Relevant bibliographies by topics / Finite-Scale Lyapunov Exponent

Academic literature on the topic 'Finite-Scale Lyapunov Exponent'

Author: Grafiati
Published: 11 March 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Contents

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Finite-Scale Lyapunov Exponent.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Finite-Scale Lyapunov Exponent"

1

HAN, R., M. LEMM, and W. SCHLAG. "Effective multi-scale approach to the Schrödinger cocycle over a skew-shift base." Ergodic Theory and Dynamical Systems 40, no. 10 (April 17, 2019): 2788–853. http://dx.doi.org/10.1017/etds.2019.19.

Full text
Abstract:
We prove a conditional theorem on the positivity of the Lyapunov exponent for a Schrödinger cocycle over a skew-shift base with a cosine potential and the golden ratio as frequency. For coupling below 1, which is the threshold for Herman’s subharmonicity trick, we formulate three conditions on the Lyapunov exponent in a finite but large volume and on the associated large-deviation estimates at that scale. Our main results demonstrate that these finite-size conditions imply the positivity of the infinite-volume Lyapunov exponent. This paper shows that it is possible to make the techniques developed for the study of Schrödinger operators with deterministic potentials, based on large-deviation estimates and the avalanche principle, effective.
APA, Harvard, Vancouver, ISO, and other styles
2

ANDRES, DANIELA SABRINA, DANIEL CERQUETTI, and MARCELO MERELLO. "FINITE DIMENSIONAL STRUCTURE OF THE GPI DISCHARGE IN PATIENTS WITH PARKINSON'S DISEASE." International Journal of Neural Systems 21, no. 03 (June 2011): 175–86. http://dx.doi.org/10.1142/s0129065711002778.

Full text
Abstract:
Stochastic systems are infinitely dimensional and deterministic systems are low dimensional, while real systems lie somewhere between these two limit cases. If the calculation of a low (finite) dimension is in fact possible, one could conclude that the system under study is not purely random. In the present work we calculate the maximal Lyapunov exponent from interspike intervals time series recorded from the internal segment of the Globus Pallidusfrom patients with Parkinson's disease. We show the convergence of the maximal Lyapunov exponent at a dimension equal to 7 or 8, which is therefore our estimation of the embedding dimension for the system. For dimensions below 7 the observed behavior is what would be expected from a stochastic system or a complex system projecting onto lower dimensional spaces. The maximal Lyapunov exponent did not show any differences between tremor and akineto-rigid forms of the disease. However, it did decay with the value of motor Unified Parkinson's Disease Rating Scale -OFF scores. Patients with a more severe disease (higher UPDRS-OFF score) showed a lower value of the maximal Lyapunov exponent. Taken together, both indexes (the maximal Lyapunov exponent and the embedding dimension) remark the importance of taking into consideration the system's non-linear properties for a better understanding of the information transmission in the basal ganglia.
APA, Harvard, Vancouver, ISO, and other styles
3

Siqueira, L., and B. Kirtman. "Nonlinear dynamics approach to the predictability of the Cane–Zebiak coupled ocean–atmosphere model." Nonlinear Processes in Geophysics 21, no. 1 (January 29, 2014): 155–63. http://dx.doi.org/10.5194/npg-21-155-2014.

Full text
Abstract:
Abstract. The predictability of the Cane–Zebiak coupled ocean–atmosphere model is investigated using nonlinear dynamics analysis. Newer theoretical concepts are applied to the coupled model in order to help quantify maximal prediction horizons for finite amplitude perturbations on different scales. Predictability analysis based on the maximum Lyapunov exponent considers infinitesimal perturbations, which are associated with errors in the smallest fastest-evolving scales of motion. However, these errors become irrelevant for the predictability of larger scale motions. In this study we employed finite-size Lyapunov exponent analysis to assess the predictability of the Cane–Zebiak coupled ocean–atmosphere model as a function of scale. We demonstrate the existence of fast and slow timescales, as noted in earlier studies, and the expected enhanced predictability of the anomalies on large scales. The final results and conclusions clarify the applicability of these new methods to seasonal forecasting problems.
APA, Harvard, Vancouver, ISO, and other styles
4

BozorgMagham, A. E., S. D. Ross, and D. G. Schmale. "Local finite-time Lyapunov exponent, local sampling and probabilistic source and destination regions." Nonlinear Processes in Geophysics 22, no. 6 (November 11, 2015): 663–77. http://dx.doi.org/10.5194/npg-22-663-2015.

