126 research outputs found
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 with
at intermediate temperatures 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
Changing Sides in Revolutionary Times: The Career of a Lower-Class CPP-NPA Leader in Negros Occidental.
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