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Parker R, Capobianchi P, Lappa M. Competing particle attractee in liquid bridges. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220302. [PMID: 36842985 PMCID: PMC9968533 DOI: 10.1098/rsta.2022.0302] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/23/2022] [Accepted: 12/19/2022] [Indexed: 06/18/2023]
Abstract
Assuming the so-called particle accumulation structures (PAS) in liquid bridges as archetypal systems for the investigation of particle self-assembly phenomena in laminar time-periodic flows, an attempt is made here to disentangle the complex hierarchy of relationships existing between the multiplicity of the loci of aggregation (streamtubes which coexist in the physical space as competing attractee) and the particle structures effectively showing up. While the former depends on purely topological (fluid-dynamic) arguments, the influential factors driving the outcomes of the fluid-particle interaction seem to obey a much more complex logic, which makes the arrangement of particles different from realization to realization. Through numerical solution of the governing Eulerian and Lagrangian equations for liquid and mass transport, we show that for a fixed aspect ratio of the liquid bridge, particles can be gradually transferred from one streamtube to another as the Stokes number and/or the Marangoni number are varied. Moreover, ranges exist where these attractors compete resulting in overlapping or intertwined particle structures, some of which, characterized by a strong degree of asymmetry, have never been reported before. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.
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Affiliation(s)
- Robert Parker
- Department of Mechanical and Aerospace Engineering, University of Strathclyde, James Weir Building, 75 Montrose Street, Glasgow G1 1XJ, UK
| | - Paolo Capobianchi
- Department of Mechanical and Aerospace Engineering, University of Strathclyde, James Weir Building, 75 Montrose Street, Glasgow G1 1XJ, UK
| | - Marcello Lappa
- Department of Mechanical and Aerospace Engineering, University of Strathclyde, James Weir Building, 75 Montrose Street, Glasgow G1 1XJ, UK
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2
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Venditti C, Giona M, Adrover A. Invariant manifold approach for quantifying the dynamics of highly inertial particles in steady and time-periodic incompressible flows. CHAOS (WOODBURY, N.Y.) 2022; 32:023121. [PMID: 35232041 DOI: 10.1063/5.0081556] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2021] [Accepted: 01/24/2022] [Indexed: 06/14/2023]
Abstract
The dynamics of finite-sized particles with large inertia are investigated in steady and time-dependent flows through the numerical solution of the invariance equation, describing the spatiotemporal evolution of the slow/inertial manifold representing the effective particle velocity field. This approach allows for an accurate reconstruction of the effective particle divergence field, controlling clustering/dispersion features of particles with large inertia for which a perturbative approach is either inaccurate or not even convergent. The effect of inertia on heavy and light particles is quantified in terms of the rate of contraction/expansion of volume elements along a particle trajectory and of the maximum Lyapunov exponent for systems exhibiting chaotic orbits, such as the time-periodic sine-flow on the 2D torus and the time-dependent 2D cavity flow.
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Affiliation(s)
- Claudia Venditti
- Dipartimento di Ingegneria Chimica Materiali Ambiente, Sapienza Università di Roma, Via Eudossiana 18, 00184 Roma, Italy
| | - Massimiliano Giona
- Dipartimento di Ingegneria Chimica Materiali Ambiente, Sapienza Università di Roma, Via Eudossiana 18, 00184 Roma, Italy
| | - Alessandra Adrover
- Dipartimento di Ingegneria Chimica Materiali Ambiente, Sapienza Università di Roma, Via Eudossiana 18, 00184 Roma, Italy
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3
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Inertial diffusivity of non-colloidal particles in unbounded suspending media and numerical simulations. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.117471] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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4
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Abstract
A small spherical rigid particle in a cylindrical cavity is considered. The harmonic rotation of the cavity wall drives the background flow characterized by the Strouhal number Str, assumed as the first parameter of our investigation. The particle immersed in the flow (assumed Stokesian) has a Stokes number St=1 and a particle-to-fluid density ratio ϱ which is assumed as the second parameter of this study. Building on the theoretical understanding of the recently discovered oscillatory switching centrifugation for inertial particles in unbounded flows, we investigate the effect of a confinement. For the first time we study how the presence of a wall affects the particle trajectory in oscillatory switching centrifugation dynamics. The emergence of two qualitatively different particle attractors is characterized for particles centrifuged towards the cavity wall. The implication of two such classes of attractors is discussed focusing on the application to microfluidics. We propose some strategies for exploiting the confined oscillatory switching centrifugation for selective particle segregation and for the enhancement of particle interaction events.
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Cartwright JHE, Piro O. The fluid mechanics of poohsticks. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190522. [PMID: 32762437 DOI: 10.1098/rsta.2019.0522] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 06/17/2020] [Indexed: 06/11/2023]
Abstract
The year 2019 marked the bicentenary of George Gabriel Stokes, who in 1851 described the drag-Stokes drag-on a body moving immersed in a fluid, and 2020 is the centenary of Christopher Robin Milne, for whom the game of poohsticks was invented; his father A. A. Milne's The House at Pooh Corner, in which it was first described in print, appeared in 1928. So this is an apt moment to review the state of the art of the fluid mechanics of a solid body in a complex fluid flow, and one floating at the interface between two fluids in motion. Poohsticks pertains to the latter category, when the two fluids are water and air. This article is part of the theme issue 'Stokes at 200 (part 2)'.
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Affiliation(s)
- Julyan H E Cartwright
- Instituto Andaluz de Ciencias de la Tierra, CSIC-Universidad de Granada, 18100 Armilla, Granada, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain
| | - Oreste Piro
- Departament de Física, Universitat de les Illes Balears, 07071 Palma de Mallorca, Spain
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6
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Grados AJ, Vilela RD. Quantitative analysis of the gain in probability of escaping for ideal phototactic swimmers due to chaotic dynamics. Phys Rev E 2020; 101:052617. [PMID: 32575183 DOI: 10.1103/physreve.101.052617] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2020] [Accepted: 04/15/2020] [Indexed: 06/11/2023]
Abstract
We study the dynamics of ideal phototactic swimmers in a steady two-dimensional model flow with transport barriers. We consider a distant light source, in which case the self-propulsion velocity of the swimmers is, at any instant, along a predetermined direction. The probability of transport along that direction emerges from the competing effects of the swimmers' self-propulsion and the flow's transport barriers. For swimmers bounded to have the same time average self-propulsion speed, temporal modulation of that speed increases the probability of escaping due to the formation of a stochastic layer which fosters transport. We use separatrix-map techniques to calculate the gain in the probability of escaping.
