Chaotic Alternation Research Articles

Address direction finding of ZigBee devices

Statement of problem. The active use of wireless technologies requires the development of means of monitoring devices and data transmission networks and, in particular, ZigBee wireless personal networks. Therefore, the detection and localization of working ZigBee devices is an urgent task of radio monitoring services. Correlation-interferometric direction finders based on two-channel radio receiving equipment cyclically connected to various pairs of elements of a multi-element antenna system can serve as a tool for bearing radio signals. For the direction finding of packet radio signals, the direction finder accumulates time samples from different antenna pairs over long time intervals; joint processing of these data allows determining the direction of arrival of radio signals. An obstacle to the direction finding of ZigBee devices is the fact that many similar devices can simultaneously operate in the same frequency range, generating a chaotic alternation of packets in the air. As a consequence, the accumulation of information from a specific ZigBee device for different antenna pairs of the direction finder becomes problematically. Purpose of the work is to develop a method for joint identification and bearing of detected devices of ZigBee networks. Results. the presented method of address bearing is implemented on the basis of the mobile direction finder ARTICLE-M, used to search for and locate unauthorized sources of radio emissions, and allows detecting signals of the 802.15.4 standard, identifying personal network devices, as well as forming estimates of directions to these sources of radio emissions. Practical importance. the use of address bearing of ZigBee network devices increases the functionality of existing radio monitoring equipment, and also allows the localization of unauthorized radio sources masquerading as Internet of Things devices.

Interior structure and complexity growth rate of holographic superconductor from M-theory

We study the interior dynamics of a top-down holographic superconductor from M-theory. The condense of the charged scalar hair necessarily removes the inner Cauchy horizon and the spacetime ends at a spacelike singularity. Although there is a smooth superconducting phase transition at the critical temperature, the onset of superconductivity is accompanied by intricate interior dynamics, including the collapse of the Einstein-Rosen bridge, the Josephson oscillations of the condensate, and the final Kasner singularity. We obtain analytically the transformation rule for the alternation of different Kasner epochs. Thanks to the nonlinear couplings of the top-down theory, there is generically a never-ending chaotic alternation of Kasner epochs towards the singularity. We compute the holographic complexity using both the complexity-action and the complexity-volume dualities. In contrast to the latter, the complexity growth rate from the complexity-action duality has a discontinuity at the critical temperature, characterizing the sudden change of the internal structure before and after the superconducting phase transition.

Quantum Kasner transition in a locally rotationally symmetric Bianchi II universe

The Belinski-Khalatnikov-Lifshitz (BKL) conjecture predicts a chaotic alternation of Kasner epochs in the evolution of generic classical spacetimes towards a spacelike singularity. As a first step towards understanding the full quantum BKL scenario, we analyze a vacuum Bianchi II model with local rotational symmetry, which presents just one Kasner transition. During the Kasner epochs, the quantum state is coherent and it is thus characterized by constant values of the different quantum fluctuations, correlations and higher-order moments. By computing the constants of motion of the system we provide, for any peaked semiclassical state, the explicit analytical transition rules that relate the parametrization of the asymptotic coherent state before and after the transition. In particular, we obtain the modification of the transition rules for the classical variables due to quantum back-reaction effects. This analysis is performed by considering a high-order truncation in moments (the full computations are performed up to fifth-order, which corresponds to neglecting terms of an order $\hbar^3$), providing a solid estimate about the quantum modifications to the classical model. Finally, in order to understand the dynamics of the state during the transition, we perform some numerical simulations for an initial Gaussian state, that show that the initial and final equilibrium values of the quantum variables are connected by strong and rapid oscillations.

Alternation of Defects and Phase Turbulence Induces Extreme Events in an Extended Microcavity Laser.

Out-of-equilibrium systems exhibit complex spatiotemporal behaviors when they present a secondary bifurcation to an oscillatory instability. Here, we investigate the complex dynamics shown by a pulsing regime in an extended, one-dimensional semiconductor microcavity laser whose cavity is composed by integrated gain and saturable absorber media. This system is known to give rise experimentally and theoretically to extreme events characterized by rare and high amplitude optical pulses following the onset of spatiotemporal chaos. Based on a theoretical model, we reveal a dynamical behavior characterized by the chaotic alternation of phase and amplitude turbulence. The highest amplitude pulses, i.e., the extreme events, are observed in the phase turbulence zones. This chaotic alternation behavior between different turbulent regimes is at contrast to what is usually observed in a generic amplitude equation model such as the Ginzburg–Landau model. Hence, these regimes provide some insight into the poorly known properties of the complex spatiotemporal dynamics exhibited by secondary instabilities of an Andronov–Hopf bifurcation.

