Topological Change in Mean Convex Mean Curvature Flow

Consider the mean curvature flow of an (n+1)-dimensional, compact, mean convex region in Euclidean space (or, if n<7, in a Riemannian manifold). We prove that elements of the m-th homotopy group of the complementary region can die only if there is a shrinking S^k x R^(n-k) singularity for some k less than or equal to m. We also prove that for each m from 1 to n, there is a nonempty open set of compact, mean convex regions K in R^(n+1) with smooth boundary for which the resulting mean curvature flow has a shrinking S^m x R^(n-m) singularity.Comment: 19 pages. This version includes a new section proving that certain kinds of mean curvature flow singularities persist under arbitrary small perturbations of the initial surface. Newest update (Oct 2013) fixes some bibliographic reference

On-board processing concepts for future satellite communications systems

The initial definition of on-board processing for an advanced satellite communications system to service domestic markets in the 1990's is discussed. An exemplar system with both RF on-board switching and demodulation/remodulation baseband processing is used to identify important issues related to system implementation, cost, and technology development. Analyses of spectrum-efficient modulation, coding, and system control techniques are summarized. Implementations for an RF switch and baseband processor are described. Among the major conclusions listed is the need for high gain satellites capable of handling tens of simultaneous beams for the efficient reuse of the 2.5 GHz 30/20 frequency band. Several scanning beams are recommended in addition to the fixed beams. Low power solid state 20 GHz GaAs FET power amplifiers in the 5W range and a general purpose digital baseband processor with gigahertz logic speeds and megabits of memory are also recommended

Double window viewing chamber assembly

A viewing chamber which permits observation of a sample retained therein includes a pair of double window assemblies mounted in opposed openings in the walls thereof so that a light beam can directly enter and exit from the chamber. A flexible mounting arrangement for the outer windows of the window assemblies enables the windows to be brought into proper alignment. An electrical heating arrangement prevents fogging of the outer windows whereas desiccated air in the volume between the outer and inner windows prevents fogging of the latter

Metallic Triple Beam Resonator with Thick-film Printed Drive and Pickup

A triple beam resonator fabricated in 430S17 stainless steel with thick-film piezoelectric elements to drive and detect the vibrations is presented. The resonator substrate was fabricated by a simultaneous, double-sided photochemical etching technique and the thick-film piezoelectric elements were deposited by a standard screen-printing process. The combination of these two batch-fabrication processes provides the opportunity for mass production of the device at low cost. The resonator, a dynamically balanced triple beam tuning fork (TBTF) structure 23.5 mm long and 6.5 mm wide, has a favoured mode at 4.96 kHz with a Q-factor of 3630 operating in air

Linear Optical CNOT Gate in the Coincidence Basis

We describe the operation and tolerances of a non-deterministic, coincidence basis, quantum CNOT gate for photonic qubits. It is constructed solely from linear optical elements and requires only a two-photon source for its demonstration.Comment: Submitted to Physical Review

Spinon-holon interactions in an anisotropic t-J chain: a comprehensive study

We consider a generalization of the one-dimensional t-J model with anisotropic spin-spin interactions. We show that the anisotropy leads to an effective attractive interaction between the spinon and holon excitations, resulting in a localized bound state. Detailed quantitative analytic predictions for the dependence of the binding energy on the anisotropy are presented, and verified by precise numerical simulations. The binding energy is found to interpolate smoothly between a finite value in the t-Jz limit and zero in the isotropic limit, going to zero exponentially in the vicinity of the latter. We identify changes in spinon dispersion as the primary factor for this non-trivial behavior.Comment: 12 pages, 13 figures, long story. The short story is cond-mat/0702213. Published versio