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Affiliation(s)
- Alfredo J Grados
- Centro de Matemática, Computação e Cognição, UFABC, Santo André, SP, Brazil
| | - Rafael D Vilela
- Centro de Matemática, Computação e Cognição, UFABC, Santo André, SP, Brazil
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7
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Borgnino M, Arrieta J, Boffetta G, De Lillo F, Tuval I. Turbulence induces clustering and segregation of non-motile, buoyancy-regulating phytoplankton. J R Soc Interface 2019; 16:20190324. [PMID: 31640498 PMCID: PMC6833313 DOI: 10.1098/rsif.2019.0324] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2019] [Accepted: 10/01/2019] [Indexed: 11/12/2022] Open
Abstract
Turbulence plays a major role in shaping marine community structure as it affects organism dispersal and guides fundamental ecological interactions. Below oceanographic mesoscale dynamics, turbulence also impinges on subtle physical-biological coupling at the single cell level, setting a sea of chemical gradients and determining microbial interactions with profound effects on scales much larger than the organisms themselves. It has been only recently that we have started to disentangle details of this coupling for swimming microorganisms. However, for non-motile species, which comprise some of the most abundant phytoplankton groups on Earth, a similar level of mechanistic understanding is still missing. Here, we explore by means of extensive numerical simulations the interplay between buoyancy regulation in non-motile phytoplankton and cellular responses to turbulent mechanical cues. Using a minimal mechano-response model, we show how such a mechanism would contribute to spatial heterogeneity and affect vertical fluxes and trigger community segregation.
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Affiliation(s)
- Matteo Borgnino
- Department of Physics and INFN, Università di Torino, via P. Giuria 1, Torino 10125, Italy
| | - Jorge Arrieta
- Instituto Mediterráneo de Estudios Avanzados, IMEDEA, UIB-CSIC, Esporles 07190, Spain
| | - Guido Boffetta
- Department of Physics and INFN, Università di Torino, via P. Giuria 1, Torino 10125, Italy
| | - Filippo De Lillo
- Department of Physics and INFN, Università di Torino, via P. Giuria 1, Torino 10125, Italy
| | - Idan Tuval
- Instituto Mediterráneo de Estudios Avanzados, IMEDEA, UIB-CSIC, Esporles 07190, Spain
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Martins Afonso M, Gama SMA. Point-source dispersion of quasi-neutrally-buoyant inertial particles. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:10. [PMID: 30684095 DOI: 10.1140/epje/i2019-11771-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2018] [Accepted: 01/04/2019] [Indexed: 06/09/2023]
Abstract
We analyze the evolution of the distribution, both in the phase space and in the physical space, of inertial particles released by a spatially-localized (punctual) source and advected by an incompressible flow. The difference in mass density between fluid and particles is assumed to be small, and represents the basic parameter for a regular perturbative expansion. By means of analytical techniques such as Hermitianization, we derive a chain of equations of the advection-diffusion-reaction type, easily solvable at least numerically. Our procedure provides results also for finite particle inertia, away from the over-damped limit of quasi-tracer dynamics.
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Affiliation(s)
- Marco Martins Afonso
- Centro de Matemática da Universidade do Porto, Rua do Campo Alegre 687, 4169-007, Porto, Portugal.
| | - Sílvio M A Gama
- Centro de Matemática da Universidade do Porto, Rua do Campo Alegre 687, 4169-007, Porto, Portugal
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9
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Particle slip velocity influences inertial focusing of particles in curved microchannels. Sci Rep 2018; 8:11852. [PMID: 30087382 PMCID: PMC6081444 DOI: 10.1038/s41598-018-30171-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2017] [Accepted: 07/12/2018] [Indexed: 11/18/2022] Open
Abstract
Size based separation and identification of particles in microfluidics through purely hydrodynamic means has gained significant interest due to a number of possible biomedical applications. Curved micro-channels, particularly spiral micro-channels with rectangular cross-section and the dynamics of particles in such channels have been extensively researched to achieve size based separation of particles. In this paper we present evidence that sheds new light on the dynamics of particles in such curved channels; that a unique particle slip velocity is associated with the focusing positions in the cross sections, which leads to a balance of forces. Our experiments therefore imply that the forces acting on the particle lead to convergence to an attractor in both the physical space (the cross section of the channel) and the slip velocity space.
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10
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Das S, Gupte N. Transport, diffusion, and energy studies in the Arnold-Beltrami-Childress map. Phys Rev E 2018; 96:032210. [PMID: 29346902 DOI: 10.1103/physreve.96.032210] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2017] [Indexed: 11/07/2022]
Abstract
We study the transport and diffusion properties of passive inertial particles described by a six-dimensional dissipative bailout embedding map. The base map chosen for the study is the three-dimensional incompressible Arnold-Beltrami-Childress (ABC) map chosen as a representation of volume preserving flows. There are two distinct cases: the two-action and the one-action cases, depending on whether two or one of the parameters (A,B,C) exceed 1. The embedded map dynamics is governed by two parameters (α,γ), which quantify the mass density ratio and dissipation, respectively. There are important differences between the aerosol (α<1) and the bubble (α>1) regimes. We have studied the diffusive behavior of the system and constructed the phase diagram in the parameter space by computing the diffusion exponents η. Three classes have been broadly classified-subdiffusive transport (η<1), normal diffusion (η≈1), and superdiffusion (η>1) with η≈2 referred to as the ballistic regime. Correlating the diffusive phase diagram with the phase diagram for dynamical regimes seen earlier, we find that the hyperchaotic bubble regime is largely correlated with normal and superdiffusive behavior. In contrast, in the aerosol regime, ballistic superdiffusion is seen in regions that largely show periodic dynamical behaviors, whereas subdiffusive behavior is seen in both periodic and chaotic regimes. The probability distributions of the diffusion exponents show power-law scaling for both aerosol and bubbles in the superdiffusive regimes. We further study the Poincáre recurrence times statistics of the system. Here, we find that recurrence time distributions show power law regimes due to the existence of partial barriers to transport in the phase space. Moreover, the plot of average particle kinetic energies versus the mass density ratio for the two-action case exhibits a devil's staircase-like structure for higher dissipation values. We explain these results and discuss their implications for realistic systems.
