Stress-energy tensor for a massless spin 1/2 field in static black hole spacetimes

The stress-energy tensor for the massless spin 1/2 field is numerically computed outside and on the event horizons of both charged and uncharged static nonrotating black holes, corresponding to the Schwarzschild, Reissner-Nordstr?m, and extreme Reissner-Nordstr?m solutions of Einstein's equations. The field is assumed to be in a thermal state at the black hole temperature. Comparison is made between the numerical results and previous analytic approximations for the stress-energy tensor in these spacetimes. For the Schwarzschild (charge zero) solution, it is shown that the stress energy differs even in sign from the analytic approximation. For the Reissner-Nordstr?m and extreme Reissner-Nordstr?m solutions, divergences predicted by the analytic approximations are shown not to exist.     

Martensitic fcc-to-hcp transformation observed in xenon at high pressure

Angle-resolved x-ray diffraction patterns of Xe to 127 GPa indicate that the fcc-to-hcp transition occurs martensitically between 3 and 70 GPa in diamond-anvil cells without an intermediate phase. These data also reveal that the transition occurs by the introduction of stacking disorder in the fcc lattice at low pressure, which grows into hcp domains with increasing pressure. The small energy difference between the hcp and the fcc structures may allow the two phases to coexist over a wide pressure range. Evidence of similar stacking disorder and incipient growth of an hcp phase are also observed in solid Kr.     

Highly optimized tolerance: robustness and design in complex systems

Highly optimized tolerance (HOT) is a mechanism that relates evolving structure to power laws in interconnected systems. HOT systems arise where design and evolution create complex systems sharing common features, including (1) high efficiency, performance, and robustness to designed-for uncertainties, (2) hypersensitivity to design flaws and unanticipated perturbations, (3) nongeneric, specialized, structured configurations, and (4) power laws. We study the impact of incorporating increasing levels of design and find that even small amounts of design lead to HOT states in percolation.     

Multiscale coherent structures and broadband waves due to parallel inhomogeneous flows

Linear theory analysis and particle-in-cell simulations show that a spatial transverse gradient in the ion drift parallel to the magnetic field, dV(di)/dxOmega(i). Nonlinearly, these waves lead to multiscale spatially coherent structures, substantial cross-field transport, ion energization, and phase-space diffusion. Large spikes are formed in the parallel electric field time series. These signatures are similar to the Fast Auroral Snapshot satellite observations in the upward current region.     

Nonlinear phase adjustment of selective excitation pulses

A continuous transformation of an RF waveform with a modified Korteweg-de Vries equation or generalization can be used to adjust the phase behavior of a selective excitation pulse while preserving the magnitude behavior of the spin response. This transformation has applications in removing or adding to the nonlinear phase properties of a selected region.     

Multivariate design

In multivariate data analysis such as principal components analysis (PCA) and projections to latent structures (PLS), it is essential that the training set systems (objects) are selected to provide data with substantial information for model parametrization, and to represent properly any future situations where the multilvariate model is used for predictions. In the framework of multivariate projections (PCA, SIMCA and PLS), elementary concepts of statistical design (fractional factorials and composite designs) can be used with the latent variables (PC or PLS scores) as design variables. The plan of action thus becomes: (1) problem formulation (specify aim and model, make a conceptual division of the investigated system into subsystems); (2) collection of multivariate data for each type of subsystems; (3) estimation of the practical dimensionality of the data for each type of subsystems by PC or PLS analysis; (4) use of the PC or PLS scores (t) as design variables in the combination of subsystems to systems in the training set; (5) measurement of responses (Y); (6) analysis of data by PCA or PLS; (7) interpretation of results with possible feedback to steps 1, 2 or 3. The procedures are illustrated by two problems: a structure/activity relationship for a family of peptides, and optimization of an organic synthesis with respect to system variables (solvent, substrate, co-reactant_) and process variables (temperature, reactant concentrations).     

Nachweis und Bestimmung der Halogensauerstoffverbindungen

Ohne Zusammenfassung