Chaotic Component Research Articles

Impact of Thermal Tests Simulating Dry Storage of VVER-1000 Fuel on the Hydride Phase Morphology in Fuel Element Claddings

In this work, we carried out metallographic studies of the lateral and longitudinal sections of the fuel element claddings used in the fuel assemblies of VVER-1000 reactors. The average fuel burnup in these fuel elements during one and six annual campaigns was ~20 and ~70 MWd/kg U, respectively. The effect of long-term thermal tests under simulated dry storage conditions of fuel elements on the hydride morphology in the lateral and longitudinal sections of E110 zirconium alloy claddings was experimentally studied. The test fuel elements were kept in helium at 380°C for 468 days under stationary conditions and from 20 to 380°C (48 cycles, holding time from 1 to 10 days at 380°C) for 427 days during thermal cycling. Metallographic studies of the microstructure of the lateral and longitudinal sections of fuel element claddings were carried out in order to determine the effect of fuel burnup and thermal testing modes on the morphology of zirconium hydrides in the fuel elements from the regions corresponding to the middle of the fuel rod and the gas collector location. It was established that the specific length of hydrides does not exceed 4.5 × 10–3 μm–1 and correlates with a low hydrogen content in the claddings. Thermal tests did not change the hydrogen content in the claddings, but caused an increase in the specific length of hydrides in the lateral sections of the claddings by 1.5–1.9 times in fuel elements with low burnup. In the longitudinal sections of the claddings of these fuel elements, as well as in the fuel elements with a high level of fuel burnup, this coagulation of hydrides was not observed. Thermal tests under stationary conditions and in thermal cycling mode did not lead to a significant change in the hydride orientation, which was predominantly tangential with a high fraction of the chaotic component in the lateral section of the claddings, whereas the axial orientation of hydrides prevailed in the longitudinal section.

Almost sure convergence on chaoses

We present several new phenomena about almost sure convergence on homogeneous chaoses that include Gaussian Wiener chaos and homogeneous sums in independent random variables. Concretely, we establish the fact that almost sure convergence on a fixed finite sum of chaoses forces the almost sure convergence of each chaotic component. Our strategy uses “extra randomness” and a simple conditioning argument. These ideas are close to the spirit of Stein’s method of exchangeable pairs. Some natural questions are left open in this note.

Nodal area distribution for arithmetic random waves

We obtain the limiting distribution of the nodal area of random Gaussian Laplace eigenfunctions on T 3 = R 3 / Z 3 \mathbb {T}^3= \mathbb {R}^3/ \mathbb {Z}^3 (three-dimensional “arithmetic random waves"). We prove that, as the multiplicity of the eigenspace goes to infinity, the nodal area converges to a universal, non-Gaussian distribution. Universality follows from the equidistribution of lattice points on the sphere. Our arguments rely on the Wiener chaos expansion of the nodal area: we show that, analogous to the two-dimensional case addressed by Marinucci et al., [Geom. Funct. Anal. 26 (2016), pp. 926–960] the fluctuations are dominated by the fourth-order chaotic component. The proof builds upon recent results from Benatar and Maffiucci [Int. Math. Res. Not. IMRN (to appear)] that establish an upper bound for the number of nondegenerate correlations of lattice points on the sphere. We finally discuss higher-dimensional extensions of our result.

Identification Method of the Time-Series Properties of the Aviation Events

The new empirical method was developed for estimating the relative contribution of the deterministic, chaotic and noise components in the time series of the accident rate of aircraft in the Armed Forces of the Russian Federation. The behavior analysis of the senior Lyapunov exponent dependencies on the parameter of “number of neighbors used” specified in the algorithm in the case of model series (deterministic, chaotic and colored noise series) enabled to estimate the boundaries of numerical values of the parameters typical for these types of series and then apply them to the noise percentage analysis in the real series of the aviation events number.

