Chaotic Layer Research Articles

Frequency-Modulated Antipodal Chaos Shift Keying Chaotic Communication on Field Program Gate Array: Prototype Design and Performance Insights

Using chaos for communication can provide more robust channel security, covert transmission, and inherent support for spread-spectrum modulation. Although numerous studies have explored this technology, its practical deployment remains limited due to substantial hardware demands, complex signal processing, and a lack of efficient modulation methods for chaotic signals. In this study, a novel chaotic digital communication system is proposed and studied. A prototype of a frequency-modulated antipodal chaos shift keying (FM-ACSK) system is implemented on an Intel Cyclone V field-programmable gate array (FPGA) along with a complete mathematical model using Matlab R2022a Simulink software. Using FPGAs to implement chaotic oscillators avoids analog system problems such as component drift and high thermal instability while providing determined system parameters, rapid prototyping, and high throughput. The employment of FM over a chaotic modulation layer provides a passband operation (currently at an intermediate frequency of 10.7 MHz) while adding the benefits of carrier frequency offset robustness and constant signal envelope. Within this study, the robustness of FM-ACSK to white noise in the channel was evaluated using bit error rate, which was tested through hardware experiments and simulations. The results show the feasibility and potential performance limitations of this approach to chaotic communication system design.

Clustered slumping in the northern South China Sea: Implications for chronology and geohazards

Seismic facies analysis is the most widely used method to identify event deposits from subaqueous environments. However, the internal structures of a chaotic or transparent seismic unit that represent event deposits are usually poorly imaged. This is primarily due to the limited resolution (usually <10 m) of commonly available multi-channel seismic reflection data. As a consequence, potential (sub)meter-thick, interbedded background sediments that may divide the chaotic layer cannot be discerned on such a seismic profile. The result of this, is that a complex of multiple moderate-thickness event layers can be misinterpreted as a single, thick event layer and this can greatly impact age-depth model reconstruction and geohazard assessment. One approach to resolve the problem is to correlate seismic data with high-resolution sediment core analysis. To address the problem in the South China Sea, we combine multiple methods to identify event deposits in the IODP holes U1499A and U1432C. Our dataset reveals that: (1) the previously interpreted ∼50 m-thick slumping unit in the region is a complex of multiple moderately sized units; (2) the slumping events are clustered between 0.6 and 0.4 Ma. Using our new understanding of event emplacement, we define event-free age models for mass wasting on the margin of the South China Sea, improving our understanding of local geohazards. Our methods here represent a sedimentological approach which could be used in other subaqueous environments to reconstruct event-free age models and geohazard histories.

A fixed point analysis of fractional dynamics of heat transfer in chaotic fluid layers

This manuscript aims to analyze the chaotic fluid layer heating from below, using the Atangana–Baleanu derivative to characterize the existence and uniqueness of this chaotic model based on the provided fixed point data. First, with suitable examples, we demonstrate the existence and uniqueness of fixed point solutions within the framework of controlled metric spaces. Secondly, we study the chaotic behavior of water with various Rayleigh numbers by experimenting with it while keeping a constant Prandtl number. Furthermore, the role of the Rayleigh number in magnifying chaotic behaviors is examined, with graphical simulations demonstrating the effect of different fractional orders of the Atangana–Baleanu derivative. This research provides insights into the dynamics of chaotic systems and their practical applications in controlled situations.

