Measure dependence of 2D simplicial quantum gravity

We study pure 2D Euclidean quantum gravity with $R^2$ interaction on spherical lattices, employing Regge's formulation. We attempt to measure the string susceptibility exponent $\gamma_{\rm str}$ by using a finite-size scaling Ansatz in the expectation value of $R^2$. To check on effects of the path integral measure we investigate two scale invariant measures, the "computer" measure $dl/l$ and the Misner measure $dl/\sqrt A$.Comment: 3 pages, self unpacking uuencoded PostScript file, contribution to LATTICE9

Parallelism in the Hanvueng: A Zhuang Verse Epic from West-Central Guangxi in Southern China

Zhuang is a Tai-Kadai language spoken in southern China. Parallelism is ubiquitous in Zhuang poetry and song,in ritual texts, and in a range of oral genres. Curiously, this salient fact has generally escaped the notice of scholars writing on the subject of Zhuang poetics. This article looks specifically at the phenomenon of parallelism in one particular Zhuang ritual text from west-central Guangxi. This is the Hanvueng, a long verse narrative that is recited at rituals intended to deal with cases of unnatural death and serious family quarrels, especially feuding between brothers. I provide a general description of the role of song and parallel verse in Zhuang oral culture. I next present a typology of poetic lines and passages exhibiting strict parallelism and quasi-parallelism, and also look at the rhetorical and rhythmical uses of non-parallel lines. As a second step in this investigation, I re-analyse these typological categories in terms of the recitation soundscape as it unfolds in real time and in ritual performance. This second step brings us back from an objectivist account to a variety of emic perspectives, and allows us to see more clearly the rhetorical and emotive power generated by the ongoing narration -- and its artistry -- for a range of participants within the ritual space.Abstract from website.David Holm is a Professor in the Department of Ethnology at National Chengchi University in Taipei. He completed a first degree in Classics at the University of Glasgow and holds a D.Phil. in Chinese from the University of Oxford. He conducted fieldwork in the northwest of China during the 1980s and published a monograph on the performing arts and Chinese Communist Party cultural policy (Art and Ideology in Revolutionary China, 1991). Since the early 1990s, he has been engaged in fieldwork on Zhuang and ritual theatre in Guangxi, and produced two collections of edited Zhuang ritual texts (Killing a Buffalo, 2003 and Recalling Lost Souls, 2004). More recently, he has conducted systematic surveys of the traditional vernacular character scripts of the Zhuang and other Tai speakers in southern China and northern Vietnam, and has published a compedium Mapping the Old Zhuang Character Script (Brill, 2013). He is currently editor-inchief, along with Professor Meng Yuanyao of Guangxi Nationalities University, of the series Zhuang Traditional Texts, published by Brill

On the persistence properties of the cross-coupled Camassa-Holm system

In this paper we examine the evolution of solutions, that initially have compact support, of a recently-derived system of cross-coupled Camassa-Holm equations. The analytical methods which we employ provide a full picture for the persistence of compact support for the momenta. For solutions of the system itself, the answer is more convoluted, and we determine when the compactness of the support is lost, replaced instead by an exponential decay rate.Comment: 13 pages, 1 figur

Measuring the string susceptibility in 2D simplicial quantum gravity using the Regge approach

We use Monte Carlo simulations to study pure 2D Euclidean quantum gravity with $R^2$-interaction on spherical topologies, employing Regge's formulation. We attempt to measure the string susceptibility exponent $\gamma_{\rm str}$ by using a finite-size scaling Ansatz in the expectation value of $R^2$, as has been done in a previous study by Bock and Vink ( hep-lat/9406018 ). By considerably extending the range and statistics of their study we find that this Ansatz is plagued by large systematic errors. The $R^2$ specific string susceptibility exponent \GS' is found to agree with theoretical predictions, but its determination also is subject to large systematic errors and the presence of finite-size scaling corrections. To circumvent this obstacle we suggest a new scaling Ansatz which in principle should be able to predict both, \GS and \GS'. First results indicate that this requires large system sizes to reduce the uncertainties in the finite-size scaling Ans\"atze. Nevertheless, our investigation shows that within the achievable accuracy the numerical estimates are still compatible with analytic predictions, contrary to the recent claim by Bock and Vink.Comment: 33 pages, self unpacking uuencoded PostScript file, including all the figures. Paper also available at http://www.physik.fu-berlin.de/~holm

Lagrange-Poincare field equations

The Lagrange-Poincare equations of classical mechanics are cast into a field theoretic context together with their associated constrained variational principle. An integrability/reconstruction condition is established that relates solutions of the original problem with those of the reduced problem. The Kelvin-Noether theorem is formulated in this context. Applications to the isoperimetric problem, the Skyrme model for meson interaction, metamorphosis image dynamics, and molecular strands illustrate various aspects of the theory.Comment: Submitted to Journal of Geometry and Physics, 45 pages, 1 figur

Fractal Structure in Two-Dimensional Quantum Regge Calculus

We study the fractal structure of the surface in two-dimensional quantum Regge calculus by performing Monte Carlo simulation with up to 200,000 triangles. The result can be compared with the universal scaling function obtained analytically in the continuum limit of dynamical triangulation, which provides us with a definite criterion whether Regge calculus serves as a proper regularization of quantum gravity. When the scale-invariant measure is taken as the measure of the link-length integration, we observe the correct scaling behavior in the data for the type of loop attached to a baby universe. The data seem to converge to the universal scaling function as the number of triangles is increased. The data for the type of loop attached to the mother universe, on the other hand, shows no scaling behavior up to the present size.Comment: 13 pages + 8 figures, LaTeX, UT-683, KEK-TH-401 (double-spacing command removed. sorry.