Undersampled Phase Retrieval with Outliers

We propose a general framework for reconstructing transform-sparse images from undersampled (squared)-magnitude data corrupted with outliers. This framework is implemented using a multi-layered approach, combining multiple initializations (to address the nonconvexity of the phase retrieval problem), repeated minimization of a convex majorizer (surrogate for a nonconvex objective function), and iterative optimization using the alternating directions method of multipliers. Exploiting the generality of this framework, we investigate using a Laplace measurement noise model better adapted to outliers present in the data than the conventional Gaussian noise model. Using simulations, we explore the sensitivity of the method to both the regularization and penalty parameters. We include 1D Monte Carlo and 2D image reconstruction comparisons with alternative phase retrieval algorithms. The results suggest the proposed method, with the Laplace noise model, both increases the likelihood of correct support recovery and reduces the mean squared error from measurements containing outliers. We also describe exciting extensions made possible by the generality of the proposed framework, including regularization using analysis-form sparsity priors that are incompatible with many existing approaches.Comment: 11 pages, 9 figure

Unified order-disorder vortex phase transition in high-Tc superconductors

The diversity of vortex melting and solid-solid transition lines measured in different high-T$_{c}$ superconductors is explained, postulating a unified order-disorder phase transition driven by both thermally- and disorder-induced fluctuations. The temperature dependence of the transition line and the nature of the disordered phase (solid, liquid, or pinned liquid) are determined by the relative contributions of these fluctuations and by the pinning mechanism. By varying the pinning mechanism and the pinning strength one obtains a spectrum of monotonic and non-monotonic transition lines similar to those measured in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$$, YBa$_{2}$Cu$_{3}$O$_{7-\delta}$, Nd$_{1.85}$Ce$_{0.15}$CuO$$, Bi$_{1.6}$Pb$_{0.4}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ and (La$_{0.937}$Sr$_{0.063}$)$_{2}$CuO$_{4}$Comment: To be published in Phys. Rev. B Rapid Com

Metastable vortex states in YBa<SUB>2</SUB>Cu<SUB>3</SUB>O<SUB>7-δ</SUB> crystal

Magnetization measurements in an untwinned YBa2Cu3O7-δ crystal reveal a range of temperatures and fields for which the magnetization exhibits unusual history-dependent behavior. This range envelopes the transition line, Bss(T), separating between the vortex quasiordered and disordered phases. The observed history effects indicate that a disordered (quasiordered) vortex state can exist as a metastable state below (above) the Bss(T) line. The fields, defining the phase transition and the borders of the metastability region, are correlated to sharp features in the magnetization loop

Disorder and thermally driven vortex-lattice melting in La{2-x}Sr{x}CuO{4} crystals

Magnetization measurements in La{2-x}Sr{x}CuO{4} crystals indicate vortex order-disorder transition manifested by a sharp kink in the second magnetization peak. The transition field exhibits unique temperature dependence, namely a strong decrease with temperature in the entire measured range. This behavior rules out the conventional interpretation of a disorder-driven transition into an entangled vortex solid phase. It is shown that the transition in La{2-x}Sr{x}CuO{4} is driven by both thermally- and disorder-induced fluctuations, resulting in a pinned liquid state. We conclude that vortex solid-liquid, solid-solid and solid to pinned-liquid transitions are different manifestations of the same thermodynamic order-disorder transition, distinguished by the relative contributions of thermal and disorder-induced fluctuations.Comment: To be published in phys. Rev. B Rapid Com

Calculation of minor hysteresis loops under metastable to stable transformations in vortex matter

We present a model in which metastable supercooled phase and stable equilibrium phase of vortex matter coexist in different regions of a sample. Minor hysteresis loops are calculated with the simple assumption of the two phases of vortex matter having field-independent critical current densities. We use our earlier published ideas that the free energy barrier separating the metastable and stable phases reduces as the magnetic induction moves farther from the first order phase transition line, and that metastable to stable transformations occur in local regions of the sample when the local energy dissipation exceeds a critical value. Previously reported anomalous features in minor hysteresis loops are reproduced, and calculated field profiles are presented.Comment: 9pages, 7 figure

Hysteretic behavior of the vortex lattice at the onset of the second peak for HgBa2_2CuO4+δ_{4+\delta} superconductor

By means of local Hall probe ac and dc permeability measurements we investigated the phase diagram of vortex matter for the HgBa$_2$CuO$_{4+\delta }$ superconductor in the regime near the critical temperature. The second peak line, $H_{\rm sp}$, in contrast to what is usually assumed, doesn't terminate at the critical temperature. Our local ac permeability measurements revealed pronounced hysteretic behavior and thermomagnetic history effects near the onset of the second peak, giving evidence for a phase transition of vortex matter from an ordered qausilattice state to a disordered glass

Peak effect in a superconducting DyBa2Cu3O7-y film at microwave frequencies

We report the observation of a peak in the microwave (9.55 GHz) surface resistance in an epitaxial DyBa2Cu3O7-y superconducting film in magnetic fields (parallel to the c axis) ranging between 0.2 to 0.9 Tesla. Such a peak is absent in the measurements done in zero-field. The temperature and field dependence of the peak suggests that this peak could be associated with the peak effect phenomenon reflecting the order-disorder transformation in the flux-line lattice. A strong dependence of this peak effect at frequencies close to the depinning frequency of the flux line lattice is observed.Comment: 1 text, 4 figures (all postscript) to be published in Phys. Rev.

An Assessment of Multilevel Governance in Cohesion Policy 2007-2013 : Volume 1, Study

This study provides an in-depth analysis of Multi-Level Governance in Cohesion Policy in the programming period of 2007-2013. It begins by examining the evolution of the concept and previous practices of implementing Multi-Level Governance in Cohesion Policy across the EU. It then provides a comparative analysis of partnership-working in nine programme case studies during the programming period and across the various stages of the policy cycle. The study identifies the advantages and disadvantages of partnership-working and formulates strategic and operational recommendations in the context of the preparation of the 2014-2020 programming period