2,437 research outputs found
A Random Multifractal Tilling
We develop a multifractal random tilling that fills the square. The
multifractal is formed by an arrangement of rectangular blocks of different
sizes, areas and number of neighbors. The overall feature of the tilling is an
heterogeneous and anisotropic random self-affine object. The multifractal is
constructed by an algorithm that makes successive sections of the square. At
each -step there is a random choice of a parameter related to the
section ratio. For the case of random choice between and we
find analytically the full spectrum of fractal dimensions
Anisotropy and percolation threshold in a multifractal support
Recently a multifractal object, , was proposed to study percolation
properties in a multifractal support. The area and the number of neighbors of
the blocks of show a non-trivial behavior. The value of the
probability of occupation at the percolation threshold, , is a function
of , a parameter of which is related to its anisotropy. We
investigate the relation between and the average number of neighbors of
the blocks as well as the anisotropy of
Subcycle squeezing of light from a time flow perspective
Light as a carrier of information and energy plays a fundamental role in both
general relativity and quantum physics, linking these areas that are still not
fully compliant with each other. Its quantum nature and spatio-temporal
structure are exploited in many intriguing applications ranging from novel
spectroscopy methods of complex many-body phenomena to quantum information
processing and subwavelength lithography. Recent access to subcycle quantum
features of electromagnetic radiation promises a new class of time-dependent
quantum states of light. Paralleled with the developments in attosecond
science, these advances motivate an urgent need for a theoretical framework
that treats arbitrary wave packets of quantum light intrinsically in the time
domain. Here, we formulate a consistent time domain theory of the generation
and sampling of few-cycle and subcycle pulsed squeezed states, allowing for a
relativistic interpretation in terms of induced changes in the local flow of
time. Our theory enables the use of such states as a resource for novel
ultrafast applications in quantum optics and quantum information.Comment: 24 pages, 7 figures (including supplementary information
Invasion Percolation Between two Sites
We investigate the process of invasion percolation between two sites
(injection and extraction sites) separated by a distance r in two-dimensional
lattices of size L. Our results for the non-trapping invasion percolation model
indicate that the statistics of the mass of invaded clusters is significantly
dependent on the local occupation probability (pressure) Pe at the extraction
site. For Pe=0, we show that the mass distribution of invaded clusters P(M)
follows a power-law P(M) ~ M^{-\alpha} for intermediate values of the mass M,
with an exponent \alpha=1.39. When the local pressure is set to Pe=Pc, where Pc
corresponds to the site percolation threshold of the lattice topology, the
distribution P(M) still displays a scaling region, but with an exponent
\alpha=1.02. This last behavior is consistent with previous results for the
cluster statistics in standard percolation. In spite of these discrepancies,
the results of our simulations indicate that the fractal dimension of the
invaded cluster does not depends significantly on the local pressure Pe and it
is consistent with the fractal dimension values reported for standard invasion
percolation. Finally, we perform extensive numerical simulations to determine
the effect of the lattice borders on the statistics of the invaded clusters and
also to characterize the self-organized critical behavior of the invasion
percolation process.Comment: 7 pages, 11 figures, submited for PR
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