Static and dynamic molecular mechanics modelling and X-ray scattering calculations for a cyclic siloxane macromolecule

A liquid crystalline system consisting of cyclic penta(methylsiloxane) cores with biphenylyl 4-propoxybenzoate mesogens is studied with respect to its molecular conformation and the intermolecular ordering of pendant groups by employing molecular mechaincs calculations, while a molecular dynamics simulation indicates the degree of conformational flexibility. The calculated X-ray scattering patterns for these structures provide insight into the origin of the experimentally observed results. A good agreement is found between the calculated and experimental reflections data, supporting the ‘cylinder’ global topology as the basis for forming a ‘columnar’ structure. Further, a comparison of the calculated and experimental meriodional sections shows a strong similarity of both the meridional intensities and d-spacings.     

The controllability problem for affine targets

We consider the problem of steering a point in Rⁿ to an affine target set with the autonomous control system $\text{x}\text{?}\text{= Ax + Bu}$. First the case of unbounded control is studied, with special attention given to targets which are cores of subspaces. For the case of compact control magnitude restraints we derive geometric properties of subspace cores and apply these to the controllability problem. Connections with stability theory are given.     

Control with conic control constraint set

A sufficient condition is given for controllability with conic control constraint set, and a control is computed which performs the transfer to the origin.     

Effects of conjugation in length and dimension on spectroscopic properties of fluorene-based chromophores from experiment and theory

A series of one-photon absorption spectra for fluorene-based donor-pi-acceptor molecules is presented and spectroscopically assigned, based upon the results obtained from time-dependent density functional theory. The computed excitation energies were generally shown to be in good agreement with experiment, particularly when compared to results from measurements carried out in a nonpolar solvent, which were available for some molecules. The computed oscillator strengths may resolve discordant experimental values in some cases, for example, for AF-380, AF-270, and AF-295. However, a quantitative comparison between computed and observed oscillator strengths is complicated by band overlapping. Thus, the computed extinction coefficients obtained by summing over the Gaussian bands are useful in such cases.     

Synthesis and crystal structure of a push-pull quinoidal porphyrin: a nanoporous framework assembled from cyclic trimer aggregates

A quinoidal porphyrin has been synthesised with such a curved pi-system that pi-pi stacking leads to the formation of cyclic trimer aggregates in the crystal, which pack to generate cylindrical channels with an internal diameter of 1.0 nm.     

Simple-motion pursuit-evasion differential games,part 2: Optimal evasion from proportional navigation guidance in the deterministic and stochastic cases

The problem of the optimal evasion from a pursuer employing proportional navigation guidance is considered. Thus, we consider the problem of maximizing the time-to-capture when the problem parameters, namely, the speed ratio and the proportional navigation constant, are such that capturability of the evader is guaranteed.     

A stochastic homicidal chauffeur pursuit-evasion differential game

A certain stochastic pursuit-evasion problem of the homicidal chauffeur type is considered. The pursuer strategy synthesized in this paper is fairly simple in contrast to the less straightforward swerve maneuver employed in the deterministic model. The analysis may partially explain why relatively simple pursuit strategies are apparently always adopted in practice.This work was partially supported by a grant from Control Data.The authors wish to thank Dr. D. H. Martin for a very enlightening discussion.     

An optimal evasion problem: Complete global solution

We consider a collision avoidance optimal control problem. The kinematics is modelled by a maneuverable pointE in the plane, with a limited rate of turn (a car à la Isaacs), that is moving at a constant speedv _E and is trying to avoid a circular disc of radiusl centered around a pointP, known to move at a constant speedv _P in the positive direction of they-axis.Global questions, answered analytically in the paper, are these: (i) the initial positions are determined ofE, relative toP, for which the capture ofE byP is assured—we characterize the capture zone in the state space; (ii) given thatE is initially in the capture zone, we solve the optimal control problem of steeringE to maximize the bearing ofE fromP at the instant of capture; (iii) we investigate the dependence of the answers to (i) and (ii) on the problem parameters v _P/v _E>1 andl.We solve completely a relatively simple, but practically meaningful, optimal evasion problem, not, to our knowledge, previously published.An earlier version of this paper was presented at the Annual Conference on Aeronautics and Astronautics held at the Technion, Haifa, Israel, February 27–28, 1985.     

Effects of conjugation in length and dimension on two-photon properties of fluorene-based chromophores

We report calculated two-photon (TPA) absorption spectra based upon results obtained from quadratic response time-dependent density functional theory for fluorene-based donor-π-acceptor molecules. Coulomb attenuated functionals with a long-range exchange contribution are applied to predict TPA excitation energies and cross-sections. Observed spectra are explained, and the effects of conjugation and multibranching on the TPA spectra are discussed. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Contribution of the Mark S. Gordon 65th Birthday Festschrift Issue.     

Analysis of mouse brain microvascular endothelium using immuno-laser capture microdissection coupled to a hybrid linear ion trap with Fourier transform-mass spectrometry proteomics platform

The purpose of this study was to identify the protein profile of the mouse brain microvascular endothelium in situ. This involved coupling of a double-label, immuno-laser capture microdissection (LCM) process with LTQ-FT mass spectrometry to perform the in situ proteomic analysis. LCM was utilized to isolate cells from frozen mouse brain tissue sections. Following cell capture, samples were solubilized and proteins separated by gel electrophoresis in preparation for enzymatic digestion and LC-MS analysis. Processed samples were subsequently analyzed using a linear IT coupled with a Fourier transform mass spectrometer (LTQ-FT MS). Overall, in this study, 881 proteins were identified from a specific cell category using immuno-guided LCM to probe these cell types along the entirety of the cerebral microvascular tree. The identification of sufficient numbers of proteins with high biological interest should allow us to study protein expression by specific cell types - as defined by certain cell markers - in complex tissues.