A map for heavy inertial particles in fluid flows

Vilela, Rafael D.; Oliveira, Vitor M. de

doi:10.1140/epjst/e2017-70035-3

Cited by 3 publications

(2 citation statements)

References 27 publications

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“…In the function findKYDim in Lagrange2D, we use estimates of the Lyapunov exponents generated by the FTLE calculation in (2), in order to produce a timescale-dependent scalar field D t KY (x, y). In fluid flows, the Kaplan-Yorke dimension quantifies the tendency of particles to cluster within subregions of the fluid's attractor: wherever the Kaplan-Yorke dimension equals the dimensionality of the dependent variables (d = 2 here), then there is no particular tendency of trajectories to localize [14,15]. In contrast, in subregions where the Kaplan-Yorke dimension is much less than the dimension of the underlying dynamics, particles will tend to cluster and form filamentary structures.…”

Section: Kaplan-yorke Fractal Dimensionmentioning

confidence: 99%

Lagrange2D: A Mathematica package for Lagrangian analysis of two-dimensional fluid flows

Gilpin¹

2019

Preprint

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We introduce Lagrange2D, a Mathematica package for analysis and characterization of complex fluid flows using Lagrangian transport metrics. La-grange2D includes built-in functions for integrating ensembles of trajectories subject to time-varying two-dimensional flows, as well as utilities for calculating various quantities of interest, such as finite-time Lyapunov exponents, stretching vector fields, the fractal dimension, and flushing times. The package also includes tools for visualizing transport and pathlines, as well as for generating videos. This package aims to ease rapid characterization of arbitrary flows, by allowing identification of Lagrangian coherent structures and other quantities of interest. The open-source code for the package is available on GitHub at: https://github.com/williamgilpin/lagrange2d

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Section: Kaplan-yorke Fractal Dimensionmentioning

confidence: 99%

Lagrange2D: A Mathematica package for Lagrangian analysis of two-dimensional fluid flows

Gilpin¹

2019

Preprint

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“…Using the so-called snapshot attractor approach enables exploitation of a time-scale separation, thus allowing the authors identifying a short-term exponential convergence and a long-term power law behavior. A description of the transport of inertial particles is also what Vilela and Oliveira [34] are concerned with. For inertial particles denser than the carrying flow (aerosols) the authors propose an effective description of the particle advection dynamics by the so-called Stokes map.…”

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confidence: 99%

Festschrift on the occasion of Ulrike Feudel’s 60th birthday

Freund

Guseva

Grebogi

2017

Eur. Phys. J. Spec. Top.

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Since the early days of chaos theory [1,2] and complexity research [3], and the boom of results obtained since the 1980s, we have witnessed a growing body of work on the applications of nonlinear dynamics, chaos and complexity in diverse fields of science, e.g., in neuronal dynamics and brain research, or laser dynamics and excitable media in chemistry, or the dynamics of ecological populations and communities, to mention but a few. On the one hand, these applications fueled a revived interest in synchronization phenomena and control of networks. On the other hand, they inspired investigations of the effects of the coupling topology in networks where each node represents a subsystem with an intrinsic nonlinear dynamics; between the classical extremes of next neighbor coupling (diffusive) and the global all-to-all coupling (mean field) interesting new phenomena can be found such as, for instance, chimera states that have come into the focus of research recently. While chaos is often defined and observed in deterministic nonlinear dynamics, the importance of temporal fluctuations and noise is widely acknowledged and, in particular, the cooperative action of noise and nonlinearities can enrich the repertoire of dynamical phenomena and the emergence of complex structures.The European Physics Journal Special Topics (EPJST) edition at hand collects a series of articles reflecting recent advances in nonlinear dynamics and complex structures. Contributors to this issue are renowned specialists in a field belonging to nonlinear research and, in fact, some of the authors even established its foundations. While some contributions of this issue still tackle fundamental aspects of nonlinear dynamics, the majority of articles in this collection uses the arsenal of nonlinear methods to model questions belonging to a topical field. We tried to map this partition by dividing the present edition into sections.A first section on Fundamental Aspects of Nonlinear Dynamics is opened with a mini-review by Lai and Grebogi [4] whose main purpose is to argue that quasiperiodicity tends to suppress multistability, as does random noise. Through an analysis of a

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Quantitative analysis of the gain in probability of escaping for ideal phototactic swimmers due to chaotic dynamics

Grados

Vilela

2020

Phys. Rev. E

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A map for heavy inertial particles in fluid flows

Cited by 3 publications

References 27 publications

Lagrange2D: A Mathematica package for Lagrangian analysis of two-dimensional fluid flows

Lagrange2D: A Mathematica package for Lagrangian analysis of two-dimensional fluid flows

Festschrift on the occasion of Ulrike Feudel’s 60th birthday

Quantitative analysis of the gain in probability of escaping for ideal phototactic swimmers due to chaotic dynamics

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