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Affiliation(s)
- Swetamber Das
- Department of Physics, Indian Institute of Technology Madras, Chennai, 600036, India
| | - Neelima Gupte
- Department of Physics, Indian Institute of Technology Madras, Chennai, 600036, India
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11
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Gunther T, Theisel H. Backward Finite-Time Lyapunov Exponents in Inertial Flows. IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2017; 23:970-979. [PMID: 27875210 DOI: 10.1109/tvcg.2016.2599016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Inertial particles are finite-sized objects that are carried by fluid flows and in contrast to massless tracer particles they are subject to inertia effects. In unsteady flows, the dynamics of tracer particles have been extensively studied by the extraction of Lagrangian coherent structures (LCS), such as hyperbolic LCS as ridges of the Finite-Time Lyapunov Exponent (FTLE). The extension of the rich LCS framework to inertial particles is currently a hot topic in the CFD literature and is actively under research. Recently, backward FTLE on tracer particles has been shown to correlate with the preferential particle settling of small inertial particles. For larger particles, inertial trajectories may deviate strongly from (massless) tracer trajectories, and thus for a better agreement, backward FTLE should be computed on inertial trajectories directly. Inertial backward integration, however, has not been possible until the recent introduction of the influence curve concept, which - given an observation and an initial velocity - allows to recover all sources of inertial particles as tangent curves of a derived vector field. In this paper, we show that FTLE on the influence curve vector field is in agreement with preferential particle settling and more importantly it is not only valid for small (near-tracer) particles. We further generalize the influence curve concept to general equations of motion in unsteady spatio-velocity phase spaces, which enables backward integration with more general equations of motion. Applying the influence curve concept to tracer particles in the spatio-velocity domain emits streaklines in massless flows as tangent curves of the influence curve vector field. We demonstrate the correlation between inertial backward FTLE and the preferential particle settling in a number of unsteady vector fields.
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12
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Aparicio Medrano E, van de Wiel B, Uittenbogaard R, Dionisio Pires L, Clercx H. Simulations of the diurnal migration of Microcystis aeruginosa based on a scaling model for physical-biological interactions. Ecol Modell 2016. [DOI: 10.1016/j.ecolmodel.2016.06.019] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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13
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Pérez-Muñuzuri V, Garaboa-Paz D, Muñuzuri AP. Nonperfect mixing affects synchronization on a large number of chemical oscillators immersed in a chemically active time-dependent chaotic flow. Phys Rev E 2016; 94:013103. [PMID: 27575213 DOI: 10.1103/physreve.94.013103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2016] [Indexed: 06/06/2023]
Abstract
The problem of synchronization of finite-size chemical oscillators described by active inertial particles is addressed for situations in which they are immersed in a reacting nonstationary chaotic flow. Active substances in the fluid will be modeled by Lagrangian particles closely following the fluid streamlines. Their interaction with the active inertial particles as well as the properties of the fluid dynamics will result in modifying the synchronization state of the chemical oscillators. This behavior is studied in terms of the exchange rate between the Lagrangian and inertial particles, and the finite-time Lyapunov exponents characterizing the flow. The coherence of the population of oscillators is determined by means of the order parameter introduced by Kuramoto. The different dynamics observed for the inertial particles (chemical oscillators) and Lagrangian particles (describing chemicals in the flow) lead to nonlinear interactions and patches of synchronized regions within the domain.
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Affiliation(s)
- V Pérez-Muñuzuri
- Group of Nonlinear Physics, Faculty of Physics, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain
| | - D Garaboa-Paz
- Group of Nonlinear Physics, Faculty of Physics, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain
| | - A P Muñuzuri
- Group of Nonlinear Physics, Faculty of Physics, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain
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14
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Sudharsan M, Brunton SL, Riley JJ. Lagrangian coherent structures and inertial particle dynamics. Phys Rev E 2016; 93:033108. [PMID: 27078448 DOI: 10.1103/physreve.93.033108] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2015] [Indexed: 06/05/2023]
Abstract
In this work we investigate the dynamics of inertial particles using finite-time Lyapunov exponents (FTLE). In particular, we characterize the attractor and repeller structures underlying preferential concentration of inertial particles in terms of FTLE fields of the underlying carrier fluid. Inertial particles that are heavier than the ambient fluid (aerosols) attract onto ridges of the negative-time fluid FTLE. This negative-time FTLE ridge becomes a repeller for particles that are lighter than the carrier fluid (bubbles). We also examine the inertial FTLE (iFTLE) determined by the trajectories of inertial particles evolved using the Maxey-Riley equations with nonzero Stokes number and density ratio. Finally, we explore the low-pass filtering effect of Stokes number. These ideas are demonstrated on two-dimensional numerical simulations of the unsteady double-gyre flow.
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Affiliation(s)
- M Sudharsan
- Department of Applied Mathematics, University of Washington, Seattle, Washington 98195-3925, USA
| | - Steven L Brunton
- Department of Applied Mathematics, University of Washington, Seattle, Washington 98195-3925, USA
- Department of Mechanical Engineering, University of Washington, Seattle, Washington 98195-2420, USA
| | - James J Riley
- Department of Applied Mathematics, University of Washington, Seattle, Washington 98195-3925, USA
- Department of Mechanical Engineering, University of Washington, Seattle, Washington 98195-2420, USA
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Pérez-Muñuzuri V. Clustering of inertial particles in compressible chaotic flows. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052906. [PMID: 26066228 DOI: 10.1103/physreve.91.052906] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2014] [Indexed: 06/04/2023]
Abstract
Clustering of inertial particles is analyzed in chaotic compressible flows. A simplified dynamical model for the motion of inertial particles in a compressible flow has been derived. Clustering enhancement has been observed for intermediate Stokes times and characterized in terms of the number of particles with negative finite-time Lyapunov exponents and the Lyapunov dimension of the model attractor. Cluster formation has been observed to depend on the nature of the flow; vortical or shear. The motion of heavy and light particles is analyzed in terms of the compressibility and correlation length of the density field.
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Affiliation(s)
- Vicente Pérez-Muñuzuri
- Group of Nonlinear Physics, Faculty of Physics, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain
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16
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Arrieta J, Barreira A, Tuval I. Microscale patches of nonmotile phytoplankton. PHYSICAL REVIEW LETTERS 2015; 114:128102. [PMID: 25860773 DOI: 10.1103/physrevlett.114.128102] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2014] [Indexed: 06/04/2023]
Abstract
Phytoplankton cells have evolved sophisticated strategies for actively responding to environmental signals, most notably to mechanical stresses of hydrodynamic origin. A largely unanswered question, however, is the significance of these cellular responses for the largely heterogeneous spatial distribution of cells found in the oceans. Motivated by the physiological regulation of buoyancy prevalent in nonmotile phytoplankton species, we solve here a minimal model for "active" sinking that incorporates these cellular responses. Within this model, we show how buoyancy regulation leads to intense patchiness for nonmotile species as compared to passive tracers, resulting in important variations in settling speeds and, as a consequence, determining escape rates to the deep ocean.
