257 research outputs found
Phase description of oscillatory convection with a spatially translational mode
We formulate a theory for the phase description of oscillatory convection in
a cylindrical Hele-Shaw cell that is laterally periodic. This system possesses
spatial translational symmetry in the lateral direction owing to the
cylindrical shape as well as temporal translational symmetry. Oscillatory
convection in this system is described by a limit-torus solution that possesses
two phase modes; one is a spatial phase and the other is a temporal phase. The
spatial and temporal phases indicate the position and oscillation of the
convection, respectively. The theory developed in this paper can be considered
as a phase reduction method for limit-torus solutions in infinite-dimensional
dynamical systems, namely, limit-torus solutions to partial differential
equations representing oscillatory convection with a spatially translational
mode. We derive the phase sensitivity functions for spatial and temporal
phases; these functions quantify the phase responses of the oscillatory
convection to weak perturbations applied at each spatial point. Using the phase
sensitivity functions, we characterize the spatiotemporal phase responses of
oscillatory convection to weak spatial stimuli and analyze the spatiotemporal
phase synchronization between weakly coupled systems of oscillatory convection.Comment: 35 pages, 14 figures. Generalizes the phase description method
developed in arXiv:1110.112
Phase reduction approach to synchronization of spatiotemporal rhythms in reaction-diffusion systems
Reaction-diffusion systems can describe a wide class of rhythmic
spatiotemporal patterns observed in chemical and biological systems, such as
circulating pulses on a ring, oscillating spots, target waves, and rotating
spirals. These rhythmic dynamics can be considered limit cycles of
reaction-diffusion systems. However, the conventional phase-reduction theory,
which provides a simple unified framework for analyzing synchronization
properties of limit-cycle oscillators subjected to weak forcing, has mostly
been restricted to low-dimensional dynamical systems. Here, we develop a
phase-reduction theory for stable limit-cycle solutions of infinite-dimensional
reaction-diffusion systems. By generalizing the notion of isochrons to
functional space, the phase sensitivity function - a fundamental quantity for
phase reduction - is derived. For illustration, several rhythmic dynamics of
the FitzHugh-Nagumo model of excitable media are considered. Nontrivial phase
response properties and synchronization dynamics are revealed, reflecting their
complex spatiotemporal organization. Our theory will provide a general basis
for the analysis and control of spatiotemporal rhythms in various
reaction-diffusion systems.Comment: 19 pages, 6 figures, see the journal for a full versio
Radion stabilization in the presence of Wilson line phase
We study the stabilization of an extra-dimensional radius in the presence of
a Wilson line phase of an extra gauge symmetry on a five-dimensional
space-time, using the effective potential relating both the radion and the
Wilson line phase at the one-loop level. We find that the radion can be
stabilized by the introduction of a small number of fermions.Comment: 12 pages, 5 figures, Comments added. References added. Typo correcte
Submucosal electrocoagulation for prolapsed hemorrhoids:a new operative approach to hemorrhoidal varices
The results of submucosal electrocoagulation (SEC), a new radical operation for prolapsed hemorrhoids, in 403 patients with third- or fourth-degree hemorrhoids are reported. After resecting the anal skin tags that coexisted with prolapsed hemorrhoids, the hemorrhoidal varices could be resected and electrically coagulated through the wound without cutting the anal canal epithelium by using a fine needle-type electric knife. The results of this series indicated that SEC could dramatically reduce the incidence of the postoperative complications that sometimes occur after conventional hemorrhoid-ectomy, such as severe anal pain, massive anal bleeding and anal stenosis. Moreover, SEC could ensure that operated patients make an early return to social activities and have a satisfactory quality of life. Relapse of prolapsed hemorrhoids after SEC was rare
Optimal waveform for fast entrainment of airfoil wakes
We obtain an optimal actuation waveform for fast entrainment of periodic
airfoil wakes through the phase reduction approach. Entrainment is the
synchronization process of the system to an external forcing input in an
asymptotic manner. Using the phase reduction approach for periodic wake flows,
the spatial sensitivity fields with respect to the phase of the vortex shedding
are obtained. The phase sensitivity fields can uncover the synchronization
properties in the presence of periodic actuation. This study seeks a periodic
actuation waveform using phase-based analysis to minimize the time for
entrainment to modify the wake-shedding frequency of NACA0012 airfoil wakes.
This fast entrainment waveform is obtained theoretically from the phase
sensitivity function by casting an optimization problem. The obtained optimal
actuation waveform becomes increasingly non-sinusoidal for higher angles of
attack. Actuation based on the obtained waveform achieves rapid entrainment
within as low as two vortex shedding cycles irrespective of the forcing
frequency whereas traditional sinusoidal actuation requires O(10) shedding
cycles. Further, we analyze the influence of actuation frequency on the vortex
shedding and the aerodynamic coefficients using force-element analysis. The
present analysis provides an efficient way to modify the vortex lock-on
properties with applications to fluid-structure interactions and unsteady flow
control
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