Separation of linear components in nonlinear boundary heat control

By means of an additional substitution a parabolic control problem with some nonlinear boundary condition will be decoupled into some control problem with linear parabolic state equations and an appropriate nonlinear mapping. This separation allows the use of efficient techniques e.g. Fourier methods, to determine the solution of linear parabolic state equations. Essential properties of the mapping used in the transformation are studied. Further, the application of piecewise constant discretizations of the controls in connection with the proposed splitting is discussed.     

Interplay of wetting and elasticity in the nucleation of carbon nanotubes

We use molecular dynamics and simple thermodynamic arguments to model the interaction between catalyst nanoparticles and carbon nanotube caps, and we illustrate how the competition between cap strain energy and adhesion plays a role in the lifting of these caps from the catalyst surface prior to tube elongation. Given a particular cap structure, we show that there is a lower bound on the catalyst size from which the cap can lift. This lower bound depends on the cap's spontaneous curvature and bending rigidity, as well as the catalyst binding strength, and it explains the mismatch between single-walled carbon nanotube and catalyst diameters observed in prior experiments. These findings offer new insight into the nucleation of carbon nanotubes, and they may lead to the design of catalysts that can better control nanotube structure.     

Subsolidus phase diagrams for the Tl<Subscript>2</Subscript>MoO<Subscript>4</Subscript>-Ln<Subscript>2</Subscript>(MoO<Subscript>4</Subscript>)<Subscript>3</Subscript>-Hf(MoO<Subscript>4</Subscript>)<Subscript>2</Subscript> systems,where Ln = La-Lu

The Tl₂MoO₄-Ln₂(MoO₄)₃-Hf(MoO₄)₂ systems where Ln = La-Lu were studied in the subsolidus region using X-ray powder diffraction. Quasi-binary joins were revealed, and triangulation carried out. New ternary molybdates were prepared: Tl₅LnHf(MoO₄)₆ (5: 1: 2) for Ln = Ce-Ho, Tl₅LnHf(MoO₄)₆ (5: 1: 2) for Ln = Er-Lu, TlLnHf_0.5(MoO₄)₃ (1: 1: 1) for Ln = Ce-Nd, and Tl₂LnHf₂(MoO₄)_6.5 (2: 1: 4) for Ln = Ce-Lu. The crystallographic parameters of Tl₅LnHf(MoO₄)₆ (5: 1: 2) compounds for Ln = Er-Lu were determined.     

Novel trans-spanned palladium complexes as efficient catalysts in mild and amine-free cyanation of aryl bromides under air

[reaction: see text] The use of a novel trans-spanned palladium complex as an efficient and selective catalyst in the cyanation of aryl halides is described. The suggested reaction conditions are mild, exhibit good scope of substrates, and circumvent the need for an inert atmosphere and amine co-ligands.     

General but discriminating fluorescent chemosensor for aliphatic amines

Aliphatic amines are sensitively and discriminatively detected through binding with demethylated naphthol AS-BI (7-bromo-3-hydroxy-2-naphth-o-hydroxyanilide, 2) and fluorescence of the resulting complex. Recognition of the amine by the chemosensor 2 occurs via proton transfer of the naphtholic proton to the amine and is facilitated by the presence of the phenol group. Amine basicity is the primary controller of detection. Poorly basic aromatic and conjugated amines such as pyridine and aniline are not detected. Hydrogen bonding within the complex allows further differentiation of aliphatic amines. Doubly primary, conformationally flexible diamines are the most sensitive to detection, followed by secondary amines.     

Simplifying the setup for vacuum‐outlet GC: Using a restriction inside the injection port

The application of vacuum GC has several advantages over pressurized GC. One of the key characteristics is that the optimal gas velocity is very high. Combined with short capillary columns of wide internal diameter, this results in short analysis times using standard GC‐MS equipment. To make vacuum GC possible using a GC‐MS system, a restriction must be positioned at the injection side of the column. This restriction is usually made of deactivated 0.1 mm i.d. fused‐silica tubing which is coupled to the analytical column. Such restrictions will work, but practical challenges are found in coupling, reducing dead volume and robustness. A new way of making restrictions is by incorporating the restriction into the injection port. Using well‐defined short pieces of fused silica with internal diameter of 0.025 mm, one can make a restriction using a Press‐Tight® type connector, and position this inside the injection port. By doing this, the restriction is very short and at high temperature all the time. Activity plays a minimal role, and also leaks will not be an issue as the coupling is in 100% inert gas. Data obtained using this concept is promising as vacuum GC becomes easier and more robust.     

Toward extracting $$\gamma $$ from $$B\rightarrow DK$$ without binning

SABRE (Sodium iodide with Active Background REjection) is a direct detection dark matter experiment based on arrays of radio-pure NaI(Tl) crystals. The experiment aims at achieving an ultra-low background rate and its primary goal is to confirm or refute the results from the DAMA/LIBRA experiment. The SABRE Proof-of-Principle phase was carried out in 2020–2021 at the Gran Sasso National Laboratory (LNGS), in Italy. The next phase consists of two full-scale experiments: SABRE South at the Stawell Underground Physics Laboratory, in Australia, and SABRE North at LNGS. This paper focuses on SABRE South and presents a detailed simulation of the detector, which is used to characterise the background for dark matter searches including DAMA/LIBRA-like modulation. We estimate an overall background of 0.72 cpd/kg/\(\hbox {keV}_{\hbox {{ee}}}\) in the energy range 1–6 \(\hbox {keV}_{\hbox {{ee}}}\) primarily due to radioactive contamination in the crystals. Given this level of background and considering that the SABRE South has a target mass of 50 kg, we expect to exclude (confirm) DAMA/LIBRA modulation at \(4~(5)\sigma \) within 2.5 years of data taking.