Manual de confessores y penitentes, que co[n]tiene quasi todas las dudas que en las confessiones suelen ocurrir de los pecados ... : con cinco comentarios de vsuras, cambios, symonia mental, defension del proximo, de hurto notable, [et] irregularidad / compuesto por el Doctor Martin de Azpilcueta nauarro ... ; con su repertorio copiosissimo.

Sign.: [calderón]8, A-Z8, 2A-2Z8, 3A-3D8, A-K8, L6, 2a-2d8

Quasi-aplanatic free-form V-groove collimators for LED colour mixing

Two quasi-aplanatic free-form solid V-groove collimators are presented in this work. Both optical designs are originally designed using the Simultaneous Multiple Surface method in three dimensions (SMS 3D). The second optically active surface in both free-form V-groove devices is designed a posteriori as a grooved surface. First two mirror (XX) design is designed in order to clearly show the design procedure and working principle of these devices. Second, RXI free-form design is comparable with existing RXI collimators; it is a compact and highly efficient design made of polycarbonate (PC) performing very good colour mixing of the RGGB LED sources placed off-axis. There have been presented rotationally symmetric non-aplanatic high efficiency collimators with colour mixing property to be improved and rotationally symmetric aplanatic devices with good colour mixing property and efficiency to be improved. The aim of this work was to design a free-form device in order to improve colour mixing property of the rotationally symmetric nonaplanatic RXI devices and the efficiency of the aplanatic ones.

Intermittency reinjection probability density function with and without noise effects.

Intermittency phenomenon is a continuous route from regular to chaotic behaviour. Intermittency is an occurrence of a signal that alternates chaotic bursts between quasi-regular periods called laminar phases, driven by the so called reinjection probability density function (RPD). In this paper is introduced a new technique to obtain the RPD for type-II and III intermittency. The new RPD is more general than the classical one and includes the classical RPD as a particular case. The probabilities of the laminar length, the average laminar lengths and the characteristic relations are determined with and without lower bound of the reinjection in agreement with numerical simulations. Finally, it is analyzed the noise effect in intermittency. A method to obtain the noisy RPD is developed extending the procedure used in the noiseless case. The analytical results show a good agreement with numerical simulations.

Self-similar motion of laser half-space plasmas. II. Thermal waves and intermediate regimes

The one-dimensional self-similar motion of an initially cold, half-space plasma of electron density n,produced by the (anomalous) absorption of a laser pulse of irradiation

regimes, the critical plane lies far in the expansion tail. The results break down when the density is so small that the plasma becomes collisionless. The analysis is also invalid for a too small. Using results previously found for a>€~4'3, a qualitative discussion of how plasma behavior changes with a, is given.

Hard transition to chaotic dynamics in Alfven wave fronts

The derivative nonlinear Schrodinger DNLS equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In a reduced three-wave model equal dampings of daughter waves, three-dimensional flow for two wave amplitudes and one relative phase, no matter how small the growth rate of the unstable wave there exists a parametric domain with the flow exhibiting chaotic relaxation oscillations that are absent for zero growth rate. This hard transition in phase-space behavior occurs for left-hand LH polarized waves, paralleling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable, with damping less than about unstable wave frequency 2/4 x ion cyclotron frequency. The structural stability of the transition was explored by going into a fully 3-wave model different dampings of daughter waves,four-dimensional flow; both models differ in significant phase-space features but keep common features essential for the transition.

Digital chaotic output from an optically processing element

Digital chaotic behavior in an optically processing element is reported. It is obtained as the result of processing two fixed trains of bits. The process is performed with an optically programmable logic gate, previously reported as a possible main block for optical computing. Outputs for some specific conditions of the circuit are given. Digital chaos is obtained using a feedback configuration. Period doublings in a Feigenbaum‐like scenario are obtained. A new method to characterize this type of digital chaos is reported.

Synchronizing chaotic optically-programmable digital circuits

In this paper an approach to the synchronization of chaotic circuits has been reported. It is based on an optically programmable logic cell and the signals involved are fully digital. It is based on the reception of the same input signal on sender and receiver and from this approach, with a posterior correlation between both outputs, an identical chaotic output is obtained in both systems. No conversion from analog to digital signals is needed. The model here presented is based on a computer simulation.