Evidence for a Middle Pleistocene glaciation of MIS 8 age in the southern North Sea

In the cores of borehole 89/2, situated at 54° 00 01′N and 5° 00 04′E about 70 km north of the Frisian Islands in the southern North Sea, two diamictons levels are found at ±70 and 100 m below sea floor (i.e. ±110 and 140 below present sea level), respectively. Both diamictons appear to be older than Saalian (=MIS 6), in contrast to earlier interpretations. The upper diamicton is overlain by about 20 m of shallow marine sands followed by a chaotic alternation of fine-grained clay-rich Eemian (MIS 5e) sediments and sands deposited in a glacially excavated basin. It was originally assumed that this diamicton was Saalian (MIS 6) in age and lined the base of the basin. Seismic lines crossing the borehole location, however, show that the upper diamicton is truncated by the basin, and, consequently must be older than Saalian. This is corroborated by new investigations on the Saalian–Eemian transition in the Netherlands and new data on the age of the molluscs and foraminifera in the sands directly overlying the upper diamicton. The age data, based on measurements of the isoleucine epimerisation of mollusc shells and foraminiferal tests favour an MIS 8 age.

Chaotic alternation of waves in ring lasers.

We intend to give an analytic description of the mechanisms involved in the periodic and chaotic wave alternation frequently observed in ring lasers. A set of amplitude equations is derived from the Maxwell-Bloch equations. These equations are studied analytically and numerically.

Bifurcation analysis of the mathematical model of the NO+CO/Pt(100) reaction

The article presents a detailed bifurcation analysis of steady and periodic states for a new mathematical model of the NO+CO/Pt(100) reaction. Various bifurcation diagrams are constructed in the planes of partial reagent pressures and surface temperature. Regions with oscillations and multiple steady solutions are investigated. Isolated branches of steady and periodic states are identified. An “explosive” bifurcation of the periodic solution leading to chaotic alternation of small-and large-amplitude oscillations is detected and analyzed for the first time. A good quantitative fit is demonstrated between modeling results and experimental data.

On the periodic and chaotic alternation of transverse patterns of photorefractive oscillators

An interpretation of periodic and chaotic alternation of transverse patterns in photorefractive oscillators is suggested: change between patterns occurs as a consequence of linear coupling of transverse modes. The numerical integration of the corresponding models yields periodic and chaotic alternation of transverse patterns. The results are tested experimentally on the q = 2 transverse mode family.

Pattern formation and competition in photorefractive oscillators.

We introduce a general model of pattern formation in optical systems made of a cavity with an active medium as a photorefractive crystal fed by a pump. The model is based on the interplay of a diffractive equation for the optical field and a diffusive equation for the medium refractivity. The aim of the model is to describe a series of experiments which have shown mode competition (periodic or chaotic alternation) for low Fresnel numbers (F) and mode coexistence, leading to short range space correlations, for high F. For low F, a linear stability analysis provides the set of modes above threshold as a function of the transverse wave number. Due to the interplay of the optical and the diffusive interactions, different behaviors result depending on the thickness of the medium as compared to the optical absorption length and diffusion length. Including the leading nonlinearities compatible with the symmetry constraints, we introduce normal form equations which describe the time-dependent mode competition. In the case of a large number of modes (high F), nonlinear mode-mode interaction is equivalent to a self-induced noise. In this limit, the relevant feature to be compared with the experiment is the power spectrum.

Periodic and chaotic alternation in systems with imperfect O(2) symmetry.

Recent experiments on an optical oscillator with photorefractive gain have shown that the output field undergoes periodic or chaotic alternations among a small number of patterns. The above features are explained by a dynamical model, based only on symmetry arguments, and hence applicable to a variety of physical situations.

An experimental study of elastic turbulence

Elastic turbulence, a phenomenon of major importance for polymers processing, is most conveniently studied under conditions of high uniformity of the stressed state. Observation of the flow of systems displaying a strong photoelastic effect, in polarized light under simple shear conditions, reveals that elastic turbulence can be detected by a continuous and chaotic alternation of interference colours. In relatively lowviscous highly elastic liquids elastic turbulence corresponds to independence or very weak dependence of the shear stresses on the deformation rates.