Abstract:
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.

Abstract:
Pattern formation of a thin layer of vertically agitated wet granular matter is investigated experimentally. Due to the strong cohesion arising from the capillary bridges formed between adjacent particles, agitated wet granular matter exhibits a different scenario compared with cohesionless dry particles. Rotating spirals with three arms, which correspond to the kinks between regions with different colliding phases with the vibrating plate, have been found to be the dominating pattern. From both top view snapshots and laser profilometry methods, the rotation frequency of the spiral arms is characterized with image processing procedures. Both methods reveal that there exists a finite rotation frequency $\nu_{\rm r}$ at a threshold vibration acceleration, above which $\nu_{\rm r}$ increases linearly with the peak vibration acceleration with a slope strongly dependent on the vibration frequency.

Abstract:
Pattern formation of a thin layer of vertically agitated wet granular matter is investigated experimentally. Rotating spirals with three arms, which correspond to the kinks between regions with different colliding phases, are the dominating pattern. This preferred number of arms corresponds to period tripling of the agitated granular layer, unlike predominantly subharmonic Faraday crispations in dry granular matter. The chirality of the spatiotemporal pattern corresponds to the rotation direction of the spirals.

Abstract:
An investigation has been made to study the reaction kinetics of gelled acids with calcite using a rotating disk apparatus. The rheological experiments revealed that all gelled acids behaved as non-Newtonian shear thinning fluids. With the rotating disk apparatus, the reaction kinetics parameters, activation energy, and effective diffusion coefficients were determined. It was found that the reaction of gelled acid with calcite was mass transfer limited at low polymer concentration and moving toward surface reaction limited at higher polymer concentration. And the diffusion rate marginally decreased, with increasing the polymer concentration.

Abstract:
It has been a puzzle that rotating detector may respond even in the appropriate vacuum defined via canonical quantization. We solve this puzzle by taking back reaction of the detector into account. The influence of the back reaction, even in the detector's mass infinite limit, appears in the response function. It makes the detector possible to respond in the vacuum if the detector is rotating, though the detector in linear uniform motion never respond in the vacuum as expected from Poincare invariance.

Abstract:
For Rayleigh-Benard convection of a fluid with Prandtl number \sigma \approx 1, we report experimental and theoretical results on a pattern selection mechanism for cell-filling, giant, rotating spirals. We show that the pattern selection in a certain limit can be explained quantitatively by a phase-diffusion mechanism. This mechanism for pattern selection is very different from that for spirals in excitable media.

Abstract:
A single merger scenario for making galaxies such as NGC 4550 possessing equal coplanar counter-rotating stellar disks is investigated by collisionless N-body technique. The scenario is successful in producing an axisymmetric disk made of two almost equal counter-rotating populations. The final disk shows a clear bimodal line profile in the outer part, which demonstrates that disk-disk mergers do not always produce ellipticals.

Abstract:
According to the cosmological model without singularity, there are s-matter and v-matter which are symmetric and have oppose gravitational masses. In V-breaking s-matter is similar to dark energy to cause expansion of the universe with an acceleration now, and v-matter is composed of v-F-matter and v-W-matter which are symmetric and have the same gravitational masses and forms the world. The ratio of s-matter to v-matter is changeable. Based on the cosmological model, we confirm that big bang nucleosynthesis is not spoiled by that the average energy density of W-matter (mirror matter) is equal to that of F-matter (ordinary matter). According to the present model, there are three sorts of dark matter which are v-W-baryon matter (4/27), unknown v-F-matter (9.5/27) and v-W-matter (9.5/27). Given v-F-baryon matter (4/27) and v-W-baryon matter can cluster and respectively form the visible galaxies and dark galaxies. Unknown v-F-matter and v-W-matter cannot cluster to form any celestial body, loosely distribute in space, are equivalent to cold dark matter, and their compositions are unknown. The number in a bracket is the ratio of the density of a sort of matter to total density of v-matter. The decisive predict is that there are dark celestial bodies and dark galaxies. The energy of F-matter can transform into the energy of W-matter by such a process in which the reaction energy is high enough.

Abstract:
An exact solution of the vacuum Einstein field equations over a nonsimply-connected manifold is presented. This solution is spherically symmetric and has no curvature singularity. It can be considered to be a regularization of the Schwarzschild solution over a simply-connected manifold, which has a curvature singularity at the center. Spherically symmetric collapse of matter in R^4 may result in this nonsingular black-hole solution, if quantum-gravity effects allow for topology change near the center.

Abstract:
We construct phantom energy models with the equation-of-state parameter $w$ such that $w<-1$, but finite-time future singularity does not occur. Such models can be divided into two classes: (i) energy density increases with time ("phantom energy" without "Big Rip" singularity) and (ii) energy density tends to constant value with time ("cosmological constant" with asymptotically de Sitter evolution). The disintegration of bound structure is confirmed in Little Rip cosmology. Surprisingly, we find that such disintegration (on example of Sun-Earth system) may occur even in asymptotically de Sitter phantom universe consistent with observational data. We also demonstrate that non-singular phantom models admit wormhole solutions as well as possibility of big trip via wormholes.