Chernoff approximations of Feller semigroups in Riemannian manifolds

Chernoff approximations of Feller semigroups and the associated diffusion processes in Riemannian manifolds are studied. The manifolds are assumed to be of bounded geometry, thus including all compact manifolds and also a wide range of non-compact manifolds. Sufficient conditions are established for a class of second order elliptic operators to generate a Feller semigroup on a (generally non-compact) manifold of bounded geometry. A construction of Chernoff approximations is presented for these Feller semigroups in terms of shift operators. This provides approximations of solutions to initial value problems for parabolic equations with variable coefficients on the manifold. It also yields weak convergence of a sequence of random walks on the manifolds to the diffusion processes associated with the elliptic generator. For parallelizable manifolds this result is applied in particular to the representation of Brownian motion on the manifolds as limits of the corresponding random walks.     

Common-path achromatic rotational-shearing coronagraph

To suppress starlight for direct exoplanet observation, we propose a common-path achromatic rotational-shearing coronagraph (CP-ARC), which is an interferocoronagraph with an angular-adjustable field rotator. The CP-ARC aims to maintain unwanted detection of stellar light, which can be suppressed incompletely by interference because of the finite diameter of the star. Compared to the previous interferocoronagraph, which had a nonadjustable 180° field rotation, the proposed CP-ARC can improve the coronagraphic contrast by several orders if the CP-ARC is combined with medium or large telescopes where the companion-star separation is optically resolved by more than a few Airy radii. The CP-ARC is made robust against mechanical disturbances due to the common-path interferometer principle.     

Probing the out-of-plane distortion of single point defects in atomically thin hexagonal boron nitride at the picometer scale

Crystalline systems often lower their energy by atom displacements from regular high-symmetry lattice sites. We demonstrate that such symmetry lowering distortions can be visualized by ultrahigh resolution transmission electron microscopy even at single point defects. Experimental investigation of structural distortions at the monovacancy defects in suspended bilayers of hexagonal boron nitride (h-BN) accompanied by first-principles calculations reveals a characteristic charge-induced pm symmetry configuration of boron vacancies. This symmetry breaking is caused by interlayer bond reconstruction across the bilayer h-BN at the negatively charged boron vacancy defects and results in local membrane bending at the defect site. This study confirms that boron vacancies are dominantly present in the h-BN membrane.     

Controlling phonon squeezing and correlation via one- and two-phonon interference

When ultrafast laser pulse strikes the crystal with a van Hove singularity in the phonon density of states, it can create a pair of anti-correlated in wave-vector phonons. As a result, the atomic fluctuations in either position or momentum become squeezed in such a way that their size might fall below the vacuum level. The ultrafast pulses can also generate a biphonon state in which the constituent phonons are correlated and/or entangled. Here we show that via the interplay between one- and two-phonon interference the bound and squeezed two-phonon state in (110) oriented ZnTe single crystal can be manipulated.     

Advances towards using finger/toenail dosimetry to triage a large population after potential exposure to ionizing radiation

Rapid and accurate retrospective dosimetry is of critical importance and strategic value for the emergency medical response to a large-scale radiological/nuclear event. One technique that has the potential for rapid and accurate dosimetry measurements is electron paramagnetic resonance (EPR) spectroscopy of relatively stable radiation-induced signals (RIS) in fingernails and toenails. Two approaches are being developed for EPR nail dosimetry. In the approach using ex vivo measurements on nail clippings, accurate estimation of the dose-dependent amplitude of the RIS is complicated by the presence of mechanically-induced signals (MIS) that are generated during the nail clipping. Recent developments in ex vivo nail dosimetry, including a thorough characterization of the MIS and an appreciation of the role of hydration and the development of effective analytic techniques, have led to improvements in the accuracy and precision of this approach. An in vivo nail dosimetry approach is also very promising, as it eliminates the problems of MIS from the clipping and it has the potential to be an effective and efficient approach for field deployment. Two types of EPR resonators are being developed for in vivo measurements of fingernails and toenails.     

Atomic and electronic structures of lutetium oxide Lu2O3

The chemical composition, electronic structure, structure, and physical properties a lutetium oxide Lu₂O₃ film are studied by X-ray photoelectron spectroscopy, ellipsometry, and X-ray absorption spectroscopy. The short-range order in Lu₂O₃ is found to correspond to its cubic modification. The binding energies of the 1s and 2p levels of oxygen and the 4d _5/2 and 4f _7/2 levels of lutetium are 529.2, 5.0 and 7.4, 195.9 eV, respectively. The energy gap determined from the electron energy loss spectrum of the film is 5.9 eV. The electron energy loss spectra have two peaks at 17.4 and 22.0 eV, which can be attributed to the excitation of bulk plasma oscillations. The dispersion of the refractive index is measured by spectral ellipsometry. The refractive index is shown to increase from 1.82 at 1.5 eV to 2.18 at 5.0 eV, and the high-frequency permittivity of Lu₂O₃ is 3.31.     