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Affiliation(s)
- Jorge Arrieta
- Área de Mecánica de Fluidos, Universidad Carlos III de Madrid, Madrid, Spain
- Instituto Mediterráneo de Estudios Avanzados, IMEDEA, UIB-CSIC, Esporles, Spain
| | - Ana Barreira
- Instituto Mediterráneo de Estudios Avanzados, IMEDEA, UIB-CSIC, Esporles, Spain
| | - Idan Tuval
- Instituto Mediterráneo de Estudios Avanzados, IMEDEA, UIB-CSIC, Esporles, Spain
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17
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Ben-Bassat D, Boymelgreen A, Yossifon G. The influence of flow intensity and field frequency on continuous-flow dielectrophoretic trapping. J Colloid Interface Sci 2015; 442:154-61. [DOI: 10.1016/j.jcis.2014.11.037] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2014] [Revised: 11/12/2014] [Accepted: 11/16/2014] [Indexed: 12/15/2022]
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18
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Das S, Gupte N. Dynamics of impurities in a three-dimensional volume-preserving map. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:012906. [PMID: 25122359 DOI: 10.1103/physreve.90.012906] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2013] [Indexed: 06/03/2023]
Abstract
We study the dynamics of inertial particles in three-dimensional incompressible maps, as representations of volume-preserving flows. The impurity dynamics has been modeled, in the Lagrangian framework, by a six-dimensional dissipative bailout embedding map. The fluid-parcel dynamics of the base map is embedded in the particle dynamics governed by the map. The base map considered for the present study is the Arnold-Beltrami-Childress (ABC) map. We consider the behavior of the system both in the aerosol regime, where the density of the particle is larger than that of the base flow, as well as the bubble regime, where the particle density is less than that of the base flow. The phase spaces in both the regimes show rich and complex dynamics with three types of dynamical behaviors--chaotic structures, regular orbits, and hyperchaotic regions. In the one-action case, the aerosol regime is found to have periodic attractors for certain values of the dissipation and inertia parameters. For the aerosol regime of the two-action ABC map, an attractor merging and widening crisis is identified using the bifurcation diagram and the spectrum of Lyapunov exponents. After the crisis an attractor with two parts is seen, and trajectories hop between these parts with period 2. The bubble regime of the embedded map shows strong hyperchaotic regions as well as crisis induced intermittency with characteristic times between bursts that scale as a power law behavior as a function of the dissipation parameter. Furthermore, we observe a riddled basin of attraction and unstable dimension variability in the phase space in the bubble regime. The bubble regime in the one-action case shows similar behavior. This study of a simple model of impurity dynamics may shed light upon the transport properties of passive scalars in three-dimensional flows. We also compare our results with those seen earlier in two-dimensional flows.
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Affiliation(s)
- Swetamber Das
- Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
| | - Neelima Gupte
- Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
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19
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Crimaldi JP, Zimmer RK. The physics of broadcast spawning in benthic invertebrates. ANNUAL REVIEW OF MARINE SCIENCE 2013; 6:141-165. [PMID: 23957600 DOI: 10.1146/annurev-marine-010213-135119] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Most benthic invertebrates broadcast their gametes into the sea, whereupon successful fertilization relies on the complex interaction between the physics of the surrounding fluid flow and the biological properties and behavior of eggs and sperm. We present a holistic overview of the impact of instantaneous flow processes on fertilization across a range of scales. At large scales, transport and stirring by the flow control the distribution of gametes. Although mean dilution of gametes by turbulence is deleterious to fertilization, a variety of instantaneous flow phenomena can aggregate gametes before dilution occurs. We argue that these instantaneous flow processes are key to fertilization efficiency. At small scales, sperm motility and taxis enhance contact rates between sperm and chemoattractant-releasing eggs. We argue that sperm motility is a biological adaptation that replaces molecular diffusion in conventional mixing processes and enables gametes to bridge the gap that remains after aggregation by the flow.
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Affiliation(s)
- John P Crimaldi
- Department of Civil, Environmental, and Architectural Engineering, University of Colorado, Boulder, Colorado 80309-0428;
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20
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Hamidi S, Rostamiyan Y, Ganji D, Fereidoon A. A novel and developed approximation for motion of a spherical solid particle in plane coquette fluid flow. ADV POWDER TECHNOL 2013. [DOI: 10.1016/j.apt.2012.11.003] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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21
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Hamidi S, Rostamiyan Y, Ganji D, Fereidoon A. WITHDRAWN: A novel and developed approximation for motion of a spherical solid particle in plane coquette fluid flow. ADV POWDER TECHNOL 2013. [DOI: 10.1016/j.apt.2013.02.008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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22
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WITHDRAWN: A novel and developed approximation for motion of a spherical solid particle in plane coquette fluid flow. ADV POWDER TECHNOL 2012. [DOI: 10.1016/j.apt.2012.07.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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23
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Crimaldi JP. The role of structured stirring and mixing on gamete dispersal and aggregation in broadcast spawning. J Exp Biol 2012; 215:1031-9. [DOI: 10.1242/jeb.060145] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
Summary
Broadcast-spawning benthic invertebrates synchronously release sperm and eggs from separate locations into the surrounding flow, whereupon the process depends on structured stirring by the flow field (at large scales), and sperm motility and taxis (at small scales) to bring the gametes together. The details of the relevant physical and biological aspects of the problem that result in successful and efficient fertilization are not well understood. This review paper includes relevant work from both the physical and biological communities to synthesize a more complete understanding of the processes that govern fertilization success; the focus is on the role of structured stirring on the dispersal and aggregation of gametes. The review also includes a summary of current trends and approaches for numerical and experimental simulations of broadcast spawning.
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24
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Daitche A, Tél T. Memory effects are relevant for chaotic advection of inertial particles. PHYSICAL REVIEW LETTERS 2011; 107:244501. [PMID: 22243003 DOI: 10.1103/physrevlett.107.244501] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2011] [Indexed: 05/31/2023]
Abstract
A systematic investigation of the effect of the history force on particle advection is carried out in a paradigmatic model flow of chaotic advection, the von Kármán flow. All investigated properties turn out to heavily depend on the presence of memory when compared to previous studies neglecting this force. We find a weaker tendency for accumulation and for caustics formation. The Lyapunov exponent of transients becomes larger, the escape rates are strongly altered. Attractors are found to be suppressed by the history force, and periodic ones have a very slow, t(-1/2)-type convergence towards the asymptotic form.
