Analyses of 4f11 Energy Levels and Transition Intensities Between Stark Levels of Er3+ in Y3Al5O12

ABSTRACT

Absorption and fluorescence spectra obtained at temperatures as low as 4 K were investigated between 200 and 1550 nm on samples containing approximately 1.2 at. wt. % Er in Y₃Al₅O₁₂ (YAG). Within this wavelength range 125 experimental energy (Stark) levels were analyzed, representing data that span 29 ^2S+1 L _J multiplet manifolds of Er³⁺(4f¹¹) in D₂ sites up to an energy of 44,000 cm^?1. Agreement between calculated and observed Stark levels was achieved with an r.m.s. deviation of 11.2 cm^?1. These transitions originate from the ground-state Stark level in the ⁴I_15/2 manifold to J + 1/2 Stark levels associated with each of the 28 excited-state manifolds. A total of 88 ground-state absorption transition line strengths were measured for 19 ^2S+1 L _J multiplet manifolds between 280 and 1550 nm. For line strength measurements, the Er³⁺ ion is assumed to be distributed homogeneously throughout the D₂ cation sites of Y³⁺ in the lattice. The line strengths were analyzed with a weighted (E _i  ? C _i )/E _i , with an r.m.s. error of 0.25. Use of a “vector crystal field” parametrization resolves ambiguities in the transition intensity parameters and allows for the definition of polarization-resolved Judd-Ofelt parameters, which may have wide-ranging applicability for future Judd-Ofelt-type intensity calculations.     

On the Approximation of the SABR Model: A Probabilistic Approach

Abstract

In this article, we derive a probabilistic approximation for three different versions of the SABR model: Normal, Log-Normal and a displaced diffusion version for the general case. Specifically, we focus on capturing the terminal distribution of the underlying process (conditional on the terminal volatility) to arrive at the implied volatilities of the corresponding European options for all strikes and maturities. Our resulting method allows us to work with a variety of parameters that cover the long-dated options and highly stress market condition. This is a different feature from other current approaches that rely on the assumption of very small total volatility and usually fail for longer than 10 years maturity or large volatility of volatility (Volvol).     

A Combination Theorem for Metric Bundles

We introduce the notion of metric (graph) bundles which provide a coarse-geometric generalization of the notion of trees of metric spaces a la Bestvina?CFeighn in the special case that the inclusions of the edge spaces into the vertex spaces are uniform coarsely surjective quasi-isometries. We prove the existence of quasi-isometric sections in this generality. Then we prove a combination theorem for metric (graph) bundles that establishes sufficient conditions, particularly flaring, under which the metric bundles are hyperbolic. We use this to give examples of surface bundles over hyperbolic disks, whose universal cover is Gromov-hyperbolic. We also show that in typical situations, flaring is also a necessary condition.     

Modulation of Kinetic Pathways of Enzyme–Substrate Interaction in a Microfluidic Channel: Nanoscopic Water Dynamics as a Switch

Enzyme-mediated catalysis is attributed to enzyme–substrate interactions, with models such as “induced fit” and “conformational selection” emphasizing the role of protein conformational transitions. The dynamic nature of the protein structure, thus, plays a crucial role in molecular recognition and substrate binding. As large-scale protein motions are coupled to water motions, hydration dynamics play a key role in protein dynamics, and hence, in enzyme catalysis. Here, microfluidic techniques and time-dependent fluorescence Stokes shift (TDFSS) measurements are employed to elucidate the role of nanoscopic water dynamics in the interaction of an enzyme, α-Chymotrypsin (CHT), with a substrate, Ala-Ala-Phe-7-amido-4-methylcoumarin (AMC) in the cationic reverse micelles of benzylhexadecyldimethylammonium chloride (BHDC/benzene) and anionic reverse micelles of sodium bis(2-ethylhexyl)sulfosuccinate (AOT/benzene). The kinetic pathways unraveled from the microfluidic setup are consistent with the “conformational selection” fit for the interaction of CHT with AMC in the cationic reverse micelles, whereas an “induced fit” mechanism is indicated for the anionic reverse micelles. In the cationic reverse micelles of BHDC, faster hydration dynamics (≈550 ps) aid the pathway of “conformational selection”, whereas in the anionic reverse micelles of AOT, the significantly slower dynamics of hydration (≈1600 ps) facilitate an “induced fit” mechanism for the formation of the final enzyme–substrate complex. The role of water dynamics in dictating the mechanism of enzyme–substrate interaction becomes further manifest in the neutral reverse micelles of Brij-30 and Triton X-100. In the former, the faster water dynamics aid the “conformational selection” pathway, whereas the significantly slower dynamics of water molecules in the latter are conducive to the “induced fit” mechanism in the enzyme–substrate interaction. Thus, nanoscopic water dynamics act as a switch in modulating the pathway of recognition of an enzyme (CHT) by the substrate (AMC) in reverse micelles.     

A metal-free iodine-mediated conversion of hydroxamates to esters

Abstract

A metal-, oxidant-, and additive-free conversion of hydroxamates to esters have been achieved using molecular iodine as the reagent using a novel but not-so-explored heron-type rearrangement. The reaction proceeds with almost equal facility with substrates having either electron-donating or electron-withdrawing substituent. Similarly, α,ß-unsaturated, and sterically hindered ortho-substituted hydroxamates also undergo the desired transformation smoothly.     

Photoacidic behavior of small phenolics in micellar media

The present work demonstrates the photophysical characterization of the interaction of two antibacterial and antimicrobial compounds, thymol and its isomer, carvacrol with different biomimetic micellar nanocavities having varying surface charge characteristics. These types of molecules are reported to be photoacids and this behavior is remarkably exhibited upon interaction with the macromolecular assemblies of micellar systems in the presence of inorganic and organic quencher molecules (silver nitrate and diethylamine) and is manifested through significant modulations of the bimolecular quenching constant values.     

Numerical simulation of conductive particle behaviour at the surface of a plate electrode affected by a DC corona field

The electric field in certain electrostatic devices can be modeled by a grounded plate electrode affected by a corona discharge generated by a series of parallel wires connected to a DC high-voltage supply. The system of differential equations that describe the behaviour (i.e., charging and motion) of the conductive particle in such an electric field has been numerically solved, using several simplifying assumptions. Thus, it was possible to investigate the effect of various electrical and mechanical factors on the trajectories of conductive particles. This model has been employed to study the behaviour of coal particles in fly-ash corona separators.     

Behaviour of charged insulating particles in contact with a rotating roll electrode

The overall economic efficiency of standard industrial roll-type separators for granular materials can be improved by operation at higher velocities of the rotating roll electrode. The aim of this paper is to estimate how high this speed could be and still have a good separation. The answer to this question implied the calculation of the electric image force, which opposes the centrifugal force and sticks the corona-charged insulating particles to the rotating roll electrode. This force depends on the residual charge carried by the particles. By estimating the decay of this charge from surface potential measurements carried out on granular layers of insulating materials dispersed on grounded plate electrodes, it was possible to simulate the particle lift-off from the rotating roll electrode under various operating conditions. The results presented in the paper were obtained for fly-ash particles, but the numerical simulation methodology employed by the authors can be successfully applied for the optimisation of other electrostatic separation applications.