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Topic: Multipoles

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	Multipole Explanation
		This is again where the multipoles come in handy: based on the multipole data, we can anticipate a reaction to the field without knowing what it true shape is, and we can gather hints about what the shape might be.
		The index is the highest order of multipoles used in that reconstruction, with zero being the monopole and six being the hexacontatetrapole.
		Each additional multipole is shown in grey and white, where grey is an addition and white is a subtraction.
	physics.unl.edu /~tgay/ns/multipoles.html (1202 words)

	BioMagnetic Research and Technology \| Full text \| Simultaneous suppression of disturbing fields and localization of ...
		Multipole expansions are used also to model spatially distributed biological sources such as brain currents [7,8].
		The application of multipoles for the localization of magnetic dipoles is described in [9,10], and is used in other technical areas without disturbing field suppression [11].
		The multipole localization is an effective algorithm because it unites a method for the suppression of disturbing fields with a localization method.
	www.biomagres.com /content/2/1/6 (2733 words)

	BioMed Central \| Full text \| Multipolar representation of protein structure
		The notion of multipoles originates in physics [13] and is closely related to the representation of functions in terms of spherical harmonics [14].
		Each multipole in the series accounts for the contribution of a certain type of deviation of the density field from a spherically symmetric distribution and, in general, the higher the order of the multipole the smaller the spatial scale of the deviation it describes.
		The use of multipoles as shape descriptors is also closely related to the more general methods of 3D moments used in the field of object recognition in computer science [21-23].
	www.biomedcentral.com /1471-2105/7/242 (7019 words)

	Background: What Are Multipoles?
		The FMA process, however, uses a Multipole Expansion (MPE) to represent the effects of a group of distant particles as a single entity.
		By using the MPE when computing forces on a particle, and doing operations to combine multipole expansions, the overall amount of computation can be reduced to an almost linear relationship with the number of particles.
		These algorithms are similar to Greengard's FMA, in that they use oct-tree based spatial decomposition and multipoles, but do not utilize the concept of combining distant multipoles into local expansions prior to computing the particle forces.
	www.ee.duke.edu /~wrankin/Dpmta/users_guide/node2.html (371 words)

	Multipole Vectors
		A paper focusing on the low l multipoles (l=2 and 3), the planarity of l=3 and the alignment of the l=2 and l=3 planes.
		The light gray stars are particular sums of the multipole vectors which are very close to the temperature minima and maxima of the octopole.
		The trajectories of the Quadrupole and Octopole multipole vectors for the TOH map as the V band synchrotron foreground map is slowly added.
	www.phys.cwru.edu /projects/mpvectors (1600 words)

	5.3 Black hole multipole moments
		Field multipoles appear in the asymptotic expansions of the fields at infinity while the source multipoles are defined in terms of the mass or charge distribution of the source.
		The knowledge of these multipole moments suffices to determine the space-time geometry in a neighborhood of spatial infinity [41, 40, 42].
		Finally, note that there is no a-priori reason for these source multipoles to agree with the field multipoles at infinity; there could be matter fields or radiation outside the horizon which contribute to the field multipoles at infinity.
	relativity.livingreviews.org /Articles/lrr-2004-10/articlesu11.html (738 words)

	EGAD: WMAP: The Cosmic Axis of Evil
		Now the bread-and-butter of CMB work is breaking this map up into multipoles, or simple functions that each encode structure on a particular scale, and which when added together give you the original map.
		Reading the maps left to right, top to bottom, the first few multipoles are shown that add up to the large-scale structure of the CMB sky.
		This sort of large-scale structure is reflected in the multipole plots; several of these low-order maps similarly have a cold peak at about this point.
	blog.lib.umn.edu /mill1974/EGAD/041107.html (1152 words)

