Chaotic Field Research Articles

Extreme multistability in a new hyperchaotic meminductive circuit and its circuit implementation

In this paper, a new hyperchaotic meminductive circuit was designed. Based on the normalized mathematical model, the origin point as the unique equilibrium point of system was calculated. Especially, using the two-dimension complexity algorithms, the dynamical behaviors of system were analyzed. In the analysis, some peculiar physical phenomenon for instance coexisting evolution and infinitely many coexisting attractors were found. Finally, the practical circuit was physically implemented and the parameters of all the components are displayed. The results of numerical simulation show that the new circuit system is extremely multistable. It provides a theoretical guidance for the research of the chaotic related field.

Optical polarization properties of February 2010 outburst of the blazar Mrk 421

In this paper, we explore the behavior of optical polarization during the multi-wavelength outburst of the blazar Mrk 421 detected in February 2010. We use optical polarization measurements in the wavelength range 500-700 nm from SPOL observations available between January 1, 2010 and March 31, 2010 (MJD 55197-55286) including the period of multi-wavelength flaring activity detected from the source around February 16-17, 2010 (MJD 55243-55244). We also use near simultaneous optical and radio flux measurements from SPOL in V and R bands and OVRO at 15 GHz respectively. We find that the emissions in the optical and radio bands do not show any significant change in the source activity unlike at X-ray and $\gamma$--ray energies during the outburst. The optical and radio flux measurements are found to be consistent with the long term quiescent state emission of the source. Moreover, the linear polarization in the wavelength range 500-700 nm decreases to a minimum value of 1.6$\%$ during the X-ray and $\gamma$--ray outburst which is significantly lower than the long term average value of $\sim$ 4.2$\%$. The angle of polarization varies between 114$^\circ$-163$^\circ$ with a preferred average value of $\sim$ 137$^\circ$ during this period. We estimate the degree of polarization intrinsic to the jet taking into account the host galaxy contamination in R band and compare this with the theoretical synchrotron polarization estimated for a power law distribution of relativistic electrons gyrating in an emission region filled with ordered and chaotic magnetic fields. The intrinsic linear polarization estimated for different epochs during the above period is found to be consistent with the theoretical synchrotron polarization produced by the relativistic electrons with power law spectral index $\sim$ 2.2.

A Chaotic Electromagnetic Field Optimization Algorithm Based on Fuzzy Entropy for Multilevel Thresholding Color Image Segmentation.

Multilevel thresholding segmentation of color images is an important technology in various applications which has received more attention in recent years. The process of determining the optimal threshold values in the case of traditional methods is time-consuming. In order to mitigate the above problem, meta-heuristic algorithms have been employed in this field for searching the optima during the past few years. In this paper, an effective technique of Electromagnetic Field Optimization (EFO) algorithm based on a fuzzy entropy criterion is proposed, and in addition, a novel chaotic strategy is embedded into EFO to develop a new algorithm named CEFO. To evaluate the robustness of the proposed algorithm, other competitive algorithms such as Artificial Bee Colony (ABC), Bat Algorithm (BA), Wind Driven Optimization (WDO), and Bird Swarm Algorithm (BSA) are compared using fuzzy entropy as the fitness function. Furthermore, the proposed segmentation method is also compared with the most widely used approaches of Otsu’s variance and Kapur’s entropy to verify its segmentation accuracy and efficiency. Experiments are conducted on ten Berkeley benchmark images and the simulation results are presented in terms of peak signal to noise ratio (PSNR), mean structural similarity (MSSIM), feature similarity (FSIM), and computational time (CPU Time) at different threshold levels of 4, 6, 8, and 10 for each test image. A series of experiments can significantly demonstrate the superior performance of the proposed technique, which can deal with multilevel thresholding color image segmentation excellently.

Reflection of radiation from an atmosphere with a chaotic magnetic field

We consider a semi-infinite turbulent atmosphere with a chaotic magnetic field. We assume that the ratio of the cyclotron frequency to the radiation frequency is small. In this case the Faraday rotation influences only the radiation polarization. The magnetic-field fluctuations are assumed to be isotropic and of Gaussian type. We present the solution of two problems – the reflection of non-polarized radiation with normal incidence to the surface and the reflection of non-polarized radiation from a point source above the surface. The latter occurs when the observed radiation escapes from the part of the jet where most of the radiation (at the relevant wavelength) arises. In this case the polarization degree depends on the level of magnetic-field fluctuations, the wavelength λ and the aperture Θ of the point source, which is determined by the height of the source and the radius of the optically thick part of an accretion disc. The calculations show that the chaotic Faraday rotations very strongly diminish the polarization degree of the emerging radiation compared to the non-magnetized atmosphere. The calculations of the intensity distribution and polarization degree can be used to estimate the level of magnetic-field fluctuations in the accretion discs in active galactic nuclei and binary systems.

