1,072 research outputs found
Multifractal Properties of the Random Resistor Network
We study the multifractal spectrum of the current in the two-dimensional
random resistor network at the percolation threshold. We consider two ways of
applying the voltage difference: (i) two parallel bars, and (ii) two points.
Our numerical results suggest that in the infinite system limit, the
probability distribution behaves for small current i as P(i) ~ 1/i. As a
consequence, the moments of i of order q less than q_c=0 do not exist and all
current of value below the most probable one have the fractal dimension of the
backbone. The backbone can thus be described in terms of only (i) blobs of
fractal dimension d_B and (ii) high current carrying bonds of fractal dimension
going from to d_B.Comment: 4 pages, 6 figures; 1 reference added; to appear in Phys. Rev. E
(Rapid Comm
Fractal dimension and size scaling of domains in thin films of multiferroic BiFeO3
We have analyzed the morphology of ferroelectric domains in very thin films
of multiferroic BiFeO3. Unlike the more common stripe domains observed in
thicker films BiFeO3 or in other ferroics, the domains tend not to be straight,
but irregular in shape, with significant domain wall roughening leading to a
fractal dimensionality. Also contrary to what is usually observed in other
ferroics, the domain size appears not to scale as the square root of the film
thickness. A model is proposed in which the observed domain size as a function
of film thickness can be directly linked to the fractal dimension of the
domains.Comment: 4 pages, 3 figure
Discrete Fracture Model with Anisotropic Load Sharing
A two-dimensional fracture model where the interaction among elements is
modeled by an anisotropic stress-transfer function is presented. The influence
of anisotropy on the macroscopic properties of the samples is clarified, by
interpolating between several limiting cases of load sharing. Furthermore, the
critical stress and the distribution of failure avalanches are obtained
numerically for different values of the anisotropy parameter and as a
function of the interaction exponent . From numerical results, one can
certainly conclude that the anisotropy does not change the crossover point
in 2D. Hence, in the limit of infinite system size, the crossover
value between local and global load sharing is the same as the one
obtained in the isotropic case. In the case of finite systems, however, for
, the global load sharing behavior is approached very slowly
Classes of behavior of small-world networks
Small-world networks are the focus of recent interest because they appear to
circumvent many of the limitations of either random networks or regular
lattices as frameworks for the study of interaction networks of complex
systems. Here, we report an empirical study of the statistical properties of a
variety of diverse real-world networks. We present evidence of the occurrence
of three classes of small-world networks: (a) scale-free networks,
characterized by a vertex connectivity distribution that decays as a power law;
(b) broad-scale networks, characterized by a connectivity distribution that has
a power-law regime followed by a sharp cut-off; (c) single-scale networks,
characterized by a connectivity distribution with a fast decaying tail.
Moreover, we note for the classes of broad-scale and single-scale networks that
there are constraints limiting the addition of new links. Our results suggest
that the nature of such constraints may be the controlling factor for the
emergence of different classes of networks
Elementary processes governing the evolution of road networks
Urbanisation is a fundamental phenomenon whose quantitative characterisation
is still inadequate. We report here the empirical analysis of a unique data set
regarding almost 200 years of evolution of the road network in a large area
located north of Milan (Italy). We find that urbanisation is characterised by
the homogenisation of cell shapes, and by the stability throughout time of
high-centrality roads which constitute the backbone of the urban structure,
confirming the importance of historical paths. We show quantitatively that the
growth of the network is governed by two elementary processes: (i)
`densification', corresponding to an increase in the local density of roads
around existing urban centres and (ii) `exploration', whereby new roads trigger
the spatial evolution of the urbanisation front. The empirical identification
of such simple elementary mechanisms suggests the existence of general, simple
properties of urbanisation and opens new directions for its modelling and
quantitative description.Comment: 10 pages, 6 figure
Topological dragging of solitons
We put forward properties of solitons supported by optical lattices featuring
topological dislocations, and show that solitons experience attractive and
repulsive forces around the dislocations. Suitable arrangements of dislocations
are even found to form soliton traps, and the properties of such solitons are
shown to crucially depend on the trap topology. The uncovered phenomenon opens
a new concept for soliton control and manipulation, e.g., in disk-shaped
Bose-Einstein condensates.Comment: 15 pages, 5 figures, to appear in Physical Review Letter
Towards two-dimensional metallic behavior at LaAlO3/SrTiO3 interfaces
Using a low-temperature conductive-tip atomic force microscope in
cross-section geometry we have characterized the local transport properties of
the metallic electron gas that forms at the interface between LaAlO3 and
SrTiO3. At low temperature, we find that the carriers do not spread away from
the interface but are confined within ~10 nm, just like at room temperature.
Simulations taking into account both the large temperature and electric-field
dependence of the permittivity of SrTiO3 predict a confinement over a few nm
for sheet carrier densities larger than ~6 10^13 cm-2. We discuss the
experimental and simulations results in terms of a multi-band carrier system.
Remarkably, the Fermi wavelength estimated from Hall measurements is ~16 nm,
indicating that the electron gas in on the verge of two-dimensionality.Comment: Accepted for publication in Physical Review Letter
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