On Higher Order Pyramidal Finite Elements

In this paper we first prove a theorem on the nonexistence of pyramidal polynomial basis functions. Then we present a new symmetric composite pyramidal finite element which yields a better convergence than the nonsymmetric one. It has fourteen degrees of freedom and its basis functions are incomplete piecewise triquadratic polynomials. The space of ansatz functions contains all quadratic functions on each of four sub-tetrahedra that form a given pyramidal element.     

Robust passive range estimation using the waveguide invariant

The waveguide invariant principle is used to estimate the range to a broadband acoustic source in a shallow-water waveguide using a single acoustic receiver towed along a path directly toward the acoustic source. A relationship between the signal processing parameters and the ocean-acoustic environmental parameters is used to increase the effective signal-to-noise ratio without requiring detailed knowledge of the environment. Heuristics are developed to estimate the minimum source bandwidth and minimum horizontal aperture required for range estimation. A range estimation algorithm is tested on experimental and simulated data for source ranges of 500-2200 m and frequencies from 350 to 700 Hz. The algorithm is accurate to within approximately 25% for the cases tested and requires only a minimal amount of a priori environmental knowledge.     

Martingales, detrending data, and the efficient market hypothesis

We discuss martingales, detrending data, and the efficient market hypothesis (EMH) for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). Beginning with x-independent drift coefficients R(t) we show that martingale stochastic processes generate uncorrelated, generally non-stationary increments. Generally, a test for a martingale is therefore a test for uncorrelated increments. A detrended process with an x-dependent drift coefficient is generally not a martingale, and so we extend our analysis to include the class of (x,t)-dependent drift coefficients of interest in finance. We explain why martingales look Markovian at the level of both simple averages and 2-point correlations. And while a Markovian market has no memory to exploit and presumably cannot be beaten systematically, it has never been shown that martingale memory cannot be exploited in 3-point or higher correlations to beat the market. We generalize our Markov scaling solutions presented earlier, and also generalize the martingale formulation of the EMH to include (x,t)-dependent drift in log returns. We also use the analysis of this paper to correct a misstatement of the ‘fair game’ condition in terms of serial correlations in Fama's paper on the EMH. We end with a discussion of Levy's characterization of Brownian motion and prove that an arbitrary martingale is topologically inequivalent to a Wiener process.     

Polarization singularities in 2D and 3D speckle fields

The 3D structure of randomly polarized light fields is exemplified by its polarization singularities: lines along which the polarization is purely circular (C lines) and surfaces on which the polarization is linear (L surfaces). We visualize these polarization singularities experimentally in vector laser speckle fields, and in numerical simulations of random wave superpositions. Our results confirm previous analytical predictions [M. R. Dennis, Opt. Commun. 213, 201 (2002)] regarding the statistical distribution of types of C points and relate their 2D properties to their 3D structure.     

The computed force constants and vibrational spectra of cubane

The geometry, complete harmonic force field, and dipole moment derivatives of cubane, C₈H₈, have been calculated at the Hartree-Fock level using a 4–21 Gaussian basis set. The infrared and Raman spectra of cubane and four deuterated derivatives were calculated and compared with previously observed spectra. A set of five scale factors for the calculated force constants was then derived by least-squares fitting of the fundamental vibrational frequencies calculated from the scaled force field to the frequencies obtained by direct experimental measurement. The resulting scaled quantum-mechanical (SQM) force field, containing 73 unique elements, is believed to give an accurate representation of the harmonic vibrational potential of cubane. In most cases, the spectral assignments previously made from purely empirical considerations were confirmed, but a few corrections are proposed. The only major alteration is for an A_2u mode revised to appear at 1030 cm^?1 in the undeuterated molecule. Coriolis constants and approximate infrared intensities are also calculated.     

Single axial mode pumping and external mirror operation of a pulsed spin-flip Raman laser at 10.6 μm

By the addition of an external cavity to a single axial mode, TEA CO₂ laser pumped, In Sb spin-flip Raman laser, a tenfold increase in first Stokes output and a twenty-five fold increase in second Stokes and anti-Stokes outputs has been observed.     

Metal atom-induced diffuse scattering from short-range order among deuterium atoms in single crystal α-phase V2D

X-ray scattering has been studied above the critical ordering temperature, T_c (133°C), in b.c.c. α-phase V₂D. At 140 and 200°C quite weak diffuse intensity was observed centered on the reciprocal lattice points of the ordered superlattice. This intensity is due to short-range order among deuterium atoms which induces a local or short-range modulation of the parent vanadium lattice and suggests the possibility of local octahedral D—D fluctuations building up well above T_c.     

Interface interactions in modulated phases,and upsilon points

Certain features in Frenkel-Kontorova and other models of phases with a one-dimensional modulation can be analyzed by assuming parallel interfaces separating sets of lattice planes belonging to two different phases, and treating the free energy to create interfaces, as well as the interaction of two, three, or more interfaces, as phenomenological parameters. A strategy employed by Fisher and Szpilka for interacting defects can be extended to the case of interfaces, allowing a systematic study of the phase diagram by ignoring all interface interactions, and then successively taking into account pair, triple, and higher-order terms. The possible phase diagrams which can occur near the point where =0 include: various sorts of endpoints analogous to critical endpoints, an accumulation point of first-order transitions and triple points, and a self-similar structure which we call an upsilon point, which turns out to be an accumulation point of an infinite number of segments of first-order transition lines, each of which terminates in two upsilon points.