Reduced three-wave model to study the hard transition to chaotic dynamics in Alfven wave-fronts

The derivative nonlinear Schrödinger (DNLS) equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In a reduced three-wave model (equal damping of daughter waves, three-dimensional flow for two wave amplitudes and one relative phase), no matter how small the growth rate of the unstable wave there exists a parametric domain with the flow exhibiting chaotic dynamics that is absent for zero growth-rate. This hard transition in phase-space behavior occurs for left-hand (LH) polarized waves, paralelling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable.

Fully 3-wave model to study the hard transition to chaotic dynamics in alfven wave-fronts

The derivative nonlinear Schrödinger (DNLS) equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. No matter how small the growth rate of the unstable wave, the four-dimensional flow for the three wave amplitudes and a relative phase, with both resistive damping and linear Landau damping, exhibits chaotic relaxation oscillations that are absent for zero growth-rate. This hard transition in phase-space behavior occurs for left-hand (LH) polarized waves, paralleling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable. The parameter domain developing chaos is much broader than the corresponding domain in a reduced 3-wave model that assumes equal dampings of the daughter waves

Multiple attractors, long chaotic transients, and failure in small-world networks of excitable neurons.

We study the dynamical states of a small-world network of recurrently coupled excitable neurons, through both numerical and analytical methods. The dynamics of this system depend mostly on both the number of long-range connections or ?shortcuts?, and the delay associated with neuronal interactions. We find that persistent activity emerges at low density of shortcuts, and that the system undergoes a transition to failure as their density reaches a critical value. The state of persistent activity below this transition consists of multiple stable periodic attractors, whose number increases at least as fast as the number of neurons in the network. At large shortcut density and for long enough delays the network dynamics exhibit exceedingly long chaotic transients, whose failure times follow a stretched exponential distribution. We show that this functional form arises for the ensemble-averaged activity if the failure time for each individual network realization is exponen- tially distributed

Defect chaos and bursts: Hexagonal rotating convection and the complex Ginzburg-Landau equation

We employ numerical computations of the full Navier-Stokes equations to investigate non-Boussinesq convection in a rotating system using water as the working fluid. We identify two regimes. For weak non- Boussinesq effects the Hopf bifurcation from steady to oscillating (whirling) hexagons is supercritical and typical states exhibit defect chaos that is systematically described by the cubic complex Ginzburg-Landau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and the oscil- lations exhibit localized chaotic bursting, which is modeled by a quintic complex Ginzburg-Landau equation.

Secure transmission of information by digital chaotic signals

Protecting signals is one of the main tasks in information transmission. A large number of different methods have been employed since many centuries ago. Most of them have been based on the use of certain signal added to the original one. When the composed signal is received, if the added signal is known, the initial information may be obtained. The main problem is the type of masking signal employed. One possibility is the use of chaotic signals, but they have a first strong limitation: the need to synchronize emitter and receiver. Optical communications systems, based on chaotic signals, have been proposed in a large number of papers. Moreover, because most of the communication systems are digital and conventional chaos generators are analogue, a conversion analogue-digital is needed. In this paper we will report a new system where the digital chaos is obtained from an optically programmable logic structure. This structure has been employed by the authors in optical computing and some previous results in chaotic signals have been reported. The main advantage of this new system is that an analogue-digital conversion is not needed. Previous works by the authors employed Self-Electrooptical Effect Devices but in this case more conventional structures, as semiconductor laser amplifiers, have been employed. The way to analyze the characteristics of digital chaotic signals will be reported as well as the method to synchronize the chaos generators located in the emitter and in the receiver.

Analysis of digital chaotic optical signals

The main objective of this paper is to present some tools to analyze a digital chaotic signal. We have proposed some of them previously, as a new type of phase diagrams with binary signals converted to hexadecimal. Moreover, the main emphasis will be given in this paper to an analysis of the chaotic signal based on the Lempel and Ziv method. This technique has been employed partly by us to a very short stream of data. In this paper we will extend this method to long trains of data (larger than 2000 bit units). The main characteristics of the chaotic signal are obtained with this method being possible to present numerical values to indicate the properties of the chaos.

Chaotic behaviour evaluation in optical logic gates with fractal concepts

A chaotic output was obtained previously by us, from an Optical Programmable Logic Cell when a feedback is added. Some time delay is given to the feedback in order to obtain the non-linear behavior. The working conditions of such a cell is obtained from a simple diagram with fractal properties. We analyze its properties as well as the influence of time delay on the characteristics of the working diagram. A further study of the chaotic obtained signal is presented.