The Gamma-limit of the two-dimensional Ohta-Kawasaki energy. II. Droplet arrangement at the sharp interface level via the renormalized energy

This is the second in a series of papers in which we derive a $\Gamma$-expansion for the two-dimensional non-local Ginzburg-Landau energy with Coulomb repulsion known as the Ohta-Kawasaki model in connection with diblock copolymer systems. In this model, two phases appear, which interact via a nonlocal Coulomb type energy. Here we focus on the sharp interface version of this energy in the regime where one of the phases has very small volume fraction, thus creating small "droplets" of the minority phase in a "sea" of the majority phase. In our previous paper, we computed the $\Gamma$-limit of the leading order energy, which yields the averaged behavior for almost minimizers, namely that the density of droplets should be uniform. Here we go to the next order and derive a next order $\Gamma$-limit energy, which is exactly the Coulombian renormalized energy obtained by Sandier and Serfaty as a limiting interaction energy for vortices in the magnetic Ginzburg-Landau model. The derivation is based on the abstract scheme of Sandier-Serfaty that serves to obtain lower bounds for 2-scale energies and express them through some probabilities on patterns via the multiparameter ergodic theorem. Without thus appealing to the Euler-Lagrange equation, we establish for all configurations which have "almost minimal energy" the asymptotic roundness and radius of the droplets, and the fact that they asymptotically shrink to points whose arrangement minimizes the renormalized energy in some averaged sense. Via a kind of $\Gamma$-equivalence, the obtained results also yield an expansion of the minimal energy for the original Ohta-Kawasaki energy. This leads to expecting to see triangular lattices of droplets as energy minimizers

Developmental and tissue-specific expression of the Q5k gene

Expression of the Q5k gene was examined by northern blot analysis and polymerase chain reaction (PCR) in the AKR mouse and various cell lines, each of the H-2k haplotype. Our results show that Q5k mRNA is present during the whole postimplantational development of the AKR embryo/fetus (gestation day 6 to 15). In the juvenile mouse (week 2 to 4) transcription of the Q5k gene persisted in all organs examined. In contrast, in the adult animal expression of the Q5k gene was limited to the thymus and uterus of the pregnant mouse. Upon malignant transformation, the amount of Q5k-specific mRNA increased dramatically in thymus and could also be observed in the spleen of thymoma bearing animals. Expression of the Q5k gene was also detectable in several transformed mouse cell lines. Mitogen stimulation or treatment with cytokines induced Q5k expression in primary spleen cell cultures. A possible explanation for the tissue-restricted expression in the adult AKR mouse is discussed

Effects of Vibration and G-Loading on Heart Rate, Breathing Rate, and Response Time

Aerospace and applied environments commonly expose pilots and astronauts to G-loading and vibration, alone and in combination, with well-known sensorimotor (Cohen, 1970) and performance consequences (Adelstein et al., 2008). Physiological variables such as heart rate (HR) and breathing rate (BR) have been shown to increase with G-loading (Yajima et al., 1994) and vibration (e.g. Guignard, 1965, 1985) alone. To examine the effects of G-loading and vibration, alone and in combination, we measured heart rate and breathing rate under aerospace-relevant conditions (G-loads of 1 Gx and 3.8 Gx; vibration of 0.5 gx at 8, 12, and 16 Hz)

Ocean Dynamics and the Inner Edge of the Habitable Zone for Tidally Locked Terrestrial Planets

Recent studies have shown that ocean dynamics can have a significant warming effect on the permanent night sides of 1 to 1 tidally locked terrestrial exoplanets with Earth-like atmospheres and oceans in the middle of the habitable zone. However, the impact of ocean dynamics on the habitable zone's boundaries (inner edge and outer edge) is still unknown and represents a major gap in our understanding of this type of planets. Here we use a coupled atmosphere-ocean global climate model to show that planetary heat transport from the day to night side is dominated by the ocean at lower stellar fluxes and by the atmosphere near the inner edge of the habitable zone. This decrease in oceanic heat transport (OHT) at high stellar fluxes is mainly due to weakening of surface wind stress and a decrease in surface shortwave energy deposition. We further show that ocean dynamics have almost no effect on the observational thermal phase curves of planets near the inner edge of the habitable zone. For planets in the habitable zone's middle range, ocean dynamics moves the hottest spot on the surface eastward from the substellar point. These results suggest that future studies of the inner edge may devote computational resources to atmosphere-only processes such as clouds and radiation. For studies of the middle range and outer edge of the habitable zone, however, fully coupled ocean-atmosphere modeling will be necessary. Note that due to computational resource limitations, only one rotation period (60 Earth days) has been systematically examined in this study; future work varying rotation period as well as other parameters such as atmospheric mass and composition is required.Comment: 34 pages, 13 figures, and 1 tabl