Tensor Distributions on Signature-changing Space-times

Irregularities in the metric tensor of a signature-changing space-time suggest that field equations on such space-times might be regarded as distributional. We review the formalism of tensor distributions on differentiable manifolds, and examine to what extent rigorous meaning can be given to field equations in the presence of signature-change, in particular those involving covariant derivatives. We find that, for both continuous and discontinuous signature-change, covariant differentiation can be defined on a class of tensor distributions wide enough to be physically interesting.     

High-speed horizontal-path atmospheric turbulence correction with a large-actuator-number microelectromechanical system spatial light modulator in an interferometric phase-conjugation engine

Results of atmospheric propagation for a high-speed, large-actuator-number adaptive optics system are presented. The system uses a microelectromechanical system- (MEMS-) based spatial light modulator correction device with 1024 actuators. Tests over a 1.35-km path achieved correction speeds in excess of 800 Hz and Strehl ratios close to 0.5. The wave-front sensor was based on a quadrature interferometer that directly measures phase. This technique does not require global wave-front reconstruction, making it relatively insensitive to scintillation and phase residues. The results demonstrate the potential of large-actuator-number MEMS-based spatial light modulators to replace conventional deformable mirrors.     

Frequency- and bias-dependent ac conductivity of charge-density waves in TaS3

The charge-density wave contribution to the dc and the small-signal ac conductivity of orthorhombic TaS₃ has been completely characterized for a single crystal. The ac conductivity is found to be independent of dc bias below threshold. The tunneling theory of charge-density wave depinning successfully predicts the real and imaginary parts of the ac conductivity as functions of both frequency and applied dc bias, using only a fit to the dc I–V data and one adjustable parameter.     

Integral Modular Categories of Frobenius-Perron Dimension <Emphasis Type="Italic">pq</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

Integral modular categories of Frobenius-Perron dimension pq ⁿ , where p and q are primes, are considered. It is already known that such categories are group-theoretical in the cases of 0 ≤ n ≤ 4. In the general case we determine that these categories are either group-theoretical or contain a Tannakian subcategory of dimension q ⁱ for i > 1. We then show that all integral modular categories \(\mathcal {C}\) with \(\text {FPdim}(\mathcal {C})=pq^{5}\) are group-theoretical, and, if in addition p < q, all with \(\text {FPdim}(\mathcal {C})=pq^{6}\) or pq ⁷ are group-theoretical. In the process we generalize an existing criterion for an integral modular category to be group-theoretical.     

Oriented noncrystalline structure in PET fibers prepared with threadline modification process

The development of an oriented noncrystalline phase in a semicrystalline polymer filament has been studied via X-ray scattering. These unique PET fibers contain a relatively high noncrystalline content and also have high tenacity, high modulus, and low breaking elongation. Fiber properties were found to be very responsive to the oriented amorphous phase content. This phase was utilized for interpreting noncrystalline orientation in PET fibers produced by a new extrusion technique. Here, the oriented noncrystalline regions in a series of PET fibers varies from 6% to 63%, depending strongly on the production conditions. In particular, samples produced with a newly developed threadline modification process possess a high content of oriented noncrystalline polymer. Measurements such as dynamic and static mechanical properties have been performed on various samples, and these properties are related to the oriented noncrystalline phase. The results provide direct evidence for the existence of highly oriented noncrystalline material in these unique PET fibers spun with a threadline modification process. © 1996 John Wiley & Sons, Inc.     

Fourier transform infrared quantification of sugars in pretreated biomass liquors

The process of converting renewable lignocellulosic biomass to ethanol requires a number of steps, and pretreatment is one of the most important. Pretreatment usually in volves a hydrolysis of the easily hydrolyzed hemicellulosic component of biomass using some form of thermal/chemical/mechanical action that results in a product that can be further hydrolyzed by cellulase enzymes (the cellulosic portion). The sugars produced can then befermented to ethanol by fermentative microorganisms. If the pretreatment step is not severe enough, the resultant residue is not as easily hydrolyzed by the cellulase enzyme. More severe pretreatment conditions result in the production of degradation products that are toxic to the fermentative microorgan ism. In this article, wereport the quantitative analysis of glucose, mannose, xylose, and acetic acid using Fourier transform infrared (FTIR) spectroscopy on liquors from dilute-acid-pretreated softwood and hard wood slurries. Comparison of FTIR and high-performance liquid chromatography quantitative analyses of these liquorsare reported. Recent developments in infrared probe technology has enabled the rapid quantification of these sugars by FTIR spectroscopy in the batch reactor during optimization of the pretreatment conditions, or interfaced to the computer controlling a continuous reactor for on-line monitoring and control.     

