736,453 research outputs found
Optimized local modes for lattice dynamical applications
We present a new scheme for the construction of highly localized lattice
Wannier functions. The approach is based on a heuristic criterion for
localization and takes the symmetry constraints into account from the start. We
compare the local modes thus obtained with those generated by other schemes and
find that they also provide a better description of the relevant vibrational
subspace.Comment: 6 pages, ReVTeX, plus four postscript files for figure
Generic effective source for scalar self-force calculations
A leading approach to the modelling of extreme mass ratio inspirals involves
the treatment of the smaller mass as a point particle and the computation of a
regularized self-force acting on that particle. In turn, this computation
requires knowledge of the regularized retarded field generated by the particle.
A direct calculation of this regularized field may be achieved by replacing the
point particle with an effective source and solving directly a wave equation
for the regularized field. This has the advantage that all quantities are
finite and require no further regularization. In this work, we present a method
for computing an effective source which is finite and continuous everywhere,
and which is valid for a scalar point particle in arbitrary geodesic motion in
an arbitrary background spacetime. We explain in detail various technical and
practical considerations that underlie its use in several numerical self-force
calculations. We consider as examples the cases of a particle in a circular
orbit about Schwarzschild and Kerr black holes, and also the case of a particle
following a generic time-like geodesic about a highly spinning Kerr black hole.
We provide numerical C code for computing an effective source for various
orbital configurations about Schwarzschild and Kerr black holes.Comment: 24 pages, 7 figures, final published versio
Nonparametric estimation of mean-squared prediction error in nested-error regression models
Nested-error regression models are widely used for analyzing clustered data.
For example, they are often applied to two-stage sample surveys, and in biology
and econometrics. Prediction is usually the main goal of such analyses, and
mean-squared prediction error is the main way in which prediction performance
is measured. In this paper we suggest a new approach to estimating mean-squared
prediction error. We introduce a matched-moment, double-bootstrap algorithm,
enabling the notorious underestimation of the naive mean-squared error
estimator to be substantially reduced. Our approach does not require specific
assumptions about the distributions of errors. Additionally, it is simple and
easy to apply. This is achieved through using Monte Carlo simulation to
implicitly develop formulae which, in a more conventional approach, would be
derived laboriously by mathematical arguments.Supported in part by NSF Grant SES-03-18184
Nonparametric estimation of mean-squared prediction error in nested-error regression models
Nested-error regression models are widely used for analyzing clustered data.
For example, they are often applied to two-stage sample surveys, and in biology
and econometrics. Prediction is usually the main goal of such analyses, and
mean-squared prediction error is the main way in which prediction performance
is measured. In this paper we suggest a new approach to estimating mean-squared
prediction error. We introduce a matched-moment, double-bootstrap algorithm,
enabling the notorious underestimation of the naive mean-squared error
estimator to be substantially reduced. Our approach does not require specific
assumptions about the distributions of errors. Additionally, it is simple and
easy to apply. This is achieved through using Monte Carlo simulation to
implicitly develop formulae which, in a more conventional approach, would be
derived laboriously by mathematical arguments.Comment: Published at http://dx.doi.org/10.1214/009053606000000579 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Assessment of the undergraduate Curriculum in Paediatrics in Malta : student feedback in Paediatrics, Malta
Aim: The study was designed to assess both satisfactory and unsatisfactory aspects of the undergraduate curriculum in Paediatrics as perceived by the students themselves. Methods: A simple questionnaire was designed to assess students' perceptions of the curriculum and was returned from 17 students from a cohort of 57 in 1999, and 32 from 39 in 2002. Results: In most aspects of the course, replies were highly satisfactory and often excellent, particularly with regard to the course organisation, attendance of lecturers, coverage of general paediatrics, tutorials and examinations. Some areas where student dissatisfaction was in excess of one third of respondents, notably the amount of neonatal coverage in 1999, have been addressed and had improved in 2002. Nevertheless, the follow up questionnaire in 2002 has shown that other issues remain problematic, particularly a lack of coverage of community paediatrics and insufficient `hands-on' teaching. Conclusions: A simple questionnaire-based format for assessing student feedback was both practical and reliable, and can be applied to assess the influence of any future changes in the curriculum. The questionnaire does not only confirm anticipated curricular deficiencies but is also effective in highlighting unexpected problems that can, therefore, be addressed appropriately.peer-reviewe
Fourth Order Algorithms for Solving the Multivariable Langevin Equation and the Kramers Equation
We develop a fourth order simulation algorithm for solving the stochastic
Langevin equation. The method consists of identifying solvable operators in the
Fokker-Planck equation, factorizing the evolution operator for small time steps
to fourth order and implementing the factorization process numerically. A key
contribution of this work is to show how certain double commutators in the
factorization process can be simulated in practice. The method is general,
applicable to the multivariable case, and systematic, with known procedures for
doing fourth order factorizations. The fourth order convergence of the
resulting algorithm allowed very large time steps to be used. In simulating the
Brownian dynamics of 121 Yukawa particles in two dimensions, the converged
result of a first order algorithm can be obtained by using time steps 50 times
as large. To further demostrate the versatility of our method, we derive two
new classes of fourth order algorithms for solving the simpler Kramers equation
without requiring the derivative of the force. The convergence of many fourth
order algorithms for solving this equation are compared.Comment: 19 pages, 2 figure
Improved Calculation of Vibrational Mode Lifetimes in Anharmonic Solids - Part I: Theory
We propose here a formal foundation for practical calculations of vibrational
mode lifetimes in solids. The approach is based on a recursion method analysis
of the Liouvillian. From this we derive the lifetime of a vibrational mode in
terms of moments of the power spectrum of the Liouvillian as projected onto the
relevant subspace of phase space. In practical terms, the moments are evaluated
as ensemble averages of well-defined operators, meaning that the entire
calculation is to be done with Monte Carlo. These insights should lead to
significantly shorter calculations compared to current methods. A companion
piece presents numerical results.Comment: 18 pages, 3 figure
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