'Bound Over to Satan’s Tyranny’ : Sin and Satan in Contemporary Reformed Hamartiology

Peer reviewedPostprin

An Exactly Soluble Model of Directed Polymers with Multiple Phase Transitions

Polymer chains with hard-core interaction on a two-dimensional lattice are modeled by directed random walks. Two models, one with intersecting walks (IW) and another with non-intersecting walks (NIW) are presented, solved and compared. The exact solution of the two models, based on a representation using Grassmann variables, leads, surprisingly, to the same analytic expression for the polymer density and identical phase diagrams. There are three different phases as a function of hopping probability and single site monomer occupancy, with a transition from the dense polymer system to a polymer liquid (A) and a transition from the liquid to an empty lattice (B). Within the liquid phase there exists a self-dual line with peculiar properties. The derivative of polymer density with respect to the single site monomer occupancy diverges at transitions A and B, but is smooth across and along the self-dual line. The density-density correlation function along the direction $x$, perpendicular to the axis of directedness has a power law decay 1/$x^2$ in the entire liquid phase, in both models. The difference between the two models shows up only in the behavior of the correlation function along the self-dual line: it decays exponentially in the IW model and as 1/$x^4$ in the NIW model.Comment: 8 pages, plain-TeX, figures available upon reques

Is the Peak Value of σxx\sigma_{xx} at the Quantum Hall Transition Universal?

The question of the universality of the longitudinal peak conductivity at the integer quantum Hall transition is considered. For this purpose, a system of 2D Dirac fermions with random mass characterised by variance $g$ is proposed as a model which undergoes a quantum Hall transition. Whilst for some specific models the longitudinal peak conductivity $\sigma_{xx}$ was found to be universal (in agreement with the conjecture of Lee et al. as well as with some numerical work), we find that $\sigma_{xx}$ is reduced by a factor $(1+g/2\pi)^{-1}$, at least for small $g$. This provides some theoretical evidence for the non-universality of $\sigma_{xx}$, as observed in a number of experiments.Comment: 2 double-column LaTeX pages, no figures, to appear in Z.Phys.

Geodynamo alpha-effect derived from box simulations of rotating magnetoconvection

The equations for fully compressible rotating magnetoconvection are numerically solved in a Cartesian box assuming conditions roughly suitable for the geodynamo. The mean electromotive force describing the generation of mean magnetic flux by convective turbulence in the rotating fluid is directly calculated from the simulations, and the corresponding alpha-coefficients are derived. Due to the very weak density stratification the alpha-effect changes its sign in the middle of the box. It is positive at the top and negative at the bottom of the convection zone. For strong magnetic fields we also find a clear downward advection of the mean magnetic field. Both of the simulated effects have been predicted by quasi-linear computations (Soward, 1979; Kitchatinov and Ruediger, 1992). Finally, the possible connection of the obtained profiles of the EMF with mean-field models of oscillating alpha^2-dynamos is discussed.Comment: 17 pages, 9 figures, submitted to Phys. Earth Planet. Inte

Convex Hulls, Oracles, and Homology

This paper presents a new algorithm for the convex hull problem, which is based on a reduction to a combinatorial decision problem POLYTOPE-COMPLETENESS-COMBINATORIAL, which in turn can be solved by a simplicial homology computation. Like other convex hull algorithms, our algorithm is polynomial (in the size of input plus output) for simplicial or simple input. We show that the ``no''-case of POLYTOPE-COMPLETENESS-COMBINATORIAL has a certificate that can be checked in polynomial time (if integrity of the input is guaranteed).Comment: 11 pages, 2 figure

A Study of Sediment Transport in Norwegian Glacial Rivers, 1969

From original report: The Norwegian Water Resources and Electricity Board, Institute of Water Resources, Department of Hydrology, Oslo. September 1970. Report No. 6/70.Permission to translate this Norwegian report was kindly given by G. Østrem, and the translation by Helga Carstens, while she was in Alaska, is greatly appreciated. Unfortunately, Mrs. Carstens returned to her homeland, Norway, before final editing of the manuscript could be completed. Consequently, any errors in translation are due to the editor, and for these errors, the editor apologizes to the authors. Not included in this translation is an English summary contained in the original report. To keep printing costs down, the original figures and tables, which fortunately had English titles, are used in this translation. This report is the first of a series of reports being prepared for the Norwegian Water Resources and Electricity Board. The second report for 1970 has been published with an English summary and contains an extension of the data contained in the 1969 report. Because this work deals with problems very similar to those in Alaska, it was decided to translate the first report and circulate a limited number of copies to workers in the U. S. and Canada. Research very similar to the Norwegian work was initiated in Alaska under the editor's direction in cooperation with the U. S. Geological Survey. -- G. L. Guymon.This work and the translation of this report were supported by funds provided by the United States Department of the Interior, Office of Water Resources Research (Proj. A-042-ALAS), as authorized under the amended Water Resources Act of 1964

3D simulations of rising magnetic flux tubes in a compressible rotating interior: The effect of magnetic tension

Context: Long-term variability in solar cycles represents a challenging constraint for theoretical models. Mean-field Babcock-Leighton dynamos that consider non-instantaneous rising flux tubes have been shown to exhibit long-term variability in their magnetic cycle. However a relation that parameterizes the rise-time of non-axisymmetric magnetic flux tubes in terms of stellar parameters is still missing. Aims: We aim to find a general parameterization of the rise-time of magnetic flux tubes for solar-like stars. Methods: By considering the influence of magnetic tension on the rise of non-axisymmetric flux tubes, we predict the existence of a control parameter referred as $\Gamma_{\alpha_1}^{\alpha_2}$. This parameter is a measure of the balance between rotational effects and magnetic effects (buoyancy and tension) acting on the magnetic flux tube. We carry out two series of numerical experiments (one for axisymmetric rise and one for non-axisymmetric rise) and demonstrate that $\Gamma_{\alpha_1}^{\alpha_2}$ indeed controls the rise-time of magnetic flux tubes. Results: We find that the rise-time follows a power law of $\Gamma_{\alpha_1}^{\alpha_2}$ with an exponent that depends on the azimuthal wavenumber of the magnetic flux loop. Conclusions: Compressibility does not impact the rise of magnetic flux tubes, while non-axisymmetry does. In the case of non-axisymmetric rise, the tension force modifies the force balance acting on the magnetic flux tube. We identified the three independent parameters required to predict the rise-time of magnetic flux tubes, that is, the stellar rotation rate, the magnetic flux density of the flux tube, and its azimuthal wavenumber. We combined these into one single relation that is valid for any solar-like star. We suggest using this generalized relation to constrain the rise-time of magnetic flux tubes in Babcock-Leighton dynamo models.Comment: 18 pages, 15 figures, 6 tabula