Approximations of relations by continuous functions

AbstractLet X be a Tychonoff space, C(X) be the space of all continuous real-valued functions defined on X and CL(X×R) be the hyperspace of all nonempty closed subsets of X×R. We prove the following result. Let X be a countably paracompact normal space. The following are equivalent: (a) dimX=0; (b) the closure of C(X) in CL(X×R) with the Vietoris topology consists of all F∈CL(X×R) such that F(x)≠∅ for every x∈X and F maps isolated points into singletons; (c) each usco map which maps isolated points into singletons can be approximated by continuous functions in CL(X×R) with the locally finite topology. From the mentioned result we can also obtain the answer to Problem 5.5 in [L'. Holá, R.A. McCoy, Relations approximated by continuous functions, Proc. Amer. Math. Soc. 133 (2005) 2173–2182] and to Question 5.5 in [R.A. McCoy, Comparison of hyperspace and function space topologies, Quad. Mat. 3 (1998) 243–258] in the realm of normal, countably paracompact, strongly zero-dimensional spaces. Generalizations of some results from [L'. Holá, R.A. McCoy, Relations approximated by continuous functions, Proc. Amer. Math. Soc. 133 (2005) 2173–2182] are also given

Edge effects in a frustrated Josephson junction array with modulated couplings

A square array of Josephson junctions with modulated strength in a magnetic field with half a flux quantum per plaquette is studied by analytic arguments and dynamical simulations. The modulation is such that alternate columns of junctions are of different strength to the rest. Previous work has shown that this system undergoes an XY followed by an Ising-like vortex lattice disordering transition at a lower temperature. We argue that resistance measurements are a possible probe of the vortex lattice disordering transition as the linear resistance $R_{L}(T)\sim A(T)/L$ with $A(T) \propto (T-T_{cI})$ at intermediate temperatures $T_{cXY}>T>T_{cI}$ due to dissipation at the array edges for a particular geometry and vanishes for other geometries. Extensive dynamical simulations are performed which support the qualitative physical arguments.Comment: 8 pages with figs, RevTeX, to appear in Phys. Rev.

Percolation in random environment

We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the system with varying degree of disorder is governed by new, random fixed points with anisotropic scaling properties. For weaker disorder both the magnetization and the anisotropy exponents are non-universal, whereas for strong enough disorder the system scales into an {\it infinite randomness fixed point} in which the critical exponents are exactly known.Comment: 8 pages, 7 figure

Random antiferromagnetic quantum spin chains: Exact results from scaling of rare regions

We study XY and dimerized XX spin-1/2 chains with random exchange couplings by analytical and numerical methods and scaling considerations. We extend previous investigations to dynamical properties, to surface quantities and operator profiles, and give a detailed analysis of the Griffiths phase. We present a phenomenological scaling theory of average quantities based on the scaling properties of rare regions, in which the distribution of the couplings follows a surviving random walk character. Using this theory we have obtained the complete set of critical decay exponents of the random XY and XX models, both in the volume and at the surface. The scaling results are confronted with numerical calculations based on a mapping to free fermions, which then lead to an exact correspondence with directed walks. The numerically calculated critical operator profiles on large finite systems (L<=512) are found to follow conformal predictions with the decay exponents of the phenomenological scaling theory. Dynamical correlations in the critical state are in average logarithmically slow and their distribution show multi-scaling character. In the Griffiths phase, which is an extended part of the off-critical region average autocorrelations have a power-law form with a non-universal decay exponent, which is analytically calculated. We note on extensions of our work to the random antiferromagnetic XXZ chain and to higher dimensions.Comment: 19 pages RevTeX, eps-figures include

Phase Stability Effects on Hydrogen Embrittlement Resistance in Martensite–Reverted Austenite Steels

Earlier studies have shown that interlath austenite in martensitic steels can enhance hydrogen embrittlement (HE) resistance. However, the improvements were limited due to microcrack nucleation and growth. A novel microstructural design approach is investigated, based on enhancing austenite stability to reduce crack nucleation and growth. Our findings from mechanical tests, X-ray diffraction, and scanning electron microscopy reveal that this strategy is successful. However, the improvements are limited due to intrinsic microstructural heterogeneity effects

Organic Superconductors: when correlations and magnetism walk in

This survey provides a brief account for the start of organic superconductivity motivated by the quest for high Tc superconductors and its development since the eighties'. Besides superconductivity found in 1D organics in 1980, progresses in this field of research have contributed to better understand the physics of low dimensional conductors highlighted by the wealth of new remarkable properties. Correlations conspire to govern the low temperature properties of the metallic phase. The contribution of antiferromagnetic fluctuations to the interchain Cooper pairing proposed by the theory is borne out by experimental investigations and supports supercondutivity emerging from a non Fermi liquid background. Quasi one dimensional organic superconductors can therefore be considered as simple prototype systems for the more complex high Tc materials.Comment: 41 pages, 21 figures to be published in Journal of Superconductivity and Novel Magnetis

Paths in spaces of homeomorphisms on the plane

AbstractThe path components and connected components are determined for the space H(C) of homeomorphisms on the complex plane C for the three cases that H(C) has the pointwise topology, the compact-open topology, and the fine topology. The space H(C) is also considered with the uniform topology, but the characterization of the path components and connected components there is left as an open question