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 the Expansions in Spin Foam Cosmology

We discuss the expansions used in spin foam cosmology. We point out that already at the one vertex level arbitrarily complicated amplitudes contribute, and discuss the geometric asymptotics of the five simplest ones. We discuss what type of consistency conditions would be required to control the expansion. We show that the factorisation of the amplitude originally considered is best interpreted in topological terms. We then consider the next higher term in the graph expansion. We demonstrate the tension between the truncation to small graphs and going to the homogeneous sector, and conclude that it is necessary to truncate the dynamics as well.Comment: 17 pages, 4 figures, published versio

Design ideation through improvised comedy processes

We argue that the processes of creating successful comedy are comparable to the processes of designing an innovative product. Our research explores how constructs of humour may be applied to the early phase of engineering design, when divergent thinking is assumed to be most valuable. During a series of exploratory workshops, the principles and processes of creating improvised comedy presented an opportunity to reinvigorate the design process, and overcome some of the common barriers to effective group brainstorming. This paper discusses the link between improvised comedy and design creativity, and the early development of a new improvisation-based approach to design ideation

An infinite genus mapping class group and stable cohomology

We exhibit a finitely generated group \M whose rational homology is isomorphic to the rational stable homology of the mapping class group. It is defined as a mapping class group associated to a surface \su of infinite genus, and contains all the pure mapping class groups of compact surfaces of genus $g$ with $n$ boundary components, for any $g\geq 0$ and $n>0$. We construct a representation of \M into the restricted symplectic group ${\rm Sp_{res}}({\cal H}_r)$ of the real Hilbert space generated by the homology classes of non-separating circles on \su, which generalizes the classical symplectic representation of the mapping class groups. Moreover, we show that the first universal Chern class in H^2(\M,\Z) is the pull-back of the Pressley-Segal class on the restricted linear group ${\rm GL_{res}}({\cal H})$ via the inclusion ${\rm Sp_{res}}({\cal H}_r)\subset {\rm GL_{res}}({\cal H})$.Comment: 14p., 8 figures, to appear in Commun.Math.Phy

The development of coal-based technologies for Department of Defense facilities. Volume 1, Technical report. Semiannual technical progress report, September 28, 1994--March 27, 1995

This program is being conducted as a cooperative agreement between the Consortium for Coal Water Mixture Technology and the U.S. Department of Energy. Activities this reporting period are summarized by phase. Phase I is nearly completed. During this reporting period, coal beneficiation/preparation studies, engineering designs and economics for retrofitting the Crane, Indiana boiler to fire coal-based fuels, and a 1,000-hour demonstration of dry, micronized coal were completed. In addition, a demonstration-scale micronized-coal water mixture (MCWM) preparation circuit was constructed and a 1,000-hour demonstration firing MCWM began. Work in Phase II focused on emissions reductions, coal beneficiation/preparation studies, and economic analyses of coal use. Emissions reductions investigations involved literature surveys of NO{sub x}, SO{sub 2}, trace metals, volatile organic compounds, and fine particulate matter capture. In addition, vendors and engineering firms were contacted to identify the appropriate emissions technologies for the installation of commercial NO{sub x} and SO{sub 2} removal systems on the demonstration boiler. Information from the literature surveys and engineering firms will be used to identify, design, and install a control system(s). Work continued on the refinement and optimization of coal grinding and MCWM preparation procedures, and on the development of advanced processes for beneficiating high ash, high sulfur coals. Work also continued on determining the basic cost estimation of boiler retrofits, and evaluating environmental, regulatory, and regional economic impacts. In addition, the feasibility of technology adoption, and the public`s perception of the benefits and costs of coal usage was studied. A coal market analysis was completed. Work in Phase III focused on coal preparation studies, emissions reductions and economic analyses of coal use

Qudit surface codes and gauge theory with finite cyclic groups

Surface codes describe quantum memory stored as a global property of interacting spins on a surface. The state space is fixed by a complete set of quasi-local stabilizer operators and the code dimension depends on the first homology group of the surface complex. These code states can be actively stabilized by measurements or, alternatively, can be prepared by cooling to the ground subspace of a quasi-local spin Hamiltonian. In the case of spin-1/2 (qubit) lattices, such ground states have been proposed as topologically protected memory for qubits. We extend these constructions to lattices or more generally cell complexes with qudits, either of prime level or of level $d^\ell$ for $d$ prime and $\ell \geq 0$, and therefore under tensor decomposition, to arbitrary finite levels. The Hamiltonian describes an exact $\mathbb{Z}_d\cong\mathbb{Z}/d\mathbb{Z}$ gauge theory whose excitations correspond to abelian anyons. We provide protocols for qudit storage and retrieval and propose an interferometric verification of topological order by measuring quasi-particle statistics.Comment: 26 pages, 5 figure

Area-charge inequality for black holes

The inequality between area and charge $A\geq 4\pi Q^2$ for dynamical black holes is proved. No symmetry assumption is made and charged matter fields are included. Extensions of this inequality are also proved for regions in the spacetime which are not necessarily black hole boundaries.Comment: 21 pages, 2 figure