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 $\zeta = 0.59 \pm 0.07$ 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, $D$, which evolves with the distance from the crack tip. For large distances, $D$ 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-μm 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^(−1), 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^(−1)) 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 YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ 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