Geometric critical exponent inequalities for general random cluster models

A set of new critical exponent inequalities,d(1 –1 /)2 –, dv(1 – 1/), andd> 1, is proved for a general class of random cluster models, which includes (independent or dependent) percolations, lattice animals (with any interactions), and various stochastic cluster growth models. The inequalities imply that the critical phenomena in the models are inevitably not mean-field-like in the dimensions one, two, and three.The present work was reported at the 56th Statistical Mechanics Meeting (Rutgers, December 1986).     

A class of interaction-round-a-face models and its equivalence with an ice-type model

A new model (called the Temperley-Lieb interactions model) is introduced, in two-dimensional lattice statistics, on a square lattice . The Temperley-Lieb equivalence of this model to the six-vertex, self-dual Potts, critical hard-hexagons and critical nonintersecting string models is established. A graphical equivalence of this model to the six-vertex model generalizes this equivalence to noncritical cases of the above models. The order parameters of a specialization of this model are studied.     

Exact results for a generalized classicalO(n) matrix spin model

A generalizedO(n) matrix version of the classical Heisenberg model, introduced by Fuller and Lenard as a classical limit of a quantum model, is solved exactly in one dimension. The free energy is analytic and the pair correlation functions decay exponentially for all finite temperatures. It is shown, however, that even for a finite number of spins the model has a phase transition in then limit. The transition features a specific heat jump, zero long-range order at all temperatures, and zero correlation length at the critical point. The Curie-Weiss version of the model is also solved exactly and shown to have standard mean-field type behavior for all finiten and to differ from the one-dimensional results in then limit.     

Sampling and local models for multivariate image analysis

Local models are a very important concept for microscopic and macroscopic imaging. Different methods of sub-sampling a multivariate image are described both in general and for three examples. The need for sub-sampling and its influence on multivariate image analysis and visualization are studied. Examples from MRI (256 × 256), satellite imaging (7 × 512 × 512) and biofuel studies (6 × 512 × 512) are used to illustrate some of the principles involved.     

Different approaches toward an automatic structural alignment of drug molecules: Applications to sterol mimics,thrombin and thermolysin inhibitors

Summary A relative comparison of the binding properties of different drug molecules requires their mutual superposition with respect to various alignment criteria. In order to validate the results of different alignment methods, the crystallographically observed binding geometries of ligands in the pocket of a common protein receptor have been used. The alignment function in the program SEAL that calculates the mutual superposition of molecules has been optimized with respect to these references. Across the reference data set, alignments could be produced that show mean rms deviations of approximately 1 Å compared to the experimental situation. For structures with obvious skeletal similarities a multiple-flexible fit, linking common pharmacophoric groups by virtual springs, has been incorporated into the molecular mechanics program MOMO. In order to combine conformational searching with comparative alignments, the optimized SEAL approach has been applied to sets of conformers generated by MIMUMBA, a program for conformational analysis. Multiple-flexible fits have been calculated for inhibitors of ergosterol biosynthesis. Sets of different thrombin and thermolysin inhibitors have been conformationally analyzed and subsequently aligned by a combined MIMUMBA/SEAL approach. Since for these examples crystallographic data on their mutual alignment are available, an objective assessment of the computed results could be performed. Among the generated conformers, one geometry could be selected for the thrombin and thermolysin inhibitors that approached reasonably well the experimentally observed alignment.     

Photoelectron Spectra of Nonmetal Compounds and Their Interpretation by MO Models

The results of (low energy) photoelectron spectroscopy render possible a better appreciation of the “Nature of the Chemical Bond”. The application of this new experimental method is demonstrated utilizing representative compounds of the nonmetal elements, and a close symbiosis delineated with molecular orbital models. In particular, general consequences are discussed concerning electron deficiency, σ- and π-interactions, electron pair delocalization, and substituent effects or geometric perturbations. Photoelectron spectroscopic ionization energies permit evaluation of parameters for specified molecular groups, allow correlation with numerous other experimental data, and are didactically valuable in the teaching of general chemistry.     

Solid-state synthesis, structural variants and transformation of three-dimensional sulfides, AGaSnS4 (A=Na, K, Rb, Cs, Tl) and Na1.263Ga1.263Sn0.737S4

New cubic-AGaSnS₄ (A=Na, K, Rb, Cs, Tl) and orthorhombic-NaGaSnS₄ compounds were synthesized by solid-state reactions and characterized by X-ray diffraction and diffuse reflectance spectroscopy. Single crystals of orthorhombic-Na_1.263Ga_1.263Sn_0.737S₄ were obtained in the crystal growth attempts of sodium compound. All six new compounds have orthorhombic AgGaGeS₄ and cubic BaGa₂S₄ structures, as determined from single crystal X-ray structures of Na_1.263Ga_1.263Sn_0.737S₄ and cubic-AGaSnS₄ (A=Na, K, Rb). Orthorhombic-NaGaSnS₄ and known layered-KGaSnS₄ undergo structural transformation to thermodynamically stable cubic form.     

Relative stability of major types of beta-turns as a function of amino acid composition: a study based on Ab initio energetic and natural abundance data

Folding properties of small globular proteins are determined by their amino acid sequence (primary structure). This holds both for local (secondary structure) and for global conformational features of linear polypeptides and proteins composed from natural amino acid derivatives. It thus provides the rational basis of structure prediction algorithms. The shortest secondary structure element, the beta-turn, most typically adopts either a type I or a type II form, depending on the amino acid composition. Herein we investigate the sequence-dependent folding stability of both major types of beta-turns using simple dipeptide models (-Xxx-Yyy-). Gas-phase ab initio properties of 16 carefully selected and suitably protected dipeptide models (for example Val-Ser, Ala-Gly, Ser-Ser) were studied. For each backbone fold most probable side-chain conformers were considered. Fully optimized 321G RHF molecular structures were employed in medium level [B3LYP/6-311++G(d,p)//RHF/3-21G] energy calculations to estimate relative populations of the different backbone conformers. Our results show that the preference for beta-turn forms as calculated by quantum mechanics and observed in Xray determined proteins correlates significantly.     

A density functional study of propylene glycol conversion to propanal and propanone of various acid-catalyzed reaction models: a water-addition effect

The acid-catalyzed models on reaction mechanisms of pinacol rearrangement of propylene glycol conversion to propanal and propanone have been investigated using the density functional method at 298.15 K. Thermodynamic quantities of activation steps of four water-addition models were obtained. The number of added water interacting with the transition states of three concerted pathways has obviously affected the product ratio. The relative energetic profiles of the conversion reactions of all solvation models have been comparatively displayed. Estimation of the percent ratio of product composition computed from activation free energies of each acid-catalyzed reaction model was carried out. The percent ratios of propanal and propanone were decreased as the number of added water increased.     

Markov processes in single molecule fluorescence

This article examines the current status of Markov processes in single molecule fluorescence. For molecular dynamics to be described by a Markov process, the Markov process must include all states involved in the dynamics and the first-passage time (FPT) distributions out of those states must be describable by a simple exponential law. The observation of non-exponential FPT distributions or other evidence of non-Markovian dynamics is common in single molecule studies and offers an opportunity to expand the Markov model to include new dynamics or states that improve understanding of the system.