and is included here with their permission. The author would also like to acknowledge the contribution made by the stimulating environment of an optimal control seminar held at The Aerospace Corporation since 1970. Principle members of the seminar have been H. E. Pickett, J. L. Searcy, R. W. Reid, and the author.     

Fragment ion formation from n-alkanes and cycloalkanes by plasma desorption

The plasma desorption of hydrogen loss fragment ions from frozen films of several classes of aliphatic volatile hydrocarbons was investigated with ²⁵²Cf plasma desorption mass spectrometry. A time-of-flight instrument suitable for the reproducible sampling and analysis of volatile hydrocarbons in the solid state was designed for this study. Representative compounds from the n-alkanes and cycloalkanes were analyzed. For all the compounds studied, radical molecular ions. M^+., and hydrogen loss fragment ions, [M ? mH]⁺ with m varying from 1 to 10, were produced. The length of the alkane chain, the size of the alkane rings and the stability of the resulting H-loss ions affected the number and abundance of these ions. Smaller molecules underwent proportionally more hydrogen loss than larger molecules of the same class.     

Selection of a Trio of Different Selective Gas Chromatographic Stationary Phases, and Use of Retention Ratios Between Phase Pairs to Indicate Some Solute Structures: “MPMS” Liquid Crystal Polysiloxane Re-assessed

Summary MPMS is a commercially marketed capillary liquid crystal Mesogenic Polymeric Methyl (poly-) Siloxane stationary phase which is selective to solute molecular shapes. It is chemically different to other types of molecularly selective phases, such as the peptide methyl-polysiloxane Chirasil-Val and the various modified cyclodextrins (CD). This study measures how different in chromatographic behaviour are the phase trio of a CD to be selected here, and the above two methyl polysiloxanes. Ten selected solutes from volatile oils are used to record relative retentions to n-undecane on each phase, and these are used in a procedure previously itemised for Chirasil-Val to seek the lowest correlation coefficients between results for pairs of phases, which leads to Chiraldex G-DA being the selected most different CD (out of 14) to MPMS and Chirasil-Val. Another 21 solutes are also examined on this phase trio, and retention ratios of the 31 solutes between pairs of phases are calculated. These are indicative of an unknown solute being an aromatic substance, or a bicyclic monoterpenoid.     

Comparison of three diacetyl-cyclodextrin gas chromatographic stationary phases: Possible indicators of the chemical nature of constituents of volatile oils

Summary Relative retention times (RR) versusn-undecane for thirty solutes from volatile oils are determined for Alpha-, Beta- and Gamma-Dex 225 capillaries. These are diacetyl-cyclodextrin phases to which some solutes respond as though they were conventional phases. However, lowest RR of the three on Beta-Dex 225 indicates a bicyclic terpenoid. Highest RR on this phase can be by an aromatic, or an acyclic terpenoid. Lowest values of correlation coefficients between pairs of variously modified-cyclodextrins for RR of ten selected diverse solutes occur with combinations of any one-Dex 225 phase, indicating that these are desirably different to many other modified-CDs, although not to each other.     

RCM-based synthesis of a variety of beta-C-glycosides and their in vitro anti-solid tumor activity

The synthesis of a number of biologically relevant C-glycosides has been carried out through the use of an esterification-ring-closing metathesis (RCM) strategy. The required acid precursors were readily prepared via a number of standard chemical transformations followed by dehydrative coupling of these acids with several olefin alcohols 1 to yield the precursor esters 3 in excellent yield. Methylenation of the esters 3 was followed by RCM and in situ hydroboration-oxidation of the formed glycals to furnish the protected beta-C-glycosides 6 in good overall yield. Several examples were converted to the corresponding C-glycoglycerolipids 17 and subsequently screened against solid-tumor cell lines for in vitro differential cytotoxicity.     

Osmium's Debye temperature

Osmium's Debye characteristic temperature Θ_D remains uncertain. We tabulate 20 reported values that average 411±94 K, for a property that one should know within about 1%. We report a new value derived from low-temperature monocrystal elastic-constant measurements extrapolated to 0 K: Θ_D=477±2 K. Our value disagrees with all previous reports except one specific-heat measurement. It agrees with Mendeleev-table expectations and with an a priori calculation.     

Longitudinal double-spin asymmetry for inclusive jet production in p[over -->] + p[over -->] collisions at sqrt[s]=200 GeV

We report a new STAR measurement of the longitudinal double-spin asymmetry A(LL) for inclusive jet production at midrapidity in polarized p + p collisions at a center-of-mass energy of sqrt[s]=200 GeV. The data, which cover jet transverse momenta 5相似文献