Darboux transformations for Lamé potentials

Irreducible second order Darboux (SUSY) transformations are applied to Lam periodic Hamiltonians in order to find physically acceptable partner potentials with the same band structure. The main differences with the usual SUSY approach of potentials allowing for a discrete spectrum are pointed out. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000. This work has been partially supported by CONACyT (project 32086-E) Mxico, DGES (PB98-0370) from MEC (Spain), Junta de Castilla y Len (CO2/199), and Universidad de Valladolid.     

Monte Carlo simulation of ion–material interactions in nuclear fusion devices

One of the key aspects regarding the technological development of nuclear fusion reactors is the understanding of the interaction between high-energy ions coming from the confined plasma and the materials that the plasma-facing components are made of. Among the multiple issues important to plasma–wall interactions in fusion devices, physical erosion and composition changes induced by energetic particle bombardment are considered critical due to possible material flaking, changes to surface roughness, impurity transport and the alteration of physicochemical properties of the near surface region due to phenomena such as redeposition or implantation. A Monte Carlo code named MATILDA (Modeling of Atomic Transport in Layered Dynamic Arrays) has been developed over the years to study phenomena related to ion beam bombardment such as erosion rate, composition changes, interphase mixing and material redeposition, which are relevant issues to plasma-aided manufacturing of microelectronics, components on object exposed to intense solar wind, fusion reactor technology and other important industrial fields. In the present work, the code is applied to study three cases of plasma material interactions relevant to fusion devices in order to highlight the code’s capabilities: (1) the Be redeposition process on the ITER divertor, (2) physical erosion enhancement in castellated surfaces and (3) damage to multilayer mirrors used on EUV diagnostics in fusion devices due to particle bombardment.     

Superelectrophilic Activation of N‐Substituted Isatins: Implications for Polymer Synthesis,a Theoretical Study

The stability and reactivity of mono‐ and multi‐protonatred N‐substituted isatin derivatives were studied at PBE0/aug‐cc‐pvtz//PBE0/6‐31+G** level of theory in triflic acid (TFSA) solution. Calculations showed that the monocationic intermediates are the principal reactive species in the reaction of hydroxyalkylation of isatin derivatives in TFSA media. Electron‐withdrawing substituents on the nitrogen atom increase the reactivity of isatin‐containing electrophiles towards aromatic hydrocarbons, in accordance with their expected electronic influence. Steric factors also play an important role in the reactivity of isatin‐containing electrophiles, especially in the second reaction step, due to their more sterically hindered reactive center.

     

The ground state energy of the Edwards-Anderson spin glass model with a parallel tempering Monte Carlo algorithm

We study the efficiency of parallel tempering Monte Carlo technique for calculating true ground states of the Edwards-Anderson spin glass model. Bimodal and Gaussian bond distributions were considered in two- and three-dimensional lattices. By a systematic analysis we find a simple formula to estimate the values of the parameters needed in the algorithm to find the GS with a fixed average probability. We also study the performance of the algorithm for single samples, quantifying the difference between samples where the GS is hard, or easy, to find. The GS energies we obtain are in good agreement with the values found in the literature. Our results show that the performance of the parallel tempering technique is comparable to more powerful heuristics developed to find the ground state of Ising spin glass systems.     

Effect of low intensity helium-neon (HeNe) laser irradiation on experimental paracoccidioidomycotic wound healing dynamics

The effect of HeNe laser on the extracellular matrix deposition, chemokine expression and angiogenesis in experimental paracoccidioidomycotic lesions was investigated. At days 7, 8 and 9 postinfection the wound of each animal was treated with a 632.8 nm HeNe laser at a dose of 3 J cm(-2). At day 10 postinfection, the wounds were examined by using histologic and immunohistochemical methods. Results revealed that laser-treated lesions were lesser extensive than untreated ones, and composed mainly by macrophages and lymphocytes. High IL-1beta expression was shown in the untreated group whereas in laser-treated animals the expression was scarce. On the other hand, the expression of CXCL-10 was found to be reduced in untreated animals and quite intensive and well distributed in the laser-treated ones. Also, untreated lesions presented vascular endothelial growth factor (VEGF) in a small area near the center of the lesion and high immunoreactivity for hypoxia-inducible factor-1 (HIF-1), whereas laser-treated lesions expressed VEGF surrounding blood vessels and little immunoreactivity for HIF-1. Laser-treated lesions presented much more reticular fibers and collagen deposition when compared with the untreated lesion. Our results show that laser was efficient in minimizing the local effects observed in paracoccidioidomycosis and can be an efficient tool in the treatment of this infection, accelerating the healing process.     

Runge–Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments

In this paper we deal with the numerical solutions of Runge–Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments. The numerical solution is given by the numerical Green’s function. It is shown that Runge–Kutta methods preserve their original order for first-order periodic boundary value differential equations with piecewise constant arguments. We give the conditions under which the numerical solutions preserve some properties of the analytic solutions, e.g., uniqueness and comparison theorems. Finally, some experiments are given to illustrate our results.     

Controllability of Semilinear Differential Systems with Nonlocal Initial Conditions in Banach Spaces

In this note, we establish a sufficient condition for the controllability of a first-order semilinear differential system with nonlocal initial conditions in Banach spaces. The approach used is the Sadovskii fixed-point theorem combined with operator semigroups. Particularly, the compactness of the operator semigroups is not needed in this article. Y.K. Chang was supported by Tianyuan Youth Fund of Mathematics in China (10826063), NNSF of China (10801065), the Scientific Research Fund of Gansu Provincial Education Department (20868), and Qing Lan Talent Engineering Funds (QL-05-16A) of Lanzhou Jiaotong University. J.J. Nieto was supported by Ministerio de Educacion y Ciencia-FEDER Project MTM2007-61724, and by Xunta de Galicia-FEDER Project PGIDIT05PXIC20702PN.     

On Impulsive Hyperbolic Differential Inclusions with?Nonlocal Initial Conditions

This paper is focused mainly upon existence of solutions for a second-order impulsive hyperbolic differential inclusions with nonlocal initial conditions. By using some well-known fixed-point theorems, existence theorems are established when the multivalued map has convex or nonconvex values. As applications of these main theorems, some consequences are given for the sublinear growth cases. Y.-K. Chang was supported by “Qing Lan” Talent Engineering Funds (QL-05-16A), by Lanzhou Jiaotong University, the Scientific Research Fund of Gansu Provincial Education Department (0704-14). J.J. Nieto was supported by Ministerio de Educacion y Ciencia and FEDER, Project MTM2007-61724, and by Xunta de Galicia and FEDER, Project PGIDIT05PXIC20702PN.     

Mechanism of the gold(I)-catalyzed Rautenstrauch rearrangement: a center-to-helix-to-center chirality transfer

The mechanism of the stereospecific gold(I)-catalyzed Rautenstrauch rearrangement of (E)-1-ethynyl-2-methyl-but-2-en-yl acetate to 3,4-dimethyl-cyclopent-2-enone has been computationally addressed using DFT (B3LYP/6-31G, SDD for Au). Our results indicate that the bond formation event follows the Au(I)-induced acetyl transfer to the vicinal alkyne and that it is the helicity of the pentadienyl cation intermediate which keeps memory of the chiral information. The fidelity of the center-to-helix-to-center chirality transfer requires that the rates of helix interconversion and pivaloyl rotation are slower than the cyclization, as calculations predict.