Field Patterns of the TE Modes in Ridge-Trough Waveguide

A single-ridge waveguide with a symmetrical longitudinal trough, designated as a ridge-trough waveguide has been used as a transition in a V-band (50-75 GHz) wafer probe recently. In this paper, the field patterns for the dominant TE mode and the first higher TE mode in ridge-trough waveguide with different configurations are presented by finite element method. The field patterns in this paper have important values for us to understand the transmission characteristics of ridge-trough waveguide, and will be of practical significance in designing ridge-trough waveguide components in microwave and millimeter wave engineering.     

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.     

Response properties at the dynamic water/dichloroethane liquid–liquid interface

ABSTRACT

We present a novel approach for calculating the static dielectric permittivity profile of a liquid–liquid interface (LLI) from molecular dynamics simulations. To obtain well-defined features, comparable to those observed at solid–liquid interfaces, we find it essential to reference to the instantaneous liquid–liquid interface rather than the more commonly used average Gibbs interface. We provide a coarse-grained approach for the practical definition of the instantaneous interface and present numerical results for the prototypical water/1,2-dichloroethane system. These results show that the parallel components of the dielectric permittivity tensor can be accurately extracted. In contrast, the perpendicular component does not converge to the correct bulk value at large distances from the LLI, highlighting a flaw in the regularly applied coarse-graining procedure.     

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.     

A class of multidimensional periodic splines

Periodic spline functions are introduced by use of reproducing kernel structure in Hilbert spaces. Minimum properties are described in interpolation and best approximation problems. A numerical method for determining interpolating splines and best approximations is proposed.Dedicated to Prof. Dr. F. Reutter on the occasion of his 70th birthday