Gibbsian dynamics and ergodicity of magnetohydrodynamics and related systems forced by random noise

The magnetohydrodynamics system consists of the Navier-Stokes equations from fluid mechanics, coupled with the Maxwell’s equations from electromagnetism through multiples of non-linear terms involving derivatives. Following the approach of [1 Weinan, E., Mattingly, J. C., Sinai, Y. (2001). Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation. Commun. Math. Phys. 224:83–106. DOI:10.1007/s002201224083.[Crossref], [Web of Science ®] , [Google Scholar]], we prove the existence of a unique invariant measure in case the forcing terms consist of the cylindrical Wiener processes with only low modes. Its proof requires taking advantage of the structure of the non-linear terms carefully and is extended to various other related models such as the magnetohydrodynamics-Boussinesq system from fluid mechanics in atmosphere and oceans, as well as the magneto-micropolar fluid system from the theory of microfluids.     

Characterization of intrinsic ultracontractivity for one dimensional Schrödinger operators

We consider a Schrödinger operator $L=?d^2/d{x}^2+V(x)$ on $\mathbb{R}$, where V is a real-valued measurable function, and give an explicit and simple characterization of intrinsic ultracontractivity (IU) of the Schrödinger semigroup generated by L for a wide class of potentials. By making use of it, we also give new examples of potentials for which the semigroups satisfy (IU) or non-(IU).     

Effects of silica nanoparticle addition on polymer semiconductor wettability and carrier mobility in solution‐processable organic transistors on hydrophobic substrates

The effects of the addition of silica nanoparticles (SNPs) on wettability of regioregular poly(3‐hexylthiophene) (P3HT) organic semiconductor solutions on hydrophobic substrates and the carrier mobility in organic field‐effect transistors (OFETs) made of these films are investigated. The dewetting of films made from P3HT solutions on hydrophobic substrates modified with octadecyltrichlorosilane (ODTS) is markedly suppressed after the addition of SNPs with phenyl surfactants. This enables us to fabricate continuous P3HT/SNPs films with high crystallinity by the conventional spin‐coating technique, leading to higher mobility compared with P3HT FETs fabricated on non‐modified substrates. Moreover, the addition of SNPs with larger diameters compensates for the degradation of mobility associated with the increase in the concentration of SNPs. Solution‐processed P3HT/SNPs FETs on ODTS‐modified substrates exhibit a field‐effect mobility of 1.3 × 10^?2 cm² V^?1 s^?1, which is almost comparable to that of P3HT FETs without SNPs (2.1 × 10^?2 cm² V^?1 s^?1). © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 509–516     

Synthesis,Properties, and Redox Behavior of 1,1,4,4‐Tetracyano‐2‐ferrocenyl‐1,3‐butadienes Connected by Aryl,Biaryl, and Teraryl Spacers

Aryl‐substituted 1,1,4,4‐tetracyano‐1,3‐butadienes (FcTCBDs) and bis(1,1,4,4‐tetracyanobutadiene)s (bis‐FcTCBDs), possessing a ferrocenyl group on each terminal, were prepared by the reaction of a variety of alkynes with tetracyanoethylene (TCNE) in a [2+2] cycloaddition reaction, followed by retro‐electrocyclization of the initially formed [2+2] cycloadducts (i.e., cyclobutene derivatives). The characteristic intramolecular charge transfer (ICT) between the donor (ferrocene) and acceptor (TCBD) moieties were investigated by using UV/Vis spectroscopy. The redox behaviors of FcTCBDs and bis‐FcTCBDs were examined by cyclic voltammetry (CV) and differential pulse voltammetry (DPV), which revealed their properties of multi‐electron transfer depending on the number of ferrocene and TCBD moieties. Moreover, significant color changes were observed by visible spectroscopy under the electrochemical reduction conditions.     

Flexible and Epitaxial Metal Oxide Thin Film Growth by Photoreaction Processing for Electrical and Optical Applications

This review summarizes the use of photoreactions that replace conventional heating processes for growing oxide thin films from chemical solutions. In particular, this review outlines key variables in photoreactions that affect epitaxial and polycrystalline thin film growth, including precursor materials, laser wavelength, laser fluence, and carbon. In addition, the features of the photoreaction process that can be controlled at a low temperature by oxygen non-stoichiometry are examined. Likewise, functions that are neither achieved by developing a gradient structure nor controlled by a thermal equilibrium reaction are detailed. Two new concepts are presented, known as photoreaction of nanoparticles (PRNP) and photoreaction of a hybrid solutions (PRHS), in which crystal nuclei are pre-dispersed in a metal–organic compound film. This method has successfully produced flexible phosphor films used as resistor or thermistor electronic components. Finally, thin film growth using different light sources such as flash lamps and femtosecond lasers (fs) is explored.     

Bifunctional Iminophosphorane-Catalyzed Enantioselective Nitroalkane Addition to Unactivated α,β-Unsaturated Esters**

Herein we describe the enantioselective intermolecular conjugate addition of nitroalkanes to unactivated α,β-unsaturated esters, catalyzed by a bifunctional iminophosphorane (BIMP) superbase. The transformation provides the most direct access to pharmaceutically relevant enantioenriched γ-nitroesters, utilizing feedstock chemicals, with unprecedented selectivity. The methodology exhibits a broad substrate scope, including β-(fluoro)alkyl, aryl and heteroaryl substituted electrophiles, and was successfully applied on a gram scale with reduced catalyst loading, and, additionally, catalyst recovery was carried out. The formal synthesis of a range of drug molecules, and an enantioselective synthesis of (S)-rolipram were achieved. Additionally, computational studies revealed key reaction intermediates and transition state structures, and provided rationale for high enantioselectivities, in good agreement with experimental results.