Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation Frank Moss; Into the Daphnia vortex. Chaos 1 December 2004; 14 (4): S10. https://doi.org/10.1063/1.1821731 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAIP Publishing PortfolioChaos: An Interdisciplinary Journal of Nonlinear Science Search Advanced Search |Citation Search

This chapter detects unstable periodic orbits (UPOs) in biological systems. In both driven and autonomous chaotic systems, the motion (or orbit) of the system in phase space can at times be almost periodic. Unstable periodic orbits can also be used for the anticontrol (or maintenance) of chaos. By analyzing the UPOs in the region of either transition, small perturbations can be used to lock the system's dynamics into one basin of attraction. The study of UPOs has enabled researchers in the field of nonlinear dynamics to work with short and noisy sets of nonlinear data. This allows the study of biological systems, which noise and nonstationarity had previously made intractable. The methods described in the chapter are very robust to the presence of dynamical noise and can operate on extremely short data files. They are also demonstrated to be capable of distinguishing between dynamical data and colored noise, something that is difficult for more traditional nonlinear techniques even when very long data files are available.

Subthreshold information carrying signals can be detected and their information content enhanced by the addition of a random process, or ''noise'', in a large class of nonlinear systems. And often a maximal enhancement is possible with the inclusion of an optimal noise intensity. This process is known as stochastic resonance. It has a history of demonstrations in a variety of physical systems and has more recently been observed in both sensory and molecular biology and in medical science. In all of these observations, the noise enhanced signal was analyzed for information content by some algorithm implemented by computer. By contrast, in this work human perception replaces computer analysis. We report the results of an extensive psychophysics experiment wherein subjects analyzed computer generated visual images enhanced by time varying noise. The images were generated in analogy to classic stochastic resonance experiments. The results are robust and can be accurately described with simple threshold stochastic resonance theory, suggesting that the brain possibly interprets spatio-temporal visual information by similar computational processes.

In a class of experiments in sensory biology sub- or slightly supra-threshold stimuli are applied at the periphery while making action potential recordings at a higher level in the nervous system. In many cases the records are largely noise but with a small coherence with the stimulus. The detection threshold for increasing stimulus intensity is frequently measured, and this threshold can often be controlled by manipulating some additional biological parameter, for example, the temperature or inherent noise intensity. How does this parameter change the detection threshold? In this note, we test three popular paradigms on an electronic Fitzhugh-Nagumo neuron model and compare the results with a simple threshold theory.

We have measured the rate v at which negative ions nucleate charged vortex rings in isotopically pure superfluid 4 He for pressures, P , temperatures, T , and electric fields, E , within the ranges: 15 < P <25 bar; 0.3 < T < 0.9 K; 5 x 10 4 < E < 10 6 V m -1 . The measurements were done by a novel electrostatic induction technique specially developed for the purpose, and this is described in some detail. It was found that: at fixed E and P , v increases rapidly with T for T ca. 0.5 K, but approaches a temperature-independent limiting value v s for T < 0.5 K; at fixed P and T , v at first increases rapidly with E but then passes through a maximum at ca. 7 x 10 5 V m -1 and decreases again for larger values of E ;at fixed E and T , v increases rapidly with decreasing P until, below ca. 15 bar, the signal becomes too small to use. In all cases, v was found to be considerably smaller than had been measured for low E by earlier workers using helium of the natural isotopic ratio ( ca. 2 x 10 -7 ). The same signals were also used for measuring ionic drift velocities, v for v < ca . 3 x 1O 4 s -1 . Values of the matrix element for roton pair emission have been deduced from the v ( E ) measurements for several pressures in the range 17 < P < 25 bar. The pressure dependence of the Landau critical velocity was measured and is compared with predictions based on accepted values of the roton parameters. Analysis of the nucleation data showed that, at fixed v and P ,( v — vs ) oc n r ,where n r is the thermal roton density, suggesting that v is the sum of contributions from two independent nucleation mechanisms: a spontaneous mechanism responsible for v s and a roton driven mechanism responsible for the increase in v with T above 0.5 K. The existence of a maximum in v ( E ) appears to be inconsistent with the peeling model of vortex nucleation; but it is entirely to be expected on the basis of the quantum transition model. It is shown that all the nucleation rate measurements reported herein are consistent with the quantum transition model, provided that due account is taken of the possibility that roton absorption may give rise to a critical velocity v r that is smaller than the critical velocity v v characteristic of the spontaneous nucleation mechanism. Values of v v and v r are deduced from the experimental data for several pressures. The fact that exponential decay of the bare ion signal still occurs even when v > v v (or v r ) constitutes the first experimental evidence that the microscopic mechanisms responsible for vortex nucleation are probabilistic in nature.

We present measurements of the equilibrium and mean-square fluctuation in vortex-line density in turbulent He II. The equilibrium values are in good agreement with the Vinen theory and other current experimental results. The fluctuating quantities are described by the general instability theory reviewed by Haken.

The first measurements of fluctuations observed with both negative-ion and second-sound probes in turbulent He II are reported. Data on the distributions are well matched by Gaussian functions. An ${\ensuremath{\omega}}^{\ensuremath{-}}$ component, and well-defined relaxation times which depend on the heat flux, are found in the spectral intensity.

Data on the capture and escape of negative ions in turbulent He II are reported for various pressures. The results are consistent with a revised version of Vinen's dimensional theory and previous experimental results on rotating He II. A model for vortex annihilation is developed which allows the turbulence theory to be expressed in terms of a single dimensionless constant which we measure.

Capture and escape of negative ions by vorticity resulting from a supercritical heat current in liquid He II are demonstrated in the temperature range between 1.6 and 1.8\ifmmode^\circ\else\textdegree\fi{}K. The vorticity is identical to that produced by rotation except for configuration of the individual lines. The escape probability was measured between 1.7 and 1.8\ifmmode^\circ\else\textdegree\fi{}K and is in agreement with the theory of Donnelly.