Mathematical models of transient processes for the distribution of resources in the system

Problems for shares of resources to be distributed in conditions of constraints, including the process of dynamic change of shares are considered. The tasks of forming and dynamically changing the composition of portfolios are considered, in particular, in the presence of group restrictions. A mathematical model for predicting the dynamics of shares for a transition process from one equilibrium state of the system to another equilibrium state is proposed. The case of the presence of a noise chaotic component in such a model is considered. An example of the application of the proposed model of the dynamic process of resource allocation is given.

Non-linear forecasting of the state of a socio-eco-oriented innovative economy in the conditions of systemic crises

The paper deals with the problem of sustainable development and innovative integral modeling and forecasting approach in the management of technogenic objects and processes (TOP) as a system of socio-eco-economic and humanitarian type (SEEH). Based on the use of information and innovation technologies in order to forecast the non-linear dynamics of eco-economic and socio-humanitarian systems, integrated stochastic models of objects and processes were developed and studied, suitable for the conditions of systemic crises. The paper handles the aspect of integration of 4 business and functioning areas of the modern complex systems. It proposes a general conceptual integrated model, generalized synergetic model of dynamics, considering different uncertainty (stochastic and chaotic components). The paper examines the aspects of integration of multiple business areas and sectors of the modern complex systems functioning and developing under the present conditions of non-linearity, instability and crises. An integrated stochastic non-linear phase-space growth dynamics model was developed and studied to forecast the development of the state of an innovative economy. The paper looks into the aspects of activity management of the modern complex systems functioning and developing under the present conditions of instability.

Dynamics of coupled nonlinear systems

Two models were studied theoretically which describe the dynamics of two nonlinear elements with linear and nonlinear interaction between them. These models correspond to the commutators in nonlinear fiber optics and artificial lattices of magnetic nanodots or magnetic layers in quasi-two dimensional compounds. The models illustrate the common situation in the nonlinear systems with two degrees of freedom. Usually the absence of additional to the total energy integrals of motion leads to the appearance of a chaotic component of the dynamics. This chaotic behaviour masks the reqular part of the total dynamics. In the studied in the paper two integrable systems the chaotic component is absent and the reqular dynamics manifest itself per se. In the paper at first the dynamics of the systems was investigated qualitatively in the corresponding phase planes. Two integrals of motion correspond to the total energy E and the number N of elementary excitations in the system (photons and spin deviations). The phase analysis demonstrates the complicated its dynamics. The excitations of different types are classified in the plane of the integrals N,E . For the fix number of excitations N in the domain of small N the dynamics is close to the linear one and divides into two regions for quasi-inphase and quasi-antiphase oscillations. But for the large level of the excitation after the definite value of N N b  in the bifurcation way the region of another dynamics appears. For N N b  the minimum of the energy corresponds to the essentially nonlinear regime with nonunifor average distribution of the energy between two oscillators. At the same time the critical point which correspond to the in-phase oscillations transforms into saddle one and in-phase regime becomes unstable. As integrable the studied systems allow the solutions in the quadratures. The exact solution of the dynamical equations for nonlinear dynamics were obtained and analysed. The main result consists in the above prediction of the nonuniform states with different energies of subsystems, their stability and instability of inphase oscillations. The nonuniform states corresponds to the solitonic excitations in the systems with distributed parameters.

The Effect of Breathing at the Resonant Frequency on the Nonlinear Dynamics of Heart Rate

Investigation of the nonlinear dynamics of the heart rate is crucial for understanding the physiological mechanisms of various functional states and understanding the adaptation capacity of the human body. The purpose of this study was to evaluate some quantitative parameters of the nonlinear parameters of resonance in the heart rate variability. The study included 70 healthy students who underwent paced breath training. The heart rate was recorded during breathing at different respiratory rates (spontaneous breathing, 4.5, 5, 5.5, 6, and 6.5 breaths/min). The resonant frequency was determined using heart-rate spectral analysis. Nonlinear analysis of HRV was performed using entropy measures (ApEn, SampEn, and MSE), Correlation dimension, Detrended Fluctuation Analysis (DFA), Recurrence Plot (REC, DET, Lmean, Lmax, and ShanEn), the Poincare plot (SD1 and SD2), and time asymmetry (GI and P). We observed a decrease in the level of complexity, an increase in the self-similarity of the RR intervals, a decrease in the chaotic component, and an increase in rhythm asymmetry during breathing at resonant frequency.

