Abstract:
We suggest that some observational features of high-energy radiation from pulsars should be explained in terms of three dimensional geometric models, e.g. the phase-resolved X-ray and $\gamma$-ray spectra and the energy dependent light curves from various pulsars. In this paper, we present a three dimensional pulsar outer-magnetospheric gap model to explain these observational features. The outer-magnetospheric gap is proposed to form near the null charged surface and extend toward the light cylinder. The other two geometric dimensions of the outer-magnetospheric gap, i.e. the vertical size and the azimuthal extension can be determined self-consistently. We apply this model to explain the observed phase-dependent spectra and the energy-dependent light curves of various pulsars.

Abstract:
In this review paper we explain the following gamma-ray emission features from the millisecond pulsars. (1)Why is the dipolar field of millisecond pulsars so weak but the magnetic pair creation process may still be able to control the size of the outergap? (2)A sub-GeV pulse component could occur in the vicinity of the radio pulse of millisecond pulsars. (3)Orbital modulated gamma-rays should exist in the black widow systems for large viewing angle.

Abstract:
This paper provides an overview of the conventional therapeutic stimulation methodologies and proposes a more effective stimulation approach based on a consideration of the inherently fractal nature of normal biological dynamics. There are varying forms of physiological stimulations including the use of electrical currents, electromagnetic fields, temperature change, ultrasound, light and so forth. These stimulation therapies can be categorized into three main modalities: electrical stimulation modalities, thermal modalities, and non-thermal modalities. Electrical stimulation modalities include therapeutic techniques where electrical current is directly applied to the body of treated subject. Direct application of electrical current to the brain also falls under this category. Thermal modalities consist of stimulations that induce temperature change on the body for therapeutic effects without the direct transfer of electrical current. Non-thermal modalities functions through energy transfer without directly applying electrical current and without the effects of temperature change. A fourth miscellaneous category for stimulation techniques consists of the stimulation effects of music along with physical stimulation as in massage therapy. Common to most of these therapeutic strategies is that the stimulation is delivered at certain fixed periods or frequencies. We introduce some rudiments of fractal dynamics, and the notions of self-similarity, scale-invariance, and long-range correlation or memory in the dynamics of a system. We present evidence that fractal dynamics is commonly observed in healthy physiological systems while unhealthy systems are shown to veer away from fractal dynamics towards periodic or random motion. This difference in dynamics can be observed in many biological signals such as in neural activity, heart rate variations, and breathing patterns. We propose that an optimal stimulation technique should thus be one that encourages an unhealthy, non-fractal pathological system towards a healthy, fractal dynamic. Given the ubiquity of fractality in healthy biological dynamics, we argue that a fractal pattern of stimulation is a more optimal approach to functional restoration than the widely used conventional periodic stimulation, which may further consolidate the existing pathological dynamics.

Abstract:
We consider the general expressions for the time delay of photons of different energies in the framework of multi-dimensional cosmological models. In models with compactified extra-dimensions (Kaluza-Klein type models), the main source of the photon time delay is the time variation of the electromagnetic coupling, due to dimensional reduction, which induces an energy-dependence of the speed of light. A similar relation between the fine structure constant and the multi-dimensional gauge couplings also appears in models with large (non-compactified) extra-dimensions. For photons of energies around 1 TeV, propagating on cosmological distances in an expanding Universe, the time delay could range from a few seconds in the case of Kaluza-Klein models to a few days for models with large extra-dimensions. As a consequence of the multi-dimensional effects, the intrinsic time profiles at the emitter rest frame differ from the detected time profiles. The formalism developed in the present paper allows the transformation of the predicted light curves of various energy ranges of the emitter into the frame of the observer, for comparison with observations. Therefore the study of energy and redshift dependence of the time delay of photons, emitted by astrophysical sources at cosmological distances, could discriminate between the different multi-dimensional models and/or quantum gravity effects.

