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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Phenomenological Model of Nonlinear Dynamics and Deterministic Chaotic Gas Migration in Bentonite: Experimental Evidence and Diagnostic Parameters

Understanding gas migration in compacted clay materials, e.g., bentonite and claystone, is important for the design and performance assessment of an engineered barrier system of a radioactive waste repository system, as well as many practical applications. Existing field and laboratory data on gas migration processes in low-permeability clay materials demonstrate the complexity of flow and transport processes, including various types of instabilities, caused by nonlinear dynamics of coupled processes of liquid–gas exchange, dilation, fracturing, fracture healing, etc., which cannot be described by classical models of fluid dynamics in porous media. We here show that the complexity of gas migration processes can be explained using a phenomenological concept of nonlinear dynamics and deterministic chaos theory. To do so, we analyzed gas pressure and gas influx (i.e., input) and outflux (i.e., output), recorded during the gas injection experiment in the compact Mx80-D bentonite sample, and calculated a set of the diagnostic parameters of nonlinear dynamics and chaos, such a global embedding dimension, a correlation dimension, an information dimension, and a spectrum of Lyapunov exponents, as well as plotted 2D and 3D pseudo-phase-space strange attractors, based on the univariate influx and outflux time series data. These results indicate the presence of phenomena of low-dimensional deterministic chaotic behavior of gas migration in bentonite. In particular, during the onset of gas influx in the bentonite core, before the breakthrough, the development of gas flow pathways is characterized by the process of chaotic gas diffusion. After the breakthrough, with inlet-to-outlet movement of gas, the prevailing process is chaotic advection. During the final phase of the experiment, with no influx to the sample, the relaxation pattern of gas outflux is resumed back to a process of chaotic diffusion. The types of data analysis and a proposed phenomenological model can be used to establish the basic principles of experimental data-gathering, modeling predictions, and a research design.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Gyroaverage effects on chaotic transport by drift waves in zonal flows

Finite Larmor radius (FLR) effects on E Multiplication-Sign B test particle chaotic transport in the presence of zonal flows is studied. The FLR effects are introduced by the gyro-average of a simplified E Multiplication-Sign B guiding center model consisting of the linear superposition of a non-monotonic zonal flow and drift waves. Non-monotonic zonal flows play a critical role on transport because they exhibit robust barriers to chaotic transport in the region(s) where the shear vanishes. In addition, the non-monotonicity gives rise to nontrivial changes in the topology of the orbits of the E Multiplication-Sign B Hamiltonian due to separatrix reconnection. The present study focuses on the role of FLR effects on these two signatures of non-monotonic zonal flows: shearless transport barriers and separatrix reconnection. It is shown that, as the Larmor radius increases, the effective zonal flow profile bifurcates and multiple shearless regions are created. As a result, the topology of the gyro-averaged Hamiltonian exhibits very complex separatrix reconnection bifurcations. It is also shown that FLR effects tend to reduce chaotic transport. In particular, the restoration of destroyed transport barriers is observed as the Larmor radius increases. A detailed numerical study is presented on the onset of global chaotic transport as function of the amplitude of the drift waves and the Larmor radius. For a given amplitude, the threshold for the destruction of the shearless transport barrier, as function of the Larmor radius, exhibits a fractal-like structure. The FLR effects on a thermal distribution of test particles are also studied. In particular, the fraction of confined particles with a Maxwellian distribution of gyroradii is computed, and an effective transport suppression is found for high enough temperatures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

Parallel heat transport in integrable and chaotic magnetic fields

The study of transport in magnetized plasmas is a problem of fundamental interest in controlled fusion, space plasmas, and astrophysics research. Three issues make this problem particularly challenging: (i) The extreme anisotropy between the parallel (i.e., along the magnetic field), {chi}{sub ||} , and the perpendicular, {chi}{sub Up-Tack }, conductivities ({chi}{sub ||} /{chi}{sub Up-Tack} may exceed 10{sup 10} in fusion plasmas); (ii) Nonlocal parallel transport in the limit of small collisionality; and (iii) Magnetic field lines chaos which in general complicates (and may preclude) the construction of magnetic field line coordinates. Motivated by these issues, we present a Lagrangian Green's function method to solve the local and non-local parallel transport equation applicable to integrable and chaotic magnetic fields in arbitrary geometry. The method avoids by construction the numerical pollution issues of grid-based algorithms. The potential of the approach is demonstrated with nontrivial applications to integrable (magnetic island), weakly chaotic (Devil's staircase), and fully chaotic magnetic field configurations. For the latter, numerical solutions of the parallel heat transport equation show that the effective radial transport, with local and non-local parallel closures, is non-diffusive, thus casting doubts on the applicability of quasilinear diffusion descriptions. General conditions for the existence of non-diffusive, multivalued flux-gradient relations in the temperature evolution are derived.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Dynamics of coupled simplest chaotic two-component electronic circuits and its potential application to random bit generation

