Dynamics of quantum crystals

The phonon spectrum in a quantum crystal, where short-range correlations are important, is obtained by adapting the general relations between the one-phonon response and the thermodynamic properties of an anharmonic crystal proposed by Götze. Specifically, the one-phonon self-energy is obtained by requiring that the elastic constants obtained by the method of long waves equal those obtained as the strain derivatives of the ground-state energy. In practice this means that the atomic force constants can be obtained by formal differentiation of the ground-state energy. We explore the effects of this conserving approximation for theT-matrix and Jastrow methods and implement it numerically for bcc helium.     

Radio wave propagation through woods

In 1997 and 1998, measurements were made of radio wave attenuation through a cottonwood plantation at the University of Illinois at Urbana-Champaign, on a number of frequencies between 27 and 411 MHz. Based on these measurements, an empirical formula that describes radio wave attenuation was developed     

Using evolutionary trees in protein secondary structure prediction and other comparative sequence analyses

Previously proposed methods for protein secondary structure prediction from multiple sequence alignments do not efficiently extract the evolutionary information that these alignments contain. The predictions of these methods are less accurate than they could be, because of their failure to consider explicitly the phylogenetic tree that relates aligned protein sequences. As an alternative, we present a hidden Markov model approach to secondary structure prediction that more fully uses the evolutionary information contained in protein sequence alignments. A representative example is presented, and three experiments are performed that illustrate how the appropriate representation of evolutionary relatedness can improve inferences. We explain why similar improvement can be expected in other secondary structure prediction methods and indeed any comparative sequence analysis method.     

Spin Injection and Transport in Magnetic-Superconducting Oxide Heterostructures

Advances in thin film deposition techniques, in particular molecular beam epitaxy, have made it possible to produce bilayer heterostructures of high-temperature superconductors and manganite perovskites. The latter exhibit the phenomenon of colossal magnetoresistance (CMR). The half-metallic character of CMR compounds results in their carriers being spin polarized. The geometry of the structures that have been fabricated is such that it is possible to measure the interface conductance–voltage characteristic G(V) as well as the current–voltage characteristic of the superconducting half of the bilayer. Injection of carriers suppresses superconductivity in the latter, with a current gain of order unity. The data exhibit qualitative features of equilibrium theories of spin-polarized transport across an interface between a ferromagnet and an anisotropic superconductor, although a detailed understanding requires generalization of the theory to include out of equilibrium effects.     

Some applications of resultants to problems in computational geometry

Resultants were originally developed in the 18th and 19th centuries to solve certain simple algebraic problems. Here we shall present some applications of resultants to several important problems in computational geometry, including the implicitization, inversion, and intersection of parametric rational polynomial curves and surfaces.This paper was first delivered orally at the International Conference on Engineering and Computer Graphics in Beijing, China, held in August 1984     

A subdivision scheme for Poisson curves and surfaces

The de Casteljau evaluation algorithm applied to a finite sequence of control points defines a Bézier curve. This evaluation procedure also generates a subdivision algorithm and the limit of the subdivision process is this same Bézier curve. Extending the de Casteljau subdivision algorithm to an infinite sequence of control points defines a new family of curves. Here, limits of this stationary non-uniform subdivision process are shown to be equivalent to curves whose control points are the original data points and whose blending functions are given by the Poisson distribution. Thus this approach generalizes standard subdivision techniques from polynomials to arbitrary analytic functions. Extensions of this new subdivision scheme from curves to tensor product surfaces are also discussed.     

Change of basis algorithms for surfaces in CAGD

The computational complexity of general change of basis algorithms from one bivariate polynomial basis of degree n to another bivariate polynomial basis of degree n using matrix multiplication is O(n⁴). Applying blossoming and duality, we derive change of basis algorithms with computational complexity O(n³) between two important classes of polynomial bases used for representing surfaces in CAGD: B-bases and L-bases. Change of basis algorithms for B-bases follow from their blossoming property; change of basis algorithms for L-bases follow from the duality between L-bases and B-bases. The Bézier and multinomial bases are special cases of both B-bases and L-bases, so these algorithms can be used to convert between the Bézier and multinomial forms. We also show that the bivariate Horner evaluation algorithm for the multinomial basis is dual to the bivariate de Boor evaluation algorithm for B-patches.     

Vignette and exposure calibration and compensation

We discuss calibration and removal of "vignetting" (radial falloff) and exposure (gain) variations from sequences of images. Even when the response curve is known, spatially varying ambiguities prevent us from recovering the vignetting, exposure, and scene radiances uniquely. However, the vignetting and exposure variations can nonetheless be removed from the images without resolving these ambiguities or the previously known scale and gamma ambiguities. Applications include panoramic image mosaics, photometry for material reconstruction, image-based rendering, and preprocessing for correlation-based vision algorithms.