On partial regularity of suitable weak solutions to the Navier–Stokes equations in unbounded domains

Consider the nonstationary Navier–Stokes equations in Ω × (0, T), where Ω is a general unbounded domain with non-compact boundary in R ³. We prove the regularity of suitable weak solutions for large |x|. It should be noted that our result also holds near the boundary. Our result extends the previous ones by Caffarelli–Kohn–Nirenberg in R ³ and Sohr-von Wahl in exterior domains to general domains.     

Explosive desorption and fragmentation of molecular ion from solid fullerene by intense nonresonant femtosecond laser pulses

Desorption of C 60 (+) and its dimer cation was investigated on irradiation with nonresonant femtosecond laser pulses at 1.4 mum. Ionization of solid C 60 revealed strikingly different features, such as the absence of multiply charged molecular ions, the emission of C (+) at low laser intensity, C 2 attachments, delayed ionization, and dimer cation formation, as compared with the gas phase experiments. The large kinetic energy distribution of ions found in this study indicated that the desorption process was mainly driven by an electrostatic mechanism rather than by thermal, photochemical, or volume expansion mechanisms. Singly charged C 60 emission by a Coulomb explosion due to the high density of C 60 (+) is suggested.     

meso-Phbox-Pd(II) catalyzed tandem carbonylative cyclization of 1-ethynyl-1-propargyl acetate

Palladium(ii) catalyzed carbonylation of 1-ethynyl-1-propargyl acetate is described; in the absence of the bisoxazoline (box) ligand, the second triple bond did not react, affording cyclic orthoesters and . The use of meso-Phbox-Pd(ii) strikingly changed the course of the reaction, yielding bicyclic lactone by tandem carbonylative cyclization as a result of insertion of the second triple bond.     

Oligonucleotide analysis by nanoparticle-assisted laser desorption/ionization mass spectrometry

We analyzed oligonucleotides by nanoparticle-assisted laser desorption/ionization (nano-PALDI) mass spectrometry (MS). To this end, we prepared several kinds of nanoparticles (Cr-, Fe-, Mn-, Co-based) and optimized the nano-PALDI MS method to analyze the oligonucleotides. Iron oxide nanoparticles with diammonium hydrogen citrate were found to serve as an effective ionization-assisting reagent in MS. The mass spectra showed both [M - H](-) and [M + xMe(2+)- H](-) (Me: transition metal) peaks. The number of metal-adducted ion signals depended on the length of the oligonucleotide. This phenomenon was only observed using bivalent metal core nanoparticles, not with any other valency metal core nanoparticles. Our pilot study demonstrated that iron oxide nanoparticles could easily ionize samples such as chemical drugs and peptides as well as oligonucleotides without the aid of an oligonucleotide-specific chemical matrix (e.g., 3-hydroxypicolinic acid) used in conventional MS methods. These results suggested that iron-based nanoparticles may serve as the assisting material of ionization for genes and other biomolecules.     

Vapochromic ionic liquids from metal-chelate complexes exhibiting reversible changes in color, thermal, and magnetic properties

Vapor- and gas-responsive ionic liquids (ILs) comprised of cationic metal-chelate complexes and bis(trifluoromethanesulfonyl)imide (Tf(2) N) have been prepared, namely, [Cu(acac)(BuMe(3) en)][Tf(2) N] (1?a), [Cu(Bu-acac)(BuMe(3) en)][Tf(2) N] (1?b), [Cu(C(12) -acac)(Me(4) en)][Tf(2) N] (1?c), [Cu(acac)(Me(4) en)][Tf(2) N] (1?d), and [Ni(acac)(BuMe(3) en)][Tf(2) N] (2?a) (acac=acetylacetonate, Bu-acac=3-butyl-2,4-pentanedionate, C(12) -acac=3-dodecyl-2,4-pentanedionate, BuMe(3) en=N-butyl-N,N',N'-tetramethylethylenediamine, and Me(4) en=N,N,N',N'-trimethylethylenediamine). These ILs exhibited reversible changes in color, thermal properties, and magnetic properties in response to organic vapors and gases. The Cu(II) -containing ILs are purple and turn blue-purple to green when exposed to organic vapors, such as acetonitrile, methanol, and DMSO, or ammonia gas. The color change is based on the coordination of the vapor molecules to the cation, and the resultant colors depend on the coordination strength (donor number, DN) of the vapor molecules. The vapor absorption caused changes in the melting points and viscosities, leading to alteration in the phase behaviors. The IL with a long alkyl chain (1?d) transitioned from a purple solid to a brown liquid at its melting point. The Ni(II) -containing IL (2?a) is a dark red diamagnetic liquid, which turned into a green paramagnetic liquid by absorbing vapors with high DN. Based on the equilibrium shift from four- to six-coordinated species, the liquid exhibited thermochromism and temperature-dependent magnetic susceptibility after absorbing methanol.     

