Cosmological perturbations in a family of deformations of general relativity

We study linear cosmological perturbations in a previously introduced family of deformations of general relativity characterized by the absence of new degrees of freedom. The homogeneous and isotropic background in this class of theories is unmodified and is described by the usual Friedmann equations. The theory of cosmological perturbations is modified and the relevant deformation parameter has the dimension of length. Gravitational perturbations of the scalar type can be described by a certain relativistic potential related to the matter perturbations just as in general relativity. A system of differential equations describing the evolution of this potential and of the stress-energy density perturbations is obtained. We find that the evolution of scalar perturbations proceeds with a modified effective time-dependent speed of sound, which, contrary to the case of general relativity, does not vanish even at the matter-dominated stage. In a broad range of values of the length parameter controlling the deformation, a specific transition from the regime of modified gravity to the regime of general relativity in the evolution of scalar perturbations takes place during the radiation domination. In this case, the resulting power spectrum of perturbations in radiation and dark matter is suppressed on the comoving spatial scales that enter the Hubble radius before this transition. We estimate the bounds on the deformation parameter for which this suppression does not lead to observable consequences. Evolution of scalar perturbations at the inflationary stage is modified but very slightly and the primordial spectrum generated during inflation is not noticeably different from the one obtained in general relativity.Comment: 45 pages, version published in JCAP; minor changes, one section moved to the appendi

Single fluxon in double stacked Josephson junctions: Analytic solution

We derive an approximate analytic solution for a single fluxon in a double stacked Josephson junctions (SJJ's) for arbitrary junction parameters and coupling strengths. It is shown that the fluxon in a double SJJ's can be characterized by two components, with different Swihart velocities and Josephson penetration depths. Using the perturbation theory we find the second order correction to the solution and analyze its accuracy. Comparison with direct numerical simulations shows a quantitative agreement between exact and approximate analytic solutions. It is shown that due to the presence of two components, the fluxon in SJJ's may have an unusual shape with an inverted magnetic field in the second junction when the velocity of the fluxon is approaching the lower Swihart velocity.Comment: 4 pages, 3 figure

On the Nature of Black Holes in Loop Quantum Gravity

A genuine notion of black holes can only be obtained in the fundamental framework of quantum gravity resolving the curvature singularities and giving an account of the statistical mechanical, microscopic degrees of freedom able to explain the black hole thermodynamical properties. As for all quantum systems, a quantum realization of black holes requires an operator algebra of the fundamental observables of the theory which is introduced in this study based on aspects of loop quantum gravity. From the eigenvalue spectra of the quantum operators for the black hole area, charge and angular momentum, it is demonstrated that a strict bound on the extensive parameters, different from the relation arising in classical general relativity, holds, implying that the extremal black hole state can neither be measured nor can its existence be proven. This is, as turns out, a result of the specific form of the chosen angular momentum operator and the corresponding eigenvalue spectrum, or rather the quantum measurement process of angular momentum. Quantum mechanical considerations and the lowest, non-zero eigenvalue of the loop quantum gravity black hole mass spectrum indicate, on the one hand, a physical Planck scale cutoff of the Hawking temperature law and, on the other hand, give upper and lower bounds on the numerical value of the Immirzi parameter. This analysis provides an approximative description of the behavior and the nature of quantum black holes

The shape of a moving fluxon in stacked Josephson junctions

We study numerically and analytically the shape of a single fluxon moving in a double stacked Josephson junctions (SJJ's) for various junction parameters. We show that the fluxon in a double SJJ's consists of two components, which are characterized by different Swihart velocities and Josephson penetration depths. The weight coefficients of the two components depend on the parameters of the junctions and the velocity of the fluxon. It is shown that the fluxon in SJJ's may have an unusual shape with an inverted magnetic field in the second junction when the velocity of the fluxon is approaching the lower Swihart velocity. Finally, we study the influence of fluxon shape on flux-flow current-voltage characteristics and analyze the spectrum of Cherenkov radiation for fluxon velocity above the lower Swihart velocity. Analytic expression for the wavelength of Cherenkov radiation is derived.Comment: 12 pages, 12 figure

