Coherent Pion Radiation From Nucleon Antinucleon Annihilation

A unified picture of nucleon antinucleon annihilation into pions emerges from a classical description of the pion wave produced in annihilation and the subsequent quantization of that wave as a coherent state. When the constraints of energy-momentum and iso-spin conservation are imposed on the coherent state, the pion number distribution and charge ratios are found to be in excellent agreement with experiment.Comment: LaTex, 8 text pages, 1 PostScript figure, PSI-PR-93-2

Steady and Stable: Numerical Investigations of Nonlinear Partial Differential Equations

Excerpt: Mathematics is a language which can describe patterns in everyday life as well as abstract concepts existing only in our minds. Patterns exist in data, functions, and sets constructed around a common theme, but the most tangible patterns are visual. Visual demonstrations can help undergraduate students connect to abstract concepts in advanced mathematical courses. The study of partial differential equations, in particular, benefits from numerical analysis and simulation

Small grid embeddings of 3-polytopes

We introduce an algorithm that embeds a given 3-connected planar graph as a convex 3-polytope with integer coordinates. The size of the coordinates is bounded by $O(2^{7.55n})=O(188^{n})$. If the graph contains a triangle we can bound the integer coordinates by $O(2^{4.82n})$. If the graph contains a quadrilateral we can bound the integer coordinates by $O(2^{5.46n})$. The crucial part of the algorithm is to find a convex plane embedding whose edges can be weighted such that the sum of the weighted edges, seen as vectors, cancel at every point. It is well known that this can be guaranteed for the interior vertices by applying a technique of Tutte. We show how to extend Tutte's ideas to construct a plane embedding where the weighted vector sums cancel also on the vertices of the boundary face

Coherent state formulation of pion radiation from nucleon antinucleon annihilation

We assume that nucleon antinucleon annihilation is a fast process leading to a classical coherent pion pulse. We develop the quantum description of such pion waves based on the method of coherent states. We study the consequences of such a description for averages of charge types and moments of distributions of pion momenta with iso-spin and four-momentum conservation taken into account. We briefly discuss the applicability of our method to annihilation at rest, where we find agreement with experiment, and suggest other avenues for its use.Comment: 24 pages, 3 figures, 1 table, PSI-preprin

Thin-Film Metamaterials called Sculptured Thin Films

Morphology and performance are conjointed attributes of metamaterials, of which sculptured thin films (STFs) are examples. STFs are assemblies of nanowires that can be fabricated from many different materials, typically via physical vapor deposition onto rotating substrates. The curvilinear--nanowire morphology of STFs is determined by the substrate motions during fabrication. The optical properties, especially, can be tailored by varying the morphology of STFs. In many cases prototype devices have been fabricated for various optical, thermal, chemical, and biological applications.Comment: to be published in Proc. ICTP School on Metamaterials (Augsut 2009, Sibiu, Romania

Correlation search for coherent pion emission in heavy ion collisions

The methods allowing to extract the coherent component of pion emission conditioned by the formation of a quasi-classical pion source in heavy ion collisions are suggested. They exploit a nontrivial modification of the quantum statistical and final state interaction effects on the correlation functions of like and unlike pions in the presence of the coherent radiation. The extraction of the coherent pion spectrum from pi+pi-, pi+pi+ and pi-pi- correlation functions and single--pion spectra is discussed in detail for large expanding systems produced in ultra-relativistic heavy ion collisions.Comment: 21 pages, 3 eps figures, ReVTeX, corrected submission abstract. Version published in PRC 65 (2002) 064904. Added is a detailed explanation of the differences between pure coherent states and charge constrained coherent states in the case of a simple example model. The expressions for two-particle spectra taking into account both the final state interaction and the coherent component of pion emission are derived in a more general and transparent wa

Solving the Uncalibrated Photometric Stereo Problem using Total Variation

International audienceIn this paper we propose a new method to solve the problem of uncalibrated photometric stereo, making very weak assumptions on the properties of the scene to be reconstructed. Our goal is to solve the generalized bas-relief ambiguity (GBR) by performing a total variation regularization of both the estimated normal field and albedo. Unlike most of the previous attempts to solve this ambiguity, our approach does not rely on any prior information about the shape or the albedo, apart from its piecewise smoothness. We test our method on real images and obtain results comparable to the state-of-the-art algorithms

Gravitational excitons from extra dimensions

Inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold are investigated under dimensional reduction. In the Einstein conformal frame, small excitations of the scale factors of the internal spaces near minima of an effective potential have a form of massive scalar fields in the external space-time. Parameters of models which ensure minima of the effective potentials are obtained for particular cases and masses of gravitational excitons are estimated.Comment: Revised version --- 12 references added, Introduction enlarged, 20 pages, LaTeX, to appear in Phys.Rev.D56 (15.11.97

The Hamiltonian limit of (3+1)D SU(3) lattice gauge theory on anisotropic lattices

The extreme anisotropic limit of Euclidean SU(3) lattice gauge theory is examined to extract the Hamiltonian limit, using standard path integral Monte Carlo (PIMC) methods. We examine the mean plaquette and string tension and compare them to results obtained within the Hamiltonian framework of Kogut and Susskind. The results are a significant improvement upon previous Hamiltonian estimates, despite the extrapolation procedure necessary to extract observables. We conclude that the PIMC method is a reliable method of obtaining results for the Hamiltonian version of the theory. Our results also clearly demonstrate the universality between the Hamiltonian and Euclidean formulations of lattice gauge theory. It is particularly important to take into account the renormalization of both the anisotropy, and the Euclidean coupling $\beta_E$, in obtaining these results.Comment: 10 pages, 11 figure