On a Speculated Relation Between Chv\'atal-Sankoff Constants of Several Sequences

It is well known that, when normalized by n, the expected length of a longest common subsequence of d sequences of length n over an alphabet of size sigma converges to a constant gamma_{sigma,d}. We disprove a speculation by Steele regarding a possible relation between gamma_{2,d} and gamma_{2,2}. In order to do that we also obtain new lower bounds for gamma_{sigma,d}, when both sigma and d are small integers.Comment: 13 pages. To appear in Combinatorics, Probability and Computin

Modeling Two Dimensional Magnetic Domain Patterns

Two-dimensional magnetic garnets exhibit complex and fascinating magnetic domain structures, like stripes, labyrinths, cells and mixed states of stripes and cells. These patterns do change in a reversible way when the intensity of an externally applied magnetic field is varied. The main objective of this contribution is to present the results of a model that yields a rich pattern structure that closely resembles what is observed experimentally. Our model is a generalized two-dimensional Ising-like spin-one Hamiltonian with long-range interactions, which also incorporates anisotropy and Zeeman terms. The model is studied numerically, by means of Monte Carlo simulations. Changing the model parameters stripes, labyrinth and/or cellular domain structures are generated. For a variety of cases we display the patterns, determine the average size of the domains, the ordering transition temperature, specific heat, magnetic susceptibility and hysteresis cycle. Finally, we examine the reversibility of the pattern evolution under variations of the applied magnetic field. The results we obtain are in good qualitative agreement with experiment.Comment: 8 pages, 12 figures, submitted to Phys. Rev.

Magnetic reordering in the vicinity of a ferromagnetic/antiferromagnetic interface

The magnetic arrangement in the vicinity of the interface between a ferromagnet and an antiferromagnet is investigated, in particular its dependence on the exchange couplings and the temperature. Applying a Heisenberg model, both sc(001) and fcc(001) lattices are considered and solved by a mean field approximation. Depending on the parameter values a variety of different magnetic configurations emerge. Usually the subsystem with the larger ordering temperature induces a magnetic order into the other one (magnetic proximity effect). With increasing temperature a reorientation of the magnetic sublattices is obtained. For coupled sc(001) systems both FM and AFM films are disturbed from their collinear magnetic order, hence exhibit a similar behavior. This symmetry is absent for fcc(001) films which, under certain circumstances, may exhibit two different critical temperatures. Analytical results are derived for simple bilayer systems.Comment: accepted for publication in Eur. Phys. J.

Detoxification of diluted azo-dyes at biocompatible pH with the oxone/Co2+ reagent in dark and light processes

Accelerated bleaching and photobleaching of diluted solutions of Methyl Orange and other dyes occur only when Co2+-ions are present in solution mediating oxone (2KHSO(5)center dot KHSO4 center dot K2SO4) decomposition. The bleaching of Methyl Orange, Orange II and Methylene Blue dyes in dilute solutions (0.01 mM) proceeds within a few minutes and occurs at biocompatible pH leading to a decrease in the toxicity of the initial solution under simulated daylight radiation. A reduction in the toxicity of 35% was observed at biocompatible pH-values when a solution Orange II (0.01 mM) was irradiated in the presence of oxone (0.06 mM)/Co2+ (0.004 mM). Only traces of Co2+ were necessary to accelerate the decomposition of the dyes in the presence of oxone in the dark and even more under daylight irradiation. The photobleaching proceeds with a photonic efficiency of similar to 0.24. The solution parameters were optimized for the photobleaching of azo-dyes by the oxone/Co2+ reagent. H2O2 generation was observed to be possible only as long as Orange II was present in the solution. The decomposition kinetics of H2O2 was followed under solar radiation. The dye decomposition was also investigated as a function of the applied light intensity. No saturation effects were observed when simulated solar light with 90% AM1 was applied. The photobleaching reaction proceeded with acceptable kinetics with light intensities 5-10 times lower than AM1. This makes the photocatalytic treatment suitable under diffuse daylight. (c) 2006 Elsevier B.V. All rights reserved

Metastable Random Field Ising model with exchange enhancement: a simple model for Exchange Bias

We present a simple model that allows hysteresis loops with exchange bias to be reproduced. The model is a modification of the T=0 random field Ising model driven by an external field and with synchronous local relaxation dynamics. The main novelty of the model is that a certain fraction f of the exchange constants between neighbouring spins is enhanced to a very large value J_E. The model allows the dependence of the exchange bias and other properties of the hysteresis loops to be analyzed as a function of the parameters of the model: the fraction f of enhanced bonds, the amount of the enhancement J_E and the amount of disorder which is controlled by the width sigma of the Gaussian distribution of the random fields.Comment: 8 pages, 11 figure

