1,016 research outputs found
Breakup of the aligned H molecule by xuv laser pulses: A time-dependent treatment in prolate spheroidal coordinates
We have carried out calculations of the triple-differential cross section for
one-photon double ionization of molecular hydrogen for a central photon energy
of ~eV, using a fully {\it ab initio}, nonperturbative approach to solve
the time-dependent \Schro equation in prolate spheroidal coordinates. The
spatial coordinates and are discretized in a finite-element
discrete-variable representation. The wave packet of the laser-driven
two-electron system is propagated in time through an effective short iterative
Lanczos method to simulate the double ionization of the hydrogen molecule. For
both symmetric and asymmetric energy sharing, the present results agree to a
satisfactory level with most earlier predictions for the absolute magnitude and
the shape of the angular distributions. A notable exception, however, concerns
the predictions of the recent time-independent calculations based on the
exterior complex scaling method in prolate spheroidal coordinates
[Phys.~Rev.~A~{\bf 82}, 023423 (2010)]. Extensive tests of the numerical
implementation were performed, including the effect of truncating the Neumann
expansion for the dielectronic interaction on the description of the initial
bound state and the predicted cross sections. We observe that the dominant
escape mode of the two photoelectrons dramatically depends upon the energy
sharing. In the parallel geometry, when the ejected electrons are collected
along the direction of the laser polarization axis, back-to-back escape is the
dominant channel for strongly asymmetric energy sharing, while it is completely
forbidden if the two electrons share the excess energy equally.Comment: 17 pages, 9 figure
Passage time distributions in large Markov chains
Accepted versio
New, efficient, and accurate high order derivative and dissipation operators satisfying summation by parts, and applications in three-dimensional multi-block evolutions
We construct new, efficient, and accurate high-order finite differencing
operators which satisfy summation by parts. Since these operators are not
uniquely defined, we consider several optimization criteria: minimizing the
bandwidth, the truncation error on the boundary points, the spectral radius, or
a combination of these. We examine in detail a set of operators that are up to
tenth order accurate in the interior, and we surprisingly find that a
combination of these optimizations can improve the operators' spectral radius
and accuracy by orders of magnitude in certain cases. We also construct
high-order dissipation operators that are compatible with these new finite
difference operators and which are semi-definite with respect to the
appropriate summation by parts scalar product. We test the stability and
accuracy of these new difference and dissipation operators by evolving a
three-dimensional scalar wave equation on a spherical domain consisting of
seven blocks, each discretized with a structured grid, and connected through
penalty boundary conditions.Comment: 16 pages, 9 figures. The files with the coefficients for the
derivative and dissipation operators can be accessed by downloading the
source code for the document. The files are located in the "coeffs"
subdirector
HDArray: Parallel Array Interface for Distributed Heterogeneous Devices
Heterogeneous clusters with nodes containing one or more accelerators, such as GPUs, have become common. While MPI provides a mechanism and management of interaddress space communication, and OpenCL provides a way to manage computation and communication within a process with access to heterogeneous computational resources, programmers are forced to write hybrid programs that manage the interaction of both of these systems. This paper describes an array programming interface that provides users with automatic or manual distributions of data and work. Using the distribution and information about what data is used and defined by kernels, communication among processes and among devices in a process is performed automatically. The interface provides a unified programming model to the user, thus simplifying program development
A Mathematical Model for Supermarket Order Picking
Order picking consists in retrieving products from storage locations to sat- isfy independent orders from multiple customers. It is generally recognized as one of the most significant activities in a warehouse (Koster et al, 2007). In fact, order picking accounts up to 50% (Frazelle, 2001) or even 80% (Van den Berg, 1999) of the total warehouse operating costs. The critical issue in today’s business environ- ment is to simultaneously reduce the cost and increase the speed of order picking. In this paper, we address the order picking process in one of the Portuguese largest companies in the grocery business. This problem was proposed at the 92nd European Study Group with Industry (ESGI92). In this setting, each operator steers a trolley on the shop floor in order to select items for multiple customers. The objective is to improve their grocery e-commerce and bring it up to the level of the best inter- national practices. In particular, the company wants to improve the routing tasks in order to decrease distances. For this purpose, a mathematical model for a faster open shop picking was developed. In this paper, we describe the problem, our proposed solution as well as some preliminary results and conclusions.info:eu-repo/semantics/publishedVersio
Batch solution of small PDEs with the OPS DSL
In this paper we discuss the challenges and optimisations opportunities when solving a large number of small, equally sized discretised PDEs on regular grids. We present an extension of the OPS (Oxford Parallel library for Structured meshes) embedded Domain Specific Language, and show how support can be added for solving multiple systems, and how OPS makes it easy to deploy a variety of transformations and optimisations. The new capabilities in OPS allow to automatically apply data structure transformations, as well as execution schedule transformations to deliver high performance on a variety of hardware platforms. We evaluate our work on an industrially representative finance simulation on Intel CPUs, as well as NVIDIA GPUs
Finding apparent horizons and other two-surfaces of constant expansion
Apparent horizons are structures of spacelike hypersurfaces that can be
determined locally in time. Closed surfaces of constant expansion (CE surfaces)
are a generalisation of apparent horizons. I present an efficient method for
locating CE surfaces. This method uses an explicit representation of the
surface, allowing for arbitrary resolutions and, in principle, shapes. The CE
surface equation is then solved as a nonlinear elliptic equation.
It is reasonable to assume that CE surfaces foliate a spacelike hypersurface
outside of some interior region, thus defining an invariant (but still
slicing-dependent) radial coordinate. This can be used to determine gauge modes
and to compare time evolutions with different gauge conditions. CE surfaces
also provide an efficient way to find new apparent horizons as they appear e.g.
in binary black hole simulations.Comment: 21 pages, 8 figures; two references adde
R.A.Fisher, design theory, and the Indian connection
Design Theory, a branch of mathematics, was born out of the experimental
statistics research of the population geneticist R. A. Fisher and of Indian
mathematical statisticians in the 1930s. The field combines elements of
combinatorics, finite projective geometries, Latin squares, and a variety of
further mathematical structures, brought together in surprising ways. This
essay will present these structures and ideas as well as how the field came
together, in itself an interesting story.Comment: 11 pages, 3 figure
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