Tsunami deposits in Tunisia contemporaneous of the large 365 CE Crete earthquake and Mediterranean Sea catastrophic event

New field investigations along the East Tunisian coastline reveal sedimentary deposits and damaged localities that may account for a catastrophic event during the late Holocene. North of Sfax city, ~ 3.4 m high cliff coastal marine and alluvial terraces show 20 to 50-cm-thick chaotic layer with sandy coarse gravels mixed with reworked pebbles, broken shells of gastropods and molluscs, organic matter and Roman pottery. The chaotic layer truncates sandy-silty paleosol, covers Roman settlements and is overlain by fire remains, a thin sandy-silty aeolian unit and ~ 1-m-thick alluvial deposits. Charcoal samples collected at 10 cm below and 4 cm above the catastrophic deposits provide radiocarbon dating that brackets the catastrophic unit between 286 and 370 CE. Other historical investigations on the Roman sites of Neapolis (Nabeul), Hadrumete (Sousse), Thyna (Sfax), Meninx in Girba (Djerba), Wadi Ennouili (Gulf of Gabes), and Sabratha (in Libya) evidenced major damage and abandonment of sites in the fourth century (16, 41, 42, 43, 44). The new identification of catastrophic deposits, offshore-onshore correlations with turbidites and modelling of tsunami waves suggest the relationship with the 21 July 365 tsunamigenic earthquake (Mw ~ 8) of west Crete (Greece) and call for a better estimate of tsunami risk on the Mediterranean coastlines.

Semi-analytical estimates for the chaotic diffusion in the Second Fundamental Model of Resonance. Application to Earth’s navigation satellites

We discuss the applicability of the Melnikov and Landau–Teller theories in obtaining semi-analytical estimates of the speed of chaotic diffusion in systems driven by the separatrix-like stochastic layers of a resonance belonging to the ‘second fundamental model’ (SFM) (Henrard and Lemaitre, 1983). Stemming from the analytic solution for the SFM in terms of Weierstrass elliptic functions, we introduce stochastic Melnikov and Landau–Teller models allowing to locally approximate chaotic diffusion as a sequence of uncorrelated ‘jumps’ observed in the time series yielding the slow evolution of an ensemble of trajectories in the space of the adiabatic actions of the system. Such jumps occur in steps of one per homoclinic loop. We show how a semi-analytical determination of the probability distribution of the size of the jumps can be arrived at by the Melnikov and Landau–Teller approximate theories. Computing also the mean time required per homoclinic loop, we arrive at estimates of the chaotic diffusion coefficient in such systems. As a concrete example, we refer to the long-term diffusion of a small object (e.g. Earth navigation satellite or space debris) within the chaotic layers of the so-called 2g+h lunisolar resonance, which is of the SFM type. After a suitable normal form reduction of the Hamiltonian, we compute estimates of the speed of diffusion of these objects, which compare well with the results of numerical experiments.

Estimation of diffusion time with the Shannon entropy approach.

The present work revisits and improves the Shannon entropy approach when applied to the estimation of an instability timescale for chaotic diffusion in multidimensional Hamiltonian systems. This formulation has already been proved efficient in deriving the diffusion timescale in 4D symplectic maps and planetary systems, when the diffusion proceeds along the chaotic layers of the resonance's web. Herein the technique is used to estimate the diffusion rate in the Arnold model, i.e., of the motion along the homoclinic tangle of the so-called guiding resonance for several values of the perturbation parameter such that the overlap of resonances is almost negligible. Thus differently from the previous studies, the focus is fixed on deriving a local timescale related to the speed of an Arnold diffusion-like process. The comparison of the current estimates with determinations of the diffusion time obtained by straightforward numerical integration of the equationsof motion reveals a quite good agreement.

Chaotic diffusion in the GJ 876 exoplanetary system

AbstractThis is a study about the dynamical stability of the GJ 876 exoplanetary system. The phase space of initial conditions (ICs) is characterized using the MEGNO indicator of chaos and the Shannon entropy approach for estimations of diffusivity. The results are compared to analyze correlations between the chaotic layers and the instability timescales. The long-term dynamical behavior of the system is reminiscent of the stable chaos, at least within the system’s lifetime.

Chaotic physical layer encryption scheme based on phase ambiguity for a DMT system.

