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DISTRIBUTED MULTIPOLE-ANALYSIS

Distributed multipole analysis

Way of describing a molecule's charge distribution

In computational chemistry, distributed multipole analysis (DMA) is a compact and accurate way of describing the spatial distribution of electric charge

Distributed multipole analysis

Distributed_multipole_analysis

Vibrational solvatochromism

Molecular changes due to solvent changes

interaction potential can be fully described by the distributed charges, dipoles, and high-order multipoles interacting with solvent electric potential and

Vibrational solvatochromism

Vibrational_solvatochromism

Crystal structure prediction

employed include simulated annealing, evolutionary algorithms, distributed multipole analysis, random sampling, basin-hopping, data mining, density functional

Crystal structure prediction

Crystal_structure_prediction

Topics referred to by the same term

Dimethylacetamide, an organic solvent Dimethylamine Dimethylaniline Distributed multipole analysis, a method to describe the charge distribution of a molecule

DMA

Fast multipole method

Numerical technique

The fast multipole method (FMM) is a numerical technique that was developed to speed up the calculation of long-ranged forces in the n-body problem. It

Fast multipole method

Fast_multipole_method

Cosmic microwave background

Trace radiation from the early universe

Górski, K. M.; Lilje, P. B. (2005). "Multipole vector anomalies in the first-year WMAP data: a cut-sky analysis". Astrophysical Journal. 635 (2): 750–60

Cosmic microwave background

Cosmic_microwave_background

Outline of algorithms

Overview of and topical guide to algorithms

— algorithm designed for parallel computation Distributed algorithm — algorithm designed for distributed systems Streaming algorithm — algorithm for processing

Outline of algorithms

Outline_of_algorithms

List of finite element software packages

Simscale.com. Retrieved 2017-05-28. "Browsing VisualFEA (Finite Element Analysis) by Title". Ecommons.cornell.edu. 2016-03-01. Retrieved 2017-05-28. GitHub

List of finite element software packages

List_of_finite_element_software_packages

List of numerical analysis topics

uses the computed solution to refine the mesh only where necessary Fast multipole method — hierarchical method for evaluating particle-particle interactions

List of numerical analysis topics

List_of_numerical_analysis_topics

Electronic filter

Electronic device

electronic components, as opposed to distributed-element filters. That is, using components and interconnections that, in analysis, can be considered to exist

Electronic filter

Electronic_filter

Boundary element method

Method of solving linear partial differential equations

with the problem size.[citation needed] Compression techniques (e.g. multipole expansions or adaptive cross approximation/hierarchical matrices) can

Boundary element method

Boundary_element_method

Electric dipole moment

Measure of positive and negative charges

Theoretically, an electric dipole is defined by the first-order term of the multipole expansion; it consists of two equal and opposite charges that are infinitesimally

Electric dipole moment

Electric_dipole_moment

Legendre polynomials

System of complete and orthogonal polynomials

recursively. The generating function approach is directly connected to the multipole expansion in electrostatics, as explained below, and is how the polynomials

Legendre polynomials

Legendre_polynomials

Fast Fourier transform

Discrete Fourier transform algorithm

communication requirements for parallel computing with the help of a fast multipole method. A wavelet-based approximate FFT by Guo and Burrus (1996) takes

Fast Fourier transform

Fast_Fourier_transform

List of algorithms

by SISC; after fast-fourier and fast-multipole) Matrix multiplication algorithms Cannon's algorithm: a distributed algorithm for matrix multiplication

List of algorithms

List_of_algorithms

Q-Chem

Computational chemistry software package

functionality as well as a growing list of features (the continuous fast multipole method, J-matrix engine, COLD PRISM for integrals, and G96 density functional

Q-Chem

Large Hadron Collider

Particle accelerator at CERN, Switzerland

the chances of interaction where the two beams cross. Magnets of higher multipole orders are used to correct smaller imperfections in the field geometry

Large Hadron Collider

Large_Hadron_Collider

Richard Vuduc

Lexing; Zorin, Denis (May 2012). "A Massively Parallel Adaptive Fast Multipole Method on Heterogeneous Architectures". Communications of the ACM. 55

Richard Vuduc

Richard_Vuduc

Ambisonics

Full-sphere surround sound format

sphere around the microphone; formally the first-order truncation of the multipole expansion. W {\displaystyle W} (the mono signal) is the zero-order information

Ambisonics

Molecular dynamics

Computer simulations to discover and understand chemical properties

an all-to-all communication. A attractive PME alternative are the fast multipole methods (FMM), which are not affected by an increase in parallelization

