Three-Dimensional Mapping of the Rotation of Interactive Virtual Objects with Eye-Tracking Data.

We present a method for real-time recording of human interaction with three-dimensional (3D) virtual objects. The approach consists of associating rotation data of the manipulated object with behavioral measures, such as eye tracking, to make better inferences about the underlying cognitive processes. The task consists of displaying two identical models of the same 3D object (a molecule), presented on a computer screen: a rotating, interactive object (iObj) and a static, target object (tObj).

Noise, transient dynamics, and the generation of realistic interspike interval variation in square-wave burster neurons.

First return maps of interspike intervals for biological neurons that generate repetitive bursts of impulses can display stereotyped structures (neuronal signatures). Such structures have been linked to the possibility of multicoding and multifunctionality in neural networks that produce and control rhythmical motor patterns. In some cases, isolating the neurons from their synaptic network reveals irregular, complex signatures that have been regarded as evidence of intrinsic, chaotic behavior.

Synchronization of two bubble trains in a viscous fluid: experiment and numerical simulation.

We investigate the interactions of two trains of bubbles, ejected by nozzles immersed in a viscous fluid, due only to the solution's circulation. The air fluxes (Q(1),Q(2)) are controlled independently, and we constructed parameter spaces of the periodicity of the attractors. We have observed complex behavior and many modes of phase synchronization that depend on these airflows as well as on the height (H) of the solution above the tops of the nozzles.

Period adding cascades: experiment and modeling in air bubbling.

Period adding cascades have been observed experimentally/numerically in the dynamics of neurons and pancreatic cells, lasers, electric circuits, chemical reactions, oceanic internal waves, and also in air bubbling. We show that the period adding cascades appearing in bubbling from a nozzle submerged in a viscous liquid can be reproduced by a simple model, based on some hydrodynamical principles, dealing with the time evolution of two variables, bubble position and pressure of the air chamber, through a system of differential equations with a rule of detachment based on force balance. The model further reduces to an iterating one-dimensional map giving the pressures at the detachments, where time between bubbles come out as an observable of the dynamics.

Bistability in bubble formation.

We obtain experimental data on time intervals of a bubble train generated from a nozzle with the air flow rate as the control parameter. Varying the length of the hose that connects the proportionating solenoid valve to the nozzle, we generate bifurcation diagrams showing period-adding cascades, among other dynamical phenomena. Then we construct a two-parameter family of one-dimensional maps whose bifurcation diagrams qualitatively match the experimental ones.