13,343 research outputs found
Dirac zero-modes in compact U(1) gauge theory
We study properties of the zero and near-zero eigenmodes of the overlap Dirac
operator in compact U(1) gauge theory. In the confinement phase the exact
zero-modes are localized as found by studying the values of the inverse
participation ratio and other features. Non-zero-eigenmodes are less localized
in the confinement phase. In the Coulomb phase no zero-modes are observed and
the eigenmodes show no localization at all.Comment: Minor corrections, 15 pages, 5 figures, LaTeX styl
On Asymptotic Global Error Estimation and Control of Finite Difference Solutions for Semilinear Parabolic Equations
The aim of this paper is to extend the global error estimation and control
addressed in Lang and Verwer [SIAM J. Sci. Comput. 29, 2007] for initial value
problems to finite difference solutions of semilinear parabolic partial
differential equations. The approach presented there is combined with an
estimation of the PDE spatial truncation error by Richardson extrapolation to
estimate the overall error in the computed solution. Approximations of the
error transport equations for spatial and temporal global errors are derived by
using asymptotic estimates that neglect higher order error terms for
sufficiently small step sizes in space and time. Asymptotic control in a
discrete -norm is achieved through tolerance proportionality and uniform
or adaptive mesh refinement. Numerical examples are used to illustrate the
reliability of the estimation and control strategies
Structural quantities of quasi-two-dimensional fluids
Quasi-two-dimensional fluids can be generated by confining a fluid between
two parallel walls with narrow separation. Such fluids exhibit an inhomogeneous
structure perpendicular to the walls due to the loss of translational symmetry.
Taking the transversal degrees of freedom as a perturbation to an appropriate
2D reference fluid we provide a systematic expansion of the -particle
density for arbitrary . To leading order in the slit width this density
factorizes into the densities of the transversal and lateral degrees of
freedom. Explicit expressions for the next-to-leading order terms are
elaborated analytically quantifying the onset of inhomogeneity. The case
yields the density profile with a curvature given by an integral over the
pair-distribution function of the corresponding 2D reference fluid, which
reduces to its 2D contact value in the case of pure excluded-volume
interactions. Interestingly, we find that the 2D limit is subtle and requires
stringent conditions on the fluid-wall interactions. We quantify the rapidity
of convergence for various structural quantities to their 2D counterparts.Comment: 12 page
BayesX: Analysing Bayesian structured additive regression models
There has been much recent interest in Bayesian inference for generalized additive and related models. The increasing popularity of Bayesian methods for these and other model classes is mainly caused by the introduction of Markov chain Monte Carlo (MCMC) simulation techniques which allow the estimation of very complex and realistic models. This paper describes the capabilities of the public domain software BayesX for estimating complex regression models with structured additive predictor. The program extends the capabilities of existing software for semiparametric regression. Many model classes well known from the literature are special cases of the models supported by BayesX. Examples are Generalized Additive (Mixed) Models, Dynamic Models, Varying Coefficient Models, Geoadditive Models, Geographically Weighted Regression and models for space-time regression. BayesX supports the most common distributions for the response variable. For univariate responses these are Gaussian, Binomial, Poisson, Gamma and negative Binomial. For multicategorical responses, both multinomial logit and probit models for unordered categories of the response as well as cumulative threshold models for ordered categories may be estimated. Moreover, BayesX allows the estimation of complex continuous time survival and hazardrate models
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