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Affiliation(s)
- Anton Daitche
- Institute for Theoretical Physics, Münster University, Wilhelm-Klemm-Straße 9, D-48149 Münster, Germany
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25
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Khurana N, Blawzdziewicz J, Ouellette NT. Reduced transport of swimming particles in chaotic flow due to hydrodynamic trapping. PHYSICAL REVIEW LETTERS 2011; 106:198104. [PMID: 21668206 DOI: 10.1103/physrevlett.106.198104] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2010] [Indexed: 05/30/2023]
Abstract
We computationally study the transport of active, self-propelled particles suspended in a two-dimensional chaotic flow. The pointlike, spherical particles have their own intrinsic swimming velocity, which modifies the dynamical system so that the particles can break the transport barriers present in the carrier flow. Surprisingly, we find that swimming does not necessarily lead to enhanced particle transport. Small but finite swimming speed can result in reduced transport, as swimmers get stuck for long times in traps that form near elliptic islands in the background flow. Our results have implications for models of transport and encounter rates for small marine organisms.
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Affiliation(s)
- Nidhi Khurana
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
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26
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Instabilities on Prey Dynamics in Jellyfish Feeding. Bull Math Biol 2010; 73:1841-56. [DOI: 10.1007/s11538-010-9594-4] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2009] [Accepted: 10/11/2010] [Indexed: 10/18/2022]
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27
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Liu SJ, Wei HH, Hwang SH, Chang HC. Dynamic particle trapping, release, and sorting by microvortices on a substrate. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:026308. [PMID: 20866906 DOI: 10.1103/physreve.82.026308] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2010] [Indexed: 05/10/2023]
Abstract
This paper examines particle trapping and release in confined microvortex flows, including those near a solid surface due to variations in the electrokinetic slip velocity and those at a liquid-gas interface due to an external momentum source. We derive a general analytical solution for a two-dimensional microvortex flow within a semicircular cap. We also use a bifurcation theory on the kinetic equation of particles under various velocity and force fields to delineate the conditions for a vortex trap, a point trap, a limit cycle trap, and the selective sorting of the particles into different traps. In the presence of only divergence-free forces on suspended particles, we find that two parameters, such as those related to Stokes drag, gravity, and flow vorticity, are sufficient to classify all the trap topologies for a given slip velocity distribution. We also show that nondivergence-free forces such as nonuniform repulsion or attraction can capture suspended particles in one trap and selectively sort a binary suspension into different traps.
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Affiliation(s)
- Shui-Jin Liu
- Department of Chemical Engineering, National Cheng Kung University, Taiwan, Republic of China
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28
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Scofield D, Huq P. Effects of large scale eddies and stagnation surfaces on microcrystallization. Chem Eng Sci 2010. [DOI: 10.1016/j.ces.2009.11.007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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29
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Sapsis T, Haller G. Clustering criterion for inertial particles in two-dimensional time-periodic and three-dimensional steady flows. CHAOS (WOODBURY, N.Y.) 2010; 20:017515. [PMID: 20370305 DOI: 10.1063/1.3272711] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
We derive an analytic condition that predicts the exact location of inertial particle clustering in three-dimensional steady or two-dimensional time-periodic flows. The particles turn out to cluster on attracting inertial Lagrangian coherent structures that are smooth deformations of invariant tori. We illustrate our results on three-dimensional steady flows, including the Hill's spherical vortex and the Arnold-Beltrami-Childress flow, as well as on a two-dimensional time and space periodic flow that models a meandering jet in a channel.
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Affiliation(s)
- Themistoklis Sapsis
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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30
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Festa R, Mazzino A, Todini M. Dynamics of light particles in oscillating cellular flows. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:035301. [PMID: 19905171 DOI: 10.1103/physreve.80.035301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2009] [Indexed: 05/28/2023]
Abstract
The dynamics of light particles in chaotic oscillating cellular flows is investigated both analytically and numerically by means of Monte Carlo simulations. At level of linear analysis (in the oscillation amplitude) we determined how the known fixed points relative to the stationary cellular flow deform into closed stable trajectories. Once the latter have been analytically determined, we numerically show that they possess the dynamical role of attracting all asymptotic trajectories for a wide range of parameters values. The robustness of the attracting trajectories is tested by adding a white-noise contribution to the particle equation of motion. As a result, attracting trajectories persist up to a critical Péclet number above which an average rising velocity sets in. Possible implications of our results on the long-standing problem related to the explanation of the observed oceanic plankton patchiness will be also discussed.
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Affiliation(s)
- Roberto Festa
- Department of Physics, University of Genova, via Dodecaneso 33, 16146 Genova, Italy
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31
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Ijzermans RHA, Reeks MW, Meneguz E, Picciotto M, Soldati A. Measuring segregation of inertial particles in turbulence by a full Lagrangian approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:015302. [PMID: 19658760 DOI: 10.1103/physreve.80.015302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2008] [Indexed: 05/28/2023]
Abstract
Preferential concentration of inertial particles in turbulence is studied numerically by evaluating the Lagrangian compressibility of the particle velocity field using the "full Lagrangian method." This is compared with the "mesoscopic Eulerian particle velocity field" both in a direct numerical simulation of turbulence and in a synthetic flow field. We demonstrate that the Lagrangian method, in contrast to the Eulerian, accurately predicts the compressibility of the particle velocity field even when the latter is characterized by singularities. In particular we use the method to evaluate the growth rates of spatial moments of the particle number density which reflect the fractal structure of segregation and the occurrence of singularities.
