Uniqueness in MHD in divergence form: right nullvectors and well-posedness

Magnetohydrodynamics in divergence form describes a hyperbolic system of covariant and constraint-free equations. It comprises a linear combination of an algebraic constraint and Faraday's equations. Here, we study the problem of well-posedness, and identify a preferred linear combination in this divergence formulation. The limit of weak magnetic fields shows the slow magnetosonic and Alfven waves to bifurcate from the contact discontinuity (entropy waves), while the fast magnetosonic wave is a regular perturbation of the hydrodynamical sound speed. These results are further reported as a starting point for characteristic based shock capturing schemes for simulations with ultra-relativistic shocks in magnetized relativistic fluids.Comment: To appear in J Math Phy

Entropic force in black hole binaries and its Newtonian limits

We give an exact solution for the static force between two black holes at the turning points in their binary motion. The results are derived by Gibbs' principle and the Bekenstein-Hawking entropy applied to the apparent horizon surfaces in time-symmetric initial data. New power laws are derived for the entropy jump in mergers, while Newton's law is shown to derive from a new adiabatic variational principle for the Hilbert action in the presence of apparent horizon surfaces. In this approach, entropy is strictly monotonic such that gravity is attractive for all separations including mergers, and the Bekenstein entropy bound is satisfied also at arbitrarily large separations, where gravity reduces to Newton's law. The latter is generalized to point particles in the Newtonian limit by application of Gibbs' principle to world-lines crossing light cones.Comment: Accepted for publication in Phys. Rev.

Differential Forms and Wave Equations for General Relativity

Recently, Choquet-Bruhat and York and Abrahams, Anderson, Choquet-Bruhat, and York (AACY) have cast the 3+1 evolution equations of general relativity in gauge-covariant and causal ``first-order symmetric hyperbolic form,'' thereby cleanly separating physical from gauge degrees of freedom in the Cauchy problem for general relativity. A key ingredient in their construction is a certain wave equation which governs the light-speed propagation of the extrinsic curvature tensor. Along a similar line, we construct a related wave equation which, as the key equation in a system, describes vacuum general relativity. Whereas the approach of AACY is based on tensor-index methods, the present formulation is written solely in the language of differential forms. Our approach starts with Sparling's tetrad-dependent differential forms, and our wave equation governs the propagation of Sparling's 2-form, which in the ``time-gauge'' is built linearly from the ``extrinsic curvature 1-form.'' The tensor-index version of our wave equation describes the propagation of (what is essentially) the Arnowitt-Deser-Misner gravitational momentum.Comment: REVTeX, 26 pages, no figures, 1 macr

Measurement of the ΔS=-ΔQ Amplitude from K_(e3)^0 Decay

We have measured the time distribution of the π^+e^-ν and π^-e^+ν modes from initial K^0's in a spark-chamber experiment performed at the Bevatron. From 1079 events between 0.2 and 7 K_S^0 lifetime, we find ReX=-0.069±0.036, ImX=+0.108_(-0.074)^(+0.092). This result is consistent with X=0 (relative probability = 0.25), but more than 4 standard deviations from the existing world average, +0.14 -0.13i

PISOX Copolyesters─Bio- and CO₂-Based Marine-Degradable High-Performance Polyesters

Oxalate esters and isosorbide serve as intriguing polymer building blocks, as they can be sourced from renewable resources, such as CO2 and glucose, and the resulting polyesters offer outstanding material properties. However, the low reactivity of the secondary hydroxyl groups makes it difficult to generate high-molecular-weight polymers from isosorbide. Combining diaryl oxalates with isosorbide appears to be a promising approach to produce high-molecular-weight isosorbide-based polyoxalates (PISOX). This strategy seems to be scalable, has a short polymerization time (<5 h), and uniquely, there is no need for a catalyst. PISOX demonstrates outstanding thermal, mechanical, and barrier properties; its barrier to oxygen is 35 times better than PLA, it possesses mechanical properties comparable to high-performance thermoplastics, and the glass transition temperature of 167 °C can be modified by comonomer incorporation. What makes this high-performance material truly exceptional is that it decomposes into CO2 and biomass in just a few months in soil under home-composting conditions and it hydrolyzes without enzymes present in less than a year in 20 °C water. This unique combination of properties has the potential to be utilized in a range of applications, such as biomedical uses, water-resistant coatings, compostable plastic bags for gardening and agriculture, and packaging plastics with diminished environmental impact

Theory and astrophysical consequences of a magnetized torus around a rapidly rotating black hole

