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

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

Spectra of Homologous Series of Monosubstituted Amides

Infrared spectra of the pure liquid and of dilute solution were observed for N‐methyl, N‐ethyl, N‐propyl, and N‐butyl acetamides and propionamides and of N‐deuterated N‐butylacetamide. Also infrared spectra of N15‐butylacetamide and N‐deuterated N15‐butylacetamide and the Raman spectra of N‐butylacetamide and N‐deuterated N‐butylacetamide were observed. In each series a band in the higher members was related to each band of the N‐methyl compound on the basis of similarity in frequency, intensity, band width, and the influence of dilution. In N‐methylacetamide and N‐butylacetamide 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

The Out‐of‐Plane 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

Microscopic Selection of Fluid Fingering Pattern

We study the issue of the selection of viscous fingering patterns in the limit of small surface tension. Through detailed simulations of anisotropic fingering, we demonstrate conclusively that no selection independent of the small-scale cutoff (macroscopic selection) occurs in this system. Rather, the small-scale cutoff completely controls the pattern, even on short time scales, in accord with the theory of microscopic solvability. We demonstrate that ordered patterns are dynamically selected only for not too small surface tensions. For extremely small surface tensions, the system exhibits chaotic behavior and no regular pattern is realized.Comment: 6 pages, 5 figure