Calculated molecular structures and electronic spectra of the geometric isomers of a model carotenoid molecule, 6,11-dimethylhexadecaheptaene

The molecular structures and the electronic spectra of the geometric isomers of a model carotenoid polyene, 6,11-dimethylhexadecaheptaene, were calculated. It was concluded that solvent effects and conformational isomerization must be taken into account in order to satisfactorily explain the observed spectra. Molecular structures were calculated using molecular mechanics (MM2), and electronic spectra using the VESCF-MO-CI method including all singly-excited configurations. A method based on the calculated and observed spectra of simple linear polyenes was devised to estimate the solvent effects.     

An Example of Problem Embedding in Deterministic Dynamic Programming

A criticism sometimes made of dynamic programming is that in deterministic problems, optimal decisions are calculated which are never needed, as the decisions relate to states which never arise. In this paper we describe how some of these "redundant" calculations have been used, in a certain problem, to derive a working rule of general validity.The problem concerns the installation and replacement of an item of electrical equipment at a large number of sites, to meet a known load at each site which increases exponentially at a known rate.     

Operational Research and Decision-Making

This paper was originally presented under the title "Decision" at the Third Operational Research Conference of the Universities of Lancaster and Sussex held at Windermere in April 1968. In it, the question of what is meant by "improved decision-making" is examined and the ways in which operational research can and does contribute to this are discussed. In the course of this the "American School" of Decision Analysis is reviewed. The paper concludes with some suggestions on computational procedures. This paper was written as a vehicle for discussion. In order to stimulate this, the authors have been deliberately provocative and presented an extreme point of view. The paper which follows this is a condensed version of some of the discussion which took place at the Conference. The authors would welcome further contributions.     

The structures of higher boron halides B8X12(X = F, Cl, Br and I) by gas-phase electron diffraction and ab initio calculations

The structure of B8F12 has been shown by gas electron diffraction and computational methods (up to MP2/6-31+G*) to have the same highly asymmetric form observed in crystalline phases. The structure can be regarded as derived from a central B2 group, bridged by two BF2 groups to give a central B4 core that is folded, not planar, and with a very short bond [164.3 pm calculated, 164.2(19) pm experimental] along the fold line. There are also four terminal BF2 groups. One of the other four bonds in the core is consistently 20-30 pm longer than the others. This asymmetry has been attributed to many intra-molecular B...F interactions, particularly those between core boron atoms and fluorines of the terminal BF2 groups. Calculations for the chloro analogue lead to a structure similar to that for B8F12, but with the long core bond extended so that one of the bridging BCl2 groups may now be regarded as terminal. With bromine as the halogen the structure changes again, with one bromine atom taking up a bridging position. With iodine, this process continues further, and there are three bridging iodine atoms. However, in this case this is not the lowest energy structure, and instead a loosely associated dimer of B4I6 is preferred. In all these cases, and particularly with the heavier halogens, there are huge differences between the results obtained with different computational methods.     

A test of the equal-loudness-ratio hypothesis using cross-modality matching functions

This study tests the Equal-Loudness-Ratio hypothesis [Florentine et al., J. Acoust. Soc. Am. 99, 1633-1644 (1996)], which states that the loudness ratio between equal-SPL long and short tones is independent of SPL. The amount of temporal integration (i.e., the level difference between equally loud short and long sounds) is maximal at moderate levels. Therefore, the Equal-Loudness-Ratio hypothesis predicts that the loudness function is shallower at moderate levels than at low and high levels. Equal-loudness matches and cross-modality string-length matches were used to assess the form of the loudness function for 5 and 200 ms tones at 1 kHz and the loudness ratio between them. Results from nine normal listeners show that (1) the amount of temporal integration is largest at moderate levels, in agreement with previous studies, and (2) the loudness functions are shallowest at moderate levels. For eight of the nine listeners, the loudness ratio between the 200 and 5 ms tones is approximately constant, except at low levels where it tends to increase. The average data show good agreement between the two methods, but discrepancies are apparent for some individuals. These findings support the Equal-Loudness-Ratio hypothesis, except at low levels.     

Measurement of the generalized polarizabilities of the proton in virtual Compton scattering at Q2=0.92 and 1.76 GeV2

We report a virtual Compton scattering study of the proton at low c.m. energies. We have determined the structure functions P(LL)-P(TT)/epsilon and P(LT), and the electric and magnetic generalized polarizabilities (GPs) alpha(E)(Q2) and beta(M)(Q2) at momentum transfer Q(2)=0.92 and 1.76 GeV2. The electric GP shows a strong falloff with Q2, and its global behavior does not follow a simple dipole form. The magnetic GP shows a rise and then a falloff; this can be interpreted as the dominance of a long-distance diamagnetic pion cloud at low Q2, compensated at higher Q2 by a paramagnetic contribution from piN intermediate states.     

Control of spatiotemporal disorder in parametrically excited surface waves

Interacting surface waves, parametrically excited by two commensurate frequencies, yield a number of nonlinear states. Near the system's bicritical point, a state, highly disordered in space and time, results from competition between nonlinear states. Experimentally, this disordered state can be rapidly stabilized to a variety of nonlinear states via open-loop control with a small-amplitude third frequency excitation, whose temporal symmetry governs the temporal and the spatial symmetry of the selected nonlinear state. This technique also excites rapid switching between nonlinear states.     

Optical microrheology using rotating laser-trapped particles

We demonstrate an optical system that can apply and accurately measure the torque exerted by the trapping beam on a rotating birefringent probe particle. This allows the viscosity and surface effects within liquid media to be measured quantitatively on a micron-size scale using a trapped rotating spherical probe particle. We use the system to measure the viscosity inside a prototype cellular structure.