(Abbrev.) We analyze the topology, lifetime, and emissions of a torus around a black hole formed in hypernovae and black hole-neutron star coalescence. The torus is ab initio uniformly magnetized, represented by two counter oriented current-rings, and develops a state of suspended accretion against a "magnetic wall" around the black hole. Magnetic stability of the torus gives rise to a new fundamental limit EB/Ek<0.1 for the ratio of poloidal magnetic field energy-to-kinetic energy. The lifetime of rapid spin of the black hole is effectively defined by the timescale of dissipation of black hole-spin energy in the horizon, and satisfies T= 40s (MH/7MSun)(R/6MH)^4(0.03MH/MT) for a black hole of mass MH surrounded by a torus of mass MT and radius R. The torus converts a major fraction Egw/Erot=0.1 into gravitational radiation through a finite number of multipole mass-moments, and a smaller fraction into MeV neutrinos and baryon-rich winds. At a source distance of 100Mpc, these emissions over N=2e4 periods give rise to a characteristic strain amplitude \sqrt{N}hchar=6e-21. We argue that torus winds create an open magnetic flux-tube on the black hole, which carries a minor and standard fraction Ej/Erot=1e-3 in baryon-poor outflows to infinity. We identify this baryon poor output of tens of seconds with GRBs with contemporaneous and strongly correlated emissions in gravitational radiation, conceivably at multiple frequencies. Ultimately, this leaves a black hole binary surrounded by a supernova remnant.Comment: To appear in ApJ (44p

Vitamin K status and physical decline in older adults—The Longitudinal Aging Study Amsterdam

Objective: We examined the association between vitamin K status and physical functioning over 13 years in the Longitudinal Aging Study Amsterdam. Study design: Longitudinal cohort study of 633 community-dwelling adults from the Longitudinal Aging Study Amsterdam (LASA) aged 55–65 years (54% women). Main outcome measures: At baseline (2002–2003), plasma desphospho-uncarboxylated matrix Gla protein (dp-ucMGP) was measured with a sandwich ELISA as a marker of vitamin K status. The outcome measures handgrip strength, calf circumference, self-reported functional limitations and functional performance were obtained at baseline and four follow-up examinations. We used generalized estimating equations to determine the relationship between dp-ucMGP tertiles and the various outcome measurements after adjusting for potential confounders. The lowest dp-ucMGP tertile reflects a high vitamin K status and was the reference. Results: Mean dp-ucMGP was 376 ± 233 pmol/L and mean follow-up was 11.1 years. Participants showed a decline in the outcome measures over time. Compared with the lowest tertile, the highest dp-ucMGP tertile had: lower handgrip strength, 1.1 kg (95% confidence interval (−2.1, −0.1; P-trend <0.001); smaller calf circumference, −0.5 cm (−0.9 −0.1; P-trend = 0.018); and, only among women, a 0.7-point poorer functional performance score (−1.1, −0.3; P-interaction = 0.002). Dp-ucMGP was not related to self-reported functional limitations. No interaction effects between time and dp-ucMGP were observed. Conclusions: Low vitamin K status was associated with lower handgrip strength, smaller calf circumference, and, in women only, with poorer functional performance score. A low vitamin K status was however not related to the 13-year decline in these measures

Gravitational radiation from gamma-ray bursts as observational opportunities for LIGO and VIRGO

Gamma-ray bursts are believed to originate in core-collapse of massive stars. This produces an active nucleus containing a rapidly rotating Kerr black hole surrounded by a uniformly magnetized torus represented by two counter-oriented current rings. We quantify black hole spin-interactions with the torus and charged particles along open magnetic flux-tubes subtended by the event horizon. A major output of Egw=4e53 erg is radiated in gravitational waves of frequency fgw=500 Hz by a quadrupole mass-moment in the torus. Consistent with GRB-SNe, we find (i) Ts=90s (tens of s, Kouveliotou et al. 1993), (ii) aspherical SNe of kinetic energy Esn=2e51 erg (2e51 erg in SN1998bw, Hoeflich et al. 1999) and (iii) GRB-energies Egamma=2e50 erg (3e50erg in Frail et al. 2001). GRB-SNe occur perhaps about once a year within D=100Mpc. Correlating LIGO/Virgo detectors enables searches for nearby events and their spectral closure density 6e-9 around 250Hz in the stochastic background radiation in gravitational waves. At current sensitivity, LIGO-Hanford may place an upper bound around 150MSolar in GRB030329. Detection of Egw thus provides a method for identifying Kerr black holes by calorimetry.Comment: to appear in PRD, 49