Warped product approach to universe with non-smooth scale factor

In the framework of Lorentzian warped products, we study the Friedmann-Robertson-Walker cosmological model to investigate non-smooth curvatures associated with multiple discontinuities involved in the evolution of the universe. In particular we analyze non-smooth features of the spatially flat Friedmann-Robertson-Walker universe by introducing double discontinuities occurred at the radiation-matter and matter-lambda phase transitions in astrophysical phenomenology.Comment: 10 page

Dynamic model for failures in biological systems

A dynamic model for failures in biological organisms is proposed and studied both analytically and numerically. Each cell in the organism becomes dead under sufficiently strong stress, and is then allowed to be healed with some probability. It is found that unlike the case of no healing, the organism in general does not completely break down even in the presence of noise. Revealed is the characteristic time evolution that the system tends to resist the stress longer than the system without healing, followed by sudden breakdown with some fraction of cells surviving. When the noise is weak, the critical stress beyond which the system breaks down increases rapidly as the healing parameter is raised from zero, indicative of the importance of healing in biological systems.Comment: To appear in Europhys. Let

Cosmological Luminosity Evolution of QSO/AGN Population

We apply the observed optical/X-ray spectral states of the Galactic black hole candidates (GBHCs) to the cosmological QSO luminosity evolution under the assumptions that QSOs and GBHCs are powered by similar accretion processes and that their emission mechanisms are also similar. The QSO luminosity function (LF) evolution in various energy bands is strongly affected by the spectral evolution which is tightly correlated with the luminosity evolution. We generate a random sample of QSOs born nearly synchronously by allowing the QSOs to have redshifts in a narrow range around an initial high redshift, black hole masses according to a power-law, and mass accretion rates near Eddington rates. The QSOs evolve as a single long-lived population on the cosmological time scale. The pure luminosity evolution results in distinct luminosity evolution features due to the strong spectral evolution. Most notably, different energy bands (optical/UV, soft X-ray, and hard X-ray) show different evolutionary trends and the hard X-ray LF in particular shows an apparent reversal of the luminosity evolution (from decreasing to increasing luminosity) at low redshifts, which is not seen in the conventional pure luminosity evolution scenario without spectral evolution. The resulting mass function of black holes (BHs), which is qualitatively consistent with the observed QSO LF evolution, shows that QSO remnants are likely to be found as BHs with masses in the range 10**8-5x10**10 solar masses. The long-lived single population of QSOs are expected to leave their remnants as supermassive BHs residing in rare, giant elliptical galaxies.Comment: 9 pages, 2 figures, ApJ

Dynamic transition and Shapiro-step melting in a frustrated Josephson-junction array

We consider a two-dimensional fully frustrated Josephson-junction array driven by combined direct and alternating currents. Interplay between the mode locking phenomenon, manifested by giant Shapiro steps in the current-voltage characteristics, and the dynamic phase transition is investigated at finite temperatures. Melting of Shapiro steps due to thermal fluctuations is shown to be accompanied by the dynamic phase transition, the universality class of which is also discussed

Characterisation of the dynamical quantum state of a zero temperature Bose-Einstein condensate

We describe the quantum state of a Bose-Einstein condensate at zero temperature. By evaluating the Q-function we show that the ground state of Bose-Einstein condensate under the Hartree approximation is squeezed. We find that multimode Schroedinger cat states are generated as the condensate evolves in a ballistic expansion.Comment: 13 pages, 6 figure

Dynamic model of fiber bundles

A realistic continuous-time dynamics for fiber bundles is introduced and studied both analytically and numerically. The equation of motion reproduces known stationary-state results in the deterministic limit while the system under non-vanishing stress always breaks down in the presence of noise. Revealed in particular is the characteristic time evolution that the system tends to resist the stress for considerable time, followed by sudden complete rupture. The critical stress beyond which the complete rupture emerges is also obtained