Asymptotic behavior of solutions of the compressible Navier‐Stokes equations in a cylinder under the slip boundary condition

The large time behavior of solutions to the compressible Navier‐Stokes equations around the motionless state is considered in a cylinder under the slip boundary condition. It is shown that if the initial data are sufficiently small, the global solution uniquely exists and the large time behavior of the solution is described by a superposition of one‐dimensional nonlinear diffusion waves and a diffusive rigid rotation.     

Remarks on the Cauchy problem for first order hyperbolic systems with constant coefficient principal part

Abstract In this article we shall introduce the results obtained in [16], i.e., we shall give a necessary and sufficient condition that the Cauchy problem for first order hyperbolic systems with constant coefficient principal part is C^∞ well-posed under the maximal rank condition (see the condition (R) below). We shall also give a simple sufficient condition without any assumptions on the rank. Keywords: Hyperbolic system, Cauchy problem, Constant coefficient principal part     

Synthesis of Oxygen‐Containing Spirobipyrrolidinium Salts for High Conductivity Room Temperature Ionic Liquids

Synthesis of ionic liquids (IL) based on oxygen‐containing spirobipyrrolidinium salts with BF₄, BF₃C₂F₅, and NTf₂ as counterions was undertaken. Their physical and electrochemical properties were evaluated for suitability for Room Temperature Ionic Liquids (RTIL) application. Reduction in melting point occurred upon exchange of C(2) by an O‐atom of spirobipyrrolidinium, without sacrificing the electrochemical stability; while introduction of alkyl groups between the N‐ and O‐atoms led to incorporation of asymmetry, and hence reduced the melting points, and viscosity.     

Efficient charge generation and collection in organic solar cells based on low band gap dyad molecules

Low band gap dyad molecules were prepared that have absorption spectra matched well with the solar spectrum, and the construction of efficient charge transport pathways was observed. Under AM 1.5 illumination, the devices have achieved the highest J(SC) (4.79 mA cm(2)) and FF (0.46) in dyad-based organic solar cells to date.     

A combined quantum mechanical and molecular mechanical method using modified generalized hybrid orbitals: implementation for electronic excited states

The generalized hybrid orbital (GHO) method is implemented at the second-order approximate coupled cluster singles and doubles (CC2) level for quantum mechanical (QM)/molecular mechanical (MM) electronic excited state calculations. The linear response function of CC2 in the GHO scheme is derived and implemented. The new implementation is applied to the first singlet excited states of three aromatic amino acids, phenylalanine, tyrosine, and tryptophan, and also bacteriorhodopsin for assessment. The results obtained for aromatic amino acids agreed well with the full QM CC2 calculations, while the calculated excitation energies of bacteriorhodopsin and its chromophore, all-trans retinal, reproduced the environmental shift of the experimental data. For the bacteriorhodopsin case, the environmental shift of GHO also showed good agreements with the experimental data. The contribution of the quantum effect of certain moieties in the excited states is elucidated by changing the partitioning of QM and MM regions.     

Asymptotic behaviors of solutions to evolution equations in the presence of translation and scaling invariance

There are wide classes of nonlinear evolution equations which possess invariant properties with respect to a scaling and translations. If a solution is invariant under the scaling then it is called a self-similar solution, which is a candidate for the asymptotic profile of general solutions at large time. In this paper we establish an abstract framework to find more precise asymptotic profiles by shifting self-similar solutions suitably.     

Geometrically associative yet electronically dissociative character in the transition state of enzymatic reversible phosphorylation

Reversible phosphorylation of proteins is a post‐translational modification that regulates diverse biological processes. The molecular mechanism underlying phosphoryl transfer catalyzed by enzymes remains a subject of active debate. In particular, the nature of transition state (TS), whether it has an associative or dissociative character, has been one of the most controversial issues. Structural evidence supports associative TS, whereas physical organic studies point to a dissociative character. Here we perform hybrid quantum mechanics/molecular mechanics simulations for the reversible phosphorylation of phosphoserine phosphatase (PSP) to study the nature of the TS. Both phosphorylation and dephosphorylation reactions are investigated based on the two‐dimensional energy surfaces along phosphoryl and proton transfer coordinates. The structures of the active site at TS in both reactions reveal compact geometries, consistent with crystal structures of PSP with phosphate analogues. However, the electron density of the phosphoryl group in both TS structures slightly decreases compared with that in the reactant states. These findings suggest that the TS of PSP has a geometrically associative yet electronically dissociative character and strongly depends on proton transfer being coupled with phosphoryl transfer. Structure and literature database, which searches on phosphotransferases, suggest that such a hybrid TS is consistent with many structures and physical organic studies and likely holds for most enzymes catalyzing phosphoryl transfer. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

The Oberbeck–Boussinesq approximation as a constitutive limit

We derive the usual Oberbeck–Boussinesq approximation as a constitutive limit of the full system describing the motion of an compressible linearly viscous fluid. To this end, the starting system is written, using the Gibbs free energy, in the variables v, θ and p. The Oberbeck–Boussinesq system is then obtained as the thermal expansion coefficient α and the isothermal compressibility coefficient β tend to zero.     

Measurements of binary diffusion coefficients for metal complexes in organic solvents by the Taylor dispersion method

Infinite dilution binary diffusion coefficients, D₁₂, of ferrocene, 1,1′-dimethylferrocene and ethylferrocene in hexane, cyclohexane and ethanol at 313.2 K and pressures from 0.2 to 19 MPa, in acetonitrile at 298.2–333.2 K and 0.2 MPa, and various metallic acetylacetonate, acac, complexes such as Co(acac)₃, Ru(acac)₃, Rh(acac)₃, Pd(acac)₂ and Pt(acac)₂ mainly in ethanol at 313.2 K and 0.2 MPa were measured by the Taylor dispersion method. The D₁₂ values in m² s⁻¹ for the three ferrocenes in the present study and those of ferrocene and 1,1′-dimethylferrocene in supercritical carbon dioxide in our previous studies were represented by the modified hydrodynamic equation over a wide range of viscosity: M^0.5D₁₂/T = 1.435 × 10⁻¹³η^−0.8446 with average absolute relative deviation of 2.40% for 316 data points, where M is the solute molecular weight, T is the temperature in K, η is the solvent viscosity in Pa s. Although the D₁₂ values for the acac complexes were roughly represented by the above hydrodynamic equation, the accuracies were lower because they were dependent on not solute molecular weight but the number of acac ligand in the complex molecules.     

Unconventional pairing originating from the disconnected Fermi surfaces of superconducting LaFeAsO1-xFx

For a newly discovered iron-based high T_{c} superconductor LaFeAsO1-xFx, we have constructed a minimal model, where inclusion of all five Fe d bands is found to be necessary. The random-phase approximation is applied to the model to investigate the origin of superconductivity. We conclude that the multiple spin-fluctuation modes arising from the nesting across the disconnected Fermi surfaces realize an extended s-wave pairing, while d-wave pairing can also be another candidate.