Singularities of Euler Flow? Not Out of the Blue!

Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time? This blowup problem is still open. After briefly reviewing what is known and pointing out some of the difficulties, we propose to tackle this issue for the class of flows having analytic initial data for which hypothetical real singularities are preceded by singularities at complex locations. We present some results concerning the nature of complex space singularities in two dimensions and propose a new strategy for the numerical investigation of blowup.     

Reporting of quantitative oxygen mapping in EPR imaging

Oxygen maps derived from electron paramagnetic resonance spectral-spatial imaging (EPRI) are based upon the relaxivity of molecular oxygen with paramagnetic spin probes. This technique can be combined with MRI to facilitate mapping of pO(2) values in specific anatomic locations with high precision. The co-registration procedure, which matches the physical and digital dimensions of EPR and MR images, may present the pO(2) map at the higher MRI resolution, exaggerating the spatial resolution of oxygen, making it difficult to precisely distinguish hypoxic regions from normoxic regions. The latter distinction is critical in monitoring the treatment of cancer by radiation and chemotherapy, since it is well-established that hypoxic regions are three or four times more resistant to treatment compared to normoxic regions. The aim of this article is to describe pO(2) maps based on the intrinsic resolution of EPRI. A spectral parameter that affects the intrinsic spatial resolution of EPRI is the full width at half maximum (FWHM) height of the gradient-free EPR absorption line in frequency-encoded imaging. In single point imaging too, the transverse relaxation times (T(2)(?)) limit the resolution since the signal decays by exp(-t(p)/T(2)(?)) where the delay time after excitation pulse, t(p), is related to the resolution. Although the spin densities of two point objects may be resolved at this separation, it is inadequate to evaluate quantitative changes of pO(2) levels since the linewidths are proportionately affected by pO(2). A spatial separation of at least twice this resolution is necessary to correctly identify a change in pO(2) level. In addition, the pO(2) values are blurred by uncertainties arising from spectral dimensions. Blurring due to noise and low resolution modulates the pO(2) levels at the boundaries of hypoxic and normoxic regions resulting in higher apparent pO(2) levels in hypoxic regions. Therefore, specification of intrinsic resolution and pO(2) uncertainties are necessary to interpret digitally processed pO(2) illustrations.     

Magneto-Optical Properties of Silica Gel Containing Magnetite Fine Particles

The magnetic composite materials that consist of transparent matrix and magnetic fine particles are expected to have large residual magnetization and coercive force because of their fine magnetic domain structure, and also to show magneto-optical effects. Silica gels containing magnetite (Fe₃O₄) fine particles were prepared by sol-gel method. The magnetic, optical and magneto-optical properties of the composites were investigated by measurements of magnetization curves, UV-visible spectra and Faraday rotation in visible range. The saturation magnetization of the composite was almost as same as that expected from the amount of magnetite fine particles in it. Although the composites had large and broad absorption at around 400 nm, they still maintained their transparency. The origins of decrement of transparency attributed to the optical absorption of magnetite and scattering due to magnetite fine particles. The whole composites showed positive Faraday rotation under external static magnetic field due to the large contribution of diamagnetic silica gel matrix. Magnetite contributed negative Faraday rotation with maximum at around 470–480 nm to the magneto-optical spectra of the composites.     

Thermal stability of cubic boron nitride films deposited by chemical vapor deposition

Thermal stability of well-crystallized cubic boron nitride (cBN) films grown by chemical vapor deposition has been investigated by cathodoluminescence (CL), Raman spectroscopy, and scanning electron microscopy (SEM) with the cBN films annealed at various temperatures up to 1,300 degrees C. The crystallinity of the cBN films further improves, as indicated by a reduction of the relevant Raman line width, when the annealing temperature exceeds 1,100 degrees C. Structural damage or amorphization was observed on the grain boundaries of the cBN crystals when annealing temperature reaches 1,300 degrees C. The CL spectra are found to be unchanged up to 1,100 degrees C after annealing at 500 degrees C, showing the stability of the cBN films in electronic properties up to this temperature. New features were observed in the CL spectra when annealing temperature reaches 1,200-1,300 degrees C.     