	The Maxwell Program package
		The program MOMENTS can perform the multipole expansion at the position of any of the atoms or it can partition the electron density into atomic contributions in a number of different ways and the perform the multipole expansion on each separately.
		The permanent multipole contribution is calculated with Campbell's generalization of the Ewald method for ionic lattices to lattices of multipoles of arbitrary order and an efficient algorithm for a sequence of calculations on the same lattice but different molecular orientations [7].
		This program computes the multipole moments and characteristic directions of a spherical harmonic representing the cartesian moments of a charge distribution as required by the Maxwell theory of the poles of a spherical harmonics [1].
	fulcrum.physbio.mssm.edu /endo/maxwell.html (10869 words)

	Properties of multipole fields
		This, of course, is an electrostatic multipole field.
		Thus, in the near zone the magnetic field associated with an electric multipole is always much smaller than the corresponding electric field.
		For magnetic multipole fields it is evident from Eqs.
	farside.ph.utexas.edu /teaching/jk1/lectures/node99.html (489 words)

	Phase Transitions in Quasi-Two-Dimensional Molecular Solids: Tilt-Induced Elastic Multipoles and Their Interaction and ... (Site not responding. Last check: 2007-10-21)
		Using a solid state approach, elastic multipoles are demonstrated to be effective for modeling the tilting of molecules in Langmuir monolayers.
		A detailed analysis of this indirect interaction and the idea of using local elastic multipoles to describe fluctuations in orientational degrees of freedom is the thrust of this work.
		Expressed in terms of spherical harmonics, elastic multipoles provide a convenient and powerful representation of the local stresses and of their interaction as mediated by the elastic field of the monolayer.
	pubs.acs.org /cgi-bin/abstract.cgi/jpchax/1996/100/i16/abs/jp953296h.html (255 words)

	Power Spectrum
		The lowest multipoles are the largest-area, continent- and ocean-size undulations on the temperature map.
		Higher multipoles are like successively smaller-area plateaus, mountains and hills (and trenches and valleys) inserted on top of the larger features.
		The entire complicated topography is the sum of the individual multipoles.
	universe-review.ca /R05-04-powerspectrum.htm (2048 words)

	Multigrid Methods (Site not responding. Last check: 2007-10-21)
		In turn, this involves the partitioning of the extended molecular charge distribution, so that charges and multipole moments can be assigned to different atoms.
		As an alternate to current approaches, we have investigated a charge partitioning scheme that is based on the maximally-localized Wannier functions.
		Tests on isolated molecules and water dimers, show that the molecular electrostatic potentials generated by such a Wannier-function based approach are in excellent agreement with the density functional-based calculations.
	nemo.physics.ncsu.edu /virgil/projects/Abinitio_calculation_of_electrostatic_multipoles.htm (270 words)

	NEIGHBOURS MANUAL
		It is essential that the calcultation uses the same orientation of the molecule as in the defined axes file.It is essentially the same definition of atomic multipole moments, as multipole expansion of electrostatic energy programmed in DMAREL.
		The atomic multipoles from the distributed multipole analysis (DMA) punch file, this can be calculated using either CADPAC or from GAUSSIAN files using GDMA.
		The multipole expansions from the punch file are changed so that all odd-z components on the inverted molecule have the sign changed.
	www.ucl.ac.uk /~ucca17p/neighmanual/input.html (718 words)

	Distributed Multipoles by Numerical Integration
		The multipole analysis discussed in the previous section is Stones's technique which distributes the multipoles by partitioning the contributions from pairs of gaussian basis functions amongst the verious centres.
		Its one disadvantage is that the individual distributed multipoles are sensitive to the basis set used, especially if diffuse basis functions are being used.
		The multipole moments are given in spherical harmonic form.
	www-theor.ch.cam.ac.uk /software/cadpac/chap6/node8.html (267 words)

	Emission by multipoles: an exact result in terms of reducible multipoles
		On the basis of an expression for the (time-averaged) radiated power comprising the radiation sources at the retarded time, an exact expression relevant to the emission by reducible multipoles is obtained, which, along with the emission from independent multipoles, accounts for the emission from the interaction between multipoles of different order.
		Whereas the former contribution is known in literature, at least for the lower-order multipoles, the latter contribution so far appears to have been overlooked.
		The result thus obtained is discussed in reference to the treatment of multipole emission in terms of irreducible multipoles, generalized to non-monochromatic sources.
	stacks.iop.org /0305-4470/30/4273 (291 words)

