Intermediate behavior of Kerr tails

The numerical investigation of wave propagation in the asymptotic domain of Kerr spacetime has only recently been possible thanks to the construction of suitable hyperboloidal coordinates. The asymptotics revealed an apparent puzzle in the decay rates of scalar fields: the late-time rates seemed to depend on whether finite distance observers are in the strong field domain or far away from the rotating black hole, an apparent phenomenon dubbed ‘splitting.’ We discuss far-field ‘splitting’ in the full field and near-horizon ‘splitting’ in certain projected modes using horizon-penetrating, hyperboloidal coordinates. For either case we propose an explanation to the cause of the ‘splitting’ behavior, and we determine uniquely decay rates that previous studies found to be ambiguous or immeasurable. The far-field ‘splitting’ is explained by competition between projected modes. The near-horizon ‘splitting’ is due to excitation of lower multipole modes that back excite the multipole mode for which ‘splitting’ is observed. In both cases ‘splitting’ is an intermediate effect, such that asymptotically in time strong field rates are valid at all finite distances. At any finite time, however, there are three domains with different decay rates whose boundaries move outwards during evolution. We then propose a formula for the decay rate of tails that takes into account the inter-mode excitation effect that we study.     

Rapid crack growth in a thermoelastic solid under mixed-mode thermomechanical loading

A two-dimensional steady-sate analysis of semi-infinite brittlecrack growth at a constant subcritical rate in an unboundedfully-coupled thermoelastic solid under mixed-mode thermomechanicalloading is made. The loading consists of normal and shear tractionsand heat fluxes applied as point sources (line loads in theout-of-plane direction). A related problem is solved exactly in an integral transformspace, and robust asymptotic forms used to reduce the originalproblem to a set of integral equations. The equations are partiallycoupled and exhibit operators of both Cauchy and Abel types,yet can be solved analytically. The temperature change field at a distance from the moving crackedge is then constructed, and its dominant term is found tobe controlled by the imposed heat fluxes. The role of this termis, indeed, enhanced if the heat fluxes serve to render thecrack as a net heat source/sink for the solid, as opposed tobeing a transmitter of heat across its plane. More generally,the influence of the thermoelastic coupling on this field, aswell as other functions, is found to increase with crack speed.     

Thermodynamic dissociation constants of silychristin, silybin, silydianin and mycophenolate by the regression analysis of spectrophotometric data

Mixed dissociation constants of four drug acids, i.e. silychristin, silybinin, silydianin and mycophenolate at various ionic strengths I of range 0.01 and 0.30 and at temperatures of 25 and 37 °C were determined using the SQUAD(84) regression analysis program applied to pH-spectrophotometric titration data. The proposed strategy of an efficient experimentation in a protonation constants determination, followed by a computational strategy for the chemical model with a protonation constants determination, is presented on the protonation equilibria of silychristin. The thermodynamic dissociation constant pK_a^T was estimated by non-linear regression of {pK_a, I} data at 25 and 37 °C: for silychristin pK_a,1^T=6.52(16) and 6.62(1), pK_a,2^T=7.22(13) and 7.41(5), pK_a,3^T=8.96(9) and 8.94(9), pK_a,4^T=10.17(7) and 10.03(8), pK_a,5^T=11.89(4) and 11.63(7); for silybin pK_a,1^T=7.00(4) and 6.86(5), pK_a,2^T=8.77(11) and 8.77(3), pK_a,3^T=9.57(8) and 9.62(1), pK_a,4^T=11.66(3) and 11.38(1); for silydianin pK_a,1^T=6.64(7) and 7.10(6), pK_a,2^T=7.78(5) and 8.93(1), pK_a,3^T=9.66(9) and 10.06(11), pK_a,4^T=10.71(7) and 10.77(7), pK_a,5^T=12.26(5) and 12.14(5); for mycophenolate pK_a^T=8.32(1) and 8.14(1). Goodness-of-fit tests for various regression diagnostics enabled the reliability of parameter estimates to be found.     

Synthetic magnetic opals

We present studies of novel nanocomposites of BiNi impregnated into the structure of opals as well as inverse opals. Atomic force microscopy and high resolution elemental analyses show a highly ordered structure and uniform distribution of the BiNi filler in the matrix. These BiNi-based nanocomposites are found to exhibit distinct ferromagnetic-like ordering with transition temperature of about 675 K. As far as we know there exists no report in literature on any BiNi compound which is magnetic.     

Comment on the Roberts Solution for the Spherically-Symmetric Einstein-Scalar Field Equations

We critically examine the Roberts homothetic solution for the spherically symmetric Einstein-scalar field equations in double null coordinates, and show that the Roberts solution indeed solves the field equations only for one non-trivial case. We generalize this solution and discuss its relations with other known exact solutions.     

A radiation scalar for numerical relativity

This Letter describes a scalar curvature invariant for general relativity with a certain, distinctive feature. While many such invariants exist, this one vanishes in regions of space-time which can be said unambiguously to contain no gravitational radiation. In more general regions which incontrovertibly support nontrivial radiation fields, it can be used to extract local, coordinate-independent information partially characterizing that radiation. While a clear, physical interpretation is possible only in such radiation zones, a simple algorithm can be given to extend the definition smoothly to generic regions of space-time.     

Black-hole singularities: a new critical phenomenon

The singularity inside a spherical charged black hole, coupled to a spherical, massless scalar field is studied numerically. The profile of the characteristic scalar field was taken to be a power of advanced time with an exponent alpha>0. A critical exponent alpha(crit) exists. For exponents below the critical one (alphaalpha(crit)) an all-encompassing, spacelike singularity evolves, which completely blocks the "tunnel" inside the black hole, preventing the use of the black hole as a portal for hyperspace travel.