Computing the Loewner driving process of random curves in the half plane

We simulate several models of random curves in the half plane and numerically compute their stochastic driving process (as given by the Loewner equation). Our models include models whose scaling limit is the Schramm-Loewner evolution (SLE) and models for which it is not. We study several tests of whether the driving process is Brownian motion. We find that just testing the normality of the process at a fixed time is not effective at determining if the process is Brownian motion. Tests that involve the independence of the increments of Brownian motion are much more effective. We also study the zipper algorithm for numerically computing the driving function of a simple curve. We give an implementation of this algorithm which runs in a time O(N^1.35) rather than the usual O(N^2), where N is the number of points on the curve.Comment: 20 pages, 4 figures. Changes to second version: added new paragraph to conclusion section; improved figures cosmeticall

The Paraldor Project

Paraldor is an experiment in bringing the power of categorical languages to lattice QCD computations. Our target language is Aldor, which allows the capture of the mathematical structure of physics directly in the structure of the code using the concepts of categories, domains and their inter-relationships in a way which is not otherwise possible with current popular languages such as Fortran, C, C++ or Java. By writing high level physics code portably in Aldor, and implementing switchable machine dependent high performance back-ends in C or assembler, we gain all the power of categorical languages such as modularity, portability, readability and efficiency.Comment: 4 pages, 2 figures, Lattice 2002 conference proceeding

Some remarks on the isoperimetric problem for the higher eigenvalues of the Robin and Wentzell Laplacians

We consider the problem of minimising the $k$th eigenvalue, $k \geq 2$, of the ($p$-)Laplacian with Robin boundary conditions with respect to all domains in $\mathbb{R}^N$ of given volume $M$. When $k=2$, we prove that the second eigenvalue of the $p$-Laplacian is minimised by the domain consisting of the disjoint union of two balls of equal volume, and that this is the unique domain with this property. For $p=2$ and $k \geq 3$, we prove that in many cases a minimiser cannot be independent of the value of the constant $\alpha$ in the boundary condition, or equivalently of the volume $M$. We obtain similar results for the Laplacian with generalised Wentzell boundary conditions $\Delta u + \beta \frac{\partial u}{\partial \nu} + \gamma u = 0$.Comment: 16 page

Making the small oblique parameters large

We compute the oblique parameters, including the three new parameters $V$, $W$ and $X$ introduced recently by the Montreal group, for the case of one scalar multiplet of arbitrary weak isospin $J$ and weak hypercharge $Y$. We show that, when the masses of the heaviest and lightest components of the multiplet remain constant, but $J$ increases, the oblique parameter $U$ and the three new oblique parameters increase like $J^3$, while $T$ only increases like $J$. For large multiplets with masses not much higher than $m_Z$, the oblique parameters $U$ and $V$ may become much larger than $T$ and $S$.Comment: 9 pages, standard LATEX, 3 figures available from the authors, report CMU-HEP93-17 and DOE-ER/40682-4

Bending vibrational data accuracy study

Computer program for predicting structural bending vibrational dat

Mission oriented study of advanced nuclear system parameters, phase 6. Volume 1 - Summary technical report Final report

Summarized study tasks, analyses, and results of advanced nuclear propulsion parameters for Mars and Venus mission

Scattering of Woods-Saxon Potential in Schrodinger Equation

The scattering solutions of the one-dimensional Schrodinger equation for the Woods-Saxon potential are obtained within the position-dependent mass formalism. The wave functions, transmission and reflection coefficients are calculated in terms of Heun's function. These results are also studied for the constant mass case in detail.Comment: 14 page

Near- to mid-infrared picosecond optical parametric oscillator based on periodically poled RbTiOAsO4

We describe a Ti:sapphire-pumped picosecond optical parametric oscillator based on periodically poled RbTiOAsO4 that is broadly tunable in the near to mid infrared. A 4.5-mm single-grating crystal at room temperature in combination with pump wavelength tuning provided access to a continuous-tuning range from 3.35 to 5 mu m, and a pump power threshold of 90 mW was measured. Average mid-infrared output powers in excess of 100 mW and total output powers of 400 mW in similar to 1-ps pulses were obtained at 33% extraction efficiency. (C) 1998 Optical Society of America.</p