Discrete models of dislocations and their motion in cubic crystals

A discrete model describing defects in crystal lattices and having the standard linear anisotropic elasticity as its continuum limit is proposed. The main ingredients entering the model are the elastic stiffness constants of the material and a dimensionless periodic function that restores the translation invariance of the crystal and influences the Peierls stress. Explicit expressions are given for crystals with cubic symmetry: sc, fcc and bcc. Numerical simulations of this model with conservative or damped dynamics illustrate static and moving edge and screw dislocations and describe their cores and profiles. Dislocation loops and dipoles are also numerically observed. Cracks can be created and propagated by applying a sufficient load to a dipole formed by two edge dislocations.Comment: 23 pages, 15 figures, to appear in Phys. Rev.

Reaching the quantum limit of sensitivity in electron spin resonance

We report pulsed electron-spin resonance (ESR) measurements on an ensemble of Bismuth donors in Silicon cooled at 10mK in a dilution refrigerator. Using a Josephson parametric microwave amplifier combined with high-quality factor superconducting micro-resonators cooled at millikelvin temperatures, we improve the state-of-the-art sensitivity of inductive ESR detection by nearly 4 orders of magnitude. We demonstrate the detection of 1700 bismuth donor spins in silicon within a single Hahn echo with unit signal-to-noise (SNR) ratio, reduced to just 150 spins by averaging a single Carr-Purcell-Meiboom-Gill sequence. This unprecedented sensitivity reaches the limit set by quantum fluctuations of the electromagnetic field instead of thermal or technical noise, which constitutes a novel regime for magnetic resonance.Comment: Main text : 10 pages, 4 figures. Supplementary text : 16 pages, 8 figure

Characterizing the relationship between land use land cover change and land surface temperature

Exploring changes in land use land cover (LULC) to understand the urban heat island (UHI) effect is valuable for both communities and local governments in cities in developing countries, where urbanization and industrialization often take place rapidly but where coherent planning and control policies have not been applied. This work aims at determining and analyzing the relationship between LULC change and land surface temperature (LST) patterns in the context of urbanization. We first explore the relationship between LST and vegetation, man-made features, and cropland using normalized vegetation, and built-up indices within each LULC type. Afterwards, we assess the impacts of LULC change and urbanization in UHI using hot spot analysis (Getis-Ord Gi∗ statistics) and urban landscape analysis. Finally, we propose a model applying non-parametric regression to estimate future urban climate patterns using predicted land cover and land use change. Results from this work provide an effective methodology for UHI characterization, showing that (a) LST depends on a nonlinear way of LULC types; (b) hotspot analysis using Getis Ord Gi∗ statistics allows to analyze the LST pattern change through time; (c) UHI is influenced by both urban landscape and urban development type; (d) LST pattern forecast and UHI effect examination can be done by the proposed model using nonlinear regression and simulated LULC change scenarios. We chose an inner city area of Hanoi as a case-study, a small and flat plain area where LULC change is significant due to urbanization and industrialization. The methodology presented in this paper can be broadly applied in other cities which exhibit a similar dynamic growth. Our findings can represent an useful tool for policy makers and the community awareness by providing a scientific basis for sustainable urban planning and management.First, the authors would like to thank the European Commission and the Erasmus Mundus Consortium for providing the master scholarship in Geospatial Technologies. We acknowledge the USGS-NASA due to their freely accessible Landsat data. Thanks are also due to the Laboratory for Geographic Information Analysis (Department of Geography, Hanoi National University of Education) for providing valuable tools and software. This work has also been partially supported by the Spanish Ministry of Economy under project ESP2013-48458-C4-3- P

Flux front penetration in disordered superconductors

We investigate flux front penetration in a disordered type II superconductor by molecular dynamics (MD) simulations of interacting vortices and find scaling laws for the front position and the density profile. The scaling can be understood performing a coarse graining of the system and writing a disordered non-linear diffusion equation. Integrating numerically the equation, we observe a crossover from flat to fractal front penetration as the system parameters are varied. The value of the fractal dimension indicates that the invasion process is described by gradient percolation.Comment: 5 pages, 4 figures, to appear in Phys. Rev. Let

Avalanches in the Weakly Driven Frenkel-Kontorova Model

A damped chain of particles with harmonic nearest-neighbor interactions in a spatially periodic, piecewise harmonic potential (Frenkel-Kontorova model) is studied numerically. One end of the chain is pulled slowly which acts as a weak driving mechanism. The numerical study was performed in the limit of infinitely weak driving. The model exhibits avalanches starting at the pulled end of the chain. The dynamics of the avalanches and their size and strength distributions are studied in detail. The behavior depends on the value of the damping constant. For moderate values a erratic sequence of avalanches of all sizes occurs. The avalanche distributions are power-laws which is a key feature of self-organized criticality (SOC). It will be shown that the system selects a state where perturbations are just able to propagate through the whole system. For strong damping a regular behavior occurs where a sequence of states reappears periodically but shifted by an integer multiple of the period of the external potential. There is a broad transition regime between regular and irregular behavior, which is characterized by multistability between regular and irregular behavior. The avalanches are build up by sound waves and shock waves. Shock waves can turn their direction of propagation, or they can split into two pulses propagating in opposite directions leading to transient spatio-temporal chaos. PACS numbers: 05.70.Ln,05.50.+q,46.10.+zComment: 33 pages (RevTex), 15 Figures (available on request), appears in Phys. Rev.

Self-organization of vortices in type-II superconductors during magnetic relaxation

We revise the applicability of the theory of self-organized criticality (SOC) to the process of magnetic relaxation in type-II superconductors. The driving parameter of self-organization of vortices is the energy barrier for flux creep and not the current density. The power spectrum of the magnetic noise due to vortex avalanches is calculated and is predicted to vary with time during relaxation.Comment: RevTex, 5 pages, 2 PS figures. Accepted in Phys. Rev.

Vortex Plastic Motion in Twinned Superconductors

We present simulations, without electrodynamical assumptions, of $B(x,y,H(t)), M(H(t))$, and $J_c(H(t))$, in hard superconductors, for a variety of twin-boundary pinning potential parameters, and for a range of values of the density and strength of the pinning sites. We numerically solve the overdamped equations of motion of up to 10^4 flux-gradient-driven vortices which can be temporarily trapped at $\sim 10^6$ pinning centers. These simulations relate macroscopic measurements (e.g., M(H), ``flame'' shaped $B(x,y)$ profiles) with the underlying microscopic pinning landscape and the plastic dynamics of individual vortices