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Theoretical and numerical analysis for the quasicontinuum approximation of a material particle model
 Mathematics of Computation
"... Abstract. In many applications materials are modeled by a large number of particles (or atoms) where any one of particles interacts with all others. Near or nearest neighbor interaction is expected to be a good simplification of the full interaction in the engineering community. In this paper we sha ..."
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Cited by 50 (1 self)
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much attention has been paid to a finiteelementlike quasicontinuum (QC) method which utilizes a mixed atomistic/continuum approximation model. No numerical analysis has been done yet. In the paper we shall estimate the error of the QC method for this onedimensional model. Possible ill
On the Continuum Approximation of the Onandoff Signal Control on Dynamic Traffic Networks
, 2013
"... In the modeling of traffic networks, a signalized junction is typically treated using a binary variable to model the onandoff nature of signal operation. One way of approximating such signal control is through a continuum approach where the onandoff control variable is replaced by a priority par ..."
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Cited by 6 (2 self)
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In the modeling of traffic networks, a signalized junction is typically treated using a binary variable to model the onandoff nature of signal operation. One way of approximating such signal control is through a continuum approach where the onandoff control variable is replaced by a priority
IMECE201165783 MULTISCALE MODELING OF RANDOM LATTICES: CRITICAL ISSUES ON CONTINUUM APPROXIMATION
"... ABSTRACT In this work, we are concerned that transmission of various boundary conditions through irregular lattices. The boundary conditions are parameterized using trigonometric Fourier series, and it is shown that, under certain conditions, transmission through irregular lattices can be well appr ..."
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approximated by that through classical continuum. It is determined that such transmission must involve the wavelength of at least 12 lattice spacings; for smaller wavelength classical continuum approximations become increasingly inaccurate. PROBLEM FORMULATION For many problems associated with fracture
A Continuum Approximation for the Excitations of the (1, 1, ..., 1) Interface in the Quantum Heisenberg model
, 1999
"... : It is shown that, with an appropriate scaling, the energy of lowlying excitations of the (1; 1; : : : ; 1) interface in the ddimensional quantum Heisenberg model are given by the spectrum of the d \Gamma 1dimensional Laplacian on an suitable domain. Keywords: Anisotropic Heisenberg ferromagnet, ..."
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: It is shown that, with an appropriate scaling, the energy of lowlying excitations of the (1; 1; : : : ; 1) interface in the ddimensional quantum Heisenberg model are given by the spectrum of the d \Gamma 1dimensional Laplacian on an suitable domain. Keywords: Anisotropic Heisenberg ferromagnet, XXZ model, interface excitations, 111 interface. MCS2000 numbers: 82B10, 82B24, 82D40 Copyright c fl 1999 Bolina, Contucci, Nachtergaele, and Starr. Reproduction of this article in its entirety, by any means, is permitted for noncommercial purposes. 2 1 Introduction and main results We consider the spin 1/2 XXZ Heisenberg model on the ddimensional lattice Z d . For any finite volume ae Z d , the Hamiltonian is given by H = \Gamma X x;y2 jx\Gammayj=1 \Delta \Gamma1 (S (1) x S (1) y + S (2) x S (2) y ) + S (3) x S (3) y ; (1.1) where \Delta ? 1 is the anisotropy. We refer to the next section for more precise definitions. By adding an appropriate boundary term o...
The stages of economic growth.
 Economic History Review , 2nd series 12,
, 1959
"... JSTOR is a notforprofit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about J ..."
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Cited by 297 (0 self)
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; and such fluctuations, along with the impact of wars, yield historical paths of growth which differ from those which the optima, calculated before the event, would have yielded. Nevertheless, the economic history of growing societies takes a part of its rude shape from the effort of societies to approximate the optimum
c ○ Copyright owned by the author(s) under the terms of the Creative Commons AttributionNonCommercialShareAlike Licence.
, 2006
"... The CKM matrix and CP violation (in the continuum approximation) ..."
On Approximation of a Continuum by Lemniscates
"... For an arbitrary continuum in the complex plane with connected complement \Omega we study the rate of its approximation from outside by lemniscates in terms of level lines of a conformal mapping of\Omega onto the exterior of the unit disk. Key Words: lemniscates; Hilbert's theorem; quasiconform ..."
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For an arbitrary continuum in the complex plane with connected complement \Omega we study the rate of its approximation from outside by lemniscates in terms of level lines of a conformal mapping of\Omega onto the exterior of the unit disk. Key Words: lemniscates; Hilbert's theorem
ATOMISTIC/CONTINUUM COUPLING APPROXIMATION
"... We present a comprehensive a priori error analysis of a practical energy based atomistic/continuum coupling method (Shapeev, arXiv:1010.0512) in two dimensions, for finiterange pairpotential interactions, in the presence of vacancy defects. The majority of the work is devoted to the analysis of co ..."
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We present a comprehensive a priori error analysis of a practical energy based atomistic/continuum coupling method (Shapeev, arXiv:1010.0512) in two dimensions, for finiterange pairpotential interactions, in the presence of vacancy defects. The majority of the work is devoted to the analysis
Deterministic and Stochastic Models for Coalescence (Aggregation, Coagulation): a Review of the MeanField Theory for Probabilists
 Bernoulli
, 1997
"... Consider N particles, which merge into clusters according to the rule: a cluster of size x and a cluster of size y merge at (stochastic) rate K(x; y)=N , where K is a specified rate kernel. This MarcusLushnikov model of stochastic coalescence, and the underlying deterministic approximation given by ..."
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Cited by 222 (13 self)
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Consider N particles, which merge into clusters according to the rule: a cluster of size x and a cluster of size y merge at (stochastic) rate K(x; y)=N , where K is a specified rate kernel. This MarcusLushnikov model of stochastic coalescence, and the underlying deterministic approximation given
Results 1  10
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1,917