	J Data for structure factor calculations using multipole form factors
		Several multipole amplitude pairs for the same atom may be given on one card.
		Words which indicate the radial form factors to be used for the different L values of multipoles describing the scattering factor with this label.
		0), where the form factor on the corresponding F card applies to the multipoles with this value of L. The form factor for L=0 is that corresponding to label.
	www.ill.fr /dif/ccsl/mk4man/c3node15.html (263 words)

	Quadrupole - Wikipedia, the free encyclopedia
		The steel is magnetized by a large electric current that flow in the coils of tubing wrapped around the poles.
		can be extended to higher orders in a multipole expansion.
		A monopole field (as for a single electric charge, or a single mass in Isaac Newton's law of universal gravitation, falls off with the inverse square law.
	en.wikipedia.org /wiki/Quadrupole (681 words)

	MOLCAS: introduction
		The force field is based on localised multipoles and polarisabilities and therefore contain many-body effects in an effective way.
		The new software also includes a module for computing local properties (multipole moments and polarizabilities), which are used to construct the NEMO force fields for MC/MD simulations of macromolecular systems, liquids, etc.
		The size of the systems that can be treated with MOLCAS have been limited due to limitations in storing two-electron integrals for large basis set.
	www.teokem.lu.se /molcas/introduction.html (1336 words)

	Selection rule - Wikipedia, the free encyclopedia
		The radiation field will be a sum of the multipole contributions; however, usually one or two multipoles dominate.
		from one multipole to the next one, so the lowest multipole transitions are most likely to occur.
		Semi-forbidden transitions (resulting in so called intercombination lines) are electric dipole (E1) transitions for which the selection rule that the spin does not change is violated.
	en.wikipedia.org /wiki/Selection_rule (378 words)

	Multipoles
		Multipoles contains procedures for calculating the atomic charges, dipole moment and dipole moment derivatives of a system.
		This module is mentioned in chapter 7 of the book
		By default or if the argument PRINT is present with a value of.TRUE., the dipole moment for the system will be printed.
	www.psc.edu /biomed/dynamo/www_v2/Modules/multipoles.html (203 words)

	publication No. 4
		What is the first nonvanishing multipole of the icosahedral buckminsterfullerene C
		The literature contains the principles of the connection between multipoles and symmetry, but their application to a wide range of multipoles and point groups seems to be lacking.
		This information is relevant for the study of intermolecular interactions in which the electrostatic energy term can be expanded in multipole/multipole interactions.
	www.mpip-mainz.mpg.de /~gelessus/pubs/pub4.html (106 words)

	e-Prints Soton - Correlations between Maxwell's multipoles for Gaussian random functions on the sphere
		Dennis, M.R. Correlations between Maxwell's multipoles for Gaussian random functions on the sphere.
		Maxwell's multipoles are a natural geometric characterization of real functions on the sphere (with fixed ℓ).
		The correlations between multipoles for Gaussian random functions are calculated by mapping the spherical functions to random polynomials.
	eprints.soton.ac.uk /29393 (154 words)

	e-Prints Soton - Canonical representation of spherical functions: Sylvester's theorem, Maxwell's multipoles and ...
		Dennis, M.R. Canonical representation of spherical functions: Sylvester's theorem, Maxwell's multipoles and Majorana's sphere.
		Any eigenfunction of the Laplacian on a sphere is given in terms of a unique set of directions: these are Maxwell's multipoles, their existence and uniqueness being known as Sylvester's theorem.
		Here, the theorem is proved by realizing the multipoles are pairs of opposite vectors in Majorana's sphere representation of quantum spins.
	eprints.soton.ac.uk /29390 (171 words)