Intra and inter-individual variability in the chaotic component and functional connectivity of the EEG signal in basal eyes closed condition

Individuality has to do with our differences and similitudes, our phenotype and genotype characteristics that make us unique in some ways, and common in others. In this study we applied linear and non-linear quantitative description of the EEG signal of 8 subjects in closed eyes, basal conditions, three times at a day (at 10:00, 13:00, and 16:00 hrs. UTC -04:00 Santiago), to provide evidence that allows us to narrow the boundaries of intra and inter-individual differences in the behavior of the oscillatory electrical signal of the brain. We applied two versions of Hurst exponent estimator of persistence/anti-persistence of the brain signal, and a Spearman R inter-correlation analysis between pairs of EEG channels to quantify and allocate the magnitude of highly correlated pairs of electrodes as an indicator of enhanced brain synchrony. Results showed differences and patterns in laterality/symmetry associated with magnitude, self-organized long-memory processes; and brain synchrony.

A Peccati-Tudor type theorem for Rademacher chaoses

In this article, we prove that in the Rademacher setting, a random vector with chaotic components is close in distribution to a centered Gaussian vector, if both themaximal influenceof the associated kernel and the fourth cumulant of each component is small. In particular, we recover the univariate case recently established in Döbler and Krokowski (2019). Our main strategy consists in a novel adaption of the exchangeable pairs couplings initiated in Nourdin and Zheng (2017), as well as its combination with estimatesviachaos decomposition.

Eccentricity Failure Detection of Brushless DC Motors From Sound Signals Based on Density of Maxima

Brushless Direct Current (BLDC) motors have been used in a wide range of fields. In some critical applications, failures in these machines can cause operational disasters and cost lives if they are not detected in advance. The classical methods for detecting incipient faults in BLDC motors perform processing of the current signal to obtain the required information. In this work, the SAC-DM (Signal Analysis based on Chaos using Density of Maxima) technique is applied for the first time in the diagnosis of failures of electromechanical systems from sound signals. Wavelet Multiresolution Analysis (WMA) is used to separate a chaotic signal component from the sound emitted by the motor. This work demonstrates that it is feasible to perform dynamic eccentricity diagnosis in BLDC motors by identifying variations of the SAC-DM of the sound signal. The technique exposed in this work requires low computational cost and achieves high success rate. To validate the method, tests were carried out on a small BLDC motor normally used in Unmanned Aerial Vehicle (UAV), demonstrating the ability of the method to detect the speed of the motor in 95.89% of the cases and to detect eccentricity problems at a fixed speed in 88.34% of the cases.

Effects of Landscape Heterogeneity on Common Shrew (Sorex araneus) Population Dynamics

The effects of landscape heterogeneity on changes in the common shrew population were researched. Multiyear (1987–2017) time series data on species abundance in the plain and piedmont areas of the Pechora-Ilych State Nature Biosphere Reserve have been analyzed using the Fourier spectral analysis method. A cyclic component of three years and another one of lower value at five years were identified in the common shrew population dynamics in the piedmont area. In the plain area, changes in the animal population are more chaotic and periodic components are poorly manifested in the time series. The influence of landscape heterogeneity on the species population and its amplitude of fluctuation were also identified; these parameters are significant in the piedmont area and negligible on the plain.

A quantitative central limit theorem for the Euler–Poincaré characteristic of random spherical eigenfunctions

We establish here a quantitative central limit theorem (in Wasserstein distance) for the Euler–Poincaré characteristic of excursion sets of random spherical eigenfunctions in dimension 2. Our proof is based upon a decomposition of the Euler–Poincaré characteristic into different Wiener-chaos components: we prove that its asymptotic behaviour is dominated by a single term, corresponding to the chaotic component of order two. As a consequence, we show how the asymptotic dependence on the threshold level $u$ is fully degenerate, that is, the Euler–Poincaré characteristic converges to a single random variable times a deterministic function of the threshold. This deterministic function has a zero at the origin, where the variance is thus asymptotically of smaller order. We discuss also a possible unifying framework for the Lipschitz–Killing curvatures of the excursion sets for Gaussian spherical harmonics.