pH sensitive adsorption of polypeptide/sodium dodecyl sulfate mixtures

Neutron reflectivity and surface tension have been used to investigate the pH sensitivity of the adsorption of poly-L-lysine hydrobromide and sodium dodecyl sulfate mixtures at the air-solution interface. The surface tension variation with surfactant concentration is complex, and between the critical aggregation concentration and critical micellar concentration there is a marked increase in the surface tension. The neutron reflectivity results show that this is associated with a depletion of the surface of polypeptide/surfactant complexes. The variations in the adsorption and surface tension with pH are attributed to changes in the polypeptide conformation at the interface and in solution.     

Adsorption of polyelectrolyte/surfactant mixtures at the air-solution interface: poly(ethyleneimine)/sodium dodecyl sulfate

Neutron reflectivity and surface tension have been used to characterize the adsorption of the polyelectrolyte/ionic surfactant mixture of poly(ethyleneimine) (PEI) and sodium dodecyl sulfate (SDS) at the air-water interface. The surface tension behavior and adsorption patterns show a strong dependence upon the solution pH. However, the SDS adsorption at the interface is unexpectedly most pronounced when the pH is high (when the polymer is essentially a neutral polymer) and when the polymer architecture is branched rather than linear. For both the branched and the linear PEI polymer/surfactant complex formation results in a significant enhancement of the amount of SDS at the interface, down to surfactant concentrations approximately 10(-6) M. For the branched PEI a transition from a monolayer to a multilayer adsorption is observed, which depends on surfactant concentration and pH. In contrast, for the linear polymer, only monolayer adsorption is observed. This substantial increase in the surface activity of SDS by complexation with PEI results in spontaneous emulsification of hexadecane in water and the efficient wetting of hydrophobic substrates such as Teflon. In regions close to charge neutralization the multilayer adsorption is accentuated, and more extensively ordered structures, giving rise to Bragg peaks in the reflectivity data, are evident.     

How to choose one-dimensional basis functions so that a very efficient multidimensional basis may be extracted from a direct product of the one-dimensional functions: energy levels of coupled systems with as many as 16 coordinates

In this paper we propose a scheme for choosing basis functions for quantum dynamics calculations. Direct product bases are frequently used. The number of direct product functions required to converge a spectrum, compute a rate constant, etc., is so large that direct product calculations are impossible for molecules or reacting systems with more than four atoms. It is common to extract a smaller working basis from a huge direct product basis by removing some of the product functions. We advocate a build and prune strategy of this type. The one-dimensional (1D) functions from which we build the direct product basis are chosen to satisfy two conditions: (1) they nearly diagonalize the full Hamiltonian matrix; (2) they minimize off-diagonal matrix elements that couple basis functions with diagonal elements close to those of the energy levels we wish to compute. By imposing these conditions we increase the number of product functions that can be removed from the multidimensional basis without degrading the accuracy of computed energy levels. Two basic types of 1D basis functions are in common use: eigenfunctions of 1D Hamiltonians and discrete variable representation (DVR) functions. Both have advantages and disadvantages. The 1D functions we propose are intermediate between the 1D eigenfunction functions and the DVR functions. If the coupling is very weak, they are very nearly 1D eigenfunction functions. As the strength of the coupling is increased they resemble more closely DVR functions. We assess the usefulness of our basis by applying it to model 6D, 8D, and 16D Hamiltonians with various coupling strengths. We find approximately linear scaling.     

Calculating intensities using effective Hamiltonians in terms of Coriolis-adapted normal modes

The calculation of rovibrational transition energies and intensities is often hampered by the fact that vibrational states are strongly coupled by Coriolis terms. Because it invalidates the use of perturbation theory for the purpose of decoupling these states, the coupling makes it difficult to analyze spectra and to extract information from them. One either ignores the problem and hopes that the effect of the coupling is minimal or one is forced to diagonalize effective rovibrational matrices (rather than diagonalizing effective rotational matrices). In this paper we apply a procedure, based on a quantum mechanical canonical transformation for deriving decoupled effective rotational Hamiltonians. In previous papers we have used this technique to compute energy levels. In this paper we show that it can also be applied to determine intensities. The ideas are applied to the ethylene molecule.