Chaos synchronization in optically programmable logic cells

A possible approach to the synchronization of chaotic circuits is reported. It is based on an Optically Programmable Logic Cell and the signals are fully digital. A method to study the characteristics of the obtained chaos is reported as well as a new technique to compare the obtained chaos from an emitter and a receiver. This technique allows the synchronization of chaotic signals. The signals received at the receiver, composed by the addition of information and chaotic signals, are compared with the chaos generated there and a pure information signal can be detected. Its application to cryptography in Optical Communications comes directly from these properties. The model here presented is based on a computer simulation.

Sequences of bifurcations and transition to chaos in an optical processing element

Digital chaotic behaviour in an Optical-Processing Element is reported. It is obtained as the result of processing two fixed trains of bits. Period doublings in a Feigenbaum-like scenario have been obtained. A new method to characterize digital chaos is reported

Digital chaos analysis in optical logic structures

Digital chaotic behavior in an optically processing element is analyzed. It was obtained as the result of processing two fixed trains of bits. The process is performed with an optically programmable logic gate. Possible outputs, for some specific conditions of the circuit, are given. Digital chaotic behavior is obtained, by using a feedback configuration. Different ways to analyze a digital chaotic signal are presented.

Sudden transition to chaos in plasma wave interactions

The coherent three-wave interaction, with linear growth in the higher frequency wave and damping in the two other waves, is reconsidered; for equal dampings, the resulting three-dimensional (3-D) flow of a relative phase and just two amplitudes behaved chaotically, no matter how small the growth of the unstable wave. The general case of different dampings is studied here to test whether, and how, that hard scenario for chaos is preserved in passing from 3-D to four-dimensional flows. It is found that the wave with higher damping is partially slaved to the other damped wave; this retains a feature of the original problem an invariant surface that meets an unstable fixed point, at zero growth rate! that gave rise to the chaotic attractor and determined its structure, and suggests that the sudden transition to chaos should appear in more complex wave interactions.

Optical digital chaos cryptography

In this work we present a new way to mask the data in a one-user communication system when direct sequence - code division multiple access (DS-CDMA) techniques are used. The code is generated by a digital chaotic generator, originally proposed by us and previously reported for a chaos cryptographic system. It is demonstrated that if the user's data signal is encoded with a bipolar phase-shift keying (BPSK) technique, usual in DS-CDMA, it can be easily recovered from a time-frequency domain representation. To avoid this situation, a new system is presented in which a previous dispersive stage is applied to the data signal. A time-frequency domain analysis is performed, and the devices required at the transmitter and receiver end, both user-independent, are presented for the optical domain.

Quasiperiodic graphs at the onset of chaos

We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identities between entropy growth rates and generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued fraction characterizes each family. We illustrate our results for the so-called golden, silver, and bronze numbers

Chaos in non lineal Alfven waves using the DNLS equations

The electro-dynamical tethers emit waves in structured denominated Alfven wings. The Derivative Nonlineal Schrödinger Equation (DNLS) possesses the capacity to describe the propagation of circularly polarized Alfven waves of finite amplitude in cold plasmas. The DNLS equation 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 this article is presented a theoretical and numerical analysis when the growth rate of the unstable wave is next to zero considering two damping models: Landau and resistive. The DNLS equation presents a chaotic dynamics when is consider only three wave truncation. The evolution to chaos possesses three routes: hard transition, period-doubling and intermittence of type I.

Digital chaos synchronization in optical networks

A possible approach to the synchronization of chaotic circuits is reported. It is based on an Optically Programmable Logic Cell and as a consequence its output is digital, its application to cryptography in Optical Communications comes directly from its properties. The model here presented is based on a computer simulation.

Analysis of crystallographic slip and grain boundary sliding in a Ti-45Al-2Nb-2Mn (at%)-0.8 vol%TiB2 alloy by high temperature in situ mechanical testing

This work aims to contribute to a further understanding of the fundamentals of crystallographic slip and grain boundary sliding in the γ-TiAl Ti–45Al–2Nb–2Mn (at%)–0.8 vol%TiB2 intermetallic alloy, by means of in situ high-temperature tensile testing combined with electron backscatter diffraction (EBSD). Several microstructures, containing different fractions and sizes of lamellar colonies and equiaxed γ-grains, were fabricated by either centrifugal casting or powder metallurgy, followed by heat treatment at 1300 °C and furnace cooling. in situ tensile and tensile-creep experiments were performed in a scanning electron microscope (SEM) at temperatures ranging from 580 °C to 700 °C. EBSD was carried out in selected regions before and after straining. Our results suggest that, during constant strain rate tests, true twin γ/γ interfaces are the weakest barriers to dislocations and, thus, that the relevant length scale might be influenced by the distance between non-true twin boundaries. Under creep conditions both grain/colony boundary sliding (G/CBS) and crystallographic slip are observed to contribute to deformation. The incidence of boundary sliding is particularly high in γ grains of duplex microstructures. The slip activity during creep deformation in different microstructures was evaluated by trace analysis. Special emphasis was placed in distinguishing the compliance of different slip events with the Schmid law with respect to the applied stress.

A genetic algorithm for slope stability analyses with concave slip surfaces using custom operators

Heuristic methods are popular tools to find critical slip surfaces in slope stability analyses. A new genetic algorithm (GA) is proposed in this work that has a standard structure but a novel encoding and generation of individuals with custom-designed operators for mutation and crossover that produce kinematically feasible slip surfaces with a high probability. In addition, new indices to assess the efficiency of operators in their search for the minimum factor of safety (FS) are proposed. The proposed GA is applied to traditional benchmark examples from the literature, as well as to a new practical example. Results show that the proposed GA is reliable, flexible and robust: it provides good minimum FS estimates that are not very sensitive to the number of nodes and that are very similar for different replications

Characterizing chaos in a type of fractional duffing's equation

We characterize the chaos in a fractional Duffing’s equation computing the Lyapunov exponents and the dimension of the strange attractor in the effective phase space of the system. We develop a specific analytical method to estimate all Lyapunov exponents and check the results with the fiduciary orbit technique and a time series estimation method.

Multistability, chaos, and random signal generation in semiconductor superlattices

Peer reviewed

Chaos, but in voting and apportionments?

Mathematical chaos and related concepts are used to explain and resolve issues ranging from voting paradoxes to the apportioning of congressional seats.

Titration of chaos with added noise

Deterministic chaos has been implicated in numerous natural and man-made complex phenomena ranging from quantum to astronomical scales and in disciplines as diverse as meteorology, physiology, ecology, and economics. However, the lack of a definitive test of chaos vs. random noise in experimental time series has led to considerable controversy in many fields. Here we propose a numerical titration procedure as a simple “litmus test” for highly sensitive, specific, and robust detection of chaos in short noisy data without the need for intensive surrogate data testing. We show that the controlled addition of white or colored noise to a signal with a preexisting noise floor results in a titration index that: (i) faithfully tracks the onset of deterministic chaos in all standard bifurcation routes to chaos; and (ii) gives a relative measure of chaos intensity. Such reliable detection and quantification of chaos under severe conditions of relatively low signal-to-noise ratio is of great interest, as it may open potential practical ways of identifying, forecasting, and controlling complex behaviors in a wide variety of physical, biomedical, and socioeconomic systems.