2,441 research outputs found
A deterministic width function model
Use of a deterministic fractal-multifractal (FM) geometric method to model width functions of natural river networks, as derived distributions of simple multifractal measures via fractal interpolating functions, is reported. It is first demonstrated that the FM procedure may be used to simulate natural width functions, preserving their most relevant features like their overall shape and texture and their observed power-law scaling on their power spectra. It is then shown, via two natural river networks (Racoon and Brushy creeks in the United States), that the FM approach may also be used to closely approximate existing width functions
A deterministic width function model
International audienceUse of a deterministic fractal-multifractal (FM) geometric method to model width functions of natural river networks, as derived distributions of simple multifractal measures via fractal interpolating functions, is reported. It is first demonstrated that the FM procedure may be used to simulate natural width functions, preserving their most relevant features like their overall shape and texture and their observed power-law scaling on their power spectra. It is then shown, via two natural river networks (Racoon and Brushy creeks in the United States), that the FM approach may also be used to closely approximate existing width functions
Interplay of couplings between antiferrodistortive, ferroelectric, and strain degrees of freedom in monodomain PbTiO/SrTiO superlattices
We report first-principles calculations on the coupling between epitaxial
strain, polarization, and oxygen octahedra rotations in monodomain
(PbTiO)/(SrTiO) superlattices. We show how the
interplay between (i) the epitaxial strain and (ii) the electrostatic
conditions, can be used to control the orientation of the main axis of the
system. The electrostatic constrains at the interface facilitate the rotation
of the polarization and, as a consequence, we predict large piezoelectric
responses at epitaxial strains smaller than those that would be required
considering only strain effects. In addition, ferroelectric (FE) and
antiferrodistortive (AFD) modes are strongly coupled. Usual steric arguments
cannot explain this coupling and a covalent model is proposed to account for
it. The energy gain due to the FE-AFD coupling decreases with the periodicity
of the superlattice, becoming negligible for .Comment: 5 pages, 4 figure
Algebraic and combinatorial aspects of sandpile monoids on directed graphs
The sandpile group of a graph is a well-studied object that combines ideas
from algebraic graph theory, group theory, dynamical systems, and statistical
physics. A graph's sandpile group is part of a larger algebraic structure on
the graph, known as its sandpile monoid. Most of the work on sandpiles so far
has focused on the sandpile group rather than the sandpile monoid of a graph,
and has also assumed the underlying graph to be undirected. A notable exception
is the recent work of Babai and Toumpakari, which builds up the theory of
sandpile monoids on directed graphs from scratch and provides many connections
between the combinatorics of a graph and the algebraic aspects of its sandpile
monoid.
In this paper we primarily consider sandpile monoids on directed graphs, and
we extend the existing theory in four main ways. First, we give a combinatorial
classification of the maximal subgroups of a sandpile monoid on a directed
graph in terms of the sandpile groups of certain easily-identifiable subgraphs.
Second, we point out certain sandpile results for undirected graphs that are
really results for sandpile monoids on directed graphs that contain exactly two
idempotents. Third, we give a new algebraic constraint that sandpile monoids
must satisfy and exhibit two infinite families of monoids that cannot be
realized as sandpile monoids on any graph. Finally, we give an explicit
combinatorial description of the sandpile group identity for every graph in a
family of directed graphs which generalizes the family of (undirected)
distance-regular graphs. This family includes many other graphs of interest,
including iterated wheels, regular trees, and regular tournaments.Comment: v2: Cleaner presentation, new results in final section. Accepted for
publication in J. Combin. Theory Ser. A. 21 pages, 5 figure
Orbital current mode in elliptical quantum dots
An orbital current mode peculiar to deformed quantum dots is theoretically
investigated; first by using a simple model that allows to interpret
analytically its main characteristics, and second, by numerically solving the
microscopic equations of time evolution after an initial perturbation within
the time-dependent local-spin-density approximation. Results for different
deformations and sizes are shown.Comment: 4 REVTEX pages, 4 PDF figures, accepted in PRB:R
Modeling geophysical complexity: a case for geometric determinism
International audienceIt has been customary in the last few decades to employ stochastic models to represent complex data sets encountered in geophysics, particularly in hydrology. This article reviews a deterministic geometric procedure to data modeling, one that represents whole data sets as derived distributions of simple multifractal measures via fractal functions. It is shown how such a procedure may lead to faithful holistic representations of existing geophysical data sets that, while complementing existing representations via stochastic methods, may also provide a compact language for geophysical complexity. The implications of these ideas, both scientific and philosophical, are stressed
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