An sp2 and sp3 hybrid nanocrystalline carbon film electrode for anodic stripping voltammetry and its application for electrochemical immunoassay

A hybridized nanocrystalline carbon film electrode consisting of sp(2) and sp(3) bonds was investigated to reveal the reduction properties of Cd(2+) and for application as a highly sensitive and reliable electrochemical immunoassay. Conductive nanocrystalline carbon film consisting of about 60% sp(2) and 40% sp(3) bonds was fabricated using electron cyclotron resonance (ECR) sputtering equipment, and then the Cd(2+) concentrations were measured with an ECR sputtered carbon (ECR nano-carbon) electrode by employing an anodic stripping voltammetry (ASV) technique. The preconcentrated Cd was analyzed with Kelvin probe force microscopy and energy dispersive X-ray spectroscopy while observing the morphology change with an atomic force microscope and a scanning electron microscope. The preconcentrated Cd on the ECR nano-carbon electrode was revealed to be a thin sheet structure, which was significantly different from the Cd on a conventional carbon material that grows with a coralloid structure. The background current during an ASV measurement maintains a low level equivalent to that found with boron-doped diamond because the surface of the ECR nano-carbon is robust and angstrom-level flat. The carbon-electrode performance for ASV was improved by controlling its structure at a nanometer scale without any metal doping or coating. Finally, the ECR nano-carbon was used for biomolecular determination by electrochemical immunoassay with a CdSe nanoparticle label. Electrochemical immunoassay results were successfully obtained with the ECR nano-carbon, and they correlated well with fluorescence results obtained for CdSe nanoparticles.     

Microfluidic devices for electrochemical measurement of photosynthetic activity of cyanobacteria microcystis cells

A microfluidic device with analytical chambers for electrochemical measurements has been employed to detect photosynthetic activity at single cell level. The flowing cells (Microcystis viridis) in a main channel are individually guided to the chamber with microelectrodes by an electrophoretic manipulation. The reduction current of oxygen was continuously monitored to determine the photosynthetic activity upon light irradiation. The average rates for oxygen generation were estimated and found to be 10(-18) mol/s level.     

Vapochromic Ionic Liquids from Metal–Chelate Complexes Exhibiting Reversible Changes in Color,Thermal, and Magnetic Properties

Vapor‐ and gas‐responsive ionic liquids (ILs) comprised of cationic metal‐chelate complexes and bis(trifluoromethanesulfonyl)imide (Tf₂N) have been prepared, namely, [Cu(acac)(BuMe₃en)][Tf₂N] ( 1 a ), [Cu(Bu‐acac)(BuMe₃en)][Tf₂N] ( 1 b ), [Cu(C₁₂‐acac)(Me₄en)][Tf₂N] ( 1 c ), [Cu(acac)(Me₄en)][Tf₂N] ( 1 d ), and [Ni(acac)(BuMe₃en)][Tf₂N] ( 2 a ) (acac=acetylacetonate, Bu‐acac=3‐butyl‐2,4‐pentanedionate, C₁₂‐acac=3‐dodecyl‐2,4‐pentanedionate, BuMe₃en=N‐butyl‐N,N′,N′‐tetramethylethylenediamine, and Me₄en=N,N,N′,N′‐trimethylethylenediamine). These ILs exhibited reversible changes in color, thermal properties, and magnetic properties in response to organic vapors and gases. The Cu^II‐containing ILs are purple and turn blue‐purple to green when exposed to organic vapors, such as acetonitrile, methanol, and DMSO, or ammonia gas. The color change is based on the coordination of the vapor molecules to the cation, and the resultant colors depend on the coordination strength (donor number, DN) of the vapor molecules. The vapor absorption caused changes in the melting points and viscosities, leading to alteration in the phase behaviors. The IL with a long alkyl chain ( 1 d ) transitioned from a purple solid to a brown liquid at its melting point. The Ni^II‐containing IL ( 2 a ) is a dark red diamagnetic liquid, which turned into a green paramagnetic liquid by absorbing vapors with high DN. Based on the equilibrium shift from four‐ to six‐coordinated species, the liquid exhibited thermochromism and temperature‐dependent magnetic susceptibility after absorbing methanol.     

Fast time-reversible algorithms for molecular dynamics of rigid-body systems

In this paper, we present time-reversible simulation algorithms for rigid bodies in the quaternion representation. By advancing a time-reversible algorithm [Y. Kajima, M. Hiyama, S. Ogata, and T. Tamura, J. Phys. Soc. Jpn. 80, 114002 (2011)] that requires iterations in calculating the angular velocity at each time step, we propose two kinds of iteration-free fast time-reversible algorithms. They are easily implemented in codes. The codes are compared with that of existing algorithms through demonstrative simulation of a nanometer-sized water droplet to find their stability of the total energy and computation speeds.     

A remark on the regularity of weak solutions to the Navier–Stokes equations in terms of the pressure in Lorentz spaces

For the incompressible Navier–Stokes equations in R³${\mathbb{R}}^3$, a regularity criterion for weak solutions is proved under the assumption that the pressure belongs to the scaling invariant Lorentz space with small norm, while corresponding results for the velocity field were proved by Sohr. The main theorem continues and extends a previous result given by the author.