Full text
Abstract:
Abstract. The finite-time Lyapunov exponent (FTLE) is a powerful Lagrangian concept widely used for describing large-scale flow patterns and transport phenomena. However, field experiments usually have modest scales. Therefore, it is necessary to bridge the gap between the concept of FTLE and field experiments. In this paper, two independent observations are discussed: (i) approximation of the local FTLE time series at a fixed location as a function of known distances between the destination (or source) points of released (or collected) particles and local velocity, and (ii) estimation of the distances between the destination (or source) points of the released (or collected) particles when consecutive release (or sampling) events are performed at a fixed location. These two observations lay the groundwork for an ansatz methodology that can practically assist in field experiments where consecutive samples are collected at a fixed location, and it is desirable to attribute source locations to the collected particles, and also in planning of optimal local sampling of passive particles for maximal diversity monitoring of atmospheric assemblages of microorganisms. In addition to deterministic flows, the more realistic case of unresolved turbulence and low-resolution flow data that yield probabilistic source (or destination) regions are studied. It is shown that, similar to deterministic flows, Lagrangian coherent structures (LCS) and local FTLE can describe the separation of probabilistic source (or destination) regions corresponding to consecutively collected (or released) particles.
APA, Harvard, Vancouver, ISO, and other styles
5

BozorgMagham, A. E., S. D. Ross, and D. G. Schmale III. "Local finite time Lyapunov exponent, local sampling and probabilistic source and destination regions." Nonlinear Processes in Geophysics Discussions 2, no. 3 (May 28, 2015): 903–37. http://dx.doi.org/10.5194/npgd-2-903-2015.

Full text
Abstract:
Abstract. The time-varying finite time Lyapunov exponent (FTLE) is a powerful Lagrangian concept widely used for describing large-scale flow patterns and transport phenomena. However, field experiments usually have modest scales. Therefore, it is necessary to bridge between the powerful concept of FTLE and (local) field experiments. In this paper a new interpretation of the local FTLE, the time series of a FTLE field at a fixed location, is proposed. This concept can practically assist in field experiments where samples are collected at a fixed location and it is necessary to attribute long distance transport phenomena and location of source points to the characteristic variation of the sampled particles. Also, results of this study have the potential to aid in planning of optimal local sampling of passive particles for maximal diversity monitoring of assemblages of microorganisms. Assuming a deterministic flow field, one can use the proposed theorem to (i) estimate the differential distances between the source (or destination) points of the collected (or released) particles when consecutive sampling (or releasing) is performed at a fixed location, (ii) estimate the local FTLE as a function of known differential distances between the source (or destination) points. In addition to the deterministic flows, the more realistic case of unresolved turbulence and low resolution flow data that yield the probabilistic source (or destination) regions are studied. It is shown that similar to deterministic flows, Lagrangian coherent structures (LCS) separate probabilistic source (or destination) regions corresponding to consecutive collected (or released) particles.
APA, Harvard, Vancouver, ISO, and other styles
6

Hidayat, A. M., U. Efendi, R. H. Virgianto, and H. A. Nugroho. "Examining optimum prediction time of rainfall dynamics based on chaotic perspective at different temporal scales: a case study in Bojonegoro, Indonesia." IOP Conference Series: Earth and Environmental Science 893, no. 1 (November 1, 2021): 012024. http://dx.doi.org/10.1088/1755-1315/893/1/012024.

Full text
Abstract:
Abstract As the driving force of the hydrological system, rain has severe impact when dealing with petroleum mining activities, especially in protecting assets and safety. Rainfall has high variability, both spatial and temporal (chaotic data). Due to this reason, ones can only create long-range prediction using the stochastic method. Here we use the Lyapunov exponent to analyze the nonlinear pattern of rainfall dynamics. This method is useful for identifying chaotic deportment in rainfall data. This study uses rainfall data for six years obtained from one of the largest petroleum mining sites in Bojonegoro, Indonesia. Rainfall dynamics have been analyzed on three different time scales, namely daily data, 5-day, and 10-day. The time delay (τ) was obtained by using the Average Mutual Information (AMI) method for the three-rainfall series (3, 2, 3, respectively). The observed rainfall data in Bojonegoro show signs of chaos as the finite correlation dimensions (m) attain values about 4 for all time scales. The maximum Lyapunov exponent λmax for each of three-rainfall series in Bojonegoro is 0.111, 0.057, 0.062, respectively. These values were analyzed to find the optimum prediction time of rainfall occurrence to perform better forecasting. The result shows that the optimum range of prediction time for daily, 5-day, and 10-day have 9, 18, and 16 times longer than their temporal scale.
APA, Harvard, Vancouver, ISO, and other styles
7

Lacorata, G., E. Aurell, and A. Vulpiani. "Drifter dispersion in the Adriatic Sea: Lagrangian data and chaotic model." Annales Geophysicae 19, no. 1 (January 31, 2001): 121–29. http://dx.doi.org/10.5194/angeo-19-121-2001.

