Nonlinear Boundary Layers of the Boltzmann Equation: I. Existence

 We study the half-space problem of the nonlinear Boltzmann equation, assigning the Dirichlet data for outgoing particles at the boundary and a Maxwellian as the far field. We will show that the solvability of the problem changes with the Mach number ℳ^∞ of the far Maxwellian. If ℳ^∞<−1, there exists a unique smooth solution connecting the Dirichlet data and the far Maxwellian for any Dirichlet data sufficiently close to the far Maxwellian. Otherwise, such a solution exists only for the Dirichlet data satisfying certain admissible conditions. The set of admissible Dirichlet data forms a smooth manifold of codimension 1 for the case −1<ℳ^∞<0, 4 for 0<ℳ^∞<1 and 5 for ℳ^∞>1, respectively. We also show that the same is true for the linearized problem at the far Maxwellian, and the manifold is, then, a hyperplane. The proof is essentially based on the macro-micro or hydrodynamics-kinetic decomposition of solutions combined with an artificial damping term and a spatially exponential decay weight. Received: 20 April 2002 / Accepted: 4 December 2002 Published online: 21 March 2003 Communicated by H.-T. Yau     

Thermodynamic Insight into the Origin of a Calix[n]arene-[60]fullerene Interaction and its Application to a Porphyrin-[60]fullerene Energy Transfer System

The calixarene-fullerene interaction,which causes only a slight change in the absorptionspectra, has been substantiated by calorimetricmeasurements: the H° values arecomparable with those obtained from the associationconstants estimated by a spectroscopic method. Furthermore, we determined the association constantbetween homooxacalix[3]arene and [60]fullerenederivatives with a porphyrin moiety by fluorescencespectra.     

Solubility of α-amino acids in water under high pressure: glycine, -alanine, -valine, -leucine, and -isoleucine

The solubility of glycine, -alanine, -valine, -leucine, and -isoleucine in water was measured at 298.15 K and pressures up to 400 MPa. The standard deviation of the logarithm of the solubility is 0.001–0.003, equal to or better than the accuracy of atmospheric pressure measurement in the literature (0.001–0.05). A variety of solubility phenomena were observed. The solubility of glycine decreased with increasing pressure, whereas that of -alanine increased. The -valine and -isoleucine have a solubility maximum at around 100 MPa, and -leucine seems to exhibit a solid-phase phase transition at around 200 MPa. Pressure coefficient of the solubilities at 0.10 MPa is compared with that thermodynamically estimated in reference to aqueous density measurements of glycine and -alanine at 298.15 K and 0.10 MPa, supporting a reliability of our high-pressure measurements.     

Radiation-induced emission from golden hamster embryo cells

Emission from high-energy-electron-irradiated golden hamster embryo (GHE) cells has been studied over the temperature range 12–300 K both by a one-shot-single-photon-counting method and by photocurrent measurements with an oscilloscope. Emission from the irradiated phosphate buffered saline (PBS) also has been studied. The emission spectra from PBS at 12 and 77 K show a maximum around 330 and 380 nm, respectively, which are the same spectra as those from irradiated pure H₂O. The emission from irradiated GHE consists of the new band at 480 nm in addition to the emission from H₂O. The 480 nm emission is observed at the temperature range of 12–300 K, though the emission at 300 K is much lower than that at low temperature. The 480 nm emission is ascribed to the transition from excited organic substances in GHE cells. The intensity of 480 nm emission at 300 K increases linearly with increasing irradiation-dose in the range of 11–600 Gy.     

Addition reactions of pendant epoxide group in poly(glycidyl methacrylate) with various active esters

Addition reactions of pendant epoxide groups in poly(glycidyl methacrylate) (PGMA) with various active esters such as 1-benzotriazolyl benzoate, S-(2-benzoxazolyl) thiobenzoate, S-(2-benzothiazolyl) thiobenzoate, 4-nitrophenyl benzoate (4NPB), and S-phenyl thiobenzoate (PTB) were carried out using quaternary salts as catalysts. The reactions of PGMA with those active esters proceeded in diglyme at 100°C for 24 h quantitatively without the formation of 2-hydroxyl pendant groups in the polymer when 10 mol % of tetraethylammonium bromide was used as a catalyst. Furthermore, it was found that the respective quaternary salts have higher catalytic activity than tertiary amines in the reaction of PGMA with the active esters, and the reaction of PGMA with 4NPB gave the corresponding polymer with the highest conversion by addition of tetrabutylammonium bromide as a catalyst, while tetraethylammonium chloride showed the highest activity for the reaction of PGMA with PTB. In addition, the rate of reaction of PGMA with 4NPB was proportional to third order kinetics of the epoxide concentration, the ester concentration and the catalyst concentration as follows: ?d[Epoxide]/dt = ?[Ester]/dt = k₃[Epoxide] [Ester] [Catalyst].     

Unexpected differences in the alpha-halogenation and related reactivity of sulfones with perhaloalkanes in KOH-t-BuOH

Most alkyl phenyl sulfones are readily alpha-chlorinated with CCl(4) and alpha-brominated with CBrCl3 in KOH-t-BuOH via radical-anion radical pair (RARP) reactions. While isopropyl mesityl sulfone (4) is easily alpha-chlorinated with CCl(4), it was completely recovered when treated with the more reactive CBrCl3. Subsequent investigations showed the latter result to be due to the poor acidity of 4 together with the rapid depletion of CBrCl3 and KOH by their reaction with each other, and led to a variety of other important results. 4-Hydroxyphenyl isopropyl sulfone (6) is unreactive with either CCl4 or CBrCl3 in KOH-t-BuOH, its phenoxide anion strongly reducing the electronegativity of the sulfonyl group, thereby inhibiting alpha-anion formation. This effect is reversed by the electron-withdrawing influence of two alpha-phenyls, so that benzhydryl 4-hydroxyphenyl sulfone (8) is readily alpha-halogenated in KOH-t-BuOH with CCl4 or CBrCl3. On further contact with KOH-t-BuOH the alpha-halogenated sulfones from 8 are decomposed into benzophenone and phenol. While the alpha-halogenated derivatives of 4-methoxyphenyl benzhydryl sulfone (9) are stable to base, they are decomposed even under mildly acidic conditions into 4-methoxyphenyl 4-methoxybenzenethiolsulfonate (9c), phenol, and benzophenone. Mono-alpha-halogenation of benzyl phenyl sulfone (10) enhances the rate of the subsequent halogenation, so that alpha,alpha-dihalogenation is attained while much substrate is still present and the mono-alpha-halogenated product is not detected. The ease of reductive debromination of alpha-bromo sulfones with Cl3C- was correlated with the stability of the formed alpha-anions, explaining the success with alpha-bromobenzylic sulfones but failure with alpha-bromoalkyl sulfones. In the presence of air and the absence of competing halogenation, formation of the alpha-anions of alkyl aryl sulfones is quickly accompanied by oxidative cleavage by atmospheric O2, leading to the formation of arenesulfonyl alcohols, arenesulfonyl halides, and haloarenes.