A variational principle for the Navier-Stokes equation

Motivated from Arnold's variational characterization of the Euler equation in terms of geodesic families of diffeomorphisms, a variational principle for the motion of incompressible viscous fluids is presented. A volume preserving diffusion process with drift velocity field subject to the Navier-Stokes equation is shown to extremize the energy functional of the fluid under a certain class of stochastic variations.     

Stochastic quantization: A review

The present status of the work on the application of the stochastic quantization procedure is reviewed. A compact mathematical introduction to the basic notions of random processes such as Markov processes, Martingales and Fokker-Planck equations is presented. The stochastic quantization procedure is explained in much detail and it is found to possess remarkable features which can not be achieved within the conventional framework of quantum theory. This admits us to give systematic analyses of irreversible quantum dynamics of dissipative systems and the vacuum tunneling phenomena in non-Abelian gauge theory     

Thermal mechanics: A quantum mechanical analogue of nonequilibrium statistical thermodynamics

A formal but not conventional equivalence between stochastic processes in nonequilibrium statistical thermodynamics and Schrödinger dynamics in quantum mechanics is shown. It is found, for each stochastic process described by a stochastic differential equation of Itô type, there exists a Schrödinger-like dynamics in which the absolute square of a wavefunction gives us the same probability distribution as the original stochastic process. In utilizing this equivalence between them, that is, rewriting the stochastic differential equation by an equivalent Schrödinger equation, it is possible to obtain the notion of deterministic limit of the stochastic process as a semi-classical limit of the “Schrödinger” equation. The deterministic limit thus obtained improves the conventional deterministic approximation in the sense of Onsager-Machlup. The present approach is valid for a general class of stochastic equations where local drifts and diffusion coefficients depend on the position. Two concrete examples are given. It should be noticed that the approach in the present form has nothing to do with the conventional one where only a formal similarity between the Fokker-Planck equation and the Schrödinger equation is considered.     

Rod-like liquid crystals of organic transition metal complexes. I. Reversible transformation between blue smectogen and red nematogen

Two novel types of transition-metal-containing liquid crystals, bis(p-n-koxydithiobenzoato)nickel(II) (abbreviated as (C_nO-DTB)₂Ni), and (p-n-alkoxydithiobenzoato)(p-n-alkoxyperthiobenzoato)nickel(II) (abbreviated as (C_nO-DTB)(C_nO-PTB)Ni), were synthesized. It was found that the (C_nO-DTB)₂Ni complex for n = 8 has smectic H and C mesophases, and that the (C_nO-DTB)₂Ni complexes for n = 4 and 8 easily transform into the corresponding monoperthio complexes, _nO-PTB)Ni, by heating at temperatures between 230°C and 285°C. It was confirmed that the transformation originates from an intermolecular reaction between the (C_nO-DTB)₂Ni complexes at high temperatures, and that the origin of the extra sulphurs in the resulting (C_nO-DTB)(C_nO-PTB)Ni complexes is the neighbouring (C_nO-DTB)₂Ni complexes. Interestingly, each of the (C_nO-DTB)(C_nO-PTB)Ni complexes (n = 4 and 8), has nematic mesophase and exhibits a unique double melting behaviour via the nematic phase, which is the first example in liquid crystals. The reversible transformation between the blue smectic rod-like (C_nO-DTB)₂Ni complex and the red nematic Λ-like (C_nO-DTB)(C_nO-PTB)Ni complex is possible.     

Macroscopic single‐domain graphene sheet on Ni(111)

We observed in situ growth of a single graphene sheet on Ni(111) by low‐energy electron microscopy. The sheet was grown epitaxially beyond the steps on the substrate. The crystalline shapes of graphene islands were clearly seen; the straight edges of the island are crossed at either 60 or 120°, and the linear edges shifted perpendicular to the edge keeping the equilibrium shape. Graphene islands were united to form a single sheet without any grain boundaries and any wrinkles. The Ni substrate of several centimeters in size was covered with a single‐domain graphene sheet. Copyright © 2011 John Wiley & Sons, Ltd.     