Chaotic encryption is a promising scheme for physical layer security. By solving the multi-dimensional chaotic equations and transforming the obtained results, both bit-level and symbol-level encryption can be realized. One of the mainstream symbol-level encryption solutions is the constellation shifting (CS) scheme, which treats the chaotic sequence as artificial noise and adds it to the QAM signal sequence to achieve encryption. However, this scheme has several technical flaws in practical application, in terms of computational complexity and coexistence with blind equalization algorithm and the probabilistic shaping (PS) technique. In this paper, we propose a novel symbol-level encryption scheme based on phase ambiguity (PA), which converts the two sequences originally used to generate artificial noise into a set of phase rotation keys and complex conjugate keys, so that the encrypted symbols are still on the ideal constellation point coordinates. Simulation verification is carried out in a discrete multi-tone (DMT) system with 64QAM modulation. Results show that the proposed scheme can fully retain the shaping gain brought by the PS technique and avoid the error convergence of the blind equalizer. Moreover, the time required to solve the chaotic equations is only 38% of the CS scheme. Experimental verification is carried out, and the obtained results once again prove the superiority of the proposed encryption algorithm, which is a practical alternative for future physical layer secure optical communications.

Heat conduction in an irregular magnetic field. Part 2. Heat transport as a measure of the effective non-integrable volume

Given the large anisotropy of transport processes in magnetized plasmas, the magnetic field structure can strongly impact heat diffusion: magnetic surfaces and cantori form barriers to transport while chaotic layers and island structures can degrade confinement. When a small but non-zero amount of perpendicular diffusion is included, the structure of the magnetic field becomes less important, allowing pressure gradients to be supported across chaotic regions and island chains. We introduce a metric for the effective volume over which the local parallel diffusion dominates based on the solution to the anisotropic heat diffusion equation. To validate this metric, we consider model fields with a single island chain and a strongly chaotic layer for which analytic predictions of the relative parallel and perpendicular transport can be made. We also analyse critically chaotic fields produced from different sets of perturbations, highlighting the impact of the mode number spectrum on the heat transport. Our results indicate that this metric coincides with the effective volume of non-integrability in the limit $\kappa _{\perp } \rightarrow 0$ , where $\kappa_{\perp}$ is the perpendicular diffusion coefficient. We propose that this metric be used to assess the impact of non-integrability on the heat transport in stellarator equilibria.

Efficient Secure NOMA Schemes Based on Chaotic Physical Layer Security for Wireless Networks

Non-orthogonal multiple access (NOMA) is considered by the 3GPP as a potential technology for beyond 5G wireless networks to support massive connectivity with robust reliability. However, the massive increase in connected users critically leads to data security problems owing to the high possibility of eavesdropping. In this paper, uplink secure NOMA (sNOMA) schemes based on chaotic physical layer security (PLS) are proposed to achieve two-fold secrecy of integrated channel coding and secret key approaches. Different code-domain and power-domain techniques are employed for sNOMA designs over realistic fading channel environments. Equal power allocation strategy is used for the transmitted chaotic signals in code-domain sNOMA (CD-sNOMA), whereas dynamic power control is employed in power-domain sNOMA (PD-sNOMA) and the hybrid code-power-domain sNOMA (CPD-sNOMA) approaches. The former design adopts joint maximum Likelihood (ML) signal detection while the later scenarios utilize integrated receiver designs based on successive interference cancellation (SIC) and ML techniques. For the proposed sNOMA schemes, power control algorithms are presented to optimize the system performance over constrained total received power and target error rate. Numerical results validate the effectiveness of sNOMA designs compared with the benchmark systems under the worst-case secrecy of unauthorized receiver with complete knowledge of the transmission scheme and associated channel,. Valuable tradeoffs are demonstrated between the achieved error rate, connectivity, security gap, and complexity. Moreover, the utilized chaotic signals offer robust and cost-effective PLS solutions with a huge key-space to combat the most powerful brute-force eavesdropping attacks.

