14,215 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
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
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
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
Nonlinear lattice model of viscoelastic Mode III fracture
We study the effect of general nonlinear force laws in viscoelastic lattice
models of fracture, focusing on the existence and stability of steady-state
Mode III cracks. We show that the hysteretic behavior at small driving is very
sensitive to the smoothness of the force law. At large driving, we find a Hopf
bifurcation to a straight crack whose velocity is periodic in time. The
frequency of the unstable bifurcating mode depends on the smoothness of the
potential, but is very close to an exact period-doubling instability. Slightly
above the onset of the instability, the system settles into a exactly
period-doubled state, presumably connected to the aforementioned bifurcation
structure. We explicitly solve for this new state and map out its
velocity-driving relation
Extinction Rates for Fluctuation-Induced Metastabilities : A Real-Space WKB Approach
The extinction of a single species due to demographic stochasticity is
analyzed. The discrete nature of the individual agents and the Poissonian noise
related to the birth-death processes result in local extinction of a metastable
population, as the system hits the absorbing state. The Fokker-Planck
formulation of that problem fails to capture the statistics of large deviations
from the metastable state, while approximations appropriate close to the
absorbing state become, in general, invalid as the population becomes large. To
connect these two regimes, a master equation based on a real space WKB method
is presented, and is shown to yield an excellent approximation for the decay
rate and the extreme events statistics all the way down to the absorbing state.
The details of the underlying microscopic process, smeared out in a mean field
treatment, are shown to be crucial for an exact determination of the extinction
exponent. This general scheme is shown to reproduce the known results in the
field, to yield new corollaries and to fit quite precisely the numerical
solutions. Moreover it allows for systematic improvement via a series expansion
where the small parameter is the inverse of the number of individuals in the
metastable state
Front Propagation up a Reaction Rate Gradient
We expand on a previous study of fronts in finite particle number
reaction-diffusion systems in the presence of a reaction rate gradient in the
direction of the front motion. We study the system via reaction-diffusion
equations, using the expedient of a cutoff in the reaction rate below some
critical density to capture the essential role of fl uctuations in the system.
For large density, the velocity is large, which allows for an approximate
analytic treatment. We derive an analytic approximation for the front velocity
depe ndence on bulk particle density, showing that the velocity indeed diverge
s in the infinite density limit. The form in which diffusion is impleme nted,
namely nearest-neighbor hopping on a lattice, is seen to have an essential
impact on the nature of the divergence
Symplectic geometry on moduli spaces of J-holomorphic curves
Let (M,\omega) be a symplectic manifold, and Sigma a compact Riemann surface.
We define a 2-form on the space of immersed symplectic surfaces in M, and show
that the form is closed and non-degenerate, up to reparametrizations. Then we
give conditions on a compatible almost complex structure J on (M,\omega) that
ensure that the restriction of the form to the moduli space of simple immersed
J-holomorphic Sigma-curves in a homology class A in H_2(M,\Z) is a symplectic
form, and show applications and examples. In particular, we deduce sufficient
conditions for the existence of J-holomorphic Sigma-curves in a given homology
class for a generic J.Comment: 16 page
Complex Systems Science: Dreams of Universality, Reality of Interdisciplinarity
Using a large database (~ 215 000 records) of relevant articles, we
empirically study the "complex systems" field and its claims to find universal
principles applying to systems in general. The study of references shared by
the papers allows us to obtain a global point of view on the structure of this
highly interdisciplinary field. We show that its overall coherence does not
arise from a universal theory but instead from computational techniques and
fruitful adaptations of the idea of self-organization to specific systems. We
also find that communication between different disciplines goes through
specific "trading zones", ie sub-communities that create an interface around
specific tools (a DNA microchip) or concepts (a network).Comment: Journal of the American Society for Information Science and
Technology (2012) 10.1002/asi.2264
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