The blue phases of cholesteric liquid crystals are liquids that exhibit orientational order characterized by crystallographic space-group symmetries. We present here a pedagogical introduction to the current understanding of the equilibrium structure of these phases accompanied by a general overview of major experimental results. Using the Ginzburg-Landau free energy appropriate to the system, we first discuss in detail the character and stability of the usual helical phase of cholesterics, showing that for certain parameter ranges the helical phase is unstable to the appearance of one or more blue phases. The two principal models for the blue phases are two limiting cases of the Ginzburg-Landau theory. We explore each limit and conclude with some general considerations of defects in both models and an exact minimization of the free energy in a curved three-dimensional space.

We describe a "neutrinogenesis" mechanism whereby, in the presence of right-handed neutrinos with sufficiently small pure Dirac masses, (B+L)-violating sphaleron processes create the baryon asymmetry of the Universe, even when B = L = 0 initially. It is shown that the resulting neutrino mass constraints are easily fulfilled by the neutrino masses suggested by current experiments. We present a simple toy model which uses this mechanism to produce the observed baryon asymmetry of the Universe.

Nightmares and sleep disturbance are fundamental concerns for victims of trauma. This study examined the efficacy of a manualized cognitive-behavioral treatment (CBT) for chronic nightmares in trauma-exposed individuals via a randomized clinical trial. Participants were randomly assigned to a treatment group or wait-list control group, with 27 participants completing the treatment. At the 6-month follow-up assessment, 84% of treated participants reported an absence of nightmares in the previous week. Significant decreases were also reported in symptoms of depression and posttraumatic stress, fear of sleep, and number of sleep problems, while sleep quality and quantity improved. The present study adds to the growing literature indicating this brief CBT as a first-line treatment for trauma-exposed individuals with chronic nightmares.

BackgroundSomitogenesis is the earliest sign of segmentation in the developing vertebrate embryo. This process starts very early, soon after gastrulation has initiated and proceeds in an anterior-to-posterior direction during body axis elongation. It is widely accepted that somitogenesis is controlled by a molecular oscillator with the same periodicity as somite formation. This periodic mechanism is repeated a specific number of times until the embryo acquires a defined specie-specific final number of somites at the end of the process of axis elongation. This final number of somites varies widely between vertebrate species. How termination of the process of somitogenesis is determined is still unknown.ResultsHere we show that during development there is an imbalance between the speed of somite formation and growth of the presomitic mesoderm (PSM)/tail bud. This decrease in the PSM size of the chick embryo is not due to an acceleration of the speed of somite formation because it remains constant until the last stages of somitogenesis, when it slows down. When the chick embryo reaches its final number of somites at stage HH 24-25 there is still some remaining unsegmented PSM in which expression of components of the somitogenesis oscillator is no longer dynamic. Finally, we identify a change in expression of retinoic acid regulating factors in the tail bud at late stages of somitogenesis, such that in the chick embryo there is a pronounced onset of Raldh2 expression while in the mouse embryo the expression of the RA inhibitor Cyp26A1 is downregulated.ConclusionsOur results show that the chick somitogenesis oscillator is arrested before all paraxial mesoderm is segmented into somites. In addition, endogenous retinoic acid is probably also involved in the termination of the process of segmentation, and in tail growth in general.

The problem of minimizing the full cholesteric free energy in flat space is difficult since the bending and bulk energies favor different forms of the order parameter. It is shown, however, that the problem can be solved exactly on the surface of a sphere in four-space, where the curvature relieves the strains induced by the "double twist." The conventional Landau bulk free energy leads to a rigorously uniaxial structure. The model is also of interest as a simple and explicit example of the ideas underlying recent theories of glasses.PACS numbers: 64.70.Ew, 61.30.Jf Equilibrium theories of cholesteric liquid crystals 1 " 3 are based on the minimization of a simple mean-field free energy, yet they display a bewildering variety of "blue phases," as do the materials themselves. 4 This complexity is the manifestation of an incompatibility in the free energy: Structures that favor bulk terms in the free energy do not take full advantage of the possibilities for minimizing the gradient energy, and vice versa. We have found that this difficulty disappears on the surface of a sphere in four dimensions with circumference given by the cholesteric pitch p: There is a unique unfrustrated texture which minimizes the free energy, providing an exact solution to a problem which has proved extremely difficult to treat in flat space. A recent proposal for a model of the blue phase , /grad=i^i(V,Q 0 -) 2 +^2(V fe Q, J .) 2 +l^^(V fe Qi,)Q i5 where sums on indicies are implied. The K 3 r as a "doubly twisted" structure threaded by a network of disclination lines is seen from this perspective to be nothing but the result of flattening out our exact curved-space solution. The cholesteric thus emerges as an extremely simple, explicit, and, in the curved space, analytically manageable continuum model of the general kinds of ideas that people have been formulating to account for the structure of glasses. 5 ' 6 The order parameter in nematic or cholesteric liquid crystals is a real traceless symmetric tensor Q {j that characterizes the deviation from isotropy of some appropriate local tensor property of the system 7 such as the dielectric constant. To second order in spatial gradients and to leading nonvanishing order in Q there are just three independent terms in the bending free-energy density:(1) term is allowed only in cholesterics, which are distinguished from nematics by the absence of microscopic inversion symmetry. The simplest model for the bulk free-energy density requires terms through fourth order in Q. Since the only independent invariants of a traceless three-tensor are TrQ 2 and TrQ 3 , this has the general form = aTrQ 2 -£TrQ 3 + y(Tr