Full text
Abstract:
Abstract. We analyze characteristics of drifter trajectories from the Adriatic Sea with recently introduced nonlinear dynamics techniques. We discuss how in quasi-enclosed basins, relative dispersion as a function of time, a standard analysis tool in this context, may give a distorted picture of the dynamics. We further show that useful information may be obtained by using two related non-asymptotic indicators, the Finite-Scale Lyapunov Exponent (FSLE) and the Lagrangian Structure Function (LSF), which both describe intrinsic physical properties at a given scale. We introduce a simple chaotic model for drifter motion in this system, and show by comparison with the model that Lagrangian dispersion is mainly driven by advection at sub-basin scales until saturation sets in.Key words. Oceanography: General (marginal and semi-closed seas) – Oceanography: Physical (turbulence, diffusion, and mixing processes; upper ocean processes)
APA, Harvard, Vancouver, ISO, and other styles
8

El Hassan, Mouhammad, and David S. Nobes. "Experimental Investigation of the Vortex Dynamics in Circular Jet Impinging on Rotating Disk." Fluids 7, no. 7 (July 1, 2022): 223. http://dx.doi.org/10.3390/fluids7070223.

Full text
Abstract:
A circular jet impinging perpendicularly onto a rotating disk is studied in order to understand the influence of centrifugal forces on the radial wall jet. Time-resolved Particle Image Velocimetry (TR-PIV) measurements are conducted in different jet regions in order to investigate the flow physics of the large-scale vortical structures and the boundary layer development on the impinging wall for both stationary and rotating impinging disks. The Reynolds number is ReD = 2480, the orifice-to-plate distance H = 4D (D is the jet-orifice diameter) and the rotation rate is 200 RPM. It is found that the rotation of the impinging wall results in strong centrifugal effects, which affect different regions of the jet. Both radial velocity profiles and turbulence intensity distributions show different behavior when comparing the stationary and rotating cases. Finite Time Lyapunov Exponent (FTLE) analysis is implemented to describe the time-resolved behavior of the large-scale vortical structures and flow separation.
APA, Harvard, Vancouver, ISO, and other styles
9

Liu, Jian, and Xiangzhe Zhu. "Chaotic mixing analysis of a novel single-screw extruder with a perturbation baffle by the finite-time Lyapunov exponent method." Journal of Polymer Engineering 39, no. 3 (February 25, 2019): 287–99. http://dx.doi.org/10.1515/polyeng-2018-0037.

Full text
Abstract:
Abstract The single-screw extruder with a perturbation baffle is a novel piece of equipment for polymer processing, in which the polymer melts undergo complex chaotic mixing. In this paper, from a new Lagrangian perspective, the fluid transporting mechanism in chaotic flow of the unwound screw channel was analyzed based on the finite element method. Firstly, two-dimensional velocity distributions in the unwound screw channel were calculated based on the mesh superposition technique. Fluid particle evolution processes in the extruder were tracked based on the fourth-order Runge-Kutta scheme. The numerical method used in this paper was validated by grid independence and experiments obtained from literature. Moreover, the finite-time Lyapunov exponent (FTLE) and Poincaré sections were adopted to discuss the chaotic mixing in the novel single-screw extruder. The effects of baffle width and height on the manifold structures in the flow dynamic system were analyzed. The results show that the homoclinic point of the manifold structure can give rise to chaotic mixing in the single-screw extruder. The height of the baffle is an important parameter to control the chaotic strength. In a way, increasing the height of the baffle can enlarge the kink scale and increase the stretching and folding actions, which results in the decrease of regular regions and an increase of the mixing efficiency in the single-screw extruder.
APA, Harvard, Vancouver, ISO, and other styles
10

Lacorata, Guglielmo, Erik Aurell, Bernard Legras, and Angelo Vulpiani. "Evidence for a k−5/3 Spectrum from the EOLE Lagrangian Balloons in the Low Stratosphere." Journal of the Atmospheric Sciences 61, no. 23 (December 1, 2004): 2936–42. http://dx.doi.org/10.1175/jas-3292.1.

Full text
Abstract:
Abstract The EOLE experiment is revisited to study turbulent processes in the lower stratosphere circulation from a Lagrangian viewpoint and to resolve a discrepancy on the slope of the atmospheric energy spectrum between the work of Morel and Larchevêque and recent studies using aircraft data. Relative dispersion of balloon pairs is studied by calculating the finite-scale Lyapunov exponent, an exit-time-based technique that is particularly efficient in cases in which processes with different spatial scales are interfering. The main goal is to reconciliate the EOLE dataset with recent studies supporting a k−5/3 energy spectrum in the 100–1000-km range. The results also show exponential separation at smaller scales, with a characteristic time of order 1 day, and agree with the standard diffusion of about 107 m2 s−1 at large scales. A remaining question is the origin of a k−5/3 spectrum in the mesoscale range between 100 and 1000 km.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Conference papers on the topic "Finite-Scale Lyapunov Exponent"

1

Winhart, Benjamin, Martin Sinkwitz, Andreas Schramm, Pascal Post, and Francesca di Mare. "Large Eddy Simulation of Periodic Wake Impact on Boundary Layer Transition Mechanisms on a Highly Loaded Low-Pressure Turbine Blade." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-14555.