Abstract:
A version of the virial theorem, which takes into account the effects of the non-compact extra-dimensions, is derived in the framework of the brane world models. In the braneworld scenario, the four dimensional effective Einstein equation has some extra terms, called dark radiation and dark pressure, respectively, which arise from the embedding of the 3-brane in the bulk. To derive the generalized virial theorem we use a method based on the collisionless Boltzmann equation. The dark radiation term generates an equivalent mass term (the dark mass), which gives an effective contribution to the gravitational energy. This term may account for the well-known virial theorem mass discrepancy in actual clusters of galaxies. An approximate solution of the vacuum field equations on the brane, corresponding to weak gravitational fields, is also obtained, and the expressions for the dark radiation and dark mass are derived. The qualitative behavior of the dark mass is similar to that of the observed virial mass in clusters of galaxies. We compare our model with the observational data for galaxy clusters, and we express all the physical parameters of the model in terms of observable quantities. In particular, we predict that the dark mass must extend far beyond the presently considered virial radius. The behavior of the galaxy cluster velocity dispersion in brane world models is also considered. Therefore the study of the matter distribution and velocity dispersion at the extragalactic scales could provide an efficient method for testing the multi-dimensional physical models.

Abstract:
We study the energy released from phase-transition induced collapse of neutron stars, which results in large amplitude stellar oscillations. To model this process we use a Newtonian hydrodynamic code, with a high resolution shock-capturing scheme. The physical process considered is a sudden phase transition from normal nuclear matter to a mixed phase of quark and nuclear matter. We show that both the temperature and the density at the neutrinosphere oscillate with time. However, they are nearly 180 degree out of phase. Consequently, extremely intense, pulsating neutrino/antineutrino and leptonic pair fluxes will be emitted. During this stage several mass ejecta can be ejected from the stellar surface by the neutrinos and antineutrinos. These ejecta can be further accelerated to relativistic speeds by the electron/positron pairs, created by the neutrino and antineutrino annihilation outside the stellar surface. We suggest that this process may be a possible mechanism for short Gamma-Ray Bursts.

Abstract:
By direct numerical simulation of the time-dependent Gross-Pitaevskii equation using the split-step Fourier spectral method we study different aspects of the localization of a cigar-shaped interacting binary (two-component) Bose-Einstein condensate (BEC) in a one-dimensional bi-chromatic quasi-periodic optical-lattice potential, as used in a recent experiment on the localization of a BEC [Roati et al., Nature 453, 895 (2008)]. We consider two types of localized states: (i) when both localized components have a maximum of density at the origin x=0, and (ii) when the first component has a maximum of density and the second a minimum of density at x=0. In the non-interacting case the density profiles are symmetric around x=0. We numerically study the breakdown of this symmetry due to inter-species and intra-species interaction acting on the two components. Where possible, we have compared the numerical results with a time-dependent variational analysis. We also demonstrate the stability of the localized symmetry-broken BEC states under small perturbation.

Abstract:
We propose an approximate description of basic parameters (radius, mass and oblateness) of general relativistic compact rotating objects in terms of the parameters of the static configuration and of the angular velocity only. The representation in terms of static properties is derived using the condition of stationary equilibrium together with some phenomenological assumptions. The predicted radius and mass of rotating neutron star (described by some realistic equations of state) and strange star (described by the bag model equation of state) are compared with data obtained by numerical integration of gravitational field equation. The obtained formulae also allow a simple derivation of the "empirical" equation relating the maximum rotation frequency $\Omega_{max}$ of uniformly rotating star models to the mass and radius of the maximum allowable mass configuration of the non-rotating model.

Abstract:
The Chandrasekhar limit for strange stars described by a linear equation of state (describing quark matter with density-dependent quark masses) is evaluated. The maximum mass and radius of the star depend on the fundamental constants and on the energy density of the quark matter at zero pressure. By comparing the expression for the mass of the star with the limiting mass formula for a relativistic degenerate stellar configuration one can obtain an estimate of the mass of the strange quark.

Abstract:
We study the localization of a cigar-shaped super-fluid Bose-Fermi mixture in a quasi-periodic bichromatic optical lattice (OL) for inter-species attraction and intra-species repulsion. The mixture is described by the Gross-Pitaevskii equation for the bosons, coupled to a hydrodynamic mean-field equation for fermions at unitarity. We confirm the existence of the symbiotic localized states in the Bose-Fermi mixture and Anderson localization of the Bose component in the interacting Bose-Fermi mixture on a bichromatic OL. The phase diagram in boson and fermion numbers showing the regions of the symbiotic and Anderson localization of the Bose component is presented. Finally, the stability of symbiotic and Anderson localized states is established under small perturbations.