Long-range chemical interactions in solid-state reactions: effect of an inert Ag interlayer on the formation of L10-FePd in epitaxial Pd(0 0 1)/Ag(0 0 1)/Fe(0 0 1) and Fe(0 0 1)/Ag(0 0 1)/Pd(0 0 1) trilayers

The effect of 0, 0.5, and 1?μm-thick Ag interlayers on the chemical interaction between Pd and Fe in epitaxial Pd(0?0?1)/Ag(0?0?1)/Fe(0?0?1)/MgO(0?0?1) and Fe(0?0?1)/Ag(0?0?1)/Pd(0?0?1)/MgO(0?0?1) trilayers has been studied using X-ray diffraction, ⁵⁷Fe Mössbauer spectroscopy, X-ray photoelectron spectroscopy, and magnetic structural measurements. No mixing of Pd and Fe occurs via the chemically inert Ag layer at annealing temperatures up to 400?°C. As the annealing temperature is increased above 400?°C, a solid-state synthesis of an ordered L1₀-FePd phase begins in the Pd(0?0?1)/Ag(0?0?1)/Fe(0?0?1) and Fe(0?0?1)/Ag(0?0?1)/Pd(0?0?1) film trilayers regardless of the thickness of the buffer Ag layer. In all samples, annealing above 500?°C leads to the formation of a disordered Fe_xPd_1?x(0?0?1) phase; however, in samples lacking the Ag layer, the synthesis of Fe_xPd_1?x is preceded by the formation of an ordered L1₂-FePd₃ phase. An analysis of the X-ray photoelectron spectroscopy results shows that Pd is the dominant moving species in the reaction between Pd and Fe. According to the preliminary results, the 2.2?μm-thick Ag film does not prevent the synthesis of the L1₀-FePd phase and only slightly increases the phase’s initiation temperature. Data showing the ultra-fast transport of Pd atoms via thick inert Ag layers are interpreted as direct evidence of the long-range character of the chemical interaction between Pd and Fe. Thus, in the reaction state, Pd and Fe interact chemically even though the distance between them is about 10⁴ times greater than an ordinary chemical bond length.     

Solute-diffusion-controlled dislocation creep in pure aluminium containing 0.026 at.% Fe

Pure aluminium containing about 200?at.ppm Fe in solution is shown to creep about 10⁶ times slower at 200°C than the same aluminium containing a negligible amount of iron in solution. The high creep resistance of the Al–200?at.ppm?Fe alloy is attributed to the presence of subgrain boundaries containing iron solute atoms. It is proposed that the opposing stress fields from subgrain boundaries and from the piled-up dislocations during creep are cyclically relaxed, by iron solute diffusion, to allow climb of the lead dislocation in the pile-up. The mechanism is a form of mechanical ratcheting. The model is applied to Al–Fe alloys and correctly predicts that the creep rate is controlled by the rate of iron solute diffusion and by a temperature dependence equal to the activation energy for iron diffusion, namely Q _c?=?221?kJ?mol^?1. Basic creep studies on solid-solution alloying with solute atoms that diffuse slowly in the lattice of aluminium (e.g. manganese, chromium, titanium and vanadium) appear worthy of study as a way of enhancing creep strength and of understanding creep mechanisms involving solute-atom-containing subgrain boundaries.     

Kinetic Study of Propylene Hydrogenation over Pt/Al2O3 by Parahydrogen-Induced Polarization

Parahydrogen-induced polarization has been successfully used for a kinetic study of propylene hydrogenation over a Pt/Al₂O₃ catalyst. It was shown that the reaction orders with respect to hydrogen are different for the pairwise and the non-pairwise hydrogen addition and are equal to 0.7 and 0.1, respectively. This observation of different reaction orders confirms the coexistence of different types of active sites which are responsible for the overall and the pairwise hydrogen addition to the propylene C=C double bond. Moreover, 0.7 reaction order with respect to H₂ for pairwise hydrogen addition indicates that the contribution of pairwise addition depends on the concentration of molecular hydrogen. Therefore, this observation can be developed into a practical tool for producing fluids with highly polarized nuclear spins by changing the hydrogen concentration.