Letter: Invariants of the Kerr Vacuum

The Kerr vacuum has two independent invariants derivable from the Riemann tensor without differentiation. Both of these invariants must be examined in order to avoid an erroneous conclusion that the ring singularity of this spacetime is directional.     

A problem concerning infinite graphs

We show that there are graphs G and H which satisfy: (I) for every integer n, H contains n disjoint graphs each isomorphic to G, and (II) H does not contain infinitely many disjoint graphs each isomorphic to G. This answers one of the questions raised by Halin in the Graph Theory Newsletter.     

Breakdown of the giant spin model in the magnetic relaxation of the Mn6 nanomagnets

We study the spin dynamics in two variants of the high-anisotropy Mn6 nanomagnet by inelastic neutron scattering, magnetic resonance spectroscopy and magnetometry. We show that a giant-spin picture is completely inadequate for these systems and that excited S multiplets play a key role in determining the effective energy barrier for the magnetization reversal. Moreover, we demonstrate the occurrence of tunneling processes involving pair of states having different total spin.     

Remark concerning spherically symmetric nonstatic solutions to the Einstein equations in the comoving frame

All nonstatic spherically symmetric fluid solutions to the Einstein equations in the comoving frame $$ds^2 = e^{\lambda (r,t)} dr^2 + e^{\mu (r,t)} d\Omega ^2 - e^{v(r,t)} dt^2$$ are found subject to the conditions: (i) \(\dot \lambda = {\rm A}\dot \mu\) ,A = const, (ii) λ,μ, andν are separable functions ofr andt, (iii) the heat flux vanishes, and (iv) the coefficient of shear viscosity vanishes. There are but two classes of solutions: (i)A= 1, in which case the metric reduces to the Robertson-Walker form, and (ii)A=0, in which case there are four solutions, all with nonvanishing acceleration, expansion, and shear. WithA=0, the solutions are either singular at the origin or degenerate into spaces of constant curvature.     

Barrier asymmetry and the mm-wave performance of resonant tunnel diodes

The effects of barrier asymmetry in a resonant tunnel diode (RTD) on the frequency response of the negative dynamical resistance are described for (i) DC biasing in the positive differential resistance (PDR) region and (ii) DC biasing in the negative differential resistance (NDR) region. Collector barriers more transparent than emitter barriers enhance performance for NDR DC-biased devices. Asymmetry has no apparent effect for PDR DC-biased devices operating in transit time mode.     

Crystal structure of the methanol solvate of (η5-cyclopentadienyl)[1,2-bis(diphenylphosphino)ethane] nitroruthunium(II) Ru(η5-C5H5)dppe)(NO2)·CH3OH

The title complex crystallizes in the centrosymmetric monoclinic space group C2/c (No. 15) withZ=8. The structure was refined toR=4.49% for those 2745 independent reflections with 2=5–50^o and |F |>6(F). Ruthenium-ligand distances are as follows: Ru-P=2.284(2) and 2.286(2) Å, Ru-NO₂=2.049(6) Å and Ru-C(Cp)=2.210(10)-2.246(9) Å. Bond lengths within the nitro ligand are N(1)-O(1)=1.226(10) Å and N(1)-O(2)=1.244(10) Å. The methanol of solvation is ordered but is subject to large thermal vibrational motions.     

Time- and space-resolved spectroscopy of dynamic hohlraum interiors

A dynamic hohlraum is created when an annular z-pinch plasma implodes onto a cylindrical 0.014 g/cc 6-mm-diameter CH₂ foam. The impact launches a radiating shock that propagates toward the axis at 350 μm/ns. The radiation trapped by the tungsten z-pinch plasma forms a 200 eV hohlraum that provides X-rays for indirect drive inertial confinement fusion capsule implosion experiments. We are developing the ability to diagnose the hohlraum interior using emission and absorption spectroscopy of Si atoms added as a tracer to the central portion of the foam. Time- and space-resolved Si spectra are recorded with an elliptical crystal spectrometer viewing the cylindrical hohlraum end-on. A rectangular aperture at the end of the hohlraum restricts the field of view so that the 1D spectrometer resolution corresponds approximately to the hohlraum radial direction. This enables distinguishing between spectra from the unshocked radiation-heated foam and from the shocked foam. Typical spectral lines observed include the Si Lyα with its He-like satellites and the He-like resonance sequence including Heα, Heβ, and Heγ, along with some of their associated Li-like satellites. Work is in progress to infer the hohlraum conditions using collisional–radiative modeling that accounts for the radiation environment and includes both opacity effects and detailed Stark broadening calculations. These 6-mm-scale radiation-heated plasmas might eventually also prove suitable for testing Stark broadening line profile calculations or for opacity measurements.     

Imaging Endogenous Metal Ions in Living Cells Using a DNAzyme–Catalytic Hairpin Assembly Probe

DNAzymes are a promising platform for metal ion detection, and a few DNAzyme-based sensors have been reported to detect metal ions inside cells. However, these methods required an influx of metal ions to increase their concentrations for detection. To address this major issue, the design of a catalytic hairpin assembly (CHA) reaction to amplify the signal from photocaged Na⁺-specific DNAzyme to detect endogenous Na⁺ inside cells is reported. Upon light activation and in the presence of Na⁺, the NaA43 DNAzyme cleaves its substrate strand and releases a product strand, which becomes an initiator that trigger the subsequent CHA amplification reaction. This strategy allows detection of endogenous Na⁺ inside cells, which has been demonstrated by both fluorescent imaging of individual cells and flow cytometry of the whole cell population. This method can be generally applied to detect other endogenous metal ions and thus contribute to deeper understanding of the role of metal ions in biological systems.     

Letter: Differential Invariants of the Kerr Vacuum

The norms associated with the gradients of the two non-differential invariants of the Kerr vacuum are examined. Whereas both locally single out the horizons, their global behavior is more interesting. Both reflect the background angular momentum as the volume of space allowing a timelike gradient decreases with increasing angular momentum becoming zero in the degenerate and naked cases. These results extend directly to the Kerr-Newman geometry.