Entropy enhancement and black hole microstates

We show that the entropy of fluctuating two-charge supertubes placed in three-charge scaling microstate solutions depends on their "effective" charges, which in strong magnetic fields can be much larger than their charges. This leads to a much larger entropy than one naively would expect. Since fluctuating supertubes source smooth geometries in certain duality frames, we propose that such an entropy enhancement mechanism might lead to a black-hole-like entropy coming entirely from configurations that are smooth and horizonless in the regime of parameters where the classical black hole exists.     

Modified method of simplest equation and its application to nonlinear PDEs

We search for traveling-wave solutions of the class of PDEswhere A_p(Q),B_r(Q),C_s(Q),D_u(Q) and F(Q) are polynomials of Q. The basis of the investigation is a modification of the method of simplest equation. The equations of Bernoulli, Riccati and the extended tanh-function equation are used as simplest equations. The obtained general results are illustrated by obtaining exact solutions of versions of the generalized Kuramoto-Sivashinsky equation, reaction-diffusion equation with density-dependent diffusion, and the reaction-telegraph equation.     

Synthesis and Photophysical Properties of Alkoxysilyl Derivatives of Dibenzoylmethanatoboron Difluoride

Alkoxysilyl derivatives of dibenzoylmethanatoboron difluoride (DBMBF₂) are synthesized by the hydrosilylation reaction of the corresponding O‐allyl derivatives of DBMBF₂ with triethoxysilane. The photophysical properties of the synthesized O‐allyl and alkoxysilyl derivatives are investigated. It is found that the absorption and fluorescence spectra of the DBMBF₂ derivatives essentially depend on the position of the O‐allyl or O‐propyl alkoxysilyl substituent. The highest fluorescence quantum yield is obtained for the para‐position, whereas the substitution at the meta‐position gives the largest bathochromic shift in the fluorescence spectrum. Density functional theory calculations of the structures and time‐dependent density functional theory calculations of the gas‐phase excitation and emission energies of alkoxysilyl derivatives are performed at the PBE0/SVP level of theory. Some spectral features of para‐, ortho‐, and meta‐substituted derivatives can be adequately explained by the overlapping of two absorption bands.     

Local Derivative-Free Approximation of Computationally Expensive Posterior Densities

Bayesian inference using Markov chain Monte Carlo (MCMC) is computationally prohibitive when the posterior density of interest, π, is computationally expensive to evaluate. We develop a derivative-free algorithm GRIMA to accurately approximate π by interpolation over its high-probability density (HPD) region, which is initially unknown. Our local approach reduces the waste of computational budget on approximation of π in the low-probability region, which is inherent in global experimental designs. However, estimation of the HPD region is nontrivial when derivatives of π are not available or are not informative about the shape of the HPD region. Without relying on derivatives, GRIMA iterates (a) sequential knot selection over the estimated HPD region of π to refine the surrogate posterior and (b) re-estimation of the HPD region using an MCMC sample from the updated surrogate density, which is inexpensive to obtain. GRIMA is applicable to approximation of general unnormalized posterior densities. To determine the range of tractable problem dimensions, we conduct simulation experiments on test densities with linear and nonlinear component-wise dependence, skewness, kurtosis and multimodality. Subsequently, we use GRIMA in a case study to calibrate a computationally intensive nonlinear regression model to real data from the Town Brook watershed. Supplemental materials for this article are available online.     

Small Data Scattering for the Nonlinear Schrödinger Equation on Product Spaces

We consider the cubic nonlinear Schrödinger equation, posed on ? ⁿ  × M, where M is a compact Riemannian manifold and n ≥ 2. We prove that under a suitable smallness in Sobolev spaces condition on the data there exists a unique global solution which scatters to a free solution for large times.     

Interfacing Formate Dehydrogenase with Metal Oxides for the Reversible Electrocatalysis and Solar‐Driven Reduction of Carbon Dioxide

The integration of enzymes with synthetic materials allows efficient electrocatalysis and production of solar fuels. Here, we couple formate dehydrogenase ( FDH ) from Desulfovibrio vulgaris Hildenborough (DvH) to metal oxides for catalytic CO₂ reduction and report an in‐depth study of the resulting enzyme–material interface. Protein film voltammetry (PFV) demonstrates the stable binding of FDH on metal‐oxide electrodes and reveals the reversible and selective reduction of CO₂ to formate. Quartz crystal microbalance (QCM) and attenuated total reflection infrared (ATR‐IR) spectroscopy confirm a high binding affinity for FDH to the TiO₂ surface. Adsorption of FDH on dye‐sensitized TiO₂ allows for visible‐light‐driven CO₂ reduction to formate in the absence of a soluble redox mediator with a turnover frequency (TOF) of 11±1 s^?1. The strong coupling of the enzyme to the semiconductor gives rise to a new benchmark in the selective photoreduction of aqueous CO₂ to formate.     

Lone pairs vs. covalent bonds: conformational effects in bicyclo[3.3.1]nonane derivatives

Structural Chemistry - Investigations on the relative energy of two least-strain conformers for bicyclo[3.3.1]nonane 1, bicyclo[3.3.1]nonan-9-one 2, and their heteroanalogues:...     

Ultralow quantum-defect eye-safe Er:Sc2O3 laser

Resonantly pumped Er(3+):Sc(2)O(3) laser operation is achieved with a quantum defect (QD) of 1.5% at liquid nitrogen temperature. The laser, in-line pumped at 1535 nm, operated at 1558 nm with a slope efficiency of over 45%. This is believed to be the lowest QD eye-safe laser ever reported. CW output of over 3.3 W was obtained in this first experiment.