The Length of an SLE - Monte Carlo Studies

The scaling limits of a variety of critical two-dimensional lattice models are equal to the Schramm-Loewner evolution (SLE) for a suitable value of the parameter kappa. These lattice models have a natural parametrization of their random curves given by the length of the curve. This parametrization (with suitable scaling) should provide a natural parametrization for the curves in the scaling limit. We conjecture that this parametrization is also given by a type of fractal variation along the curve, and present Monte Carlo simulations to support this conjecture. Then we show by simulations that if this fractal variation is used to parametrize the SLE, then the parametrized curves have the same distribution as the curves in the scaling limit of the lattice models with their natural parametrization.Comment: 18 pages, 10 figures. Version 2 replaced the use of "nu" for the "growth exponent" by 1/d_H, where d_H is the Hausdorff dimension. Various minor errors were also correcte

New continua for absorption spectroscopy from 40 to 2000 Å

The spectra of plasmas produced by focusing the output of a Q-switched ruby laser (output 1 J) on the rare-earth metals have been studied. From samarium (Z = 70), strong quasi-uniform continua are emitted in the wavelength range 40–2000 Å. Line emission from the target elements is absent over most of this wavelength region, particularly below about 600 Å. The use of these continua as simple, reliable background sources for absorption spectroscopy in the vacuum-ultraviolet and soft x-ray region down to 40 Å is demonstrated

Transforming fixed-length self-avoiding walks into radial SLE_8/3

We conjecture a relationship between the scaling limit of the fixed-length ensemble of self-avoiding walks in the upper half plane and radial SLE with kappa=8/3 in this half plane from 0 to i. The relationship is that if we take a curve from the fixed-length scaling limit of the SAW, weight it by a suitable power of the distance to the endpoint of the curve and then apply the conformal map of the half plane that takes the endpoint to i, then we get the same probability measure on curves as radial SLE. In addition to a non-rigorous derivation of this conjecture, we support it with Monte Carlo simulations of the SAW. Using the conjectured relationship between the SAW and radial SLE, our simulations give estimates for both the interior and boundary scaling exponents. The values we obtain are within a few hundredths of a percent of the conjectured values

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

Farm syndication has advantages

Sharing of single items of plant between farmers is common in Australian Agriculture but it is quite rare for farmers to amalgamate their holdings and farm them as a single unit. This article looks at the advantages of syndicate farming. It is based on a study of four whole farm syndicates in the Wimmera of Victoria

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

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

Stripe phases in the two-dimensional Falicov-Kimball model

The observation of charge stripe order in the doped nickelate and cuprate materials has motivated much theoretical effort to understand the underlying mechanism of the stripe phase. Numerical studies of the Hubbard model show two possibilities: (i) stripe order arises from a tendency toward phase separation and its competition with the long-range Coulomb interaction or (ii) stripe order inherently arises as a compromise between itinerancy and magnetic interactions. Here we determine the restricted phase diagrams of the two-dimensional Falicov-Kimball model and see that it displays rich behavior illustrating both possibilities in different regions of the phase diagram.Comment: (5 pages, 3 figures

Structural model optimization using statistical evaluation

The results of research in applying statistical methods to the problem of structural dynamic system identification are presented. The study is in three parts: a review of previous approaches by other researchers, a development of various linear estimators which might find application, and the design and development of a computer program which uses a Bayesian estimator. The method is tried on two models and is successful where the predicted stiffness matrix is a proper model, e.g., a bending beam is represented by a bending model. Difficulties are encountered when the model concept varies. There is also evidence that nonlinearity must be handled properly to speed the convergence

Changing the Order of Mathematics Test Items: Helping or Hindering Student Performance?

This paper recounts an experiment by a mathematics professor who primarily teaches mathematics majors. The main question explored is whether the ordering of the questions makes a difference as to how students perform in a test. More specifically we focus here on the following research questions:\ (1) Does arranging a math test with easy-to-hard items versus hard-to-easy items impact student performance? and (2) If so, does item order impact male and female mathematics majors and non-majors in unique ways? We examine data collected over multiple semesters with several different classes. We find that for most of the mathematics students who were examined, the ordering of the questions on a test did not impact performance. However, female majors performed better on classroom exams when the test was arranged with the more difficult questions presented first. Readers who are interested in teaching mathematics, educational psychology, or gender issues in the classroom may find our results intriguing