Dynamics Of Relative Phase Research Articles

Granger Geweke Causality reveals information exchange during physical interaction is modulated by task difficulty

The haptic sense is an important mode of communication during physical interactions, and it is known to enable humans to estimate key features of their partner's behavior. It is proposed that such estimations are based upon the exchange of information mediated by the interaction forces, resulting in role distribution and coordination between partners. In the present study, we examined whether the information exchange is functionally modified to adapt to the task, or whether it is a fixed process, leaving the adaptation to individual's behaviors. We analyzed the forces during an empirical dyadic interaction task using Granger-Geweke causality analysis, which allowed us to quantify the causal influence of each individual's forces on their partner's. The dynamics of relative phase were also examined. We observed an increase of inter-partner influence with an increase in the spatial accuracy required by the task, demonstrating an adaptation of information flow to the task. This increase of exchange with the spatial accuracy constraint was accompanied by an increase of errors and of the variability of the relative phase between forces. The influence was dominated by participants in a specific role, showing a clear role division as well as task division between the dyad partners. Moreover, the influence occurred in the [2.15–7] Hz frequency band, demonstrating its importance as a frequency band of interest during cooperation involving haptic interaction. Several interpretations are introduced, ranging from sub-division of motion control to phase–amplitude coupling.

Phase dynamics of discrete breathers periodically tunneling in weakly coupled nonlinear chains

We present a brief discussion of the phase-coherent dynamics of discrete breathers (intrinsic localized modes) in a system of two weakly coupled nonlinear chains and its comparison with periodic tunneling of quantum particles in a double-well potential and with macroscopic quantum tunneling of two weakly linked Bose–Einstein condensates. We consider the dynamics of relative phase of classically-tunneling discrete breathers in two weakly coupled nonlinear chains and show that the dynamics of the relative phase in the π/2 tunneling mode coincides with the experimentally observed dynamics of the relative phase of quantum particles, periodically tunneling in a double-well potential, both for noninteracting and strongly repulsively interacting particles. The observed coincidence demonstrates the correspondence between the dynamics of classical localized excitations in two weakly coupled nonlinear chains and tunneling dynamics of quantum object in the double-well potential. We show that in both π/2 and winding tunneling modes the relative phase experiences periodic jumps by π in the instants of complete depopulation of one of the weakly coupled chains or potential wells. The connection of the observed phase dynamics with the non-quantum uncertainty principle is discussed.

The perception-action dynamics of action competency are altered by both physical and observational training.

Action competency is defined as the ability of an individual to self-evaluate their own performance capabilities. The current experiment demonstrated that physical and observational training with a motor skill alters action competency ratings in a similar manner. Using a pre-test and post-test protocol, the results revealed that action competency is constrained prior to training by the intrinsic dynamics of relative phase (ϕ), with in-phase (ϕ = 0°) and anti-phase (ϕ = 180°) patterns receiving higher competency ratings than other relative phase patterns. After 2 days of training, action competency ratings for two trained relative phase patterns, +60° and +120°, increased following physical practice or observational practice. A transfer test revealed that both physical performance ability and action competency ability transferred to the symmetry partners (-60° and -120°) of the two trained relative phase patterns following physical or observational training. The findings also revealed that relative motion direction acts as categorical information that helps to organize action production and facilitate action competency. The results are interpreted based on the coordination dynamics theory of perception-action coupling, and extend this theory by showing that visual perception, action production, and action competency are all constrained in a consistent manner by the dynamics of the order parameter relative phase. As a whole, the findings revealed that relative motion, relative phase, and possibly relative amplitude information are all distinct sources of information that contribute to the emergence of a kinematic understanding of action in the nervous system.

Energy transfer in coupled nonlinear phononic waveguides: transition from wandering breather to nonlinear self-trapping

We consider, both analytically and numerically, the dynamics of stationary and slowly-moving breathers (localized short-wavelength excitations) in two weakly coupled nonlinear oscillator chains (nonlinear phononic waveguides). We show that there are two qualitatively different dynamical regimes of the coupled breathers: the oscillatory exchange of the low-amplitude breather between the phononic waveguides (wandering breather), and one-waveguide-localization (nonlinear self-trapping) of the high-amplitude breather. We also show that phase-coherent dynamics of the coupled breathers in two weakly linked nonlinear phononic waveguides has a profound analogy, and is described by a similar pair of equations, to the tunnelling quantum dynamics of two weakly linked Bose-Einstein condensates in a symmetric double-well potential (single bosonic Josephson junction). The exchange of phonon energy and excitations between the coupled phononic waveguides takes on the role which the exchange of atoms via quantum tunnelling plays in the case of the coupled condensates. On the basis of this analogy, we predict a new tunnelling mode of the coupled Bose-Einstein condensates in a single bosonic Josephson junction in which their relative phase oscillates around π/2. The dynamics of relative phase of two weakly linked Bose-Einstein condensates can be studied by means of interference, while the dynamics of the exchange of lattice excitations in coupled nonlinear phononic waveguides can be observed by means of light scattering.

Superimposition in interlimb rhythmic coordination

Von Holst (1939/1973) identified three processes of intersegmental rhythmic coordination: the magnet effect, the maintenance tendency, and superimposition. Superimposition, the augmenting or diminishing of amplitude ( A), is believed to interact with the other two processes in such a way that the most stable organization will maximize A. The present experiment tests this hypothesis by having subjects oscillate hand-held pendulums in three different modes, one uncoupled (single pendulum oscillations) and two coupled (inphase (φ = 0) and antiphase (φ = π)). The order parameter dynamics of relative phase predict an increased phase attraction at φ = 0 resulting in greater A. In agreement with predictions, oscillations at φ = 0 were shown to (i) be more stable (that is, lower SD φ) and (ii) possess a greater A than at φ = π. Additionally, uncoupled A was only slightly greater than coupled A suggesting weak coupling. These results support the hypothesized relation between superimposition and the magnet effect and the strategy of modelling coupled oscillators without reference to A.