Conformal Field Theories, Representations and Lattice Constructions

An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and $Z_2$-twisted theories, $H(\Lambda)$ and $\tilde H(\Lambda)$ respectively, which may be constructed from a suitable even Euclidean lattice $\Lambda$. Similarly, one may construct lattices $\Lambda_C$ and $\tilde\Lambda_C$ by analogous constructions from a doubly-even binary code $C$. In the case when $C$ is self-dual, the corresponding lattices are also. Similarly, $H(\Lambda)$ and $\tilde H(\Lambda)$ are self-dual if and only if $\Lambda$ is. We show that $H(\Lambda_C)$ has a natural ``triality'' structure, which induces an isomorphism $H(\tilde\Lambda_C)\equiv\tilde H(\Lambda_C)$ and also a triality structure on $\tilde H(\tilde\Lambda_C)$. For $C$ the Golay code, $\tilde\Lambda_C$ is the Leech lattice, and the triality on $\tilde H(\tilde\Lambda_C)$ is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories $H(\Lambda)$ and $\tilde H(\Lambda)$ with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.Comment: 65 page

Understanding β-Hydride Eliminations from Heteroatom Functional Groups

Using density functional theory, we investigated detailed aspects of the quintessential organometallic process, β-hydride elimination (BHE). In general, we find that most BHE processes from alkyl functional group β-atoms are facile, while BHE processes from heteroatom functional groups (N and O) are prohibitively high in energy. We present calculated molecular orbitals and atomic NBO charges obtained from snapshots along reaction profiles to present a qualitative overview for how heteroatoms adversely affect these processes. We discuss these results to provide an illustration for how these processes proceed, clarifying a sometimes oversimplified model for these reactions

A strongly goal-directed close-range vision system for spacecraft docking

In this presentation, we will propose a strongly goal-oriented stereo vision system to establish proper docking approach motions for automated rendezvous and capture (AR&C). From an input sequence of stereo video image pairs, the system produces a current best estimate of: contact position; contact vector; contact velocity; and contact orientation. The processing demands imposed by this particular problem and its environment dictate a special case solution; such a system should necessarily be, in some sense, minimalist. By this we mean the system should construct a scene description just sufficiently rich to solve the problem at hand and should do no more processing than is absolutely necessary. In addition, the imaging resolution should be just sufficient. Extracting additional information and constructing higher level scene representations wastes energy and computational resources and injects an unnecessary degree of complexity, increasing the likelihood of malfunction. We therefore take a departure from most prior stereopsis work, including our own, and propose a system based on associative memory. The purpose of the memory is to immediately associate a set of motor commands with a set of input visual patterns in the two cameras. That is, rather than explicitly computing point correspondences and object positions in world coordinates and trying to reason forward from this information to a plan of action, we are trying to capture the essence of reflex behavior through the action of associative memory. The explicit construction of point correspondences and 3D scene descriptions, followed by online velocity and point of impact calculations, is prohibitively expensive from a computational point of view for the problem at hand. Learned patterns on the four image planes, left and right at two discrete but closely spaced instants in time, will be bused directly to infer the spacecraft reaction. This will be a continuing online process as the docking collar approaches

A rheological study of glass fibers in a Newtonian oil Semiannual status report, 1 Dec. 1966 - 31 May 1967

Rheological study of glass fibers in Newtonian oi

EFFECTS OF ADVERTISING, FOOD SAFETY AND HEALTH CONCERNS ON MEAT DEMAND IN CANADA

Food Consumption/Nutrition/Food Safety, Marketing,

DREIDING: A generic force field for molecular simulations

We report the parameters for a new generic force field, DREIDING, that we find useful for predicting structures and dynamics of organic, biological, and main-group inorganic molecules. The philosophy in DREIDING is to use general force constants and geometry parameters based on simple hybridization considerations rather than individual force constants and geometric parameters that depend on the particular combination of atoms involved in the bond, angle, or torsion terms. Thus all bond distances are derived from atomic radii, and there is only one force constant each for bonds, angles, and inversions and only six different values for torsional barriers. Parameters are defined for all possible combinations of atoms and new atoms can be added to the force field rather simply. This paper reports the parameters for the "nonmetallic" main-group elements (B, C, N, 0, F columns for the C, Si, Ge, and Sn rows) plus H and a few metals (Na, Ca, Zn, Fe). The accuracy of the DREIDING force field is tested by comparing with (i) 76 accurately determined crystal structures of organic compounds involving H, C, N, 0, F, P, S, CI, and Br, (ii) rotational barriers of a number of molecules, and (iii) relative conformational energies and barriers of a number of molecules. We find excellent results for these systems

