Reduced Dynamics from the Unitary Group to Some Flag Manifolds : Interacting Matrix Riccati Equations

In this paper we treat the time evolution of unitary elements in the N level system and consider the reduced dynamics from the unitary group U(N) to flag manifolds of the second type (in our terminology). Then we derive a set of differential equations of matrix Riccati types interacting with one another and present an important problem on a nonlinear superposition formula that the Riccati equation satisfies. Our result is a natural generalization of the paper {\bf Chaturvedi et al} (arXiv : 0706.0964 [quant-ph]).Comment: Latex ; 13 pages ; no figur

More on the Isomorphism SU(2)⊗SU(2)≅SO(4)SU(2)\otimes SU(2)\cong SO(4)

In this paper we revisit the isomorphism $SU(2)\otimes SU(2)\cong SO(4)$ to apply to some subjects in Quantum Computation and Mathematical Physics. The unitary matrix $Q$ by Makhlin giving the isomorphism as an adjoint action is studied and generalized from a different point of view. Some problems are also presented. In particular, the homogeneous manifold $SU(2n)/SO(2n)$ which characterizes entanglements in the case of $n=2$ is studied, and a clear-cut calculation of the universal Yang-Mills action in (hep-th/0602204) is given for the abelian case.Comment: Latex ; 19 pages ; 5 figures ; minor changes. To appear in International Journal of Geometric Methods in Modern Physics (vol.4, no.3

Thermodynamic effects on cryogenic cavitating flow in an orifice

Temperature depression in a cavitating orifice flow was experimentally investigated with liquid nitrogen in order to clarify the influence of turbulent flow around a bubble on thermodynamic effects on cavitation. The temperature began to decrease at the outlet of the orifice when the cavitation number decreased below 0. Moreover, the temperature depression became larger as the cavitation number became smaller. In addition, the temperature depression also became greater as the flow velocity became lower when the cavitation numbers were equal. Based on theoretical considerations and experimental results, the difference of temperature depression can be considered to be caused by the enhancement of thermal transport around bubbles due to the turbulent flow. In addition, if thermal transport is enhanced as mentioned above, the temperature in the area where the cavitation collapses can become higher than that upstream of the orifice due to the temporary breakdown of the heat balance between the inception and collapse of cavity bubbles.http://deepblue.lib.umich.edu/bitstream/2027.42/84237/1/CAV2009-final36.pd

Feeding Cues and Injected Nutrients Induce Acute Expression of Multiple Clock Genes in the Mouse Liver

The circadian clock is closely associated with energy metabolism. The liver clock can rapidly adapt to a new feeding cycle within a few days, whereas the lung clock is gradually entrained over one week. However, the mechanism underlying tissue-specific clock resetting is not fully understood. To characterize the rapid response to feeding cues in the liver clock, we examined the effects of a single time-delayed feeding on circadian rhythms in the liver and lungs of Per2::Luc reporter knockin mice. After adapting to a night-time restricted feeding schedule, the mice were fed according to a 4, 8, or 13 h delayed schedule on the last day. The phase of the liver clock was delayed in all groups with delayed feeding, whereas the lung clock remained unaffected. We then examined the acute response of clock and metabolism-related genes in the liver using focused DNA-microarrays. Clock mutant mice were bred under constant light to attenuate the endogenous circadian rhythm, and gene expression profiles were determined during 24 h of fasting followed by 8 h of feeding. Per2 and Dec1 were significantly increased within 1 h of feeding. Real-time RT-PCR analysis revealed a similarly acute response in hepatic clock gene expression caused by feeding wild type mice after an overnight fast. In addition to Per2 and Dec1, the expression of Per1 increased, and that of Rev-erbα decreased in the liver within 1 h of feeding after fasting, whereas none of these clock genes were affected in the lung. Moreover, an intraperitoneal injection of glucose combined with amino acids, but not either alone, reproduced a similar hepatic response. Our findings show that multiple clock genes respond to nutritional cues within 1 h in the liver but not in the lung