The Yang-Mills Heat Semigroup on Three-Manifolds with Boundary

Long time existence and uniqueness of solutions to the Yang-Mills heat equation is proven over a compact 3-manifold with smooth boundary. The initial data is taken to be a Lie algebra valued connection form in the Sobolev space H ₁. Three kinds of boundary conditions are explored, Dirichlet type, Neumann type and Marini boundary conditions. The last is a nonlinear boundary condition, specified by setting the normal component of the curvature to zero on the boundary. The Yang-Mills heat equation is a weakly parabolic nonlinear equation. We use gauge symmetry breaking to convert it to a parabolic equation and then gauge transform the solution of the parabolic equation back to a solution of the original equation. Apriori estimates are developed by first establishing a gauge invariant version of the Gaffney-Friedrichs inequality. A gauge invariant regularization procedure for solutions is also established. Uniqueness holds upon imposition of boundary conditions on only two of the three components of the connection form because of weak parabolicity. This work is motivated by possible applications to quantum field theory.     

The effect of thermal reactor neutron irradiation on semi-insulating GaN

Semi-insulating Gallium nitride was irradiated by fast and thermal neutrons with fluences from 10¹⁴ to 10¹⁶ n/cm². Depth-resolved cathodoluminescence spectroscopy was used to determine defects changes before and after irradiation. The results revealed two kinds of defects affected near-band emission recombination from two opposite directions. One was attributed to irradiation-induced N vacancies that contribute to near-band emission recombination. Another was attributed to irradiation-induced deep level defects that contribute to sub-band gap recombination and thus decrease the near-band emission recombination.     

A General Deterministic Treatment of Derivatives in Particle Methods

A unified approach to approximating spatial derivatives in particle methods using integral operators is presented. The approach is an extension of particle strength exchange, originally developed for treating the Laplacian in advection–diffusion problems. Kernels of high order of accuracy are constructed that can be used to approximate derivatives of any degree. A new treatment for computing derivatives near the edge of particle coverage is introduced, using “one-sided” integrals that only look for information where it is available. The use of these integral approximations in wave propagation applications is considered and their error is analyzed in this context using Fourier methods. Finally, simple tests are performed to demonstrate the characteristics of the treatment, including an assessment of the effects of particle dispersion, and their results are discussed.     

Diffusion-limited aggregation: A kinetic critical phenomenon?

Diffusion-limited aggregation (DLA) is a model which represents noisy growth limited by diffusion. This process is quite common in nature and the simple algorithm gives a good representation of the large-scale structure of many natural objects. The clusters grown in the computer and the real objects in question are tenuous and approximately self-similar. A good deal is known about the algorithm, but a complete theory is not yet available. I review the current state of knowledge about the model, its applications and theoretical analysis of the results.     

1+1 dimensional compactifications of string theory

We argue that stable, maximally symmetric compactifications of string theory to 1+1 dimensions are in conflict with holography. In particular, the finite horizon entropies of the Rindler wedge in 1+1 dimensional Minkowski and anti-de Sitter space, and of the de Sitter horizon in any dimension, are inconsistent with the symmetries of these spaces. The argument parallels one made recently by the same authors, in which we demonstrated the incompatibility of the finiteness of the entropy and the symmetries of de Sitter space in any dimension. If the horizon entropy is either infinite or zero, the conflict is resolved.     

Fluctuations of permeable interfaces in water-in-water emulsions

The fluctuations of highly permeable interfaces, encountered in phase-separated biopolymer solutions, liposomes, polymersomes, or colloidosomes, are investigated. An expression for the power spectrum of the height correlation function is derived for a multicomponent system, incorporating the effects of mass transfer across the interface, using nonequilibrium thermodynamics. We also derive an expression for the relaxation time of the height correlation function, and calculate the relaxation time for a phase-separated gelatin-dextran-water system. Comparing our expression with the expression for an impermeable interface shows that mass transfer has a significant impact on the relaxation time of the interface.     

Guided wave helical ultrasonic tomography of pipes

Ultrasonic guided waves have been used for a wide variety of ultrasonic inspection techniques. We describe here a new variation called helical ultrasound tomography (HUT) that uses guided ultrasonic waves along with tomographic reconstruction algorithms that have been developed by seismologists for what they call "cross borehole" tomography. In HUT, the Lamb-like guided waves travel the various helical criss-cross paths between two parallel circumferential transducer arrays instead of the planar criss-cross seismic paths between two boreholes. Although the measurement itself is fairly complicated, the output of the tomographic reconstruction is a readily interpretable map of a quantity of interest such as pipe wall thickness. In this paper we demonstrate HUT via laboratory scans on steel pipe segments into which controlled thinnings have been introduced.     

Thermal analysis of some metal benzohydroxamates

The preparation and thermal analysis of metal chelates of benzohydroxarnic acid (BHA) with Al(III), Cd(II), Co(II), Cu(II) (two compounds), Fe(III), La(III), Pb(II), Mn(II), Ni(II), U(VI) and Zn(II) is discussed. The Al(III), La(III), Pb(II) and Mn(II) chelates are new compounds. DTA and TGA curves of the chelates and of BHA are presented, and the heats of decomposition of the chelates are estimated.     

Substituted chromans and tetrahydrofuro[2,3-b]benzofurans (trapped tetrahedral intermediates) from 3-phenyl-2-benzofuranones

The previously discovered neighboring group reaction has been extended to the synthesis of chroman derivatives (i.e., 4, 5, 6) containing geminal methyls in the 2-position, a feature common to certain physiologically active natural chromans. In two instances, cyclic ortho ester by-products (8), not observed in previous work, were formed as a result of the intramolecular trapping of tetrahedral intermediates. Reasons for the incursion of this unexpected side reaction are discussed.