Molecular dynamics

Molecular_dynamics

Partial charge

Electric charge which is not an integer multiple of elementary charge

Alexander; Liedl, Klaus R. (2014). "Charge Anisotropy: Where Atomic Multipoles Matter Most". Journal of Chemical Theory and Computation. 10 (10): 4488–4496

Partial charge

Partial_charge

Kerr–Newman metric

Solution of Einstein field equations

equations. The solution contains a singularity in the shape of a ring. The multipole structure of the solution suggests that the solution represents the field

Kerr–Newman metric

Kerr–Newman_metric

N-body simulation

Simulation of a dynamical system of particles

particle centered at the distant cell's center of mass (or as a low-order multipole expansion). This can dramatically reduce the number of particle pair interactions

N-body simulation

N-body_simulation

List of abbreviations in oil and gas exploration and production

MAASP – maximum acceptable [or allowable] annular surface pressure MAC – multipole acoustic log or multiarm caliper log MACL – multiarm caliper log MAE –

List of abbreviations in oil and gas exploration and production

List_of_abbreviations_in_oil_and_gas_exploration_and_production

Lanczos algorithm

Numerical eigenvalue calculation

{\displaystyle T} in O ( m 2 ) {\displaystyle O(m^{2})} operations. The Fast Multipole Method can compute all eigenvalues in just O ( m log ⁡ m ) {\displaystyle

Lanczos algorithm

Lanczos_algorithm

Bessel function

Family of solutions to related differential equations

in problems involving spherical wave propagation, for example in the multipole expansion of the electromagnetic field. Riccati–Bessel functions only

Bessel function

Bessel_function

Timeline of algorithms

Piet Hut for fast approximate simulation of n-body problems 1987 – Fast multipole method developed by Leslie Greengard and Vladimir Rokhlin 1988 – Special

Timeline of algorithms

Timeline_of_algorithms

Discrete element method

Numerical method

to deal with long-range force include: Barnes–Hut simulation, the fast multipole method. Following the work by Munjiza and Owen, the combined finite-discrete

Discrete element method

Discrete_element_method

Force field (chemistry)

Concept on molecular modeling

Gaussian electrostatic model: extension to arbitrary angular momentum, distributed multipoles, and speedup with reciprocal space methods". The Journal of Chemical

Force field (chemistry)

Force_field_(chemistry)

Inertial electrostatic confinement

Fusion power research concept

turning, spending much time there, leading to high conduction losses. The multipole ion-beam experiment (MIX) accelerated ions and electrons into a negatively

Inertial electrostatic confinement

Inertial_electrostatic_confinement

Vibrational spectroscopic map

Data models for IR probes

frequency maps include electric potentials, electric fields, distributed higher multipole moments, and other relevant factors evaluated at specific points

Vibrational spectroscopic map

Vibrational_spectroscopic_map

Lambda-CDM model

Mathematical model of the Big Bang

of the Wilkinson Microwave Anisotropy Probe power spectrum data at low multipoles". The Astrophysical Journal. 714 (2): L265–L267. arXiv:1001.4613. Bibcode:2010ApJ

Lambda-CDM model

Lambda-CDM_model

Diaphragm pacing

Medical intervention

muscle paralysis" in patients of all ages. In the 1980s, "sequential multipole stimulation" was developed in Tampere, Finland. This technology was commercialized

Diaphragm pacing

Diaphragm_pacing

Timeline of computational mathematics

four colour theorem, the first theorem to be proved by computer. Fast multipole method invented by Rokhlin and Greengard (voted one of the top 10 algorithms

Timeline of computational mathematics

Timeline_of_computational_mathematics

Gravitational wave

Aspect of relativity in physics

derivative of the quadrupole moment (or the l-th time derivative of the l-th multipole moment) of an isolated system's stress–energy tensor must be non-zero

Gravitational wave

Gravitational_wave

Timeline of scientific computing

Computational science history

four colour theorem, the first theorem to be proved by computer. Fast multipole method (voted one of the top 10 algorithms of the 20th century) invented

Timeline of scientific computing

Timeline_of_scientific_computing

Cosmic inflation

Theory of rapid universe expansion

the quadrupole moment of the CMB is unexpectedly low and the other low multipoles appear to be preferentially aligned with the ecliptic plane. Some have

Cosmic inflation

Cosmic_inflation

List of textbooks in electromagnetism

List of physics and engineering textbooks covering electromagnetism

Advanced Classical Electrodynamics: Green Functions, Regularizations, Multipole Decompositions, World Scientific, 2017. Landau LD, Lifshitz EM, Pitaevskii

List of textbooks in electromagnetism