Broadband Characteristics of Chaotic Pulse Trains Associated With Sequential Dart Leaders in a Rocket‐Triggered Lightning Flash

AbstractBased on simultaneous measurements of fast E‐field change, very high frequency radiation and channel mapping, channel base current, and high‐speed video, the characteristics of chaotic pulse trains (CPTs) during propagation of dart leaders in a rocket‐triggered lightning were analyzed. The triggered lightning involved 16 subsequent leader‐return strokes traversing in the same grounding channel. At least five dart leaders showed significant CPT signals during its propagation, with much larger intensity than that in normal leader stage at broadband of low‐frequency–medium‐frequency, very high frequency, and visible light band. All CPTs occurred in the final stage of the leader development, within 150 μs prior to the return strokes. The leader velocity and the charge transfer are both related to the instantaneous intensity of CPT, but the relationship is not always solid when the two parameters are considered individually. Nevertheless, the large product of return stroke charge to 1 ms and the velocity of the leader (QV) could be a reliable proxy/indicator for CPT. All CPTs correspond to a larger local QV with a threshold higher than 1 × 107 C · m/s when CPT is determined as chaotic electric field pulses with magnitude larger than 3 std of the magnitude of E‐fluctuation waveform of the whole flash.

Radiation intensity and polarization in an atmosphere with a chaotic magnetic field

We consider the influence of Faraday rotation in chaotic magnetic field on the intensity and linear polarization of multiple scattered radiation. All fluctuations are assumed as Gaussian type and isotropic. The values of magnetic field are less than $10^5$Gauss. In this case the parameter $ \omega_B/\omega=(eB/m_ec)/\omega\simeq 0.93\cdot 10^{-8}\lambda$($\mu$m)$B($G$)$ is small and the radiation scatterings are the usual scatterings on free electrons. Only the Faraday rotation influences on the intensity and polarization of radiation. We consider the Milne problem in the electron magnetized atmosphere without the mean magnetic field. We found that chaotic magnetic field does not increase the number of H-functions, describing the Milne problem. There are four H-functions as in the Milne problem for non-magnetized case. The calculations demonstrate that the polarization of outgoing radiation diminishes strongly with the increasing of the level of magnetic fluctuations. The calculations can be used for estimations of inclination angle $i$ of accretion discs and the level of magnetic fluctuations.

Neoclassical quasilinear theory and universal collision frequency landscape in wave-particle interaction in tokamaks

The neoclassical quasilinear theory is extended to the collisional boundary layer and 1/ν regimes. The theory is for electromagnetic waves with frequencies lower than the bounce frequency of the trapped particles and wavelengths either comparable to or shorter than the width of bananas, but much longer than the gyro-radius. Here, ν is the collision frequency. This is accomplished by solving the banana kinetic equation. The results can be used to model energetic alpha particle and thermal particle losses in the presence of the electromagnetic waves in fusion relevant tokamak plasmas. They can also be employed to quantify transport losses in chaotic magnetic fields; these regimes are not known to exist in the theory of the chaotic magnetic field induced transport. The results of the theory together with those of the theory for neoclassical toroidal plasma viscosity reveal the existence of a universal collision frequency scaling law that governs the physics of the wave-particle interaction. The detailed collision frequency landscape in the theory for neoclassical toroidal viscosity is the universal feature of the wave-particle interaction in non-axisymmetric tori.

Characteristic analysis of the fractional-order hyperchaotic memristive circuit based on the Wien bridge oscillator

In this paper, a new hyperchaotic memristive circuit based on the Wien bridge oscillator is built. The numerical solution of the new fractional-order memristive system is calculated by using the Adomian decomposition method. By using the spectral entropy (SE) complexity algorithm and the $ C_0$ complexity algorithm, the dynamic characteristics of the fractional-order system are analyzed. Especially, the fractional-order coexisting attractors are found and the coexisting bifurcation diagrams with different order are presented. With varying the order q , the phenomenon of coexisting evolution is observed. Finally, the practical circuit is realized. The results of the theoretical analysis and the numerical simulation show that the fractional-order Wien bridge hyperchaotic memristive circuit system has very complex dynamical characteristics. It provides a theoretical guidance for the chaotic related field.

Characterization of magnetic field lines in connection with their transport in Beltrami magnetic fields

Single and double curl Beltrami magnetic fields are studied numerically in connection with their transport properties, and the results are compared and analyzed by characterizing the magnetic field lines. In the phase space of the single curl Beltrami field, islands of regular field lines are embedded into the chaotic sea, whereas the field lines for certain solutions of the double curl Beltrami field are chaotic over the entire space. Due to the presence of regular islands in phase space, the chaotic trajectories show stickiness phenomena which are characterized by the distribution of a chaotic field line. The dynamical traps in chaotic orbits due to stickiness phenomena are also characterized by the distribution of finite distance Lyapunov exponents. Finally, the recurrence length distribution of chaotic trajectories is plotted to understand their global behaviour.