Full text
Abstract:
Abstract In the proposed paper the transient interaction between periodic incoming wakes and the laminar separation bubble located on the rear suction surface of a typical, highly loaded LPT blade is investigated by means of highly resolved large-eddy simulations. An annular, large scale, 1.5-stage LPT test-rig, equipped with a modified T106 turbine blading and an upstream rotating vortex generator is considered and the numerical predictions are compared against hot film array measurements. In order to accurately assess both baseline transition and wake impact, simulations were conducted with unperturbed and periodically perturbed inflow conditions. Main mechanisms of transition and wake-boundary layer interaction are investigated utilizing a frequency-time domain analysis. Finally visualizations of the main flow structures and shear layer instabilities are provided utilizing the q-criterion as well as the finite-time Lyapunov exponent.
APA, Harvard, Vancouver, ISO, and other styles
2

Attiya, Bashar, I.-Han Liu, Muhannad Altimemy, Cosan Daskiran, and Alparslan Oztekin. "Investigation of Three-Dimensional Lagrangian Coherent Structures in Flow Past Single and Arrays of Plate: Linear Energy Harvesting Applications." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86332.

Full text
Abstract:
Large Eddy Simulations (LES) are performed to investigate the coherent structures in flows past a single and an array of tandem plates. Lagrangian coherent structures (LCS) are used to investigate the nonlinear vortex dynamics of flow past a single plate. The Finite-Time Lyapunov Exponent (FTLE) is calculated using the velocity data obtained from Large Eddy Simulations (LES). All simulations are conducted at Reynolds number of 50,000. LCS for a single plate is presented in this study to elucidate and comprehend highly turbulent flow interactions in these flows. The LCS is compared against most commonly used Eulerian structures which are contours of the vorticity and the Q-criterion. The FTLE fields reveal much clearer turbulent structures compared to the Eulerian structures. FTLE better describes the evolution of larger scale eddies. The Q-criterion of flows past an array of plates is also presented.
APA, Harvard, Vancouver, ISO, and other styles
3

Sampath, Ramgopal, and S. R. Chakravarthy. "Effect of Acoustic Feedback on Lagrangian Coherent Structures in a Backward Facing Step Combustor With a Partially Premixed Flame." In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gt2017-64856.

Full text
Abstract:
The thermoacoustic oscillations of a partially premixed flame stabilized in a backward facing step combustor are studied at a constant equivalence ratio in long and short combustor configurations corresponding to with and without acoustic feedback respectively. We perform simultaneous time-resolved particle image velocimetry (TR-PIV) and chemiluminescence for selected flow conditions based on the acoustic characterization in the long combustor. The acoustic characterization shows a transition in the dominant pressure amplitudes from low to high magnitudes with an increase in the inlet flow Reynolds number. This is accompanied by a shift in the dominant frequencies. For the intermittent pressure oscillations in the long combustor, the wavelet analysis indicates a switch between the acoustic and vortex modes with silent zones of relatively low-pressure amplitudes. The short combustor configuration indicates the presence of the vortex shedding frequency and an additional band comprising the Kelvin Helmholtz mode. Next, we apply the method of finite-time Lyapunov exponent (FTLE) to the time-resolved velocity fields to extract features of the Lagrangian coherent structures (LCS) of the flow. In the long combustor post transition with the time instants with dominant acoustic mode, a large-scale modulation of the FTLE boundaries over one cycle of pressure oscillation is evident. Further, the FTLEs and the flame boundaries align each other for all phases of the pressure oscillation. In the short combustor, the FTLEs indicate the presence of small wavelength waviness that overrides the large-scale vortex structure, which corresponds to the vortex shedding mode. This behaviour contrasts with the premixed flame in the short combustor reported earlier in which such large scales were found to be seldom present. The presence of the large-scale structures even in the absence of acoustic feedback in a partially premixed flame signifies its inherent unstable nature leading to large pressure amplitudes during acoustic feedback. Lastly, the FTLE boundaries provide the frequency information of the identified coherent structure and also acts as the surrogate flame boundaries that are estimated from just the velocity fields.
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Finite-Scale Lyapunov Exponent' for particular source types:
Journal articles
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography