Topic

# Multipole expansion

About: Multipole expansion is a(n) research topic. Over the lifetime, 9675 publication(s) have been published within this topic receiving 214783 citation(s).

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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.

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3,016 citations

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

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

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2,771 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.

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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.

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1,732 citations

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01 Nov 2016-

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

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1,592 citations

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Abstract: A new component of the cosmic medium, a light scalar field or ''quintessence '', has been proposed recently to explain cosmic acceleration with a dynamical cosmological constant Such a field is expected to be coupled explicitely to ordinary matter, unless some unknown symmetry prevents it I investigate the cosmological consequences of such a coupled quintessence (CQ) model, assuming an exponential potential and a linear coupling This model is conformally equivalent to Brans-Dicke Lagrangians with power-law potential I evaluate the density perturbations on the cosmic microwave background and on the galaxy distribution at the present and derive bounds on the coupling constant from the comparison with observational data A novel feature of CQ is that during the matter dominated era the scalar field has a finite and almost constant energy density This epoch, denoted as $\phi $MDE, is responsible of several differences with respect to uncoupled quintessence: the multipole spectrum of the microwave background is tilted at large angles, the acoustic peaks are shifted, their amplitude is changed, and the present 8Mpc$/h$ density variance is diminished The present data constrain the dimensionless coupling constant to $|\beta |\leq 01$

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1,464 citations