Non-Supersymmetric Attractors

We consider theories with gravity, gauge fields and scalars in four-dimensional asymptotically flat space-time. By studying the equations of motion directly we show that the attractor mechanism can work for non-supersymmetric extremal black holes. Two conditions are sufficient for this, they are conveniently stated in terms of an effective potential involving the scalars and the charges carried by the black hole. Our analysis applies to black holes in theories with ${\cal N} \le 1$ supersymmetry, as well as non-supersymmetric black holes in theories with ${\cal N} = 2$ supersymmetry. Similar results are also obtained for extremal black holes in asymptotically Anti-de Sitter space and in higher dimensions.Comment: 55 pages, LaTeX, 7 eps figures. v3: references and some additional comments added, minor correction

Long-term and blow-up behaviors of exponential moments in multi-dimensional affine diffusions

This paper considers multi-dimensional affine processes with continuous sample paths. By analyzing the Riccati system, which is associated with affine processes via the transform formula, we fully characterize the regions of exponents in which exponential moments of a given process do not explode at any time or explode at a given time. In these two cases, we also compute the long-term growth rate and the explosion rate for exponential moments. These results provide a handle to study implied volatility asymptotics in models where returns of stock prices are described by affine processes whose exponential moments do not have an explicit formula.Comment: 36 pages, 5 figure

Porosome: the universal secretory portal in cells

In the past 50 years it was believed that during cell secretion, membrane-bound secretory vesicles completely merge at the cell plasma membrane resulting in the diffusion of intra-vesicular contents to the cell exterior and the compensatory retrieval of the excess membrane by endocytosis. This explanation made no sense or logic, since following cell secretion partially empty vesicles accumulate as demonstrated in electron micrographs. Furthermore, with the 'all or none' mechanism of cell secretion by complete merger of secretory vesicle membrane at the cell plasma membrane, the cell is left with little regulation and control of the amount of content release. Moreover, it makes no sense for mammalian cells to possess such 'all or none' mechanism of cell secretion, when even single-cell organisms have developed specialized and sophisticated secretory machinery, such as the secretion apparatus of Toxoplasma gondii, the contractile vacuoles in paramecium, or the various types of secretory structures in bacteria. Therefore, in the 1960's, experimental data concerning neurotransmitter release mechanisms by B. Katz and B. Folkow brilliantly hypothesized that limitation of the quantal packet may be set by the nerve membrane, in which case the size of the packet may actually correspond to just a fraction of the vesicle content. This conundrum in the molecular mechanism of cell secretion was finally resolved in 1997 following discovery of the porosome, the universal secretory machinery in the cell. Porosomes are supramolecular lipoprotein structures at the cell plasma membrane, where membrane-bound secretory vesicles transiently dock and fuse to release inravesicular contents to the outside during cell secretion. In the past decade, the composition of the porosome, its structure and dynamics at nanometer (nm) resolution and in real time, and its functional reconstitution into artificial lipid membrane, have all been elucidated. Since porosomes in exocrine and neuroendocrine cells measure 100-180 nm, and only 20-45% increase in porosome diameter is demonstrated following the docking and fusion of secretory vesicles (0.2-1.2 μm in diameter), it is concluded that secretory vesicles "transiently" dock and fuse, rather than completely merge at the base of the porosome complex to release their contents to the outside. In agreement, it has been demonstrated that "secretory granules are recaptured largely intact after stimulated exocytosis in cultured endocrine cells"; that "single synaptic vesicles fuse transiently and successively without loss of identity"; and that "zymogen granule (the secretory vesicle in exocrine pancreas) exocytosis is characterized by long fusion pore openings and preservation of vesicle lipid identity". In this review, the discovery of the porosome, resulting in a paradigm shift in our understanding of cell secretion, is briefly presented.Biomedical Reviews 2010; 21: 1-15

Warm Asymmetric Nuclear Matter and Proto-Neutron Star

Asymmetric nuclear matter equation of state at finite temperature is studied in SU(2) chiral sigma model using mean field approximation. The effect of temperature on effective mass, entropy, and binding energy is discussed. Treating the system as one with two conserved charges the liquid-gas phase transition is investigated. We have also discussed the effect of proton fraction on critical temperature with and without $\rho$-meson contribution. We have extended our work to study the structure of proto-neutron star with neutron free charge-neutral matter in beta-equilibrium. We found that the mass and radius of the star decreases as it cools from the entropy per baryon S = 2 to S = 0 and the maximum temperature of the core of the star is about 62 MeV for S = 2.Comment: 25 pages, 16 figure

Novel electronic and magnetic properties of BN sheet decorated with hydrogen and fluorine

First principles calculations based on density functional theory reveal some unusual properties of BN sheet functionalized with hydrogen and fluorine. These properties differ from those of similarly functionalized graphene even though both share the same honeycomb structure. (1) Unlike graphene which undergoes a metal to insulator transition when fully hydrogenated, the band gap of the BN sheet significantly narrows when fully saturated with hydrogen. Furthermore, the band gap of the BN sheet can be tuned from 4.7 eV to 0.6 eV and the system can be a direct or an indirect semiconductor or even a half-metal depending upon surface coverage. (2) Unlike graphene, BN sheet has hetero-atomic composition, when co-decorated with H and F, it can lead to anisotropic structures with rich electronic and magnetic properties. (3) Unlike graphene, BN sheets can be made ferromagnetic, antiferromagnetic, or magnetically degenerate depending upon how the surface is functionalized. (4) The stability of magnetic coupling of functionalized BN sheet can be further modulated by applying external strain. Our study highlights the potential of functionalized BN sheets for novel applications.Comment: 18 pages, 6 figures, and 1 tabl

SU(2) Chiral Sigma Model Study of Phase Transition in Hybrid Stars

We use a modified SU(2) chiral sigma model to study nuclear matter component and simple bag model for quark matter constituting a neutron star. We also study the phase transition of nuclear matter to quark matter with the mixed phase characterized by two conserved charges in the interior of highly dense neutron stars. Stable solutions of Tolman-Oppenheimer-Volkoff equations representing hybrid stars are obtained with a maximum mass of 1.67$M_{\odot}$ and radius around 8.9 km.Comment: 14 pages, 5 figure