Sound Generated by Cellular Flames

Pelcé, Pierre; Rochwerger, Daniel

doi:10.1007/978-1-4684-1357-1_23

Cited by 7 publications

(10 citation statements)

References 6 publications

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“…When there are multiple dimples in the veil, they move toward one another. These dynamics bear a loose similarity to another application of the KPP equation, the dynamics of a flame front in a tube (40). Flames, like a veil, also move up an oxygen gradient.…”

Section: Resultsmentioning

confidence: 73%

“…The KPP equation was originally used to understand the motion of nonchemotactic bacteria (i.e., χ ¼ 0) in an evolving nutrient gradient. The formulation has since been used to gain insight into a wide range of phenomena (40,45). The important difference between this model and the original KPP equation is the inclusion of chemotaxis to a particular oxygen concentration.…”

Section: Resultsmentioning

confidence: 99%

“…To quantify the effectiveness of a cell or community at transporting oxygen through the diffusive boundary layer, it is useful to define the Péclet number Pe (40). This dimensionless number compares the rate at which nutrients are transported by fluid flow and the rate at which nutrients are transported by diffusion.…”

Section: Significancementioning

confidence: 99%

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Hydrodynamics and collective behavior of the tethered bacteriumThiovulum majus

Petroff

Libchaber

2014

Proc. Natl. Acad. Sci. U.S.A.

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Significance In this paper we examine the dynamics underlying a form of collective behavior exhibited by bacteria. In a nutrient gradient, Thiovulum majus cells aggregate into a community in which cells attach to one another using mucus tethers. As tethered cells beat their flagella, they pull nutrient-laden water through the community. The flow of water created by many cells gives rise to variations in the nutrient concentration. As cells reorganize in response to these nutrient gradients, they change the flow of water. We show that the coupling between the motion of water, nutrients, and cells generates large-scale flows that dramatically increase the rate at which nutrients are pulled to the cells.

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Section: Resultsmentioning

confidence: 73%

Section: Resultsmentioning

confidence: 99%

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Hydrodynamics and collective behavior of the tethered bacteriumThiovulum majus

Petroff

Libchaber

2014

Proc. Natl. Acad. Sci. U.S.A.

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“…In particular, the invasion of a viscous fluid by an inviscid one is one of the most famous of all pattern formation problems [9,10]. The general result is that the inviscid fluid forms a finger, the Saffman-Taylor finger, which fills a fraction, λ, of the channel.…”

Section: The Averaging Conjecture and Mean-field Theory A Saffmamentioning

confidence: 99%

Random walks, diffusion limited aggregation in a wedge, and average conformal maps

Sander

Somfai

2005

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We investigate diffusion-limited aggregation (DLA) in a wedge geometry. Arneodo and collaborators have suggested that the ensemble average of DLA cluster density should be close to the noise-free selected Saffman-Taylor finger. We show that a different, but related, ensemble average, that of the conformal maps associated with random clusters, yields a non-trivial shape which is also not far from the Saffman-Taylor finger. However, we have previously demonstrated that the same average of DLA in a channel geometry is not the Saffman-Taylor finger. This casts doubt on the idea that the average of noisy diffusion-limited growth is governed by a simple transcription of noise-free results. * Electronic address: lsander@umich.edu † Electronic address: ellak@lorentz.leidenuniv.nl 1The diffusion-limited aggregation model uses aggregating random walkers to form a random fractal pattern. We can also use random walkers to generate a conformal map from the exterior of the cluster to the exterior of the unit circle.The map contains all the information about the growth probabilities for various points on the cluster. We define the pattern generated by the ensemble average of the conformal maps as a kind of mean-field pattern for DLA. In previous work we showed that there seemed to be an intriguing relationship between DLA in a channel and the noise-free Saffman-Taylor finger. We show here that this relationship is much more ambiguous when we apply it to DLA in a wedge geometry. This result casts doubt on the 'averaging conjecture' which holds that the average of noisy growth 'remembers' noise-free results.

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“…Interfacial instabilities are a driving force of many pattern-forming processes in nature, be it in the realm of fluid mechanics, flame propagation or directional solidification [1][2][3]. A large body of work has been devoted to the analysis of these processes throughout the last decades.…”

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confidence: 99%

Effective description of the interaction between anisotropic viscous fingers

Budek¹,

Szymczak²

2014

EPL

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We study patterns formed by viscous fingering in a rectangular network of microfluidic channels. Due to the strong anisotropy of such a system, the emerging patterns have a form of thin needle-like fingers, which interact with each other, competing for an available flow. We develop an upscaled description of this system in which only the fingers are tracked and the effective interactions between them are introduced, mediated through the evolving pressure field. Due to the quasi-2d geometry of the system, this is conveniently accomplished using conformal mapping techniques. A complex two-phase flow problem is thus reduced to a much simpler task of tracking evolving shapes in a 2d complex plane. This description, although simplified, turns out to capture all the key features of the system's dynamics and allows for the effective prediction of the resulting growth patterns.

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Sound Generated by Cellular Flames

Cited by 7 publications

References 6 publications

Hydrodynamics and collective behavior of the tethered bacteriumThiovulum majus

Hydrodynamics and collective behavior of the tethered bacteriumThiovulum majus

Random walks, diffusion limited aggregation in a wedge, and average conformal maps

Effective description of the interaction between anisotropic viscous fingers

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