The shadow of a collapsing dark star

The shadow of a black hole is usually calculated, either analytically or numerically, on the assumption that the black hole is eternal, i.e., that it has existed for all time. Here we ask the question of how this shadow comes about in the course of time when a black hole is formed by gravitational collapse. To that end we consider a star that is spherically symmetric, dark and non-transparent and we assume that it begins, at some instant of time, to collapse in free fall like a ball of dust. We analytically calculate the dependence on time of the angular radius of the shadow, first for a static observer who is watching the collapse from a certain distance and then for an observer who is falling towards the centre following the collapsing star.     

Validation of an extractive, airborne, compact TDL spectrometer for atmospheric humidity sensing by blind intercomparison

Accuracy, precision, repeatability and long-term stability, are the most important requirements to enable reliable airborne humidity measurements, which are needed for climate models or to validate e.g. remote sensing instrumentation like satellites. However, various hygrometer artifacts which depend on the individual sensor principle and the application profile frequently cause problems and significantly complicate the hygrometer choice. Sensor intercomparisons are one way of providing the information for an optimal choice. In this paper we present the first part of a blind, static, laboratory-based intercomparison of a new, calibration-free, 1.4 μm diode laser-based, optical hygrometer (SEALDH) with the two most important measurement principles for airborne hygrometry (frost-point hygrometers, FPH, and Lyman-alpha fluorescence hygrometers, LAFH). During three days of measurement, the TDL-hygrometer achieved a H₂O resolution of up to 0.5 ppmv (Δt=2 sec) at tropospheric pressure and H₂O concentration levels (100–800 hPa, 10 to 8000 ppmv H₂O). Its absolute accuracy was investigated via blind intercomparison with two reference FPHs and a LAFH. Without any calibration of SEALDH, i.e. without a comparison to a water vapor standard, we achieve an excellent agreement with the reference sensors, with an average systematic offset (over all three days) of ?3.9 %±1.5 %, which is fully consistent with the sensor’s uncertainty bounds. Further we also reevaluated the SEALDH data of day 2 and 3 in a calibrated mode using an independent set of FPH data from the first day and found an 8-fold accuracy improvement, yielding an excellent overall relative deviation of only 0.52 %±1.5 % with respect to a LAFH and a D/FH sensor.     

Self-Similar 2d Euler Solutions with Mixed-Sign Vorticity

We construct a class of self-similar 2d incompressible Euler solutions that have initial vorticity of mixed sign. The boundaries between regions of positive and negative vorticity form algebraic spirals, similar to the Kaden spiral and as opposed to Prandtl’s logarithmic vortex spirals. Also unlike the Prandtl case, spirals are not initially present.     

Logunov–Tavkhelidze equation in the relativistic quark model

Based on the relativistic Logunov–Tavkhelidze equation, we obtain the mass spectra and probabilities of radiative decays of heavy quarkonia in the framework of the constituent quark model of hadrons.     

A Study of Ammonium Mono-, Di- and Triphosphate Heterogeneous Systems in View of their Use as Liquid Fertilizers

Abstract

Ammonium phosphates belong among principal compounds of multicomponent liquid fertilizers and thus this study has been directed toward agrochemical application. For this reason, in the system of NH⁺ ₄, H⁺ PO³ ₄, P₂O⁴ ₇, P₃O^5- ₁₀ - H₂O, the subsystem, NH₄H₂PO₄ - (NH₄)₂H₂P₂O₇ - (NH₄)₃H₂P₃O₁₀?(NH₄)₃PO₄ - (NH₄)₄P₂O₇ - (NH₄)₅P₃O₁₀ - H₂O, was studied in which the pH of saturated solutions varies from 5 to 8. The solubility was studied in the partial pseudoternary systems. The experimental temperatures were selected immediately above the corresponding cryohydratic points, from 0 to -8°C. The sum of the results obtained can be schematically represented as a set of the curves of simultaneous crystallization of two solids on the mantle of a trigonal prism which represents the salt composition of the studied system.     

A Two-Step Synthesis of the “Queen Substance” of the Honey Bee

A synthesis of the “queen substance” was accomplished in two steps from readily available starting materials. The key step was a novel one-pot reduction of 7-oxooctanoic acid to 7-oxooctanal followed by condensation with malonic acid.     

Spatiotemporal Studies of the One-Dimensional Coordination Polymer [Fe(ebtz)2(C2H5CN)2](BF4)2: Tug of War between the Nitrile Reorientation Versus Crystal Lattice as a Tool for Tuning the Spin Crossover Properties**

Reaction of 1,2-di(tetrazol-2-yl)ethane (ebtz) with Fe(BF₄)₂⋅6 H₂O in different nitriles yields one-dimensional coordination polymers [Fe(ebtz)₂(RCN)₂](BF₄)₂⋅nRCN (n=2 for R=CH₃ ( 1 ) and n=0 for R=C₂H₅ ( 2 ) C₃H₇ ( 3 ), C₃H₅ ( 4 ), CH₂Cl ( 5 )) exhibiting spin crossover (SCO). SCO in 1 and 3 – 5 is complete and occurs above 160 K. In 2 , it is shifted to lower temperatures and is accompanied by wide hysteresis (T_1/2^↓=78 K, T_1/2^↑=123 K) and proceeds extremely slowly. Isothermal (80 K) time-resolved single-crystal X-ray diffraction studies revealed a complex nature for the HS→LS transition in 2 . An initial, slow stage is associated with shrinkage of polymeric chains and with reduction of volume at 77 % (in relation to the difference between cell volumes V_HS−V_LS) whereas only 16 % of iron(II) ions change spin state. In the second stage, an abrupt SCO occurs, associated with breathing of the crystal lattice along the direction of the Fe–nitrile bonds, while the nitriles reorient. HS→LS switching triggered by light (808 nm) reveals the coupling of spin state and nitrile orientation. The importance of this coupling was confirmed by studies of [Fe(ebtz)₂(C₂H₅CN/C₃H₇CN)₂](BF₄)₂ mixed crystals ( 2 a , 2 b ), showing a shift of T_1/2 to higher values and narrowing of the hysteresis loop concomitant with an increase of the fraction of butyronitrile. This increase reduces the capability of nitrile molecules to reorient. Density functional theory (DFT) studies of models of 1 – 5 suggest a particular possibility of 2 to adopt a low (140–145°) value of its Fe-N-C(propionitrile) angle.