From Continuous-Time Chaotic Systems to Pseudo Random Number Generators: Analysis and Generalized Methodology

The use of chaotic systems in electronics, such as Pseudo-Random Number Generators (PRNGs), is very appealing. Among them, continuous-time ones are used less because, in addition to having strong temporal correlations, they require further computations to obtain the discrete solutions. Here, the time step and discretization method selection are first studied by conducting a detailed analysis of their effect on the systems’ statistical and chaotic behavior. We employ an approach based on interpreting the time step as a parameter of the new “maps”. From our analysis, it follows that to use them as PRNGs, two actions should be achieved (i) to keep the chaotic oscillation and (ii) to destroy the inner and temporal correlations. We then propose a simple methodology to achieve chaos-based PRNGs with good statistical characteristics and high throughput, which can be applied to any continuous-time chaotic system. We analyze the generated sequences by means of quantifiers based on information theory (permutation entropy, permutation complexity, and causal entropy × complexity plane). We show that the proposed PRNG generates sequences that successfully pass Marsaglia Diehard and NIST (National Institute of Standards and Technology) tests. Finally, we show that its hardware implementation requires very few resources.     

Carbon-13 NMR spectra of taxane-type diterpenes: Oxiranes and oxetanes

The ¹³C NMR spectra of a series of nine taxane derivatives are reported. A detailed analysis of the assignments is presented. Observed long-range substituent effects are explained on the basis of the proximity of rings A and C in this type of molecules.     

Thin silica films on Ru(0001): monolayer, bilayer and three-dimensional networks of [SiO4] tetrahedra

The atomic structure of thin silica films grown over a Ru(0001) substrate was studied by X-ray photoelectron spectroscopy, infrared reflection absorption spectroscopy, low energy electron diffraction, helium ion scattering spectroscopy, CO temperature programmed desorption, and scanning tunneling microscopy in combination with density functional theory calculations. The films were prepared by Si vapor deposition and subsequent oxidation at high temperatures. The silica film first grows as a monolayer of corner-sharing [SiO(4)] tetrahedra strongly bonded to the Ru(0001) surface through the Si-O-Ru linkages. At increasing amounts of Si, the film forms a bilayer of corner-sharing [SiO(4)] tetrahedra which is weakly bonded to Ru(0001). The bilayer film can be grown in either the crystalline or vitreous state, or both coexisting. Further increasing the film thickness leads to the formation of vitreous silica exhibiting a three-dimensional network of [SiO(4)]. The principal structure of the films can be monitored by infrared spectroscopy, as each structure shows a characteristic vibrational band, i.e., ～1135 cm(-1) for a monolayer film, ～1300 cm(-1) for the bilayer structures, and ～1250 cm(-1) for the bulk-like vitreous silica.     

Radiation induced microstructural evolution and amorphization of intermetallic compounds

Abstract

A theoretical model is developed to study the influence of radiation-induced microstructural evolution on the amorphization kinetics of intermetallic compounds. The amorphization mechanism is assumed to be the buildup to a critical level of defect complexes. A complex consists of a coupled interstitial-vacancy pair. It is shown that the process of amorphization under particle bombardment is obstructed in alloy systems in which interstitials exhibit a tendency to cluster. In these systems, interstitial clustering delays the buildup of complexes. Under electron irradiation, the complex concentration attains a very low level after high doses, and the crystalline-to-amorphous transition is inhibited down to fairly low temperatures. During heavy ion bombardment, cascade damage produces an enhancement of complex formation and the transition takes place. It is shown that the kinetics of amorphization under ion bombardment depends on temperature at low temperatures, where amorphization is mostly due to complex accumulation. On the other hand, the present analyses indicate that direct in-cascade amorphization becomes more important as the bombardment temperature increases. Zr₃Al is used as a model system. The theoretical calculations yield good agreement with experimental results.     

Interior point method for long-term generation scheduling of large-scale hydrothermal systems

This paper presents an interior point method for the long-term generation scheduling of large-scale hydrothermal systems. The problem is formulated as a nonlinear programming one due to the nonlinear representation of hydropower production and thermal fuel cost functions. Sparsity exploitation techniques and an heuristic procedure for computing the interior point method search directions have been developed. Numerical tests in case studies with systems of different dimensions and inflow scenarios have been carried out in order to evaluate the proposed method. Three systems were tested, with the largest being the Brazilian hydropower system with 74 hydro plants distributed in several cascades. Results show that the proposed method is an efficient and robust tool for solving the long-term generation scheduling problem.     

Factorization at higher twist in hadron-hadron scattering

We study one-loop soft gluon effects in a scalar quark QCD model of the Drell-Yan process. We find that factorization of the type suggested by Politzer holds at order m²/s, but fails at order m⁴/s². We suggest that this pattern holds to higher orders, and that the non-factoring terms are not suppressed by form factors. We compute the non-factoring contributions, and give a classical interpretation of our results.     

Stable boundary layers in a diffusion problem with nonlinear reaction at the boundary

We prove the existence of nonconstant stable stationary solutions of an evolution problem with a nonlinear reaction acting on the boundary. These solutions present layers at certain points of the boundary. We also study the behavior of these solutions as the small parameter appearing in the equation approaches zero and show some stability properties of the profiles given by these equilibrium solutions.     

Specific heat of the anisotropic rigid rotator

The exact (numerical) thermal evolution of the specific heatC of the single anisotropic (not necessarily equal inertial momentaI _x I _y I _xy andI ₂) quantum rigid rotator is calculated. For values ofI _xy /I _z low enough,C presents an unexpectedly high maximum; for sufficiently high values ofI _xy /I _z a second peak emerges. Also a quite rich T0 asymptotic behavior is exhibited.