A variety of spin-crossover behaviors depending on the counter anion: two-dimensional complexes constructed by NH...Cl- hydrogen bonds, [FeIIH3LMe]Cl.X (X = PF6 -, AsF6 -, SbF6 -, CF3SO3 -; H3L(Me) = Tris[2-{[(2-methylimidazol-4-yl)methylidene]amino}ethyl]amine)

A family of spin-crossover (SC) complexes, [Fe(II)H(3)L(Me)]Cl.X (X(-) = PF(6) (-), AsF(6) (-), SbF(6) (-), CF(3)SO(3) (-)), 1-4, has been synthesized, in which H(3)L(Me) denotes the hexadentate N(6) tripod-like ligand tris[2-{[(2-methylimidazol-4-yl)methylidene]amino}ethyl]amine, containing three imidazole groups, with a view to establishing the effect of the counter anion on the SC behavior. These complexes have been found to crystallize in the same monoclinic crystal system with similar cell dimensions. The general crystal structure consists of a two-dimensional (2D) extended network constructed by NH...Cl- hydrogen bonds between Cl- and the imidazole NH groups of three neighboring [Fe(II)H(3)L(Me)]2+ ions, while the anion X exists as an isolated counter anion and occupies the space between the 2D sheets. Magnetic susceptibilities and M?ssbauer spectra have revealed a variety of SC behaviors depending on the counter anion, including a one-step HS<==>(HS + LS)/2 (1, X = PF(6) (-)), a two-step HS<==>(HS + LS)/2<==>LS with a slow thermal relaxation (2, X = AsF(6) (-)), a gradual one-step HS<==>LS (3, X = SbF(6) (-)), and a steep one-step HS<==>LS with hysteresis (4, X = CF(3)SO(3) (-)). The complexes assume the space group P2(1)/n in the HS state, P2(1) in the HS + LS state, and P2(1)/n in the LS state. The Fe-N bond lengths and the N-Fe-N bond angles are indicative of the HS, HS + LS, and LS states. The molecular volumes, V, of the counter anions have been evaluated by quantum-chemical calculations as follows: 53.4 A(3) (BF(4) (-)), 54.4 A(3) (ClO(4) (-)), 73.0 A(3) (PF(6) (-)), 78.5 A(3) (AsF(6) (-)), 88.7 A(3) (SbF(6) (-)), and 86.9 A(3) (CF(3)SO(3) (-)). The size and shape of the counter anion affects the flexible 2D network structure constructed by the hydrogen bonds, leading to modifications of the SC behavior. These estimated relative sizes of the counter anions correlate well with the observed SC behaviors.     

Conformation of solvent N,N-dimethylpropionamide in the coordination sphere of the zinc(II) ion studied by Raman spectroscopy and DFT calculations

Solvation structure of the zinc(II) ion in N,N-dimethylpropionamide (DMPA) was studied by Raman spectroscopy at varying temperature and by quantum mechanical calculations. No significant ion-pair formation was found for the Zn(ClO4)2 solution in the molality range m(Zn) < 1.5 mol kg(-1), and the solvation number of the zinc(II) ion was determined to be 4, indicating that 6-coordination of DMPA is sterically hindered. Interestingly, DMPA molecules are under equilibrium between planar cis and nonplanar staggered conformers, and the latter is more preferred in the coordination sphere, while the reverse is the case in the bulk. The DeltaG degrees , DeltaH degrees , and TDeltaS degrees values of conformational change from planar cis to nonplanar staggered in the coordination sphere were obtained to be -0.9, -8.5, and -7.5 kJ mol(-1), respectively. Density functional theory (DFT) calculations show that the planar cis conformer is more favorable than the nonplanar staggered one in the 1:2 cluster, as is the case for a single DMPA molecule and H(DMPA)+, indicating that there hardly occurs solvent-solvent interaction through the metal ion in the Zn2+-DMPA 1:2 cluster. On the other hand, the SCF energy of [Zn(planar cis-DMPA)4-n(nonplanar staggered DMPA)n]2+ (n = 0-4) decreases with increasing n, implying that the nonplanar staggered conformer is preferred in the solvate ion. It is thus concluded that solvent-solvent interaction through space, or solvation steric effect, plays a crucial role in the conformational equilibrium in the coordination sphere of the four-solvate metal ion.     