Time evolution of two-mode squeezed vacuum in a single-mode diffusion channel

Based on the infinite sum solution of the master equation corresponding to the diffusion channel we derive the law of time evolution of a two-mode squeezed vacuum state in a single-mode (say a -mode) diffusion channel. We find that the squeezing effect decreases, while two different chaotic field modes emerge. After t time period of the diffusion, the a -mode photon number is larger than b -mode photon number by tκ, where κ is the diffusion coefficient, thus by adjusting κ, photon number can controlled. Therefore, the diffusion process can be considered a quantum controlling scheme through photon addition.

Effect of realistic ballasted track in the underbody flow of a high-speed train via CFD simulations

The underbody flow of high-speed trains is a matter of concern in the railway industry because of its relation to the ballast flight phenomenon, and several experimental campaigns are focused on evaluating its characteristics. Computational simulations are considered as a flexible and economical alternative. However, the aforementioned simulations include only simplified track models with a flat ground that do not include the sleepers or the profiles of stones. The present study uses a previously developed methodology to reproduce the passing of a high-speed train over a scanned real profile of stones and sleepers and determines the effect on the surrounding flow and compares the results relative to those of a flat ballast bed. The simulations are validated relative to experimental data published in the bibliography with satisfactory results. The results confirm expected differences between flat and rough configurations, thereby revealing a more chaotic velocity field near the rough ballast and the presence of a larger number and smaller size of turbulence structures. The rough configuration also allows for the measurement of the pressure on the surface of the stones and the application of a predictive model for ballast flight. The obtained results are similar to those in experimental tests.

Bursting oscillations as well as the bifurcation mechanism in a non-smooth chaotic geomagnetic field model**Project supported by the National Natural Science Foundation of China (Grant No. 11472116), the Key Program of the National Natural Science Foundation of China (Grant No. 11632008), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province, China (Grant No. KYCX17 1784).

Based on the chaotic geomagnetic field model, a non-smooth factor is introduced to explore complex dynamical behaviors of a system with multiple time scales. By regarding the whole excitation term as a parameter, bifurcation sets are derived, which divide the generalized parameter space into several regions corresponding to different kinds of dynamic behaviors. Due to the existence of non-smooth factors, different types of bifurcations are presented in spiking states, such as grazing-sliding bifurcation and across-sliding bifurcation. In addition, the non-smooth fold bifurcation may lead to the appearance of a special quiescent state in the interface as well as a non-smooth homoclinic bifurcation phenomenon. Due to these bifurcation behaviors, a special transition between spiking and quiescent state can also occur.

Effective field theory for chaotic CFTs

We derive an effective field theory for general chaotic two-dimensional conformal field theories with a large central charge. The theory is a specific and calculable instance of a more general framework recently proposed in [1]. We discuss the gauge symmetries of the model and how they relate to the Lyapunov behaviour of certain correlators. We calculate the out-of-time-ordered correlators diagnosing quantum chaos, as well as certain more fine-grained higher-point generalizations, using our Lorentzian effective field theory. We comment on potential future applications of the effective theory to real-time thermal physics and conformal field theory.

Peregrine Solitons Beyond the Threefold Limit and Their Two-Soliton Interactions.

Within the coupled Fokas-Lenells equations framework, we show explicitly that, in contrast to the expected threefold-amplitude magnification, Peregrine solitons can reach a peak amplitude as high as 5 times the background level. Besides, the interaction of two such anomalous Peregrine solitons can generate a spikelike rogue wave of extremely high peak amplitude, depending on the parameters used. We numerically confirm that the Peregrine soliton beyond the threefold limit can be reproduced from either a deterministic initial profile or a chaotic background field, hence anticipating the feasibility of its experimental observation.

A model-based velocity controller for chaotization of flexible joint robot manipulators

This article presents a model-based velocity controller able to induce a chaotic motion on n-degrees of freedom flexible joint robot manipulators. The proposed controller allows the velocity link vector of a robot manipulator to track an arbitrary, chaotic reference vector field. A rigorous theoretical analysis based on Lyapunov’s theory is used to prove the asymptotic stability of the tracking error signals when using the proposed controller, which implies that a chaotic motion is induced to the robotic system. Experimental results are provided using a flexible joint robot manipulator of two degrees of freedom. Finally, by using Poincaré maps and Lyapunov exponents, it is shown that the behavior exhibited by the robot joint positions is chaotic.

