There\u27s a light shining bright : in the window to-night

https://digitalcommons.library.umaine.edu/mmb-vp/4560/thumbnail.jp

Electron Beam Deflection Without Off-Axis Aberrations

A novel focusing/deflection system for high accuracy, high throughput E-beam lithography, denoted as Variable Axis Immersion Lens (VAIL), has been successfully demonstrated. The main attributes of this system include: l) Perpendicular landing at all points of a deflection field \u3e (10 x 10 mm), 2) Elimination of transverse chromatic aberration, 3) High resolution ( \u3c 0.2μm edge slope) over the entire deflection field, 4) Elimination of eddy current effects in the target area, and 5) Total magnetic shielding of the target from external fields

Normandy Chimes

https://digitalcommons.library.umaine.edu/mmb-ps/1106/thumbnail.jp

A spin foam model for pure gauge theory coupled to quantum gravity

We propose a spin foam model for pure gauge fields coupled to Riemannian quantum gravity in four dimensions. The model is formulated for the triangulation of a four-manifold which is given merely combinatorially. The Riemannian Barrett--Crane model provides the gravity sector of our model and dynamically assigns geometric data to the given combinatorial triangulation. The gauge theory sector is a lattice gauge theory living on the same triangulation and obtains from the gravity sector the geometric information which is required to calculate the Yang--Mills action. The model is designed so that one obtains a continuum approximation of the gauge theory sector at an effective level, similarly to the continuum limit of lattice gauge theory, when the typical length scale of gravity is much smaller than the Yang--Mills scale.Comment: 18 pages, LaTeX, 1 figure, v2: details clarified, references adde

Dual variables and a connection picture for the Euclidean Barrett-Crane model

The partition function of the SO(4)- or Spin(4)-symmetric Euclidean Barrett-Crane model can be understood as a sum over all quantized geometries of a given triangulation of a four-manifold. In the original formulation, the variables of the model are balanced representations of SO(4) which describe the quantized areas of the triangles. We present an exact duality transformation for the full quantum theory and reformulate the model in terms of new variables which can be understood as variables conjugate to the quantized areas. The new variables are pairs of S^3-values associated to the tetrahedra. These S^3-variables parameterize the hyperplanes spanned by the tetrahedra (locally embedded in R^4), and the fact that there is a pair of variables for each tetrahedron can be viewed as a consequence of an SO(4)-valued parallel transport along the edges dual to the tetrahedra. We reconstruct the parallel transport of which only the action of SO(4) on S^3 is physically relevant and rewrite the Barrett-Crane model as an SO(4) lattice BF-theory living on the 2-complex dual to the triangulation subject to suitable constraints whose form we derive at the quantum level. Our reformulation of the Barrett-Crane model in terms of continuous variables is suitable for the application of various analytical and numerical techniques familiar from Statistical Mechanics.Comment: 33 pages, LaTeX, combined PiCTeX/postscript figures, v2: note added, TeX error correcte

Critical properties of loop percolation models with optimization constraints

We study loop percolation models in two and in three space dimensions, in which configurations of occupied bonds are forced to form closed loop. We show that the uncorrelated occupation of elementary plaquettes of the square and the simple cubic lattice by elementary loops leads to a percolation transition that is in the same universality class as the conventional bond percolation. In contrast to this an optimization constraint for the loop configurations, which then have to minimize a particular generic energy function, leads to a percolation transition that constitutes a new universality class, for which we report the critical exponents. Implication for the physics of solid-on-solid and vortex glass models are discussed.Comment: 8 pages, 8 figure

Diameter selective characterization of single-wall carbon nanotubes

A novel method is presented which allows the characterization of diameter selective phenomena in SWCNTs. It is based on the transformation of fullerene peapod materials into double-wall carbon nanotubes and studying the diameter distribution of the latter. The method is demonstrated for the diameter selective healing of nanotube defects and yield from C$_{70}$ peapod samples. Openings on small diameter nanotubes are closed first. The yield of very small diameter inner nanotubes from C$_{70}$ peapods is demonstrated. This challenges the theoretical models of inner nanotube formation. An anomalous absence of mid-diameter inner tubes is observed and explained by the suppressed amount of C$_{70}$ peapods due to the competition of the two almost equally stable standing and lying C$_{70}$ peapod configurations