Phase diagram of the vortex system in layered superconductors with strong columnar pinning

We present the results of a detailed investigation of the low-temperature properties of the vortex system in strongly anisotropic layered superconductors with a random array of columnar pinning centers. Our method involves numerical minimization of a free energy functional in terms of the time-averaged local vortex density. It yields the detailed vortex density distribution for all local free-energy minima, and therefore allows the computation of any desired correlation function of the time-averaged local vortex density. Results for the phase diagram in the temperature vs. pin concentration plane at constant magnetic induction are presented. We confirm that for very low pin concentrations, the low-temperature phase is a Bragg glass, which melts into an interstitial liquid phase via two first-order steps, separated by a Bose glass phase. At higher concentrations, however, the low-temperature phase is a Bose glass, and the melting transition becomes continuous. The transition is then characterized by the onset of percolation of liquid-like regions across the sample. Inhomogeneous local melting of the Bose glass is found to occur. There is also a depinning crossover between the interstitial liquid and a completely unpinned liquid at higher temperatures. At sufficiently large pin concentrations, the depinning line merges with the Bose glass to interstitial liquid transition. Many of the features we find have been observed experimentally and in simulations. We discuss the implications of our results for future experimental and theoretical work.Comment: 15 pages including Figure

The phase diagram of vortex matter in layered superconductors with tilted columnar pinning centers

We study the vortex matter phase diagram of a layered superconductor in the presence of columnar pinning defects, {\it tilted} with respect to the normal to the layers. We use numerical minimization of the free energy written as a functional of the time averaged vortex density of the Ramakrishnan-Yussouff form, supplemented by the appropriate pinning potential. We study the case where the pin density is smaller than the areal vortex density. At lower pin concentrations, we find, for temperatures of the order of the melting temperature of the unpinned lattice, a Bose glass type phase which at lower temperatures converts, via a first order transition, to a Bragg glass, while, at higher temperatures, it crosses over to an interstitial liquid. At somewhat higher concentrations, no transition to a Bragg glass is found even at the lowest temperatures studied. While qualitatively the behavior we find is similar to that obtained using the same procedures for columnar pins normal to the layers, there are important and observable quantitative differences, which we discuss.Comment: 12 pages, including figure

Phase diagram of vortex matter in layered superconductors with random point pinning

We study the phase diagram of the superconducting vortex system in layered high-temperature superconductors in the presence of a magnetic field perpendicular to the layers and of random atomic scale point pinning centers. We consider the highly anisotropic limit where the pancake vortices on different layer are coupled only by their electromagnetic interaction. The free energy of the vortex system is then represented as a Ramakrishnan-Yussouff free energy functional of the time averaged vortex density. We numerically minimize this functional and examine the properties of the resulting phases. We find that, in the temperature ($T$) -- pinning strength ($s$) plane at constant magnetic induction, the equilibrium phase at low $T$ and $s$ is a Bragg glass. As one increases $s$ or $T$ a first order phase transition occurs to another phase that we characterize as a pinned vortex liquid. The weakly pinned vortex liquid obtained for high $T$ and small $s$ smoothly crosses over to the strongly pinned vortex liquid as $T$ is decreased or $s$ increased -- we do not find evidence for the existence, in thermodynamic equilibrium, of a distinct vortex glass phase in the range of pinning parameters considered here. %cdr We present results for the density correlation functions, the density and defect distributions, and the local field distribution accessible via $\mu$SR experiments. These results are compared with those of existing theoretical, numerical and experimental studies.Comment: 15 pages, including figures. Higher resolution files for Figs 3a and 11 available from author

Enhancement of Writeback Caching by changes in flush and its parameters

Achievement of high performance in computing or accessing of data is the aim of any system. Reduction of access time to a particular data which is present in the device is very important for the enhancement in the performance. Caching is implemented to do the same. The group of cache device and the virtual device is made as a cache group to enhance the performance of the system. The system may not be on the same condition different instances of time. There will always be a variation in io rates of the application, which is not utilized for the full extent. These differences in the io rates can be utilized effectively for the enhancement of the performance of the system. When the system is idle of with less io then the system will force the flush so that the inconsistency of data is reduced. When the system is being bombarded with io then less threads are given for the flush io. These variations in the threads assigned for the implementation of flush io will enhance the overall performance of the system

