Symmetries of a Certain Periodic Chain

For the discussion of the size dependence of the third-order nonlinear susceptibility χ(3) for confined electronic systems, the result of numerical study is given for an exactly soluble model of noninteracting Frenkel excitons in a periodic chain. The case of pump-probe type nonlinear effect is explicitly treated in the long-wavelength approximation, and Im [χ(3)] is evaluated as a function of chain size N, transfer energy b, and damping constants. For a given value of b(N), there is an enhancement of χ(3) with increasing value of N(b), followed by a saturation behavior. The range of the enhancement is determined by the damping constants. This provides a consistent view of the size and transfer dependence of χ(3), its saturation behavior, and the previously discussed cancellation problem.

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Periodic chain clusters of two-dimensional bubbles

Journal of Physics Condensed Matter ◽

10.1088/0953-8984/14/23/306 ◽

2002 ◽

Vol 14 (23) ◽

pp. 5719-5730 ◽

Cited By ~ 3

Author(s):

P I C Teixeira ◽

M A Fortes

Keyword(s):

Two Dimensional ◽

Periodic Chain

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Integration of equation of Toda periodic chain kind

Ufimskii Matematicheskii Zhurnal ◽

10.13108/2017-9-2-17 ◽

2017 ◽

Vol 9 (2) ◽

pp. 17-24

Author(s):

Bazar Atajanovich Babajanov ◽

Aknazar Bekdurdievich Khasanov

Keyword(s):

Periodic Chain

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A PRIORI ERROR ESTIMATES FOR ENERGY-BASED QUASICONTINUUM APPROXIMATIONS OF A PERIODIC CHAIN

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202511005817 ◽

2011 ◽

Vol 21 (12) ◽

pp. 2491-2521 ◽

Cited By ~ 5

Author(s):

CHRISTOPH ORTNER ◽

HAO WANG

Keyword(s):

Error Estimates ◽

A Priori ◽

A Priori Error Estimates ◽

Stability Estimates ◽

Norm Estimates ◽

Priori Error Estimates ◽

Sharp Stability ◽

Consistency Error ◽

Periodic Chain ◽

Homogeneous Strain

We derive a priori error estimates for three prototypical energy-based quasicontinuum (QC) methods: the local QC method, the energy-based QC method, and the quasi-nonlocal QC method. Our analysis decomposes the consistency error into modeling and coarsening errors. While previous results on estimating the modeling error exist, we present a new and simpler proof based on negative-norm estimates. Our stability analysis extends previous results on sharp stability estimates under homogeneous strain to the nonlinear setting. Finally, we present numerical experiments to illustrate the results of our analysis.

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