Constraining spacetime torsion with LAGEOS

We compute the corrections to the orbital Lense-Thirring effect (or frame-dragging) in the presence of spacetime torsion. We analyze the motion of a test body in the gravitational field of a rotating axisymmetric massive body, using the parametrized framework of Mao, Tegmark, Guth and Cabi. In the cases of autoparallel and extremal trajectories, we derive the specific approximate expression of the corresponding system of ordinary differential equations, which are then solved with methods of Celestial Mechanics. We calculate the secular variations of the longitudes of the node and of the pericenter. We also show how the LAser GEOdynamics Satellites (LAGEOS) can be used to constrain torsion parameters. We report the experimental constraints obtained using both the nodes and perigee measurements of the orbital Lense-Thirring effect. This makes LAGEOS and Gravity Probe B complementary frame-dragging and torsion experiments, since they constrain three different combinations of torsion parameters.     

Quantum scalar field in quantum gravity: the propagator and Lorentz invariance in the spherically symmetric case

We recently studied gravity coupled to a scalar field in spherical symmetry using loop quantum gravity techniques. Since there are local degrees of freedom one faces the “problem of dynamics”. We attack it using the “uniform discretization technique”. We find the quantum state that minimizes the value of the master constraint for the case of weak fields and curvatures. The state has the form of a direct product of Gaussians for the gravitational variables times a modified Fock state for the scalar field. In this paper we do three things. First, we verify that the previous state also yields a small value of the master constraint when one polymerizes the scalar field in addition to the gravitational variables. We then study the propagators for the polymerized scalar field in flat space-time using the previously considered ground state in the low energy limit. We discuss the issue of the Lorentz invariance of the whole approach. We note that if one uses real clocks to describe the system, Lorentz invariance violations are small. We discuss the implications of these results in the light of Hořava’s Gravity at the Lifshitz point and of the argument about potential large Lorentz violations in interacting field theories of Collins et al.     

Rapid Convergence to Frequency for Substitution Tilings of the Plane

This paper concerns self-similar tilings of the Euclidean plane. We consider the number of occurrences of a given tile in any domain bounded by a Jordan curve. For a large class of self-similar tilings, including many well-known examples, we give estimates of the oscillation of this number of occurrences around its average frequency times the total number of tiles in the domain, which depend only on the Jordan curve.     

Testing Super-Deterministic Hidden Variables Theories

We propose to experimentally test non-deterministic time evolution in quantum mechanics by consecutive measurements of non-commuting observables on the same prepared state. While in the standard theory the measurement outcomes are uncorrelated, in a super-deterministic hidden variables theory the measurements would be correlated. We estimate that for macroscopic experiments the correlation time is too short to have been noticed yet, but that it may be possible with a suitably designed microscopic experiment to reach a parameter range where one would expect a super-deterministic modification of quantum mechanics to become relevant.     

Matrix theory of gravitation

A new classical theory of gravitation within the framework of general relativity is presented. It is based on a matrix formulation of four-dimensional Riemann-spaces and uses no artificial fields or adjustable parameters. The geometrical stress-energy tensor is derived from a matrix-trace Lagrangian, which is not equivalent to the curvature scalar R. To enable a direct comparison with the Einstein-theory a tetrad formalism is utilized, which shows similarities to teleparallel gravitation theories, but uses complex tetrads. Matrix theory might solve a 27-year-old, fundamental problem of those theories (Sect. 4.1). For the standard test cases (PPN scheme, Schwarz schild-solution) no differences to the Einstein-theory are found. However, the matrix theory exhibits novel, interesting vacuum solutions.     

Three-dimension direct writing TiO<Subscript>2</Subscript> crystalline patterns in Bi-free glass using femtosecond laser

Crystalline TiO₂ was induced three dimensionally inside Bi-free glass sample by an 800 nm, 250-kHz femtosecond laser irradiation. Micro-Raman spectra analysis indicated that the laser-induced crystals in the focal point of the laser beam were monophase TiO₂ rutile. Continuous crystalline lines were written through moving the focal point of the laser beam inside the glass. The results demonstrate that this technique is a convenient method to engrave three-dimensional patterns of crystals for fabricating integrated optical devices in transparent materials.     

A microfluidic chip integrated with a microoptical lens fabricated by femtosecond laser micromachining

We report on the integration of microlens and microfluidic channels in fused silica glass chip using femtosecond laser micromachining. The main process includes three procedures: (1) femtosecond laser scanning for forming a hemispherical surface and a Y-shaped channel in the fused silica glass; (2) chemical etching of the sample for removal of the modified areas; and (3) oxyhydrogen (OH) flame polish for smoothening the surface of the microlens. In addition, we demonstrate that the fabricated microlens exhibits good imaging performance with a 5× magnification, showing great potential in future lab-on-a-chip applications.     

Tomographic implementation of astronomical speckle imaging from bispectra

A bispectral method for astronomical speckle imaging utilizes an average speckle bispectrum of an object to derive its Fourier phase. There has been, however, a problem in conventional bispectral algorithm owing to difficulty in processing bispectral data in a four-dimensional (4D) space. In this paper, we propose an implementation to overcome this problem, where a one-dimensional (1D) object projection is reconstructed from a two-dimensional (2D) average bispectrum of speckle projections, and object projections so obtained at various angles are then tomographically combined into a 2D object image. In this tomographic approach, processes are separable into those for individual projection angles, implying that bispectral data required to be stored at a time are from 4D to 2D and computation time can be substantially reduced by parallelizing angle-by-angle processes. We have performed experiments using simulated and observed data, and have demonstrated the feasibility of the present approach with an achievable accuracy comparable to that of a conventional approach.     

Evaluation of influence of anisotropic diffusion near a wall in near-field fluorescence correlation spectroscopy of nanoparticles

Fluorescence correlation spectroscopy (FCS) of colloidal nanoparticles using a near-field fiber probe was numerically simulated. The near-wall dynamics was simulated by accounting for the anisotropic mobility of nanoparticles owing to hydrodynamic interaction with a wall (Stokes viscous force). By comparing the simulation results with theoretical model calculations, we found that the influence of anisotropic diffusion is insignificant in near-field FCS autocorrelation analysis.     

Investigation on the flameholding mechanisms in supersonic flows: backward-facing step and cavity flameholder

Abstract  

As effective devices to extend the fuel residence time in supersonic flow and prolong the duration time for hypersonic vehicles cruising in the near-space with power, the backward-facing step and the cavity are widely employed in hypersonic airbreathing propulsive systems as flameholders. The two-dimensional coupled implicit RANS equations, the standard k-ε turbulence model, and the finite-rate/eddy-dissipation reaction model have been used to generate the flow field structures in the scramjet combustors with the backward-facing step and the cavity flameholders. The flameholding mechanism in the combustor has been investigated by comparing the flow field in the corner region of the backward-facing step with that around the cavity flameholder. The obtained results show that the numerical simulation results are in good agreement with the experimental data, and the different grid scales make only a slight difference to the numerical results. The vortices formed in the corner region of the backward-facing step, in the cavity and upstream of the fuel injector make a large difference to the enhancement of the mixing between the fuel and the free airstream, and they can prolong the residence time of the mixture and improve the combustion efficiency in the supersonic flow. The size of the recirculation zone in the scramjet combustor partially depends on the distance between the injection and the leading edge of the cavity. Further, the shock waves in the scramjet combustor with the cavity flameholder are much stronger than those that occur in the scramjet combustor with the backward-facing step, and this causes a large increase in the static pressure along the walls of the combustor.