Accelerating Staggered Fermion Dynamics with the Rational Hybrid Monte Carlo (RHMC) Algorithm

Improved staggered fermion formulations are a popular choice for lattice QCD calculations. Historically, the algorithm used for such calculations has been the inexact R algorithm, which has systematic errors that only vanish as the square of the integration step-size. We describe how the exact Rational Hybrid Monte Carlo (RHMC) algorithm may be used in this context, and show that for parameters corresponding to current state-of-the-art computations it leads to a factor of approximately seven decrease in cost as well as having no step-size errors.Comment: 4 pages, 2 figures, 1 tabl

The Rational Hybrid Monte Carlo Algorithm

The past few years have seen considerable progress in algorithmic development for the generation of gauge fields including the effects of dynamical fermions. The Rational Hybrid Monte Carlo (RHMC) algorithm, where Hybrid Monte Carlo is performed using a rational approximation in place the usual inverse quark matrix kernel is one of these developments. This algorithm has been found to be extremely beneficial in many areas of lattice QCD (chiral fermions, finite temperature, Wilson fermions etc.). We review the algorithm and some of these benefits, and we compare against other recent algorithm developements. We conclude with an update of the Berlin wall plot comparing costs of all popular fermion formulations.Comment: 15 pages. Proceedings from Lattice 200

Asymptotics of Fixed Point Distributions for Inexact Monte Carlo Algorithms

We introduce a simple general method for finding the equilibrium distribution for a class of widely used inexact Markov Chain Monte Carlo algorithms. The explicit error due to the non-commutivity of the updating operators when numerically integrating Hamilton's equations can be derived using the Baker-Campbell-Hausdorff formula. This error is manifest in the conservation of a ``shadow'' Hamiltonian that lies close to the desired Hamiltonian. The fixed point distribution of inexact Hybrid algorithms may then be derived taking into account that the fixed point of the momentum heatbath and that of the molecular dynamics do not coincide exactly. We perform this derivation for various inexact algorithms used for lattice QCD calculations.Comment: 24 pages, accepted for publication in Physics Review

A history of the city of Somerville for the first four grades

Thesis (Ed.M.)--Boston Universit

The RHMC algorithm for theories with unknown spectral bounds

The Rational Hybrid Monte Carlo (RHMC) algorithm extends the Hybrid Monte Carlo algorithm for lattice QCD simulations to situations involving fractional powers of the determinant of the quadratic Dirac operator. This avoids the updating increment ($dt$) dependence of observables which plagues the Hybrid Molecular-dynamics (HMD) method. The RHMC algorithm uses rational approximations to fractional powers of the quadratic Dirac operator. Such approximations are only available when positive upper and lower bounds to the operator's spectrum are known. We apply the RHMC algorithm to simulations of 2 theories for which a positive lower spectral bound is unknown: lattice QCD with staggered quarks at finite isospin chemical potential and lattice QCD with massless staggered quarks and chiral 4-fermion interactions ($\chi$QCD). A choice of lower bound is made in each case, and the properties of the RHMC simulations these define are studied. Justification of our choices of lower bounds is made by comparing measurements with those from HMD simulations, and by comparing different choices of lower bounds.Comment: Latex(Revtex 4) 25 pages, 8 postscript figure

Utilization of community resources in the intermediate grades.

Thesis (Ed.M.)--Boston Universit

The government's child poverty target: how much progress has been made?

Before the 2001 election the Treasury said that `tax and benefit reforms announced in this Parliament will lift over 1.2 million children out of relative poverty'. But official figures released on 11 April show a smaller fall in child poverty, of only 0.5 million since 1996-97. This commentary attempts to explain the discrepancy. Using the data that lie behind the official Households Below Average Income publications, we analyse trend in child poverty, measured against various poverty lines, since 1979. We show how the government's choice of a relative poverty line is making its goal to abolish child poverty more difficult and more expensive. We also discuss how easy the government will find it to make further reductions in child poverty