We numerically investigate the possibility of using a coupling to increase the complexity in simplest chaotic two-component electronic circuits operating at high frequency. We subsequently show that complex behaviors generated in such coupled systems, together with the post-processing are suitable for generating bit-streams which pass all the NIST tests for randomness. The electronic circuit is built up by unidirectionally coupling three two-component (one active and one passive) oscillators in a ring configuration through resistances. It turns out that, with such a coupling, high chaotic signals can be obtained. By extracting points at fixed interval of 10 ns (corresponding to a bit rate of 100 Mb/s) on such chaotic signals, each point being simultaneously converted in 16-bits (or 8-bits), we find that the binary sequence constructed by including the 10(or 2) least significant bits pass statistical tests of randomness, meaning that bit-streams with random properties can be achieved with an overall bit rate up to 10×100 Mb/s =1Gbit/s (or 2×100 Mb/s =200 Megabit/s). Moreover, by varying the bias voltages, we also investigate the parameter range for which more complex signals can be obtained. Besides being simple to implement, the two-component electronic circuit setup is very cheap as compared to optical and electro-optical systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Chaotic dynamics of flexible Euler-Bernoulli beams

Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c{sup 2}) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions is carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q{sub 0} and frequency ω{sub p} of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Intermittent and sustained periodic windows in networked chaotic Rössler oscillators

Route to chaos (or periodicity) in dynamical systems is one of fundamental problems. Here, dynamical behaviors of coupled chaotic Rössler oscillators on complex networks are investigated and two different types of periodic windows with the variation of coupling strength are found. Under a moderate coupling, the periodic window is intermittent, and the attractors within the window extremely sensitively depend on the initial conditions, coupling parameter, and topology of the network. Therefore, after adding or removing one edge of network, the periodic attractor can be destroyed and substituted by a chaotic one, or vice versa. In contrast, under an extremely weak coupling, another type of periodic window appears, which insensitively depends on the initial conditions, coupling parameter, and network. It is sustained and unchanged for different types of network structure. It is also found that the phase differences of the oscillators are almost discrete and randomly distributed except that directly linked oscillators more likely have different phases. These dynamical behaviors have also been generally observed in other networked chaotic oscillators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Controlled transitions between cupolets of chaotic systems

We present an efficient control scheme that stabilizes the unstable periodic orbits of a chaotic system. The resulting orbits are known as cupolets and collectively provide an important skeleton for the dynamical system. Cupolets exhibit the interesting property that a given sequence of controls will uniquely identify a cupolet, regardless of the system's initial state. This makes it possible to transition between cupolets, and thus unstable periodic orbits, simply by switching control sequences. We demonstrate that although these transitions require minimal controls, they may also involve significant chaotic transients unless carefully controlled. As a result, we present an effective technique that relies on Dijkstra's shortest path algorithm from algebraic graph theory to minimize the transients and also to induce certainty into the control of nonlinear systems, effectively providing an efficient algorithm for the steering and targeting of chaotic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Fault Diagnosis of Hybrid Computing Systems Using Chaotic-Map Method

Computing systems are becoming increasingly complex with nodes consisting of a combination of multi-core central processing units (CPUs), many integrated core (MIC) and graphics processing unit (GPU) accelerators. These computing units and their interconnections are subject to different classes of hardware and software faults, which should be detected to support mitigation measures. We present the chaotic-map method that uses the exponential divergence and wide Fourier properties of the trajectories, combined with memory allocations and assignments to diagnose component-level faults in these hybrid computing systems. We propose lightweight codes that utilize highly parallel chaotic-map computations tailored to isolate faults in arithmetic units, memory elements and interconnects. The diagnosis module on a node utilizes pthreads to place chaotic-map threads on CPU and MIC cores, and CUDA C and OpenCL kernels on GPU blocks. We present experimental diagnosis results on five multi-core CPUs; one MIC; and, seven GPUs with typical diagnosis run-times under a minute.

