On the convergence of Regge calculus to general relativity

Motivated by a recent study casting doubt on the correspondence between Regge calculus and general relativity in the continuum limit, we explore a mechanism by which the simplicial solutions can converge whilst the residual of the Regge equations evaluated on the continuum solutions does not. By directly constructing simplicial solutions for the Kasner cosmology we show that the oscillatory behaviour of the discrepancy between the Einstein and Regge solutions reconciles the apparent conflict between the results of Brewin and those of previous studies. We conclude that solutions of Regge calculus are, in general, expected to be second order accurate approximations to the corresponding continuum solutions.Comment: Updated to match published version. Details of numerical calculations added, several sections rewritten. 9 pages, 4 EPS figure

Fast algorithms for computing defects and their derivatives in the Regge calculus

Any practical attempt to solve the Regge equations, these being a large system of non-linear algebraic equations, will almost certainly employ a Newton-Raphson like scheme. In such cases it is essential that efficient algorithms be used when computing the defect angles and their derivatives with respect to the leg-lengths. The purpose of this paper is to present details of such an algorithm.Comment: 38 pages, 10 figure

Is the Regge Calculus a consistent approximation to General Relativity?

We will ask the question of whether or not the Regge calculus (and two related simplicial formulations) is a consistent approximation to General Relativity. Our criteria will be based on the behaviour of residual errors in the discrete equations when evaluated on solutions of the Einstein equations. We will show that for generic simplicial lattices the residual errors can not be used to distinguish metrics which are solutions of Einstein's equations from those that are not. We will conclude that either the Regge calculus is an inconsistent approximation to General Relativity or that it is incorrect to use residual errors in the discrete equations as a criteria to judge the discrete equations.Comment: 27 pages, plain TeX, very belated update to match journal articl

Academic achievement : the role of praise in motivating students

The motivation of students is an important issue in higher education, particularly in the context of the increasing diversity of student populations. A social-cognitive perspective assumes motivation to be dynamic, context-sensitive and changeable, thereby rendering it to be a much more differentiated construct than previously understood. This complexity may be perplexing to tutors who are keen to develop applications to improve academic achievement. One application that is within the control of the tutor, at least to some extent, is the use of praise. Using psychological literature the article argues that in motivating students, the tutor is not well served by relying on simplistic and common sense understandings of the construct of praise and that effective applications of praise are mediated by students' goal orientations, which of themselves may be either additive or interactive composites of different objectives and different contexts

High-accuracy relativistic many-body calculations of van der Waals coefficients C_6 for alkaline-earth atoms

Relativistic many-body calculations of van der Waals coefficients C_6 for dimers correlating to two ground state alkaline-earth atoms at large internuclear separations are reported. The following values and uncertainties were determined : C_6 = 214(3) for Be, 627(12) for Mg, 2221(15) for Ca, 3170(196) for Sr, and 5160(74) for Ba in atomic units.Comment: 5 pages, submitted to Phys. Rev.

Mammals of the Roosevelt Brazilian Expedition

p. 559-610 : ill. ; 24 cm.Includes bibliographical references