A Triangulation Approach to Checking the Reliability of Estimation of Oscillatory Modes Embedded in an ECG Signal

Abstract—It is important to perform an analytical study of the oscillatory modes embedded in an ECG signal on individuals in certain occupations (power station operators, pilots, military officers, drivers, sportspeople, etc.) and those who experience pronounced emotional stress while carrying out important work. Reliability of studying the oscillatory modes was achieved by using and comparing several methods (triangulation), thus allowing evaluation of the results obtained by studying spatio-temporal variances, the ordered vs. stochastic character, and the periodic vs. stochastic character of the dynamics of an ECG signal. The oscillatory modes of the ECG signal structure were studied in various conditions using graphic illustrations obtained by converting the ECG signal in the phase plane. The orderliness, periodicity, and stochastic features of a time series of R–R intervals were examined using the entropy-dynamic approach and the phase-plane and phase-curve methodologies. Nonlinear phenomena were qualitatively described using the elementary part of the theory of catastrophes. Dysfunctional and pathological conditions were associated with either a significant expansion of the phase graph (PG) shape with significant variations in amplitude and time parameters and an increase in the degree of chaos or a distinct periodicity with a loss of variability, a decrease in the chaotic component, and a mathematical degeneration of the cycle. The results of the ECG-based entropy analysis and its PG were quantitatively comparable with data obtained by a rheographic recording of the biological signal; this finding supporting the reliability of the results. Constructing a phase curve using a nonparametric method helped us to detect hidden functional features of the cardiodynamics system. This study substantially contributes to the development of preventive methods based on testing cardiac activity in the primary medical and social care system.

Structure, size, and statistical properties of chaotic components in a mixed-type Hamiltonian system.

We perform a detailed study of the chaotic component in mixed-type Hamiltonian systems on the example of a family of billiards [introduced by Robnik in J. Phys. A: Math. Gen. 16, 3971 (1983)JPHAC50305-447010.1088/0305-4470/16/17/014]. The phase space is divided into a grid of cells and a chaotic orbit is iterated a large number of times. The structure of the chaotic component is discerned from the cells visited by the chaotic orbit. The fractal dimension of the border of the chaotic component for various values of the billiard shape parameter is determined with the box-counting method. The cell-filling dynamics is compared to a model of uncorrelated motion, the so-called random model [Robnik et al. J.Phys. A: Math. Gen. 30, L803 (1997)JPHAC50305-447010.1088/0305-4470/30/23/003], and deviations attributed to sticky objects in the phase space are found. The statistics of the number of orbit visits to the cells is analyzed and found to be in agreement with the random model in the long run. The stickiness of the various structures in the phase space is quantified in terms of the cell recurrence times. The recurrence time distributions in a few selected cells as well as the mean and standard deviation of recurrence times for all cells are analyzed. The standard deviation of cell recurrence time is found to be a good quantifier of stickiness on a global scale. Three methods for determining the measure of the chaotic component are compared and the measure is calculated for various values of the billiard shape parameter. Lastly, the decay of correlations and the diffusion of momenta is analyzed.

Axial-flow-induced vibration experiments on cantilevered rods for nuclear reactor applications

Abstract Axial-flow-induced vibration has been experimentally investigated with clamped-free cantilevered cylindrical rods confined in a tube and subjected to axial water flow directed from the rod free-end towards the clamped end: a simplified configuration relevant for water-cooled nuclear reactor cores. Non-contact optical techniques have been used to simultaneously detect the rods vibration and the flow field around the vibrating rods free-end. The source of excitation is turbulent buffeting at low flow velocity, while a movement induced excitation component is present at large flow velocities. The rods flow-induced vibration consists of a fuzzy period-1 motion: a periodic (period-1) motion with a chaotic component that increases in relative importance as the flow velocity is increased. The experimental data provided here are particularly suited for numerical fluid-structure model development and benchmarking, as they combine a rich fluid-structure multi-physics interaction with a relatively simple configuration and include both the flow field and the mechanical response of the vibrating rods.