	The Charge Capacity Limitations of Radio Frequency Ion Guides in Their Use for Improved Ion Accumulation and Trapping ...
		Comparisons are made between the rf quadrupole ion guide, higher-order rf multipoles and rf stacked ring ion guides, in terms of the charge capacity limitations due to the instability of ions, rf focusing efficiency limits, and effects due to rf ion heating (i.e., collisional activation due to rf oscillations of ions).
		The ion density spatial distribution is derived, an exponential form of which proved to provide a good approximation for high-order rf multipoles and stacked ring rf ion guides.
		The limit on the stored charge dependence upon rf is shown to be directly related to the thermal dissociation thresholds for the ions being studied; the limitation is weaker for higher-order multipoles and stacked ring ion guides.
	www.emsl.pnl.gov /docs/msd/mass_spec/home/publications/155.html (289 words)

	Citebase - Deconstructing Functions on Quadratic Surfaces into Multipoles (Site not responding. Last check: 2007-10-21)
		In this paper we consider similar multipole representations of polynomial and analytic functions on other quadratic surfaces Q(x, y, z) = c, real and complex.
		We study their intricate geometry and topology using methods of algebraic geometry and singularity theory.
		The multipole spaces are ramified over vector or projective spaces, and the compliments to the ramification sets give rise to a rich family of K(π, 1)-spaces, where π runs over a variety of modified braid groups.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0508124 (265 words)

	2 The contribution of the multipoles (Site not responding. Last check: 2007-10-21)
		Next: References Up: A Proton and multipole Previous: 1 The contribution of
		The sum in the last term has to be extended over all
		Finally, we want to mention that the sum over L in the second term of (18) includes L=(0,0) too, yielding a constant shift in the spherical symmetric potential.
	www.lrz-muenchen.de /~Fehrenbach/sapwscfpaper/node13.html (118 words)

	[astro-ph/0604346] Alignment tests for low CMB multipoles
		Abstract: We investigate the large scale anomalies in the angular distribution of the cosmic microwave background radiation as measured by WMAP using several tests.
		These tests, based on the multipole vector expansion, measure correlations between the phases of the multipoles as expressed by the directions of the multipole vectors and their associated normal planes.
		We have computed the probability distribution functions for 46 such tests, for the multipoles l=2-5.
	arxiv.org /abs/astro-ph/0604346 (259 words)

	Mini Multipoles
		Designated the 76 Series, the new miniature Multipole metal hoods and housings are silicon-free and carry an IP 55 protection rating.
		This series is vibration resistant and effective in heavy duty OEM and control applications.
		Minature Multipoles provide all of the standard features available in Wieland's Multipole family of rectangular connectors, including:
	www.plantautomation.com /Content/ProductShowcase/product.asp?DocID={DCF10DC9-1E03-11D5-A770-00D0B7694F32}&VNETCOOKIE=NO (199 words)

	MATHnetBASE: Mathematics Online (Site not responding. Last check: 2007-10-21)
		The study of inverse scattering, in particular, has developed rapidly with the ability to perform computational simulations of scattering processes and led to remarkable advances in a range of applications, from medical imaging and radar to remote sensing and seismic exploration.
		Point Sources and Multipoles in Inverse Scattering Theory provides a survey of recent developments in inverse acoustic and electromagnetic scattering theory.
		With interest in extracting information about an object through scattered waves at an all-time high, Point Sources and Multipoles in Inverse Scattering Theory provides a valuable source of information from both the mathematical and applications perspectives.
	www.mathnetbase.com /ejournals/books/book_summary/summary.asp?id=1199 (226 words)

	ax01946o.aw
		Atomic multipoles through the quadrupole and induced dipole polarization, as well as simpler electrostatic models, are implemented.
		Restraint potentials may be included in all types of computations or partial structures can be frozen in space.
		The molecular volume and surface area as well as their derivatives are included.
	dasher.wustl.edu /tinker/summary.html (627 words)

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