Long hydrogen-bonded rod of molecular oxide: a hexatantalate tetramer

A tetra-n-butylammonium (TBA) salt of [H(4.5)(Ta(6)O(19))](3.5-) was synthesized by reacting hydrous tantalum oxide with TBAOH. X-ray structural analysis of TBA(3.5)[H(4.5)(Ta(6)O(19))]·2THF·5.5H(2)O (THF = tetrahydrofuran) revealed that this compound consists of a hydrogen-bonded, rod-shaped tetramer of hexatantalate that is almost 30 ? long together with TBA cations and solvent molecules of crystallization [a = 20.6354(5) ?, b = 25.5951(7) ?, c = 37.2058(8) ?, α = 77.092(1)°, β = 86.177(1)°, γ = 88.683(1)°, V = 19110.9(8) ?(3), Z = 8, and space group P ?1]. (1)H NMR spectra showed that this tetrameric structure is maintained in solution.     

Physicochemical properties and plastic crystal structures of phosphonium fluorohydrogenate salts

Fluorohydrogenate salts of quaternary phosphonium cations with alkyl and methoxy groups (tetraethylphosphonium (P(2222)(+)), triethyl-n-pentylphosphonium (P(2225)(+)), triethyl-n-octylphosphonium (P(2228)(+)), and triethylmethoxymethylphosphonium (P(222(101))(+))) have been synthesized by the metatheses of anhydrous hydrogen fluoride and the corresponding phosphonium bromide or chloride precursors. The three salts with asymmetric cations, P(222m)(FH)(2.1)F (m = 5, 8, and 101), are room temperature ionic liquids (ILs) and are characterized by differential scanning calorimetry, density, viscosity, and conductivity measurements. Linear sweep voltammetry using a glassy carbon working electrode shows these phosphonium fluorohydrogenate ILs have wide electrochemical windows (>4.9 V) with the lowest viscosity and highest conductivity in the known phosphonium-based ILs. Thermogravimetry shows their thermal stabilities are also improved compared to previously reported alkylammonium cation-based fluorohydrogenate salts. Differential scanning calorimetry and X-ray diffraction revealed that tetraethylphosphonium fluorohydrogenate salt, P(2222)(FH)(2)F, exhibits two plastic crystal phases. The high temperature phase has a hexagonal lattice, which is the first example of a plastic crystal phase with an inverse nickel arsenide-type structure, and the low-temperature phase has an orthorhombic lattice. The high-temperature plastic crystal phase exhibits a conductivity of 5 mS cm(-1) at 50 °C, which is the highest value for the neat plastic crystals.     

Highly-controlled regiospecific free-radical copolymerization of 1,3-diene monomers with sulfur dioxide

The free-radical copolymerization of alkyl-substituted 1,3-butadienes with sulfur dioxide using a redox initiating system in toluene at -78 °C produced poly(diene sulfone)s consisting of a highly alternating and 1,4-regiospecific repeating structure, irrespective of the position and number of alkyl substituents, and the highly regioselective propagation via a free radical reaction mechanism is well accounted for by DFT calculations using model reactions.     

Organic reactions mediated by electrochemically generated ArS+

Low-temperature electrochemical oxidation of ArSSAr was carried out to generate a pool of "ArS(+)". Spectroscopic studies ((1)H NMR and CSI-MS) of the resulting solution revealed the accumulation of ArS(ArSSAr)(+). The resulting "ArS(+)" pool reacted with alkenes and alkynes to give diarylthio-substituted products. The "ArS(+)" pool rapidly reacted with thioacetals to give the corresponding alkoxycarbenium ion pools, which reacted with various carbon nucleophiles (indirect cation pool method). The reaction of the alkoxycarbenium ion pools with stilbene derivatives in the presence of ArSSAr gave thiochroman derivatives. In addition to such stoichiometric reactions, a catalytic amount of "ArS(+)" serves as an initiator and a chain carrier of some cationic chain reactions involving intramolecular carbon-carbon bond formation. In situ generation of "ArS(+)" by electrochemical oxidation of ArSSAr with a catalytic amount of electricity in the presence of a substrate is also effective for such cationic chain reactions.