Выживаемость изолированных кожных эксплантатов при дистанционном взаимодействии со слоистыми периодическими структурами

Full-thickness skin grafts are used in reconstructive surgeries. Objectives Experimental study of the possibility of long-term preservation of viable skin grafts in severely impaired trophics at remote interaction with entities having stratiform periodic structure. Material and methods Full-thickness skin was excised from the rabbits' backside and dissected into explants sized 1.0 × 1.0 cm. The samples (n = 81) were divided into three groups and thermostated for 2 days at 37 °C at a various distance from the metal (aluminum) presented as a 20-layer package of smooth foil forming a stratiform periodic structure (SPS) (series I), chaotic layers of squeezed foil (series II) and a single-piece sheet (series III). Histological analysis was performed for the three series to evaluate the explants' viability after the thermostating. Results The highest survival estimates were seen in experimental explants of series I that interacted with the SPS of stratified foil layers. The wave nature of such remote interaction was suggested with delayed dystrophic and necrotic processes developing in the skin samples. Experimental samples of series III appeared to be less viable. The explant vitality in series II was sharply reduced due to rapidly spreading necrosis. Conclusion Skin explants were shown to retain viability for a longer time when interacting remotely with stratiform periodic structures in the absent trophics. These promising results can be practical for the development of wound dressings to improve survival of full-thickness skin transplantation in reconstruction of deep skin defects.

An insight into shallow gas hydrates in the Dongsha area, South China Sea

Previous studies of gas hydrate in the Dongsha area mainly focused on the deep-seated gas hydrates that have a high energy potential, but cared little about the shallow gas hydrates occurrences. Shallow gas hydrates have been confirmed by drill cores at three sites (GMGS2 08, GMGS2 09 and GMGS2 16) during the GMGS2 cruise, which occur as veins, blocky nodules or massive layers, at 8–30 m below the seafloor. Gas chimneys and faults observed on the seismic sections are the two main fluid migration pathways. The deep-seated gas hydrate and the shallow hydrate-bearing sediments are two main seals for the migrating gas. The occurrences of shallow gas hydrates are mainly controlled by the migration of fluid along shallow faults and the presence of deep-seated gas hydrates. Active gas leakage is taking place at a relatively high-flux state through the vent structures identified on the geophysical data at the seafloor, although without resulting in gas plumes easily detectable by acoustic methods. The presence of strong reflections on the high-resolution seismic profiles and dim or chaotic layers in the sub-bottom profiles are most likely good indicators of shallow gas hydrates in the Dongsha area. Active cold seeps, indicated by either gas plume or seepage vent, can also be used as indicators for neighboring shallow gas hydrates and the gas hydrate system that is highly dynamic in the Dongsha area.

Minimal length effects on motion of a particle in Rindler space * *Supported in part by NSFC (11875196, 11375121, 11005016), the Fundamental Research Funds for the Central Universities, Natural Science Foundation of Chengdu University of TCM (ZRYY1729, ZRYY1921), Discipline Talent Promotion Program of /Xinglin Scholars(QNXZ2018050), the key fund project for Education Department of Sichuan (18ZA0173), the open fund of State

Various quantum theories of gravity predict the existence of a minimal measurable length. In this paper, we study effects of the minimal length on the motion of a particle in the Rindler space under a harmonic potential. This toy model captures key features of particle dynamics near a black hole horizon and allows us to make three observations. First, we find that chaotic behavior becomes stronger with increases in minimal length effects, leading predominantly to growth in the maximum Lyapunov characteristic exponents, while the KAM curves on Poincaré surfaces of a section tend to disintegrate into chaotic layers. Second, in the presence of the minimal length effects, it can take a finite amount of Rindler time for a particle to cross the Rindler horizon, which implies a shorter scrambling time of black holes. Finally, the model shows that some Lyapunov characteristic exponents can be greater than the surface gravity of the horizon, violating the recently conjectured universal upper bound. In short, our results reveal that quantum gravity effects may make black holes prone to more chaos and faster scrambling.

