12,946 research outputs found
Scattering Calculations with Wavelets
We show that the use of wavelet bases for solving the momentum-space
scattering integral equation leads to sparse matrices which can simplify the
solution. Wavelet bases are applied to calculate the K-matrix for
nucleon-nucleon scattering with the s-wave Malfliet-Tjon V potential. We
introduce a new method, which uses special properties of the wavelets, for
evaluating the singular part of the integral. Analysis of this test problem
indicates that a significant reduction in computational size can be achieved
for realistic few-body scattering problems.Comment: 26 pages, Latex, 6 eps figure
Application of wavelets to singular integral scattering equations
The use of orthonormal wavelet basis functions for solving singular integral
scattering equations is investigated. It is shown that these basis functions
lead to sparse matrix equations which can be solved by iterative techniques.
The scaling properties of wavelets are used to derive an efficient method for
evaluating the singular integrals. The accuracy and efficiency of the wavelet
transforms is demonstrated by solving the two-body T-matrix equation without
partial wave projection. The resulting matrix equation which is characteristic
of multiparticle integral scattering equations is found to provide an efficient
method for obtaining accurate approximate solutions to the integral equation.
These results indicate that wavelet transforms may provide a useful tool for
studying few-body systems.Comment: 11 pages, 4 figure
Tunable Superconducting Phase Transition in Metal-Decorated Graphene Sheets
Using typical experimental techniques it is difficult to separate the effects
of carrier density and disorder on the superconducting transition in two
dimensions. Using a simple fabrication procedure based on metal layer
dewetting, we have produced graphene sheets decorated with a non-percolating
network of nanoscale tin clusters. These metal clusters both efficiently dope
the graphene substrate and induce long-range superconducting correlations. This
allows us to study the superconducting transition at fixed disorder and
variable carrier concentration. We find that despite structural inhomogeneity
on mesoscopic length scales (10-100 nm), this material behaves electronically
as a homogenous dirty superconductor. Our simple self-assembly method
establishes graphene as an ideal tunable substrate for studying induced
two-dimensional electronic systems at fixed disorder and our technique can
readily be extended to other order parameters such as magnetism
Spectra of Homologous Series of Monosubstituted Amides
Infrared spectra of the pure liquid and of dilute solution were observed for Nâmethyl, Nâethyl, Nâpropyl, and Nâbutyl acetamides and propionamides and of Nâdeuterated Nâbutylacetamide. Also infrared spectra of N15âbutylacetamide and Nâdeuterated N15âbutylacetamide and the Raman spectra of Nâbutylacetamide and Nâdeuterated Nâbutylacetamide were observed. In each series a band in the higher members was related to each band of the Nâmethyl compound on the basis of similarity in frequency, intensity, band width, and the influence of dilution. In Nâmethylacetamide and Nâbutylacetamide bands thus related were found to have also similar Raman activities and similar shifts on replacing the peptide hydrogen by deuterium. The extra bands could be related systematically to the extra CH2 groups. The implications of these results in protein spectroscopy and in the spectroscopic study of homologous series is discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70627/2/JCPSA6-29-5-1097-1.pd
Velocity Fluctuations in Dynamical Fracture: the Role of Microcracks
We address the velocity fluctuations of fastly moving cracks in stressed
materials. One possible mechanism for such fluctuations is the interaction of
the main crack with micro cracks (irrespective whether these are existing
material defects or they form during the crack evolution). We analyze carefully
the dynamics (in 2 space dimensions) of one macro and one micro crack, and
demonstrate that their interaction results in a {\em large} and {\em rapid}
velocity fluctuation, in qualitative correspondence with typical velocity
fluctuations observed in experiments. In developing the theory of the dynamical
interaction we invoke an approximation that affords a reduction in mathematical
complexity to a simple set of ordinary differential equations for the positions
of the cracks tips; we propose that this kind of approximation has a range of
usefulness that exceeds the present context.Comment: 7 pages, 7 figure
The OutâofâPlane Deformation Frequency of the NH Group in the Peptide Link
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70613/2/JCPSA6-21-3-570-2.pd
Tip Splittings and Phase Transitions in the Dielectric Breakdown Model: Mapping to the DLA Model
We show that the fractal growth described by the dielectric breakdown model
exhibits a phase transition in the multifractal spectrum of the growth measure.
The transition takes place because the tip-splitting of branches forms a fixed
angle. This angle is eta dependent but it can be rescaled onto an
``effectively'' universal angle of the DLA branching process. We derive an
analytic rescaling relation which is in agreement with numerical simulations.
The dimension of the clusters decreases linearly with the angle and the growth
becomes non-fractal at an angle close to 74 degrees (which corresponds to eta=
4.0 +- 0.3).Comment: 4 pages, REVTex, 3 figure
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