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Affiliation(s)
- R H A Ijzermans
- School of Mechanical and Systems Engineering, Newcastle University, Newcastle-upon-Tyne NE1 7RU, UK
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32
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Nirmal Thyagu N, Gupte N. Transport and diffusion in the embedding map. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:066203. [PMID: 19658579 DOI: 10.1103/physreve.79.066203] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2008] [Revised: 04/20/2009] [Indexed: 05/28/2023]
Abstract
We study the transport properties of passive inertial particles in two-dimensional (2D) incompressible flows. Here, the particle dynamics is represented by the four-dimensional dissipative embedding map of the 2D area-preserving standard map which models the incompressible flow. The system is a model for impurity dynamics in a fluid and is characterized by two parameters, the inertia parameter alpha and the dissipation parameter gamma . The aerosol regime, where the particles are denser than the fluid, and the bubble regime, where they are less dense than the fluid, correspond to the parameter regimes alpha>1 and alpha<1 , respectively. Earlier studies of this system show a rich phase diagram with dynamical regimes corresponding to periodic orbits, chaotic structures, and mixed regimes. We obtain the statistical characterizers of transport for this system in these dynamical regimes. These are the recurrence time statistics, the diffusion exponent, and the distribution of jump lengths. The recurrence time distribution shows a power-law tail in the dynamical regimes, where there is preferential concentration of particles in sticky regions of the phase space, and an exponential decay in mixing regimes. The diffusion exponent shows behavior of three types-normal, subdiffusive, and superdiffusive, depending on the parameter regimes. Phase diagrams of the system are constructed to differentiate different types of diffusion behavior, as well as the behavior of the absolute drift. We correlate the dynamical regimes seen for the system at different parameter values with the transport properties observed at these regimes and in the behavior of the transients. This system also shows the existence of a crisis and unstable dimension variability at certain parameter values. The signature of the unstable dimension variability is seen in the statistical characterizers of transport. We discuss the implications of our results for realistic systems.
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Affiliation(s)
- N Nirmal Thyagu
- Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India.
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33
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Cartwright JH, Piro N, Piro O, Tuval I. Fluid dynamics of nodal flow and left-right patterning in development. Dev Dyn 2008; 237:3477-90. [DOI: 10.1002/dvdy.21672] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
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34
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Ouellette NT, O'Malley PJJ, Gollub JP. Transport of finite-sized particles in chaotic flow. PHYSICAL REVIEW LETTERS 2008; 101:174504. [PMID: 18999753 DOI: 10.1103/physrevlett.101.174504] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2008] [Indexed: 05/27/2023]
Abstract
By extending traditional particle tracking techniques, we study the dynamics of neutrally buoyant finite-sized particles in a spatiotemporally chaotic flow. We simultaneously measure the flow field and the trajectories of millimeter-scale particles so that the two can be directly compared. While the single-point statistics of the particles are indistinguishable from the flow statistics, the particles often move in directions that are systematically different from the underlying flow. These differences are especially evident when Lagrangian statistics are considered.
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35
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Escribano B, Vanyo J, Tuval I, Cartwright JHE, González DL, Piro O, Tél T. Dynamics of tidal synchronization and orbit circularization of celestial bodies. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:036216. [PMID: 18851130 DOI: 10.1103/physreve.78.036216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2007] [Revised: 08/19/2008] [Indexed: 05/26/2023]
Abstract
We take a dynamical-systems approach to study the qualitative dynamical aspects of the tidal locking of the rotation of secondary celestial bodies with their orbital motion around the primary. We introduce a minimal model including the essential features of gravitationally induced elastic deformation and tidal dissipation that demonstrates the details of the energy transfer between the orbital and rotovibrational degrees of freedom. Despite its simplicity, our model can account for both synchronization into the 1:1 spin-orbit resonance and the circularization of the orbit as the only true asymptotic attractors, together with the existence of relatively long-lived metastable orbits with the secondary in p:q synchronous rotation.
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Affiliation(s)
- Bruno Escribano
- Instituto Andaluz de Ciencias de la Terra, CSIC-Universidad de Granada, Campus Fuentenueva, E-18071 Granada, Spain
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36
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Tallapragada P, Ross SD. Particle segregation by Stokes number for small neutrally buoyant spheres in a fluid. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:036308. [PMID: 18851144 DOI: 10.1103/physreve.78.036308] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2008] [Revised: 06/14/2008] [Indexed: 05/26/2023]
Abstract
It is a commonly observed phenomenon that spherical particles with inertia in an incompressible fluid do not behave as ideal tracers. Due to the inertia of the particle, the planar dynamics are described in a four-dimensional phase space and thus can differ considerably from the ideal tracer dynamics. Using finite-time Lyapunov exponents, we compute the sensitivity of the final position of a particle with respect to its initial velocity, relative to the fluid, and thus partition the relative velocity subspace at each point in configuration space. The computations are done at every point in the relative velocity subspace, thus giving a sensitivity field. The Stokes number, being a measure of the independence of the particle from the underlying fluid flow, acts as a parameter in determining the variation in these partitions. We demonstrate how this partition framework can be used to segregate particles by Stokes number in a fluid. The fluid model used for demonstration is a two-dimensional cellular flow.
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Affiliation(s)
- Phanindra Tallapragada
- Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, (VPISU), Blacksburg, VA 24061, USA.
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37
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Calzavarini E, Cencini M, Lohse D, Toschi F. Quantifying turbulence-induced segregation of inertial particles. PHYSICAL REVIEW LETTERS 2008; 101:084504. [PMID: 18764623 DOI: 10.1103/physrevlett.101.084504] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2008] [Indexed: 05/26/2023]
Abstract
Particles with different density from the advecting turbulent fluids cluster due to the different response of light and heavy particles to turbulent fluctuations. This study focuses on the quantitative characterization of the segregation of dilute polydisperse inertial particles evolving in turbulent flow, as obtained from direct numerical simulation of homogeneous isotropic turbulence. We introduce an indicator of segregation amongst particles of different inertia and/or size, from which a length scale r_{seg}, quantifying the segregation degree between two particle types, is deduced.
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Affiliation(s)
- Enrico Calzavarini
- Department of Applied Physics, JMBC Burgers Center for Fluid Dynamics, and IMPACT Institute, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
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38
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Zahnow JC, Vilela RD, Feudel U, Tél T. Aggregation and fragmentation dynamics of inertial particles in chaotic flows. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:055301. [PMID: 18643122 DOI: 10.1103/physreve.77.055301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2007] [Indexed: 05/26/2023]
Abstract
Inertial particles advected in chaotic flows often accumulate in strange attractors. While moving in these fractal sets they usually approach each other and collide. Here we consider inertial particles aggregating upon collision. The new particles formed in this process are larger and follow the equation of motion with a new parameter. These particles can in turn fragment when they reach a certain size or shear forces become sufficiently large. The resulting system consists of a large set of coexisting dynamical systems with a varying number of particles. We find that the combination of aggregation and fragmentation leads to an asymptotic steady state. The asymptotic particle size distribution depends on the mechanism of fragmentation. The size distributions resulting from this model are consistent with those found in raindrop statistics and in stirring tank experiments.
