Topic
Operator (computer programming)
About: Operator (computer programming) is a research topic. Over the lifetime, 40896 publications have been published within this topic receiving 671452 citations. The topic is also known as: operator symbol & operator name.
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01 May 1999
TL;DR: In this paper, the authors show that the construction of a discrete Hodge is a central problem and interpret finite element techniques as a realization of the Hodge operator in the Whitney complex, and view the Galerkin method as a way to set up circuit equations, the metric of space being encoded in the values of branch impedances.
Abstract: In this paper, some structures which underlie the numerical treatment of second-order boundary value problems are studied using magnetostatics as an example. The authors show that the construction of a discrete Hodge is a central problem. In this light, they interpret finite element techniques as a realization of the discrete Hodge operator in the Whitney complex. This enables one to view the Galerkin method as a way to set up circuit equations, the metric of space being encoded in the values of branch impedances.
159 citations
159 citations
TL;DR: In this article, the authors construct a holographic map between asymptotically AdS5 × S5 solutions of 10d supergravity and vacuum expectation values of gauge invariant operators of the dual QFT.
Abstract: We construct a holographic map between asymptotically AdS5 × S5 solutions of 10d supergravity and vacuum expectation values of gauge invariant operators of the dual QFT. The ingredients that enter in the construction are (i) gauge invariant variables so that the KK reduction is independent of any choice of gauge fixing; (ii) the non-linear KK reduction map from 10 to 5 dimensions (constructed perturbatively in the number of fields); (iii) application of holographic renormalization. A non-trivial role in the last step is played by extremal couplings. This map allows one to reliably compute vevs of operators dual to any KK fields. As an application we consider a Coulomb branch solution and compute the first two non-trivial vevs, involving operators of dimension 2 and 4, and reproduce the field theory result, in agreement with non-renormalization theorems. This constitutes the first quantitative test of the gravity/gauge theory duality away from the conformal point involving a vev of an operator dual to a KK field (which is not one of the gauged supergravity fields).
159 citations
TL;DR: A recursive algorithm for solving the dynamical equations of motion for molecular systems using internal variable models which have been shown to reduce the computation times of molecular dynamics simulations by an order of magnitude when compared with Cartesian models.
159 citations
01 Jan 1999
TL;DR: In this paper, the Renormalization Group Method in the Stochastic Model of Isotropic Turbulence was used for operator expansion in the first Kolmogorov Hypothesis.
Abstract: 1 The Renormalization Group Method in the Stochastic Model of Isotropic Turbulence 2 Composite Operators, Operator Expansions, and the First Kolmogorov Hypothesis 3 Multicharge Problems in the Stochastic Theory of Turbulence
158 citations