Elasticity, fluctuations and vortex pinning in ferromagnetic superconductors: A "columnar elastic glass"

We study the elasticity, fluctuations and pinning of a putative spontaneous vortex solid in ferromagnetic superconductors. Using a rigorous thermodynamic argument, we show that in the idealized case of vanishing crystalline pinning anisotropy the long-wavelength tilt modulus of such a vortex solid vanishes identically, as guaranteed by the underlying rotational invariance. The vanishing of the tilt modulus means that, to lowest order, the associated tension elasticity is replaced by the softer, curvature elasticity. The effect of this is to make the spontaneous vortex solid qualitatively more susceptible to the disordering effects of thermal fluctuations and random pinning. We study these effects, taking into account the nonlinear elasticity, that, in three dimensions, is important at sufficiently long length scales, and showing that a ``columnar elastic glass'' phase of vortices results. This phase is controlled by a previously unstudied zero-temperature fixed point and it is characterized by elastic moduli that have universal strong wave-vector dependence out to arbitrarily long length scales, leading to non-Hookean elasticity. We argue that, although translationally disordered for weak disorder, the columnar elastic glass is stable against the proliferation of dislocations and is therefore a topologically ordered {\em elastic} glass. As a result, the phenomenology of the spontaneous vortex state of isotropic magnetic superconductors differs qualitatively from a conventional, external-field-induced mixed state. For example, for weak external fields $H$, the magnetic induction scales {\em universally} like $B(H)\sim B(0)+ c H^{\alpha}$, with $\alpha\approx 0.72$.Comment: Minor editorial changes, version to be published in PRB, 39 pages, 7 figure

A tale of one city: intra-institutional variations in migrating VLE platform

City University London committed in 2009 to make Moodle the Virtual Learning Environment (VLE) at the core of a new Strategic Learning Environment (SLE) comprised of VLE, externally facing website and related systems such as video streaming and virtual classrooms. Previously, the WebCT VLE had been separate from most of the other systems at the institution with very limited connections to other tools. Each of the schools within the institution was able to pursue their own strategy and timeframe for the migration and embedding of Moodle within their subject areas, within an absolute limit of 2 years. This paper outlines the approaches taken by the various schools, highlighting similarities and differences, and draws out common aspects from the project to make recommendations for institutions seeking to undertake similar migrations

Eurasian watermilfoil biomass associated with insect herbivores in New York

A study of aquatic plant biomass within Cayuga Lake, New York spans twelve years from 1987-1998. The exotic Eurasian watermilfoil ( Myriophyllum spicatum L.) decreased in the northwest end of the lake from 55% of the total biomass in 1987 to 0.4% in 1998 and within the southwest end from 50% in 1987 to 11% in 1998. Concurrent with the watermilfoil decline was the resurgence of native species of submersed macrophytes. During this time we recorded for the first time in Cayuga Lake two herbivorous insect species: the aquatic moth Acentria ephemerella , first observed in 1991, and the aquatic weevil Euhrychiopsis lecontei , first found in 1996 . Densities of Acentria in southwest Cayuga Lake averaged 1.04 individuals per apical meristem of Eurasian watermilfoil for the three-year period 1996-1998. These same meristems had Euhrychiopsis densities on average of only 0.02 individuals per apical meristem over the same three-year period. A comparison of herbivore densities and lake sizes from five lakes in 1997 shows that Acentria densities correlate positively with lake surface area and mean depth, while Euhrychiopsis densities correlate negatively with lake surface area and mean depth. In these five lakes, Acentria densities correlate negatively with percent composition and dry mass of watermilfoil. However, Euhrychiopsis densities correlate positively with percent composition and dry mass of watermilfoil. Finally, Acentria densities correlate negatively with Euhrychiopsis densities suggesting interspecific competition

Softer than normal, but not as soft as one might think: Spontaneous flux lattices in ferromagnetic spin-triplet superconductors

A theory is developed for the spontaneous vortex lattice that is expected to occur in the ferromagnetic superconductors ZrZn_2, UGe_2, and URhGe, where the superconductivity is likely of spin-triplet nature. The long-wavelength fluctuations of this spontaneous flux lattice are predicted to be huge compared to those of a conventional flux lattice, and to be the same as those for spin-singlet ferromagnetic superconductors. It is shown that these fluctuations lead to unambiguous experimental signatures which may provide the easiest way to observe the spontaneous flux lattice.Comment: 4pp, 1 eps fi