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Affiliation(s)
- Jens C Zahnow
- Theoretical Physics/Complex Systems, ICBM, University of Oldenburg, 26129 Oldenburg, Germany
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39
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Thyagu NN, Gupte N. Clustering, chaos, and crisis in a bailout embedding map. Phys Rev E 2007; 76:046218. [PMID: 17995093 DOI: 10.1103/physreve.76.046218] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2007] [Indexed: 11/07/2022]
Abstract
We study the dynamics of inertial particles in two-dimensional incompressible flows. The particle dynamics is modeled by four-dimensional dissipative bailout embedding maps of the base flow which is represented by 2-d area preserving maps. The phase diagram of the embedded map is rich and interesting both in the aerosol regime, where the density of the particle is larger than that of the base flow, as well as the bubble regime, where the particle density is less than that of the base flow. The embedding map shows three types of dynamic behavior, periodic orbits, chaotic structures, and mixed regions. Thus, the embedding map can target periodic orbits as well as chaotic structures in both the aerosol and bubble regimes at certain values of the dissipation parameter. The bifurcation diagram of the 4-d map is useful for the identification of regimes where such structures can be found. An attractor merging and widening crisis is seen for a special region for the aerosols. At the crisis, two period-10 attractors merge and widen simultaneously into a single chaotic attractor. Crisis induced intermittency is seen at some points in the phase diagram. The characteristic times before bursts at the crisis show power-law behavior as functions of the dissipation parameter. Although the bifurcation diagram for the bubbles looks similar to that of aerosols, no such crisis regime is seen for the bubbles. Our results can have implications for the dynamics of impurities in diverse application contexts.
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40
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Ouellette NT, Gollub JP. Curvature fields, topology, and the dynamics of spatiotemporal chaos. PHYSICAL REVIEW LETTERS 2007; 99:194502. [PMID: 18233080 DOI: 10.1103/physrevlett.99.194502] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2007] [Indexed: 05/25/2023]
Abstract
The curvature field is measured from tracer-particle trajectories in a two-dimensional fluid flow that exhibits spatiotemporal chaos and is used to extract the hyperbolic and elliptic points of the flow. These special points are pinned to the forcing when the driving is weak, but wander over the domain and interact in pairs at stronger driving, changing the local topology of the flow. Their behavior reveals a two-stage transition to spatiotemporal chaos: a gradual loss of spatial and temporal order followed by an abrupt onset of topological changes.
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41
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Kivotides D, Barenghi CF, Mee AJ, Sergeev YA. Interaction of solid particles with a tangle of vortex filaments in a viscous fluid. PHYSICAL REVIEW LETTERS 2007; 99:074501. [PMID: 17930898 DOI: 10.1103/physrevlett.99.074501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2007] [Indexed: 05/25/2023]
Abstract
Homogeneous isotropic turbulence consists of coherent filamentary vortex structures superimposed to a more incoherent background. The question which we address is the effect of these structures on the dynamics of small, neutrally buoyant solid particles. Rather than generating the turbulence by direct numerical simulation (DNS) of the Navier-Stokes equations, we use a model of turbulence based entirely on viscous vortex filaments which interact via inertial forces and reconnect with each other. Using this model, we show that solid particles can become trapped around vortex filaments, something difficult to achieve with DNS. Unlike most studies, we have not neglected inviscid inertial effects. By comparing the Stokes, local, and convective components of the particle's acceleration, we also show that the convective part clearly identifies the trapping.
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Affiliation(s)
- Demosthenes Kivotides
- Center for Risk Studies and Safety, University of California, Santa Barbara, California 93117, USA
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42
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Seoane JM, Sanjuán MAF, Lai YC. Fractal dimension in dissipative chaotic scattering. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:016208. [PMID: 17677544 DOI: 10.1103/physreve.76.016208] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2006] [Revised: 02/06/2007] [Indexed: 05/16/2023]
Abstract
The effect of weak dissipation on chaotic scattering is relevant to situations of physical interest. We investigate how the fractal dimension of the set of singularities in a scattering function varies as the system becomes progressively more dissipative. A crossover phenomenon is uncovered where the dimension decreases relatively more rapidly as a dissipation parameter is increased from zero and then exhibits a much slower rate of decrease. We provide a heuristic theory and numerical support from both discrete-time and continuous-time scattering systems to establish the generality of this phenomenon. Our result is expected to be important for physical phenomena such as the advection of inertial particles in open chaotic flows, among others.
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Affiliation(s)
- Jesús M Seoane
- Nonlinear Dynamics and Chaos Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.
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43
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Vilela RD, Tél T, de Moura APS, Grebogi C. Signatures of fractal clustering of aerosols advected under gravity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:065203. [PMID: 17677314 DOI: 10.1103/physreve.75.065203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2006] [Revised: 03/02/2007] [Indexed: 05/16/2023]
Abstract
Aerosols under chaotic advection often approach a strange attractor. They move chaotically on this fractal set but, in the presence of gravity, they have a net vertical motion downwards. In practical situations, observational data may be available only at a given level, for example, at the ground level. We uncover two fractal signatures of chaotic advection of aerosols under the action of gravity. Each one enables the computation of the fractal dimension D(0) of the strange attractor governing the advection dynamics from data obtained solely at a given level. We illustrate our theoretical findings with a numerical experiment and discuss their possible relevance to meteorology.
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Affiliation(s)
- Rafael D Vilela
- Max Planck Institute for the Physics of Complex Systems, D-01187 Dresden, Germany
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44
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Cartwright JH, Piro N, Piro O, Tuval I. Embryonic nodal flow and the dynamics of nodal vesicular parcels. J R Soc Interface 2007; 4:49-55. [PMID: 17015289 PMCID: PMC2358960 DOI: 10.1098/rsif.2006.0155] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
We address with fluid-dynamical simulations using direct numerical techniques three important and fundamental questions with respect to fluid flow within the mouse node and left-right development. First, we consider the differences between what is experimentally observed when assessing cilium-induced fluid flow in the mouse node in vitro and what is to be expected in vivo. The distinction is that in vivo, the leftward fluid flow across the mouse node takes place within a closed system and is consequently confined, while this is no longer the case on removing the covering membrane and immersing the embryo in a fluid-filled volume to perform in vitro experiments. Although there is a central leftward flow in both instances, we elucidate some important distinctions about the closed in vivo situation. Second, we model the movement of the newly discovered nodal vesicular parcels (NVPs) across the node and demonstrate that the flow should indeed cause them to accumulate on the left side of the node, as required for symmetry breaking. Third, we discuss the rupture of NVPs. Based on the biophysical properties of these vesicles, we argue that the morphogens they contain are likely not delivered to the surrounding cells by their mechanical rupture either by the cilia or the flow, and rupture must instead be induced by an as yet undiscovered biochemical mechanism.