Investigating landscape phase transitions in Mediterranean rangelands by recurrence analysis

Socio-ecological landscapes typically characterized by non-linear dynamics in space and time are difficult to be analyzed using standard quantitative methods, due to multiple processes interacting on different spatial and temporal scales. This poses a challenge to the identification of appropriate approaches for analyzing time series that can evaluate system properties of landscape dynamics in the face of disturbances, such as uncontrolled fires. The purpose is the application of non-linear methods such as recurrence quantification analysis (RQA) to landscape ecology. The examples concern the time series of burnt and unburnt Mediterranean rangelands, to highlight potential and limits of RQA. We used RQA together with joint recurrence analysis (JRA) to compare the evolutionary behavior of different land uses. Time series of forests and grasslands in rangelands present both periodic and chaotic components with a rather similar behavior after the fire and clear transitions from less to more regular/predictable dynamics/succession. Results highlight the impacts of fire, the recovery capacity of land covers to pre-burnt levels, and the decay of synchronization towards the previous regime associated with vegetation secondary succession consistent with early successional species. RQA and JRA with their set of indices (recurrence rate: RR, laminarity: LAM, determinism: DET, and divergence: DIV) can represent new sensitive measures that may monitor the adaptive capacity and the resilience of landscapes. However, future applications are needed to standardize the analysis by strengthening the accuracy of this approach in describing the ongoing transformations of natural and man-managed landscapes.

Separation of Trend and Chaotic Components of Time Series and Estimation of Their Characteristics by Linear Splines

This paper considers the problem of separating the trend and the chaotic component of chaotic time series in the absence of information on the characteristics of the chaotic component. Such a problem arises in nuclear physics, biomedicine, and many other applied fields. The scheme has two stages. At the first stage, smoothing linear splines with different values of smoothing parameter are used to separate the “trend component.” At the second stage, the method of least squares is used to find the unknown variance σ2 of the noise component.

Novel Multi-Step Short-Term Wind Power Prediction Framework Based on Chaotic Time Series Analysis and Singular Spectrum Analysis

Decomposition methods are widely applied as a prestage of wind power prediction (WPP) to reduce the prediction errors caused by the nonstationarity and nonlinearity of wind power time series (TS); however, they cannot address the issues posed by the chaotic behavior of wind power TS. This paper, therefore, proposes a novel decomposition approach to take the chaotic nature of wind power TS into account and to improve WPP accuracy. In this decomposition approach, as a primary step, the wind power TS is separated into several components with different time-frequency characteristics (scales) by means of ensemble empirical mode decomposition. Chaotic TS analysis is then applied to determine which components are chaotic, and then singular spectrum analysis (SSA) is applied thereto. This multi-scale SSA (MSSSA) can maintain the general trend of chaotic components, which become smoother by eliminating extremely rapid changes with low amplitudes, and thus several steps ahead WPP with higher accuracy can be realized. Following the proposed decomposition, a novel short-term WPP method comprised of localized direct and iterative prediction is proposed to perform multi-step prediction for the chaotic and nonchaotic components of MSSSA, respectively. The proposed framework is finally validated using historical data related to overall wind power generation for Alberta (Canada), the Sotavento wind farm (Spain), and Centennial wind farm in Saskatchewan (Canada).

Analysis of multiple time scales feature and chaotic property for time series of relative sunspot numbers

Using observational data of the relative sunspot numbers from January 1749 to December 2016, the multiple time scales and chaotic characteristics have been analyzed based on the ensemble empirical mode decomposition method and chaotic dynamics theory, then the differences between the relative sunspot numbers and the time series with the periodic components removed are especially compared. The results show that the relative sunspot numbers are mainly composed of periodic components, chaotic components and a trend component, and they have multi-time scale and chaotic characteristics. Therefore, the long-term solar activity is the result of the physical mechanism of periodic phenomenon and the factors of chaotic dynamical characteristics. In the mul-me scale analysis, the results are still the same as the relative sunspot numbers removed chaotic components, but chaotic characteristics become stronger if the periodic components are removed.