much attention has been paid to a finite-element-like 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 one-dimensional model. Possible ill

In the modeling of traffic networks, a signalized junction is typically treated using a binary variable to model the on-and-off nature of signal operation. One way of approximating such signal control is through a continuum approach where the on-and-off control variable is replaced by a priority

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

: It is shown that, with an appropriate scaling, the energy of lowlying excitations of the (1; 1; : : : ; 1) interface in the d-dimensional quantum Heisenberg model are given by the spectrum of the d \Gamma 1-dimensional 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 non-commercial purposes. 2 1 Introduction and main results We consider the spin 1/2 XXZ Heisenberg model on the d-dimensional 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...

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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

The CKM matrix and CP violation (in the continuum approximation)

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

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 finite-range pair-potential interactions, in the presence of vacancy defects. The majority of the work is devoted to the analysis

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