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Affiliation(s)
| | - Nicolas Piro
- ICFO-Institut de Ciéncies Fotóniques, Mediterranean Technology Park08860 Castelldefels (Barcelona), Spain
| | - Oreste Piro
- Institut Mediterrani d'Estudis Avançats, CSIC-UIB07071 Palma de Mallorca, Spain
- Center for Studies in Physics and Biology, Rockefeller UniversityNew York, NY 10021, USA
| | - Idan Tuval
- Bio5 Institute, University of ArizonaTucson, AZ 85721, USA
- Author for correspondence ()
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45
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Benczik IJ, Károlyi G, Scheuring I, Tél T. Coexistence of inertial competitors in chaotic flows. CHAOS (WOODBURY, N.Y.) 2006; 16:043110. [PMID: 17199388 DOI: 10.1063/1.2359231] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
We investigate the dynamics of inertial particles immersed in open chaotic flows. We consider the generic problem of competition between different species, e.g., phytoplankton populations in oceans. The strong influence from inertial effects is shown to result in the persistence of different species even in cases when the passively advected species cannot coexist. Multispecies coexistence in the ocean can be explained by the fact that the unstable manifold is different for each advected competitor of different size.
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Affiliation(s)
- I J Benczik
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany and Physics Department, Virginia Tech, Blacksburg, Virginia 24061, USA
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46
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Lan Y, Chandre C, Cvitanović P. Newton's descent method for the determination of invariant tori. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:046206. [PMID: 17155152 DOI: 10.1103/physreve.74.046206] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2005] [Revised: 02/06/2006] [Indexed: 05/12/2023]
Abstract
We formulate a fictitious-time-flow equation which drives an initial guess torus to a torus invariant under a given dynamics, provided such a torus exists. The method is general and applies in principle to continuous time flows and discrete time maps in arbitrary dimension and to both Hamiltonian and dissipative systems.
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Affiliation(s)
- Y Lan
- Center for Nonlinear Science, School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA
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47
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Seoane JM, Aguirre J, Sanjuán MAF, Lai YC. Basin topology in dissipative chaotic scattering. CHAOS (WOODBURY, N.Y.) 2006; 16:023101. [PMID: 16822004 DOI: 10.1063/1.2173342] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
Chaotic scattering in open Hamiltonian systems under weak dissipation is not only of fundamental interest but also important for problems of current concern such as the advection and transport of inertial particles in fluid flows. Previous work using discrete maps demonstrated that nonhyperbolic chaotic scattering is structurally unstable in the sense that the algebraic decay of scattering particles immediately becomes exponential in the presence of weak dissipation. Here we extend the result to continuous-time Hamiltonian systems by using the Henon-Heiles system as a prototype model. More importantly, we go beyond to investigate the basin structure of scattering dynamics. A surprising finding is that, in the common case where multiple destinations exist for scattering trajectories, Wada basin boundaries are common and they appear to be structurally stable under weak dissipation, even when other characteristics of the nonhyperbolic scattering dynamics are not. We provide numerical evidence and a geometric theory for the structural stability of the complex basin topology.
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Affiliation(s)
- Jesús M Seoane
- Nonlinear Dynamics and Chaos Group, Departamento de Matemáticas y Física Aplicadas y Ciencias de la Naturaleza, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.
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Vilela RD, de Moura APS, Grebogi C. Finite-size effects on open chaotic advection. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:026302. [PMID: 16605449 DOI: 10.1103/physreve.73.026302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2005] [Indexed: 05/08/2023]
Abstract
We study the effects of finite-sizeness on small, neutrally buoyant, spherical particles advected by open chaotic flows. We show that, when observed in the configuration or physical space, the advected finite-size particles disperse about the unstable manifold of the chaotic saddle that governs the passive advection. Using a discrete-time system for the dynamics, we obtain an expression predicting the dispersion of the finite-size particles in terms of their Stokes parameter at the onset of the finite-size induced dispersion. We test our theory in a system derived from a flow and find remarkable agreement between our expression and the numerically measured dispersion.
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Affiliation(s)
- Rafael D Vilela
- Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05315-970, São Paulo, São Paulo, Brazil
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Do Y, Lai YC. Stability of attractors formed by inertial particles in open chaotic flows. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:036203. [PMID: 15524608 DOI: 10.1103/physreve.70.036203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2004] [Indexed: 05/24/2023]
Abstract
Particles having finite mass and size advected in open chaotic flows can form attractors behind structures. Depending on the system parameters, the attractors can be chaotic or nonchaotic. But, how robust are these attractors? In particular, will small, random perturbations destroy the attractors? Here, we address this question by utilizing a prototype flow system: a cylinder in a two-dimensional incompressible flow, behind which the von Kármán vortex street forms. We find that attractors formed by inertial particles behind the cylinder are fragile in that they can be destroyed by small, additive noise. However, the resulting chaotic transient can be superpersistent in the sense that its lifetime obeys an exponential-like scaling law with the noise amplitude, where the exponent in the exponential dependence can be large for small noise. This happens regardless of the nature of the original attractor, chaotic or nonchaotic. We present numerical evidence and a theory to explain this phenomenon. Our finding makes direct experimental observation of superpersistent chaotic transients feasible and it also has implications for problems of current concern such as the transport and trapping of chemically or biologically active particles in large-scale flows.
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Affiliation(s)
- Younghae Do
- Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287, USA
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Tél T, Nishikawa T, Motter AE, Grebogi C, Toroczkai Z. Universality in active chaos. CHAOS (WOODBURY, N.Y.) 2004; 14:72-78. [PMID: 15003046 DOI: 10.1063/1.1626391] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Many examples of chemical and biological processes take place in large-scale environmental flows. Such flows generate filamental patterns which are often fractal due to the presence of chaos in the underlying advection dynamics. In such processes, hydrodynamical stirring strongly couples into the reactivity of the advected species and might thus make the traditional treatment of the problem through partial differential equations difficult. Here we present a simple approach for the activity in inhomogeneously stirred flows. We show that the fractal patterns serving as skeletons and catalysts lead to a rate equation with a universal form that is independent of the flow, of the particle properties, and of the details of the active process. One aspect of the universality of our approach is that it also applies to reactions among particles of finite size (so-called inertial particles).
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Affiliation(s)
- Tamás Tél
- Institute for Theoretical Physics, Eotvos University, P.O. Box 32, H-1518, Budapest, Hungary
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