Attitude motion of a space object during its contactless ion beam transportation

The development of systems for transporting space objects by an active spacecraft is an urgent task of modern astronautics. One of the promising areas in this field is contactless ion beam transport systems. The goals of this work are to study a space object attitude motion dynamics during its contactless transportation and the influence of this motion on the magnitude of the force transmitted by the ion beam. A mathematical model of a mechanical system consisting of the space object and the active spacecraft was developed using the Lagrange formalism. A simplified equation of the object's angular motion in Kepler's orbit was obtained. The influence of the object's center of mass position and the ratio of ion beam and gravity gradient torques on the phase portrait view in the case of cylindrical object in a circular orbit was studied. The most favorable areas on phase portrait from the point of view of the magnitude of the force transferred by the ion beam to the object were found. It is shown that in the case of an elliptical orbit chaos exists. Entering a phase trajectory in a chaotic layer can lead to a noticeable decrease in the ion beam force.

Lagrangian chaos in steady three-dimensional lid-driven cavity flow.

Steady three-dimensional flows in lid-driven cavities are investigated numerically using a high-order spectral-element solver for the incompressible Navier-Stokes equations. The focus is placed on critical points in the flow field, critical limit cycles, their heteroclinic connections, and on the existence, shape, and dependence on the Reynolds number of Kolmogorov-Arnold-Moser (KAM) tori. In finite-length cuboidal cavities at small Reynolds numbers, a thin layer of chaotic streamlines covers all walls. As the Reynolds number is increased, the chaotic layer widens and the complementary KAM tori shrink, eventually undergoing resonances, until they vanish. Accurate data for the location of closed streamlines and of KAM tori are provided, both of which reach very close to the moving lid. For steady periodic Taylor-Görtler vortices in spanwise infinitely extended cavities with a square cross section, chaotic streamlines occupy a large part of the flow domain immediately after the onset of Taylor-Görtler vortices. As the Reynolds number increases, the remaining KAM tori vanish from the Taylor-Görtler vortices, while KAM tori grow in the central region further away from the solid walls.

Language as Gesture in Merleau-Ponty: Some implications for method in therapeutic practice and research

ABSTRACT The unexpected invention of a game with my grandchildren provided a new way of thinking about the nature of such unpredictable moments in therapy. The experience brought together a number of ideas, considered through the view of language taken by Merleau-Ponty where the chaotic primitive layers that pervade language are seen as having primacy over the rules of linguistics such as those set out by Saussure. Saussure is seen as providing a way of understanding linguistic structure whilst at the same time opening a number of ambiguities that then allow a way for thinking about language differently through Merleau-Ponty’s emphasis on the usage of language (la parole) as opposed the structural aspects of language (la langue). Initially, Winnicott’s ideas around the ‘spontaneous gesture’ are utilised to help show how this kind of unpredictable expression appears as something alive. Merleau-Ponty then shows how language as gestural phenomena takes hold of us through our bodies. Further questions then arise about the method in therapeutic practice and research. Here, it is argued that when the method is given primacy over experience, we are in a position that seeks the already known, which will not, therefore, permit some new expression to break through.

GEOMETRIA E CARATTERI STRATIGRAFICI DELLA SEQUENZA CENOMANIANA NEL BACINO LOMBARDO (ALPI MERIDIONALI)