Electromagnetic field application to underground power cable detection

Before commencing excavation or other work where power or other cables may be buried, it is important to determine the location of cables to ensure that they are not damaged. This paper describes a method of power-cable detection and location that uses measurements of the magnetic field produced by the currents in the cable, and presents the results of tests performed to evaluate the method. The cable detection and location program works by comparing the measured magnetic field signal with values predicted using a simple numerical model of the cable. Search coils are used as magnetic field sensors, and a measurement system is setup to measure the magnetic field of an underground power cable at a number of points above the ground so that it can detect the presence of an underground power cable and estimate its position. Experimental investigations were carried out using a model and under real site test conditions. The results show that the measurement system and cable location method give a reasonable prediction for the position of the target cable

Time Domain Studies of X-ray Shot Noise in Cygnus X-1

We investigate the variability of Cygnus X-1 in the context of shot moise models, and employ a peak detection algorithm to select individual shots. For a long observation of the low, hard state, the distribution of time intervals between shots is found to be consistent with a purely random process, contrary to previous claims in the literature. The detected shots are fit to several model templates and found to have a broad range of shapes. The fitted shots have a distribution of timescales from below 10 milliseconds to above 1 second. The coherence of the cross spectrum of light curves of these data in different energy bands is also studied. The observed high coherence implies that the transfer function between low and high energy variability is uniform. The uniformity of the tranfer function implies that the observed distribution of shot widths cannot have been acquired through Compton scattering. Our results in combination with other results in the literature suggest that shot luminosities are correlated with one another. We discuss how our experimental methodology relates to non-linear models of variability.Comment: Accepted for publication in Astrophysical Journal on July 16, 200

High H_2 Uptake in Li-, Na-, K-Metalated Covalent Organic Frameworks and Metal Organic Frameworks at 298 K

The Yaghi laboratory has developed porous covalent organic frameworks (COFs), COF102, COF103, and COF202, and metal–organic frameworks (MOFs), MOF177, MOF180, MOF200, MOF205, and MOF210, with ultrahigh porosity and outstanding H2 storage properties at 77 K. Using grand canonical Monte Carlo (GCMC) simulations with our recently developed first principles based force field (FF) from accurate quantum mechanics (QM), we calculated the molecular hydrogen (H2) uptake at 298 K for these systems, including the uptake for Li-, Na-, and K-metalated systems. We report the total, delivery and excess amount in gravimetric and volumetric units for all these compounds. For the gravimetric delivery amount from 1 to 100 bar, we find that eleven of these compounds reach the 2010 DOE target of 4.5 wt % at 298 K. The best of these compounds are MOF200-Li (6.34) and MOF200-Na (5.94), both reaching the 2015 DOE target of 5.5 wt % at 298 K. Among the undoped systems, we find that MOF200 gives a delivery amount as high as 3.24 wt % while MOF210 gives 2.90 wt % both from 1 to 100 bar and 298 K. However, none of these compounds reach the volumetric 2010 DOE target of 28 g H_2/L. The best volumetric performance is for COF102-Na (24.9), COF102-Li (23.8), COF103-Na (22.8), and COF103-Li (21.7), all using delivery g H_2/L units for 1–100 bar. These are the highest volumetric molecular hydrogen uptakes for a porous material under these thermodynamic conditions. Thus, one can obtain outstanding H_2 uptakes with Li, Na, and K doping of simple frameworks constructed from simple, cheap organic linkers. We present suggestions for strategies for synthesis of alkali metal-doped MOFs or COFs

Formation of Two Glass Phases in Binary Cu-Ag Liquid

The glass transition is alternatively described as either a dynamic transition in which there is a dramatic slowing down of the kinetics, or as a thermodynamic phase transition. To examine the physical origin of the glass transition in fragile Cu-Ag liquids, we employed molecular dynamics (MD) simulations on systems in the range of 32,000 to 2,048,000 atoms. Surprisingly, we identified a 1st order freezing transition from liquid (L) to metastable heterogenous solid-like phase, denoted as the G-glass, when a supercooled liquid evolves isothermally below its melting temperature at deep undercooling. In contrast, a more homogenous liquid-like glass, denoted as the L-glass, is achieved when the liquid is quenched continuously to room temperature with a fast cooling rate of ∼10¹¹ K/sec. We report a thermodynamic description of the L-G transition and characterize the correlation length of the heterogenous structure in the G-glass. The shear modulus of the G-glass is significantly higher than the L-glass, suggesting that the first order L-G transition is linked fundamentally to long-range elasticity involving elementary configurational excitations in the G-glass