19,996 research outputs found
Coupling geometry on binary bipartite networks: hypotheses testing on pattern geometry and nestedness
Upon a matrix representation of a binary bipartite network, via the
permutation invariance, a coupling geometry is computed to approximate the
minimum energy macrostate of a network's system. Such a macrostate is supposed
to constitute the intrinsic structures of the system, so that the coupling
geometry should be taken as information contents, or even the nonparametric
minimum sufficient statistics of the network data. Then pertinent null and
alternative hypotheses, such as nestedness, are to be formulated according to
the macrostate. That is, any efficient testing statistic needs to be a function
of this coupling geometry. These conceptual architectures and mechanisms are by
and large still missing in community ecology literature, and rendered
misconceptions prevalent in this research area. Here the algorithmically
computed coupling geometry is shown consisting of deterministic multiscale
block patterns, which are framed by two marginal ultrametric trees on row and
column axes, and stochastic uniform randomness within each block found on the
finest scale. Functionally a series of increasingly larger ensembles of matrix
mimicries is derived by conforming to the multiscale block configurations. Here
matrix mimicking is meant to be subject to constraints of row and column sums
sequences. Based on such a series of ensembles, a profile of distributions
becomes a natural device for checking the validity of testing statistics or
structural indexes. An energy based index is used for testing whether network
data indeed contains structural geometry. A new version block-based nestedness
index is also proposed. Its validity is checked and compared with the existing
ones. A computing paradigm, called Data Mechanics, and its application on one
real data network are illustrated throughout the developments and discussions
in this paper
A Multiscale Diffuse-Interface Model for Two-Phase Flow in Porous Media
In this paper we consider a multiscale phase-field model for
capillarity-driven flows in porous media. The presented model constitutes a
reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model,
valid in situations where interest is restricted to dynamical and equilibrium
behavior in an aggregated sense, rather than a precise description of
microscale flow phenomena. The model is based on averaging of the equation of
motion, thereby yielding a significant reduction in the complexity of the
underlying Navier-Stokes-Cahn-Hilliard equations, while retaining its
macroscopic dynamical and equilibrium properties. Numerical results are
presented for the representative 2-dimensional capillary-rise problem
pertaining to two closely spaced vertical plates with both identical and
disparate wetting properties. Comparison with analytical solutions for these
test cases corroborates the accuracy of the presented multiscale model. In
addition, we present results for a capillary-rise problem with a non-trivial
geometry corresponding to a porous medium
Towards physical cosmology: geometrical interpretation of Dark Energy, Dark Matter and Inflation without fundamental sources
We outline the key-steps towards the construction of a physical, fully
relativistic cosmology, in which we aim to trace Dark Energy and Dark Matter
back to physical properties of space. The influence of inhomogeneities on the
effective evolution history of the Universe is encoded in backreaction terms
and expressed through spatially averaged geometrical invariants. These are
absent and interpreted as missing dark fundamental sources in the standard
model. In the inhomogeneous case they can be interpreted as energies of an
emerging scalar field (the morphon). These averaged invariants vanish for a
homogeneous geometry, where the morphon is in an unstable equilibrium state. If
this state is perturbed, the morphon can act as a classical inflaton in the
Early Universe and its de-balanced energies can mimic the dark sources in the
Late Universe, depending on spatial scale as Dark Energy or as Dark Matter,
respectively. We lay down a line of arguments that is qualitatively conclusive,
and we outline open problems of quantitative nature, related to the
interpretation of observations.Comment: 14 pages, 6 figures; presented at the International Conference on Two
Cosmological Models, Universidad Iberoamericana Ciudad de M\'exico -
Department of Physics and Mathematics, November 19 (2010
Fracton pairing mechanism for "strange" superconductors: Self-assembling organic polymers and copper-oxide compounds
Self-assembling organic polymers and copper-oxide compounds are two classes
of "strange" superconductors, whose challenging behavior does not comply with
the traditional picture of Bardeen, Cooper, and Schrieffer (BCS)
superconductivity in regular crystals. In this paper, we propose a theoretical
model that accounts for the strange superconducting properties of either class
of the materials. These properties are considered as interconnected
manifestations of the same phenomenon: We argue that superconductivity occurs
in the both cases because the charge carriers (i.e., electrons or holes)
exchange {\it fracton excitations}, quantum oscillations of fractal lattices
that mimic the complex microscopic organization of the strange superconductors.
For the copper oxides, the superconducting transition temperature as
predicted by the fracton mechanism is of the order of K. We suggest
that the marginal ingredient of the high-temperature superconducting phase is
provided by fracton coupled holes that condensate in the conducting
copper-oxygen planes owing to the intrinsic field-effect-transistor
configuration of the cuprate compounds. For the gate-induced superconducting
phase in the electron-doped polymers, we simultaneously find a rather modest
transition temperature of K owing to the limitations imposed by
the electron tunneling processes on a fractal geometry. We speculate that
hole-type superconductivity observes larger onset temperatures when compared to
its electron-type counterpart. This promises an intriguing possibility of the
high-temperature superconducting states in hole-doped complex materials. A
specific prediction of the present study is universality of ac conduction for
.Comment: 12 pages (including separate abstract page), no figure
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