The Cenomanian Sequence in the area between the lakes of Lecco and Iseo (Lombardy Basin, Southern Alps) represents a depositional unit bounded by two main unconformities and relative conformities. The unconformities progressively develop from SW to NE, with hiatuses spanning in age the Early Cenomanian and the Late Cenomanian-Turonian respectively.&#x0D; A complete section of the Cenomanian Sequence consists of Early Cenomanian red marls with pelagic turbidites and pebbly mudstones (Marne rosse) followed by two calcareous chaotic layers enclosing a succession of thin bedded, fine grained siliciclastic turbidites (Torbiditi Sottili), of Middle to Late Cenomanian age.&#x0D; The association of chaotic layers with the enclosed wedge shaped body of turbidites and the development of unconformities towards the north, point out that the Cenomanian basin developed in a mobile area where deposition was controlled by sinsedimentary tectonics. Moreover, the Cenomanian basin is, so far, the youngest Cretaceous basin clearly documented in the Southern Alps, oriented east-west, therefore crosswise to the structures related to the Jurassic rifting. Stratigraphic data strongly suggest that the tectonic evolution of the northern margin of the Cenomanian Lombardy Basin was generated by compression with the development of antiform structures.The sandstone unit pinches out towards the north and east, and thins more gradually towards the south. It represents a wedge shaped body, which parallels E-W paleocurrent trends and onlaps onto the northern margin of the Cenomanian basin. The two chaotic layers are basinally extended and show facies changes and thinning from north to south. They derived from sliding and slumping of the northern slope of the basin.

The current orbit of Atlas (SXV)

AbstractWith the success of the Cassini-Huygens mission, the dynamic complexity surrounding natural satellites of Saturn began to be elucidated. New ephemeris could be calculated with a higher level of precision, which made it possible to study in detail the resonant phenomena and, in particular, the 54:53 near mean-motion resonance between Prometheus and Atlas. For this task, we have mapped in details the domains of the resonance with dense sets of initial conditions and distinct ranges of parameters. Our initial goal was to identify possible regions in the phase space of Atlas for which some critical angles, associated with the 54:53 mean motion have a stable libration. Our investigations revealed that there is no possibility for the current Atlas orbital configuration to have any regular behavior since it is in a chaotic region located at the boundary of the 54:53 mean-motion resonance phase space. This result is in accordance with previous works (Cooper et al. 2015; Renner et al. 2016). In this work, we generalize such investigations by showing detailed aspects of the Atlas-Prometheus 54:53 mean-motion resonance, like the extension of the chaotic layers, the thin domain of the center of the 54:53 resonance, the proximity of other neighborhood resonances, among other secondary conclusions. In particular, we have also shown that even in the deep interior of the resonance, it is difficult to map periodic motion of the resonant pair for very long time spans.

Non-integrability of generalised Charlier and Saint-Germain problem

Certain generalisation of a classical problem of celestial mechanics is considered. A material point moves in the potential force field that is a superposition of a radial force and a constant force. The potential of the central forces is proportional to an integer power −n of the distance from the origin. For all positive integers n except n=1 non-integrability in meromorphic functions is proved. Case n=1 is integrable. For negative integer n analysis is much more complex: for n=−1 non-integrability is proved, for n=−2 additional first integral is found, for n=−3 although the system meets the necessary integrability conditions Poincaré cross-sections show presence of chaotic layers in phase space.

Chaotic motion and control of a tethered-sailcraft system orbiting an asteroid

Chaotic motion and control of tethered-sailcraft system orbiting an asteroid is examined. A sailcraft is hanged at the end of the tethered satellite system which can be utilized for asteroid exploring missions. The highly irregular shape of the asteroids can lead to complex motions of the system. The dynamics of in-plane libration is established using the Lagrangian equation method with the harmonic coefficients C20 and C22 of the gravity field of the asteroid. In addition, we use the Melnikov method to analytically predict the occurrence of chaos. This paper focuses on the influence of eccentricity, orbital radius and tether length on the libration characteristics of the tethered system. The time history of libration, the phase plane, the Poincaré section and power spectral density (PSD) are presented numerically for verifying the validity of the Melnikov method in predicting occurrence of chaos. Besides, numerical simulation results indicate that larger eccentricity, smaller orbit radius and longer tether length can make the system more chaotic, i.e., the chaotic layers will become thicker. To show the effect of variation of eccentricity on the libration characteristics, a corresponding bifurcation diagram is given. In order to avoid chaotic motions causing uncertainties and high risks, we propose a chaos control method of inerter-damper for the tethered-sailcraft system. Finally, numerical simulation results verify the effectiveness of the proposed chaos control method.