Rao, Nageswara↗
DOE OSTI2019

Interaction-induced transition in the quantum chaotic dynamics of a disordered metal

We demonstrate that a weakly disordered metal with short-range interactions exhibits a transition in the quantum chaotic dynamics when changing the temperature or the interaction strength. For weak interactions, the system displays exponential growth of the out-of-time-ordered correlator (OTOC) of the current operator. The Lyapunov exponent of this growth is temperature-independent in the limit of vanishing interaction. With increasing the temperature or the interaction strength, the system undergoes a transition to a non-chaotic behaviour, for which the exponential growth of the OTOC is absent. We conjecture that the transition manifests itself in the quasiparticle energy-level statistics and also discuss ways of its explicit observation in cold-atom setups.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Relation between delayed feedback and delay-coupled systems and its application to chaotic lasers

We present a systematic approach to identify the similarities and differences between a chaotic system with delayed feedback and two mutually delay-coupled systems. We consider the general case in which the coupled systems are either unsynchronized or in a generally synchronized state, in contrast to the mostly studied case of identical synchronization. We construct a new time-series for each of the two coupling schemes, respectively, and present analytic evidence and numerical confirmation that these two constructed time-series are statistically equivalent. From the construction, it then follows that the distribution of time-series segments that are small compared to the overall delay in the system is independent of the value of the delay and of the coupling scheme. By focusing on numerical simulations of delay-coupled chaotic lasers, we present a practical example of our findings.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Competitive autocatalytic reactions in chaotic flows with diffusion: Prediction using finite-time Lyapunov exponents

We investigate chaotic advection and diffusion in autocatalytic reactions for time-periodic sine flow computationally using a mapping method with operator splitting. We specifically consider three different autocatalytic reaction schemes: a single autocatalytic reaction, competitive autocatalytic reactions, which can provide insight into problems of chiral symmetry breaking and homochirality, and competitive autocatalytic reactions with recycling. In competitive autocatalytic reactions, species B and C both undergo an autocatalytic reaction with species A such that A+B→2B and A+C→2C. Small amounts of initially spatially localized B and C and a large amount of spatially homogeneous A are advected by the velocity field, diffuse, and react until A is completely consumed and only B and C remain. We find that local finite-time Lyapunov exponents (FTLEs) can accurately predict the final average concentrations of B and C after the reaction completes. The species that starts in the region with the larger FTLE has, with high probability, the larger average concentration at the end of the reaction. If B and C start in regions with similar FTLEs, their average concentrations at the end of the reaction will also be similar. When a recycling reaction is added, the system evolves towards a single species state, with the FTLE often being useful in predicting which species fills the entire domain and which is depleted. The FTLE approach is also demonstrated for competitive autocatalytic reactions in journal bearing flow, an experimentally realizable flow that generates chaotic dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Parameter estimation for chaotic systems using a hybrid adaptive cuckoo search with simulated annealing algorithm

This paper introduces a novel hybrid optimization algorithm to establish the parameters of chaotic systems. In order to deal with the weaknesses of the traditional cuckoo search algorithm, the proposed adaptive cuckoo search with simulated annealing algorithm is presented, which incorporates the adaptive parameters adjusting operation and the simulated annealing operation in the cuckoo search algorithm. Normally, the parameters of the cuckoo search algorithm are kept constant that may result in decreasing the efficiency of the algorithm. For the purpose of balancing and enhancing the accuracy and convergence rate of the cuckoo search algorithm, the adaptive operation is presented to tune the parameters properly. Besides, the local search capability of cuckoo search algorithm is relatively weak that may decrease the quality of optimization. So the simulated annealing operation is merged into the cuckoo search algorithm to enhance the local search ability and improve the accuracy and reliability of the results. The functionality of the proposed hybrid algorithm is investigated through the Lorenz chaotic system under the noiseless and noise condition, respectively. The numerical results demonstrate that the method can estimate parameters efficiently and accurately in the noiseless and noise condition. Finally, the results are compared with the traditional cuckoo search algorithm, genetic algorithm, and particle swarm optimization algorithm. Simulation results demonstrate the effectiveness and superior performance of the proposed algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Modulated heat pulse propagation and partial transport barriers in chaotic magnetic fields

Direct numerical simulations of the time dependent parallel heat transport equation modeling heat pulses driven by power modulation in three-dimensional chaotic magnetic fields are presented. The numerical method is based on the Fourier formulation of a Lagrangian-Green's function method that provides an accurate and efficient technique for the solution of the parallel heat transport equation in the presence of harmonic power modulation. The numerical results presented provide conclusive evidence that even in the absence of magnetic flux surfaces, chaotic magnetic field configurations with intermediate levels of stochasticity exhibit transport barriers to modulated heat pulse propagation. In particular, high-order islands and remnants of destroyed flux surfaces (Cantori) act as partial barriers that slow down or even stop the propagation of heat waves at places where the magnetic field connection length exhibits a strong gradient. Results on modulated heat pulse propagation in fully stochastic fields and across magnetic islands are also presented. In qualitative agreement with recent experiments in large helical device and DIII-D, it is shown that the elliptic (O) and hyperbolic (X) points of magnetic islands have a direct impact on the spatio-temporal dependence of the amplitude of modulated heat pulses.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS)

