2,564 research outputs found
Numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions
We study numerically the small dispersion limit for the Korteweg-de Vries
(KdV) equation for and give a
quantitative comparison of the numerical solution with various asymptotic
formulae for small in the whole -plane. The matching of the
asymptotic solutions is studied numerically
Daubechies Wavelets for Linear Scaling Density Functional Theory
We demonstrate that Daubechies wavelets can be used to construct a minimal
set of optimized localized contracted basis functions in which the Kohn-Sham
orbitals can be represented with an arbitrarily high, controllable precision.
Ground state energies and the forces acting on the ions can be calculated in
this basis with the same accuracy as if they were calculated directly in a
Daubechies wavelets basis, provided that the amplitude of these contracted
basis functions is sufficiently small on the surface of the localization
region, which is guaranteed by the optimization procedure described in this
work. This approach reduces the computational costs of DFT calculations, and
can be combined with sparse matrix algebra to obtain linear scaling with
respect to the number of electrons in the system. Calculations on systems of
10,000 atoms or more thus become feasible in a systematic basis set with
moderate computational resources. Further computational savings can be achieved
by exploiting the similarity of the contracted basis functions for closely
related environments, e.g. in geometry optimizations or combined calculations
of neutral and charged systems
Unusual localisation effects in quantum percolation
We present a detailed study of the quantum site percolation problem on simple
cubic lattices, thereby focussing on the statistics of the local density of
states and the spatial structure of the single particle wavefunctions. Using
the Kernel Polynomial Method we refine previous studies of the metal-insulator
transition and demonstrate the non-monotonic energy dependence of the quantum
percolation threshold. Remarkably, the data indicates a ``fragmentation'' of
the spectrum into extended and localised states. In addition, the observation
of a chequerboard-like structure of the wavefunctions at the band centre can be
interpreted as anomalous localisation.Comment: 5 pages, 7 figure
Nonlinear stability analysis of plane Poiseuille flow by normal forms
In the subcritical interval of the Reynolds number 4320\leq R\leq R_c\equiv
5772, the Navier--Stokes equations of the two--dimensional plane Poiseuille
flow are approximated by a 22--dimensional Galerkin representation formed from
eigenfunctions of the Orr--Sommerfeld equation. The resulting dynamical system
is brought into a generalized normal form which is characterized by a
disposable parameter controlling the magnitude of denominators of the normal
form transformation. As rigorously proved, the generalized normal form
decouples into a low--dimensional dominant and a slaved subsystem. {}From the
dominant system the critical amplitude is calculated as a function of the
Reynolds number. As compared with the Landau method, which works down to
R=5300, the phase velocity of the critical mode agrees within 1 per cent; the
critical amplitude is reproduced similarly well except close to the critical
point, where the maximal error is about 16 per cent. We also examine boundary
conditions which partly differ from the usual ones.Comment: latex file; 4 Figures will be sent, on request, by airmail or by fax
(e-mail address: rauh at beta.physik.uni-oldenburg.de
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