The chaotic behavior of the leaky faucet

Martien, P.; Pope, S.C.; Scott, P. L.; Shaw, Robert S.

doi:10.1016/0375-9601(85)90065-9

Cited by 107 publications

(51 citation statements)

References 2 publications

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“…Let DT (n) be the time interval that separates the (n + 1)th droplet from the nth droplet. The time series of interdrop intervals DT (n) connects the study of the formation and dynamics of droplets in ants to that of a dripping faucet, which was introduced as an early and simple example of a chaotic system (Shaw, 1984;Martien et al, 1985;Austin, 1991;Sartorelli et al, 1994;Penna et al, 1995;Sanchez-Ortiz and Salas-Brito, 1995). The physics of the dripping faucet involves surface tension, which decreases the dripping rate, and gravity, which acts as a nonlinearly coupled competitive force.…”

Section: Resultsmentioning

confidence: 99%

Model of Droplet Dynamics in the Argentine Ant Linepithema Humile(Mayr)

Théraulaz

Bonabeau

Sauwens

et al. 2001

Bulletin of Mathematical Biology

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The formation of droplets of ants Linepithema humile (Mayr) is observed under certain experimental conditions: a fluctuating aggregate forms at the end of a rod and a droplet containing up to 40 ants eventually falls down. When the flux of incoming ants is sufficient, this process can continue for several hours, leading to the formation and fall of tens of droplets. Previous work indicates that the time series of drop-to-drop intervals may result from a nonlinear low-dimensional dynamics, and the interdrop increments exhibit long-range anticorrelations. A model of aggregation and droplet formation, based on experimental observations, is introduced and shown to reproduce these properties.

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Section: Resultsmentioning

confidence: 99%

Model of Droplet Dynamics in the Argentine Ant Linepithema Humile(Mayr)

Théraulaz

Bonabeau

Sauwens

et al. 2001

Bulletin of Mathematical Biology

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“…If the seemingly random florescence gives rise to a distinct structure in phase space, with noninteger fractal dimension, onto which the phase space points are concentrated, it would be a clear indication that it is actually the consequence of dynamical deterministic chaos (i.e., hidden variables), in direct analogy to how [11,12] revealed deterministic chaos in the dynamics of the dripping water faucet ( Figure 6). For examples of qualitatively typical chaotic attractors/structures see, for example, the figures in [11,12] or the famous examples presented in the figures in this article : "The Lorenz map"-when successive, erratically fluctuating, amplitude maxima were plotted for the Lorenz attractor (previous figure) using a technique analogous to the one described in this article, the surprising result was this nearly one-dimensional attractor; hidden order in chaos [20], and a concrete simple example of the relation between continuous dynamics and discrete mappings.…”

mentioning

confidence: 95%

“…For examples of qualitatively typical chaotic attractors/structures see, for example, the figures in [11,12] or the famous examples presented in the figures in this article : "The Lorenz map"-when successive, erratically fluctuating, amplitude maxima were plotted for the Lorenz attractor (previous figure) using a technique analogous to the one described in this article, the surprising result was this nearly one-dimensional attractor; hidden order in chaos [20], and a concrete simple example of the relation between continuous dynamics and discrete mappings.…”

mentioning

confidence: 99%

Reality or Locality? Proposed Test to Decide How Nature Breaks Bell's Inequality

Hansson

2012

Physics Research International

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Bell's theorem, and its experimental tests, has shown that the two premises for Bell's inequality—locality and objective reality—cannot both hold in nature, as Bell's inequality is broken. A simple test is proposed, which for the first time may decide which alternative nature actually prefers on the fundamental, quantum level. If each microscopic event is truly random (e.g., as assumed in orthodox quantum mechanics) objective reality is not valid whereas if each event is described by an unknown but deterministic mechanism (“hidden variables”) locality is not valid. This may be analyzed and decided by the well-known reconstruction method of Ruelle and Takens; in the former case no structure should be discerned, in the latter a reconstructed structure should be visible. This could in principle be tested by comparing individual “hits” in a double-slit experiment, but in practice a single fluorescent atom, and its (seemingly random) temporal switching between active/inactive states would possibly be better/more practical, easier to set up, observe, and analyze. However, only imagination limits the list of possible experimental setups.

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“…First, one asks the question of whether this system, which seems inherently to be a predictable, periodic flow, can yield complex dynamics? Evidence exists that this is indeed the case, and that the capillary jet can serve as a model dynamical system for chaos studies (Martien et al 1985).…”

Section: Introductionmentioning

confidence: 99%

Lock-in states in the dripping mode of the capillary jet

Olinger

1993

Experiments in Fluids

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Experimental observations of a new phenomenon, lock-in states in the dripping mode of a capillary jet are presented. An externally forced capillary jet is studied within a deterministic chaos framework. The jet at low Weber numbers exhibits different behaviors depending on the amplitude of forcing and the ratio of the drip and forcing frequencies. Lock-in regions, which widen in extent with increase in forcing amplitude, along with quasiperiodic states are observed. These results suggest preliminarily that the capillary jet can be modeled by circle map dynamics, and support the idea that absolutely unstable flows are amenable to description by a 'dynamical systems' approach.

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The chaotic behavior of the leaky faucet

Cited by 107 publications

References 2 publications

Model of Droplet Dynamics in the Argentine Ant Linepithema Humile(Mayr)

Model of Droplet Dynamics in the Argentine Ant Linepithema Humile(Mayr)

Reality or Locality? Proposed Test to Decide How Nature Breaks Bell's Inequality

Lock-in states in the dripping mode of the capillary jet

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