Conserved Tyr223(5.58) plays different roles in the activation and G-protein interaction of rhodopsin

Rhodopsin, a seven transmembrane helix (TM) receptor, binds its ligand 11-cis-retinal via a protonated Schiff base. Coupling to the G-protein transducin (G(t)) occurs after light-induced cis/trans-retinal isomerization, which leads through photoproducts into a sequence of metarhodopsin (Meta) states: Meta I ? Meta IIa ? Meta IIb ? Meta IIbH(+). The structural changes behind this three-step activation scheme are mediated by microswitch domains consisting of conserved amino acids. Here we focus on Tyr223(5.58) as part of the Y(5.58)X(7)K(R)(5.66) motif. Mutation to Ala, Phe, or Glu results in specific impairments of G(t)-activation measured by intrinsic G(t) fluorescence. UV-vis/FTIR spectroscopy of rhodopsin and its complex with a C-terminal G(t)α peptide allows the assignment of these deficiencies to specific steps in the activation path. Effects of mutation occur already in Meta I but do not directly influence deprotonation of the Schiff base during formation of Meta IIa. Absence of the whole phenol ring (Y223A) allows the activating motion of TM6 in Meta IIb but impairs the coupling to G(t). When only the hydroxyl group is lacking (Y223F), Meta IIb does not accumulate, but the activity toward G(t) remains substantial. From the FTIR features of Meta IIbH(+) we conclude that proton uptake to Glu134(3.49) is mandatory for Tyr223(5.58) to engage in the interaction with the key player Arg135(3.50) predicted by X-ray analysis. This polar interaction is partially recovered in Y223E, explaining its relatively high activity. Only the phenol side chain of tyrosine provides all characteristics for accumulation of the active state and G-protein activation.     

(6Li,d) reactions on 24Mg and 26Mg at 73 MeV

The ^{24, 26}Mg(⁶Li, d)^{28, 30}Si reactions have been studied at 73 MeV bombarding energy. The angular distributions were analyzed with exact finite-range distorted wave Born approximation calculations assuming a direct α-cluster transfer. Extracted spectroscopic strengths leading to low-lying levels of ²⁸Si and relative spectroscopic strengths between transitions to ²⁸Si and ³⁰Si ground states are consistent with those previously obtained by several α-transfer reactions. Many strongly populated levels have been observed at E_x ? 10 MeV for ²⁸Si. A marked similarity was found between the deuteron spectrum and the ²⁴Mg(α, α)²⁴Mg excitation function in this excitation energy region. A brief comparison of the present α-transfer results with previous two-nucleon transfer data leading to ^28,30Si is also presented.     

Structure–Activity Studies on the Fluorescent Indicator in a Displacement Assay for the Screening of Small Molecules Binding to RNA

A series of xanthone and thioxanthone derivatives with aminoalkoxy substituents were synthesized as fluorescent indicators for a displacement assay in the study of small‐molecule–RNA interactions. The RNA‐binding properties of these molecules were investigated in terms of the improved binding selectivity to the loop region in the RNA secondary structure relative to 2,7‐bis(2‐aminoethoxy)xanthone (X2S) by fluorimetric titration and displacement assay. An 11‐mer double‐stranded RNA and a hairpin RNA mimicking the stem loop IIB of Rev response element (RRE) RNA of HIV‐1 mRNA were used. The X2S derivatives with longer aminoalkyl substituents showed a higher affinity to the double‐stranded RNA than the parent molecule. Introduction of a methyl group on the aminoethoxy moiety of X2S effectively modulated the selectivity to the RNA secondary structure. Methyl group substitution at the C1′ position suppressed the binding to the loop regions. Substitution with two methyl groups on the amino nitrogen atom resulted in reducing the affinity to the double‐stranded region by a factor of 40 %. The effect of methyl substitution on the amino nitrogen atom was also observed for a thioxanthone derivative. Titration experiments, however, suggested that thioxanthone derivatives showed a more prominent tendency of multiple binding to RNA than xanthone derivatives. The selectivity index calculated from the affinity to the double‐stranded and loop regions suggested that the N,N‐dimethyl derivative of X2S would be suitable for the screening of small molecules binding to RRE.