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 $U(1)$ 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