Abatement of an Azo Dye on Structured C-Nafion/Fe-Ion Surfaces by Photo-Fenton Reactions Leading to Carboxylate Intermediates with a Remarkable Biodegradability Increase of the Treated Solution

A novel C-Nafton/Fe-ion structured fabric capable of mediating Orange II decomposition in Fenton-immobilized photoassisted reactions is presented. The catalyst preparation requires the right balance between the amount of the Nafion necessary to protect the C-surface and the minimum encapsulation of the Fe-cluster catalytic sites inside the Nafion to allow the photocatalysis to proceed. The C-Nafion/Fe fabric can be used up to pH 10 under light to photocatalyze the disappearance of Orange II in the presence of H2O2. The photocatalysis mediated by the C-Nafion/Fe-ion fabric increased with the applied light intensity and reaction temperature in the reaction needing an activation energy of 9.8 kcal/mol. This indicates that ion- and radical-molecule reactions take place during Orange II disappearance. The build up and decomposition of intermediate iron complexes under light involves the recycling of Fe2+ and was detected by infrared spectroscopy (FTIR). This observation, along with other experimental results, allows us to suggest a surface mechanism for the dye degradation on the C-Nafion/Fe-ion fabrics. The C-Nafion/Fe-ion fabric in the presence of H2O2 under solar simulated light transforms the totally nonbiodegradable Orange II into a biocompatible material with a very high BOD5/COD value. X-ray photoelectron spectroscopy (XPS) and sputtering by Ar+-ions of the upper surface layer of the C-Nafion/Fe-ion fabric allow us to describe the intervention of the photocatalyst down to the molecular level. Most of the Fe clusters examined by transmission electron microscopy (TEM) showed particle sizes close to 4 nm due to their encapsulation into the Gierke cages of the Nafion thin film observed by scanning electron microscopy (SEM) and optical microscopy (OM)

Mechanism of photocatalytic bacterial inactivation on TiO2 films involving cell-wall damage and lysis

This article addresses the cell wall damage of Escherichia coil (from now on E. coil) by TiO2 suspensions. The dynamics of TiO2 photocatalysis by thin films layers is described. The films were characterized by FTIR spectroscopy and atomic force microscopy (AFM). The E coil complete inactivation is shown to be due to the partial damage of the cell-wall components (peroxidation). A small increase in the cell wall disorder concomitant with a decrease of the cell wall functional groups leads to higher cell wall fluidity as the precursor step preceding cell lysis. (C) 2012 Elsevier B.V. All rights reserved

Accelerated photodegradation (minute range) of the commercial azo-dye Orange II mediated by Co3O4/Raschig rings in the presence of oxone

The accelerated discoloration of Orange II by an innovative Co3O4/Raschig ring photocatalyst (from now on Co3O4/RR) is feasible and proceeds to completion using oxone as an oxidant within the surprisingly short time of ∼5 min. The preparation of Co3O4 small clusters (2–10 nm in size) on RR is reported. The discoloration/mineralization of the azo-dye Orange II was carried out in a concentric coaxial photo-reactor and was a function of the Orange II and oxone concentrations, the solution pH and the recirculation rate. At bio-compatible pH-values, the concentration of Co-ions in solution after photocatalysis (15 min) was found to be between 0.5 and 2 ppm, within the limits allowed for treated waters. The generation of peroxide was observed as long as Orange II was still available in solution. By elemental analysis (EA), the amount of Co of the Raschig rings was determined to be ∼65% (w/w) before and after the photocatalysis. This confirms the stability observed during long-term operation of the Co3O4/RR catalyst. The sizes of the Co3O4 clusters on the RR surface were determined by transmission electron spectroscopy (TEM). A non-uniform distribution of Co3O4 particles on RR with sizes between 2 and 10 nm was found. The presence of Co-clusters on the RR-surface was confirmed by electron dispersive spectroscopy (EDS) showing 12.6% surface Co-enrichment before the photocatalysis and 18.8% surface enrichment after the photocatalysis. By confocal microscopy the irregularly thick shaped Co3O4 on the Raschig rings was analyzed. The most striking observation is very large shift of Co2p3/2 line from 779.6 eV at time zero to 782.2 eV within 10 min after due to the photocatalysis taking place. This indicates a strong reduction of electron density on the cobalt atoms of Co3O4/RR and providing the evidence for the strong oxidation properties of this catalyst