The Smectic AA-CC Phase Transition in Biaxial Disordered Environments

We study the smectic $A$-$C$ phase transition in biaxial disordered environments, e.g. fully anisotropic aerogel. We find that both the $A$ and $C$ phases belong to the universality class of the "XY Bragg glass", and therefore have quasi-long-ranged translational smectic order. The phase transition itself belongs to a new universality class, which we study using an $\epsilon=7/2-d$ expansion. We find a stable fixed point, which implies a continuous transition, the critical exponents of which we calculate

Non-Ergodic Dynamics of the 2D Random-phase Sine-Gordon Model: Applications to Vortex-Glass Arrays and Disordered-Substrate Surfaces

The dynamics of the random-phase sine-Gordon model, which describes 2D vortex-glass arrays and crystalline surfaces on disordered substrates, is investigated using the self-consistent Hartree approximation. The fluctuation-dissipation theorem is violated below the critical temperature T_c for large time t>t* where t* diverges in the thermodynamic limit. While above T_c the averaged autocorrelation function diverges as Tln(t), for T<T_c it approaches a finite value q* proportional to 1/(T_c-T) as q(t) = q* - c(t/t*)^{-\nu} (for t --> t*) where \nu is a temperature-dependent exponent. On larger time scales t > t* the dynamics becomes non-ergodic. The static correlations behave as Tln{x} for T>T_c and for T<T_c when x < \xi* with \xi* proportional to exp{A/(T_c-T)}. For scales x > \xi*, they behave as (T/m)ln{x} where m is approximately T/T_c near T_c, in general agreement with the variational replica-symmetry breaking approach and with recent simulations of the disordered-substrate surface. For strong- coupling the transition becomes first-order.Comment: 12 pages in LaTeX, Figures available upon request, NSF-ITP 94-10

Transversely Driven Charge Density Waves and Striped Phases of High-Tc_c Superconductors: The Current Effect Transistor

We show that a normal (single particle) current density $J_x$ {\em transverse} to the ordering wavevector $2k_F{\bf\hat{z}}$ of a charge density wave (CDW) has dramatic effects both above and {\em below} the CDW depinning transition. It exponentially (in $J_x$) enhances CDW correlations, and exponentially suppresses the longitudinal depinning field. The intermediate longitudinal I-V relation also changes, acquiring a {\em linear} regime. We propose a novel ``current effect transistor'' whose CDW channel is turned on by a transverse current. Our results also have important implications for the recently proposed ``striped phase'' of the high-T$_c$ superconductors.Comment: change of title and minor corrections, 4 RevTeX pgs, to appear in Phys. Rev. Lett., 81, 3711 (1998

Vortex Glass Phase and Universal Susceptibility Variations in Planar Array of Flux Lines

Some of the properties of the low temperature vortex-glass phase of randomly-pinned flux lines in 1+1 dimensions are studied. The flux arrays are found to be sensitive to small changes in external parameters such as the magnetic field or temperature. These effects are captured by the variations in the magnetic response and noise, which have universal statistics and should provide an unambiguous signature of the glass phase.Comment: 11 pages and no figures; revtex 3.

Sliding Columnar Phase of DNA-Lipid Complexes

We introduce a simple model for DNA-cationic-lipid complexes in which galleries between planar bilayer lipid lamellae contain DNA 2D smectic lattices that couple orientationally and positionally to lattices in neighboring galleries. We identify a new equilibrium phase in which there are long-range orientational but not positional correlations between DNA lattices. We discuss properties of this new phase such as its X-ray structure factor S(r), which exhibits unusual exp(- const.ln^2 r) behavior as a function of in-plane separation r.Comment: This file contains 4 pages of double column text and one postscript figure. This version includes interactions between dislocations in a given gallery and presents an improved estimate of the decoupling temperature. It is the published versio

A variational study of the random-field XY model

A disorder-dependent Gaussian variational approach is applied to the $d$-dimensional ferromagnetic XY model in a random field. The randomness yields a non extensive contribution to the variational free energy, implying a random mass term in correlation functions. The Imry-Ma low temperature result, concerning the existence ($d>4$) or absence ($d < 4$) of long-range order is obtained in a transparent way. The physical picture which emerges below $d=4$ is that of a marginally stable mixture of domains. We also calculate within this variational scheme, disorder dependent correlation functions, as well as the probability distribution of the Imry-Ma domain size.Comment: 14 pages, latex fil