Hydrodynamics of superfluids confined in blocked rings and wedges

Motivated by many recent experimental studies of non-classical rotational inertia (NCRI) in superfluid and supersolid samples, we present a study of the hydrodynamics of a superfluid confined in the two-dimensional region (equivalent to a long cylinder) between two concentric arcs of radii $b$ and $a$ ($b<a$) subtending an angle $\beta$, with $0 \le \beta \le 2\pi$. The case $\beta= 2 \pi$ corresponds to a blocked ring. We discuss the methodology to compute the NCRI effects, and calculate these effects both for small angular velocities, when no vortices are present, and in the presence of a vortex. We find that, for a blocked ring, the NCRI effect is small, and that therefore there will be a large discontinuity in the moment of inertia associated with blocking or unblocking circular paths. For blocked wedges ($b=0$) with $\beta > \pi$, we find an unexpected divergence of the velocity at the origin, which implies the presence of either a region of normal fluid or a vortex for {\it any} nonzero value of the angular velocity. Implications of our results for experiments on "supersolid" behavior in solid $^4{\rm He}$ are discussed. A number of mathematical issues are pointed out and resolved.Comment: 15 pages, including figures. To appear in Phys. Rev.

Melting and structure of the vortex solid in strongly anisotropic layered superconductors with random columnar pins

We study the melting transition of the low-temperature vortex solid in strongly anisotropic layered superconductors with a concentration of random columnar pinning centers small enough so that the areal density of the pins is much less than that of the vortex lines. Both the external magnetic field and the columnar pins are assumed to be oriented perpendicular to the layers Our method, involving numerical minimization of a model free energy functional, yields not only the free energy values at the local minima of the functional but also the detailed density distribution of the system at each minimum: this allows us to study in detail the structure of the different phases. We find that at these pin concentrations and low temperatures, the thermodynamically stable state is a topologically ordered Bragg glass. This nearly crystalline state melts into an interstitial liquid (a liquid in which a small fraction of vortex lines remain localized at the pinning centers) in two steps, so that the Bragg glass and the liquid are separated by a narrow phase that we identify from analysis of its density structure as a polycrystalline Bose glass. Both the Bragg glass to Bose glass and the Bose glass to interstitial liquid transitions are first-order. We also find that a local melting temperature defined using a criterion based on the degree of localization of the vortex lines exhibits spatial variations similar to those observed in recent experiments.Comment: 17 page

Microscopic mechanism for fluctuating pair density wave

In weakly coupled BCS superconductors, only electrons within a tiny energy window around the Fermi energy, $E_F$, form Cooper pairs. This may not be the case in strong coupling superconductors such as cuprates, FeSe, SrTiO$_3$ or cold atom condensates where the pairing scale, $E_B$, becomes comparable or even larger than $E_F$. In cuprates, for example, a plausible candidate for the pseudogap state at low doping is a fluctuating pair density wave, but no microscopic model has yet been found which supports such a state. In this work, we write an analytically solvable model to examine pairing phases in the strongly coupled regime and in the presence of anisotropic interactions. Already for moderate coupling we find an unusual finite temperature phase, below an instability temperature $T_i$, where local pair correlations have non-zero center-of-mass momentum but lack long-range order. At low temperature, this fluctuating pair density wave can condense either to a uniform $d$-wave superconductor or the widely postulated pair-density wave phase depending on the interaction strength. Our minimal model offers a unified microscopic framework to understand the emergence of both fluctuating and long range pair density waves in realistic systems.Comment: 13 pages, 6 figures including Supplemental Materia

Energy3D: Guiding Engineering Design with Science Simulations

The Purdue P-12 Networking Summit gives Purdue faculty and staff engaged with P-12 schools a forum to interact with each other, share ideas, and develop collaborations that make programs more effective. Faculty and staff are invited to attend

Characterization of the Dynamics of Glass-forming Liquids from the Properties of the Potential Energy Landscape

We develop a framework for understanding the difference between strong and fragile behavior in the dynamics of glass-forming liquids from the properties of the potential energy landscape. Our approach is based on a master equation description of the activated jump dynamics among the local minima of the potential energy (the so-called inherent structures) that characterize the potential energy landscape of the system. We study the dynamics of a small atomic cluster using this description as well as molecular dynamics simulations and demonstrate the usefulness of our approach for this system. Many of the remarkable features of the complex dynamics of glassy systems emerge from the activated dynamics in the potential energy landscape of the atomic cluster. The dynamics of the system exhibits typical characteristics of a strong supercooled liquid when the system is allowed to explore the full configuration space. This behavior arises because the dynamics is dominated by a few lowest-lying minima of the potential energy and the potential energy barriers between these minima. When the system is constrained to explore only a limited region of the potential energy landscape that excludes the basins of attraction of a few lowest-lying minima, the dynamics is found to exhibit the characteristics of a fragile liquid.Comment: 13 pages, 6 figure