Symplectic Maps for Diverted Plasmas

Nowadays, divertors are used in the main tokamaks to control the magnetic field and to improve the plasma confinement. In this article, we present analytical symplectic maps describing Poincar\'e maps of the magnetic field lines in confined plasmas with a single null poloidal divertor. Initially, we present a divertor map and the tokamap for a diverted configuration. We also introduce the Ullmann map for a diverted plasma, whose control parameters are determined from tokamak experiments. Finally, an explicit, area-preserving and integrable magnetic field line map for a single-null divertor tokamak is obtained using a trajectory integration method to represent toroidal equilibrium magnetic surfaces. In this method, we also give examples of onset of chaotic field lines at the plasma edge due to resonant perturbations.

Coherent transport structures in magnetized plasmas. II. Numerical results

In a pair of linked articles (called Papers I and II, respectively), we apply the concept of Lagrangian Coherent Structures borrowed from the study of Dynamical Systems to chaotic magnetic field configurations in order to separate regions where field lines have different kinds of behavior. In the present article, Paper II, by means of a numerical procedure, we investigate the Lagrangian Coherent Structures in the case of a two-dimensional magnetic configuration with two island chains that are generated by magnetic reconnection and evolve nonlinearly in time. The comparison with previous results, obtained by assuming a fixed magnetic field configuration, allows us to explore the dependence of transport barriers on the particle velocity.

ALMA Observations of Molecular Clouds in Three Group-centered Elliptical Galaxies: NGC 5846, NGC 4636, and NGC 5044

Abstract We present new ALMA CO(2–1) observations of two well-studied group-centered elliptical galaxies: NGC 4636 and NGC 5846. In addition, we include a revised analysis of Cycle 0 ALMA observations of the central galaxy in the NGC 5044 group. We find evidence that molecular gas is a common presence in bright group-centered galaxies (BGG). CO line widths are broader than Galactic molecular clouds, and using the reference Milky Way X CO, the total molecular mass ranges from 2.6 × 105 M ⊙ in NGC 4636 to 6.1 × 107 M ⊙ in NGC 5044. Complementary observations using the ALMA Compact Array do not exhibit any detection of a CO diffuse component at the sensitivity level achieved by current exposures. The origin of the detected molecular features is still uncertain, but these ALMA observations suggest that they are the end product of the hot gas cooling process and not the result of merger events. Some of the molecular clouds are associated with dust features as revealed by HST dust extinction maps, suggesting that these clouds formed from dust-enhanced cooling. The global nonlinear condensation may be triggered via the chaotic turbulent field or buoyant uplift. The large virial parameter of the molecular structures and correlation with the warm ( )/hot (≥106) phase velocity dispersion provide evidence that they are unbound giant molecular associations drifting in the turbulent field, consistent with numerical predictions of the chaotic cold accretion process. Alternatively, the observed large CO line widths may be generated by molecular gas flowing out from cloud surfaces due to heating by the local hot gas atmosphere.

Vacuum birefringence and the x-ray polarization from black-hole accretion disks

In the next decade, x-ray polarimetry will open a new window on the high-energy Universe, as several missions that include an x-ray polarimeter are currently under development. Observations of the polarization of x-rays coming from the accretion disks of stellar-mass and supermassive black holes are among the new polarimeters' major objectives. In this paper, we show that these observations can be affected by the quantum electrodynamic (QED) effect of vacuum birefringence: after an x-ray photon is emitted from the accretion disk, its polarization changes as the photon travels through the accretion disk's magnetosphere, as a result of the vacuum becoming birefringent in presence of a magnetic field. We show that this effect can be important for black holes in the energy band of the upcoming polarimeters, and has to be taken into account in a complete model of the x-ray polarization that we expect to detect from black-hole accretion disks, both for stellar mass and for supermassive black holes. We find that, for a chaotic magnetic field in the disk, QED can significantly decrease the linear polarization fraction of edge-on photons, depending on the spin of the hole and on the strength of the magnetic field. This effect can provide, for the first time, a direct way to probe the magnetic field strength close to the innermost stable orbit of black-hole accretion disks and to study the role of magnetic fields in astrophysical accretion in general.

Control of molecular breakup by an infrared pulse and a femtosecond pulse train

We investigate the dissociation dynamics of diatomic molecules subjected to both a femtosecond infrared (IR) laser pulse and a femtosecond pulse train (FPT) within the framework of the Morse potential model. When the IR and FPT are phase delayed, we observe well-resolved oscillations in dissociation probability, corresponding to multiple integers of the IR period, exhibiting enhancement and suppression of bond dissociation. These oscillations reveal a rich dynamics as a function of the IR and FPT parameters including chaotic fields. A frequency-resolved profile of dressed molecular states shows that these oscillations are due to interference of many quantum paths analogous to the recently observed control of photoionization of atoms under IR and XUV pulses. By manipulating phases of FPTs we demonstrate an enhancement of molecular dissociation compared to the transform-limited case.