Modeling of flow of two-phase mixture in curved channel pipeline

This article describes the three-dimensional modeling of steady motion of gas and condensed phase particles of varying severity in a curvilinear orthogonal coordinate system gas channels. A numerical method for solving the equations that describe the motion of the particles, based on the difference scheme and the application of the two-level iterative process. Built multivariate mathematical model of viscous steady flow of gas and the equilibrium of hydrate particles in axisymmetric taking into account transport and energy dissipation. Obtained pressure field in the pipe by solving the model equations using SIMPLE method. Numerical calculations of the velocity field of the gas and the dispersed phase, the trajectory of the mass flow deposited on particles of different sizes with the wall during the wet gas in the curved pipe. The calculation of particle trajectories in different kinds of process equipment show at the option of either abrasive wear parts located in a stream, or an intense build-up and accumulation of hydrates. The results can be applied in the analysis of impact of solid particles of various sizes on the elements of gas pipelines

Modeling of flow two-phase mixture in curved channel pipeline

The article describes a three-dimensional simulation of the stationary motion of the gas and condensed phase particles of varying severity in a curvilinear orthogonal coordinate system of channels of gas pipelines. A numerical method for solving the equations that describe the motion of the particles, based on obtaining difference schemes and the use of a two-level iterative process. Built a multi-dimensional mathematical model of the steady flow of viscous gas hydrate particles in equilibrium axisymmetric taking into account transport and energy dissipation. Numerical calculations of the velocity field and the dispersed gas phase trajectory of mass flow of particles deposited on the walls of various sizes in a wet gas flow in a curved pipe

Zero Order Correction of Shift-multiplexed Computer Generated Fourier Holograms Recorded in Incoherent Projection Scheme

Application of computer holography methods provides the possibility to obtain the high quality holograms of objects that exist as digital models without the necessity of complex and high precision optical schemes. Computer generated Fourier holograms (CGFH) are widely used for record and optical restoration of relatively simple 2D raster objects. Application of incoherent photolithography methods such as incoherent projection allows the record of CGFHs as micro-holograms onto the photosensitiv medium with desired reduction of hologram sizes using relatively simple optical setup. The reconstruction optical schemes of CGFHs can be implemented in augmented reality displays and optical sight indicators. In this article the specificity of CGFH shift-multiplexed record process and particularly the method of zero order correction is discussed. Keywords: computer generated hologram, Fourier hologram, incoherent projection scheme

Collapse of thermal activation in moderately damped Josephson junctions

We study switching current statistics in different moderately damped Josephson junctions: a paradoxical collapse of the thermal activation with increasing temperature is reported and explained by interplay of two conflicting consequences of thermal fluctuations, which can both assist in premature escape and help in retrapping back into the stationary state. We analyze the influence of dissipation on the thermal escape by tuning the damping parameter with a gate voltage, magnetic field, temperature and an in-situ capacitor.Comment: 4 pages, 4 figure

The Universal Phase Space of AdS3 Gravity

We describe what can be called the "universal" phase space of AdS3 gravity, in which the moduli spaces of globally hyperbolic AdS spacetimes with compact spatial sections, as well as the moduli spaces of multi-black-hole spacetimes are realized as submanifolds. The universal phase space is parametrized by two copies of the Universal Teichm\"uller space T(1) and is obtained from the correspondence between maximal surfaces in AdS3 and quasisymmetric homeomorphisms of the unit circle. We also relate our parametrization to the Chern-Simons formulation of 2+1 gravity and, infinitesimally, to the holographic (Fefferman-Graham) description. In particular, we obtain a relation between the generators of quasiconformal deformations in each T(1) sector and the chiral Brown-Henneaux vector fields. We also relate the charges arising in the holographic description (such as the mass and angular momentum of an AdS3 spacetime) to the periods of the quadratic differentials arising via the Bers embedding of T(1)xT(1). Our construction also yields a symplectic map from T*T(1) to T(1)xT(1) generalizing the well-known Mess map in the compact spatial surface setting.Comment: 41 pages, 2 figures, revised version accepted for publication in Commun.Math.Phy