Topic

# Multipole expansion

About: Multipole expansion is a research topic. Over the lifetime, 9675 publications have been published within this topic receiving 214783 citations.

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TL;DR: In this paper, a program for evaluating the solution scattering from macromolecules with known atomic structure is presented, which uses multipole expansion for fast calculation of the spherically averaged scattering pattern and takes into account the hydration shell.

Abstract: A program for evaluating the solution scattering from macromolecules with known atomic structure is presented. The program uses multipole expansion for fast calculation of the spherically averaged scattering pattern and takes into account the hydration shell. Given the atomic coordinates (e.g. from the Brookhaven Protein Data Bank) it can either predict the solution scattering curve or fit the experimental scattering curve using only two free parameters, the average displaced solvent volume per atomic group and the contrast of the hydration layer. The program runs on IBM PCs and on the major UNIX platforms.

3,272 citations

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08 May 1969-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences

TL;DR: In this article, sound generation by turbulence and surfaces in arbitrary motion is discussed, and sound and multipole fields and governing equations are discussed. But sound generation is not discussed in this paper.

Abstract: Monograph on sound generation by turbulence and surfaces in arbitrary motion, discussing sound and multipole fields and governing equations

3,121 citations

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TL;DR: The current state of the art on post-Newtonian methods as applied to the dynamics and gravitational radiation of general matter sources (including the radiation reaction back onto the source) and inspiralling compact binaries is presented.

Abstract: The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the postNewtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many nonlinear multipole interactions, among them those associated with the tails (and tails-of-tails) of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail eects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary’s orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.

2,067 citations

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01 Nov 2016

TL;DR: In this paper, Cartesian tensors and spherical tensors are used to model the intermolecular potentials in the presence of many-body effects and intermolescular forces.

Abstract: Introduction 1. Molecules in Electrostatic Fields 2. Electrostatic Interactions between Molecules 3. Perturbation Theory of Intermolecular Forces at Long Range 4. Ab Initio Methods 5. Perturbation Theory of Intermolecular Forces at Short Range 6. Distributed Multipole Expansions 7. Distributed Polarizabilities 8. Many-body Effects and Intermolecular Forces in Solution 9. Interactions Involving Excited States 10. Practical Models for Intermolecular Potentials 11. Sources of Experimental Data Appendices: A Cartesian Tensors B Spherical Tensors C Introduction to Perturbation Theory D Conversion Factors E Cartesian-Spherical Conversion Tables F Interaction Functions

1,643 citations

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TL;DR: Using these techniques, the FMM and MLFMA can solve the problem of electromagnetic scattering by large complex three-dimensional objects such as an aircraft on a small computer.

Abstract: The fast multipole method (FMM) and multilevel fast multipole algorithm (MLFMA) are reviewed. The number of modes required, block-diagonal preconditioner, near singularity extraction, and the choice of initial guesses are discussed to apply the MLFMA to calculating electromagnetic scattering by large complex objects. Using these techniques, we can solve the problem of electromagnetic scattering by large complex three-dimensional (3-D) objects such as an aircraft (VFY218) on a small computer.

1,562 citations