This paper develops the Non-Intrusive Least Squares Shadowing (NILSS) method, which computes the sensitivity for long-time averaged objectives in chaotic dynamical systems. In NILSS, we represent a tangent solution by a linear combination of one inhomogeneous tangent solution and several homogeneous tangent solutions. Next, we solve a least squares problem using this representation; thus, the resulting solution can be used for computing sensitivities. NILSS is easy to implement with existing solvers. In addition, for chaotic systems with many degrees of freedom but few unstable modes, NILSS has a low computational cost. NILSS is applied to two chaotic PDE systems: the Lorenz 63 system and a CFD simulation of flow over a backward-facing step. In both cases, the sensitivities computed by NILSS reflect the trends in the long-time averaged objectives of dynamical systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Experimental investigation of quasiperiodic-chaotic-quasiperiodic-chaotic transition in a direct current magnetron sputtering plasma

Floating potential fluctuations from a direct current magnetron sputtering plasma have been analysed using time series analysis techniques like phase space plots, power spectra, frequency bifurcation plot, etc. The system exhibits quasiperiodic-chaotic-quasiperiodic-chaotic transitions as the discharge voltage was increased. The transitions of the fluctuations, quantified using the largest Lyapunov exponent, have been corroborated by Hurst exponent and the Shannon entropy. The Shannon entropy is high for quasiperiodic and low for chaotic oscillations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Criteria for stochastic pinning control of networks of chaotic maps

This paper investigates the controllability of discrete-time networks of coupled chaotic maps through stochastic pinning. In this control scheme, the network dynamics are steered towards a desired trajectory through a feedback control input that is applied stochastically to the network nodes. The network controllability is studied by analyzing the local mean square stability of the error dynamics with respect to the desired trajectory. Through the analysis of the spectral properties of salient matrices, a toolbox of conditions for controllability are obtained, in terms of the dynamics of the individual maps, algebraic properties of the network, and the probability distribution of the pinning control. We demonstrate the use of these conditions in the design of a stochastic pinning control strategy for networks of Chirikov standard maps. To elucidate the applicability of the approach, we consider different network topologies and compare five different stochastic pinning strategies through extensive numerical simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Tunable power law in the desynchronization events of coupled chaotic electronic circuits

We study the statistics of the amplitude of the synchronization error in chaotic electronic circuits coupled through linear feedback. Depending on the coupling strength, our system exhibits three qualitatively different regimes of synchronization: weak coupling yields independent oscillations; moderate to strong coupling produces a regime of intermittent synchronization known as attractor bubbling; and stronger coupling produces complete synchronization. In the regime of moderate coupling, the probability distribution for the sizes of desynchronization events follows a power law, with an exponent that can be adjusted by changing the coupling strength. Such power-law distributions are interesting, as they appear in many complex systems. However, most of the systems with such a behavior have a fixed value for the exponent of the power law, while here we present an example of a system where the exponent of the power law is easily tuned in real time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Chaoticity threshold in magnetized plasmas: Numerical results in the weak coupling regime

The present paper is a numerical counterpart to the theoretical work [Carati et al., Chaos 22, 033124 (2012)]. We are concerned with the transition from order to chaos in a one-component plasma (a system of point electrons with mutual Coulomb interactions, in a uniform neutralizing background), the plasma being immersed in a uniform stationary magnetic field. In the paper [Carati et al., Chaos 22, 033124 (2012)], it was predicted that a transition should take place when the electron density is increased or the field decreased in such a way that the ratio ω{sub p}/ω{sub c} between plasma and cyclotron frequencies becomes of order 1, irrespective of the value of the so-called Coulomb coupling parameter Γ. Here, we perform numerical computations for a first principles model of N point electrons in a periodic box, with mutual Coulomb interactions, using as a probe for chaoticity the time-autocorrelation function of magnetization. We consider two values of Γ (0.04 and 0.016) in the weak coupling regime Γ ≪ 1, with N up to 512. A transition is found to occur for ω{sub p}/ω{sub c} in the range between 0.25 and 2, in fairly good agreement with the theoretical prediction. These results might be of interest for the problem of the breakdown of plasma confinement in fusion machines.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