3,841 research outputs found
Multifractal metal in a disordered Josephson Junction Array
We report the results of the numerical study of the non-dissipative quantum
Josephson junction chain with the focus on the statistics of many-body wave
functions and local energy spectra. The disorder in this chain is due to the
random offset charges. This chain is one of the simplest physical systems to
study many-body localization. We show that the system may exhibit three
distinct regimes: insulating, characterized by the full localization of
many-body wavefunctions, fully delocalized (metallic) one characterized by the
wavefunctions that take all the available phase volume and the intermediate
regime in which the volume taken by the wavefunction scales as a non-trivial
power of the full Hilbert space volume. In the intermediate, non-ergodic regime
the Thouless conductance (generalized to many-body problem) does not change as
a function of the chain length indicating a failure of the conventional
single-parameter scaling theory of localization transition. The local spectra
in this regime display the fractal structure in the energy space which is
related with the fractal structure of wave functions in the Hilbert space. A
simple theory of fractality of local spectra is proposed and a new scaling
relationship between fractal dimensions in the Hilbert and energy space is
suggested and numerically tested.Comment: 11 page
Numerical study of the temperature and porosity effects on the fracture propagation in a 2D network of elastic bonds
This article reports results concerning the fracture of a 2d triangular
lattice of atoms linked by springs. The lattice is submitted to controlled
strain tests and the influence of both porosity and temperature on failure is
investigated. The porosity is found on one hand to decrease the stiffness of
the material but on the other hand it increases the deformation sustained prior
to failure. Temperature is shown to control the ductility due to the presence
of cavities that grow and merge. The rough surfaces resulting from the
propagation of the crack exhibit self-affine properties with a roughness
exponent over a range of length scales which increases
with temperature. Large cavities also have rough walls which are found to be
fractal with a dimension, , which evolves with the distance from the crack
tip. For large distances, is found to be close to 1.5, and close to 1.0 for
cavities just before their coalescence with the main crack
Fractal capacitors
A linear capacitor structure using fractal geometries is described. This capacitor exploits both lateral and vertical electric fields to increase the capacitance per unit area. Compared to standard parallel-plate capacitors, the parasitic bottom-plate capacitance is reduced. Unlike conventional metal-to-metal capacitors, the capacitance density increases with technology scaling. A classic fractal structure is implemented with 0.6-ÎŒm metal spacing, and a factor of 2.3 increase in the capacitance per unit area is observed. It is shown that capacitance boost factors in excess of ten may be possible as technology continues to scale. A computer-aided-design tool to automatically generate and analyze custom fractal layouts has been developed
Investigation of the relationships between basin morphology, tectonic uplift, and denudation from the study of an active fold belt in the Siwalik Hills, central Nepal
The present study investigates correlations between an extensive range of geomorphic properties that can be estimated from a digital elevation model and the uplift rate on geological timescales. The analysis focuses on an area in the Siwalik Hills (central Nepal), where lithology and climate can be considered as uniform. This area undergoes rapid tectonic uplift at rates of up to 15 mm yr^(â1), which are derived from the geometric pattern of a fault-bend model of fold growth. The selected geomorphic properties can be divided in two categories, depending on whether or not the vertical dimension is taken into account. None of the planar properties are significantly correlated to uplift rate, unlike those that include the vertical dimension, such as the mean elevation of basins, hypsometric curve, and hypsometric integral, and relief defined by the amplitude factor of length scaling analysis. Correlation between relief and uplift rate is observed for all length scales of topography shorter than 600 m, which suggests that all orders of the streams are able to adjust to the tectonic signal. Simple mass balance considerations imply that the average elevation is only 10% of surface uplift, suggesting that a dynamic equilibrium has been reached quite rapidly. Using a simple two-process model for erosion, we find that fairly high diffusion coefficients (order of 10 m^2 yr^(â1)) and efficient transport of the material by rivers are required. This unusually high value for mass diffusivity at small length scales may be obtained by either a very efficient linear diffusion or by landsliding. Actually, both processes may be active, which appears likely given the nature of the unconsolidated substratum and the favorable climatic conditions. Local relief in the study area may therefore be used to predict either uplift or denudation, but the prediction is calibrated only for that specific climatic and lithologic conditions and cannot be systematically applied to other contexts
Scaling Behavior of Quasi-One-Dimensional Vortex Avalanches in Superconducting Films
Scaling behaviour of dynamically driven vortex avalanches in superconducting
YBaCuO films deposited on tilted crystalline
substrates has been observed using quantitative magneto-optical imaging. Two
films with different tilt angles are characterized by the probability
distributions of avalanche size in terms of the number of moving vortices. It
is found in both samples that these distributions follow power-laws over up to
three decades, and have exponents ranging between 1.0 and 1.4. The
distributions also show clear finite-size scaling, when the system size is
defined by the depth of the flux penetration front -- a signature of
self-organized criticality. A scaling relation between the avalanche size
exponent and the fractal dimension, previously derived theoretically from
conservation of the number of magnetic vortices in the stationary state and
shown in numerical simulations, is here shown to be satisfied also
experimentally.Comment: 7 pages, 5 figure
Harnessing Geometric Frustration to Form Band Gaps in Acoustic Channel Lattices
We demonstrate both numerically and experimentally that geometric frustration
in two-dimensional periodic acoustic networks consisting of arrays of narrow
air channels can be harnessed to form band gaps (ranges of frequency in which
the waves cannot propagate in any direction through the system). While resonant
standing wave modes and interferences are ubiquitous in all the analyzed
network geometries, we show that they give rise to band gaps only in the
geometrically frustrated ones (i.e. those comprising of triangles and
pentagons). Our results not only reveal a new mechanism based on geometric
frustration to suppress the propagation of pressure waves in specific frequency
ranges, but also opens avenues for the design of a new generation of smart
systems that control and manipulate sound and vibrations
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