Higher order differentiability of solutions to backward stochastic differential equations

In this paper, we consider the differentiability in the sense of the Malliavin calculus of solutions to backward stochastic differential equations (BSDEs for short). It is known that a solution is differentiable in the sense of the Malliavin calculus and the derivative is also a solution to a linear BSDE. Under additional conditions, we will show that the higher order differentiability of a solution to a BSDE and that it also becomes a solution to a linear BSDE.     

Vortex dynamics and the Fulde-Ferrell-Larkin-Ovchinnikov state in a magnetic-field-induced organic superconductor

Under special conditions, a superconducting state where the order parameter oscillates in real space, the so-called FFLO state, is theoretically predicted to exist near the upper critical field, as first proposed by Fulde and Ferrell, and Larkin and Ovchinnikov. We report systematic measurements of the interlayer resistance in high magnetic fields to 45 T in the two-dimensional magnetic-field-induced organic superconductor lambda-(BETS)2FeCl4, where BETS is bis(ethylenedithio)tetraselenafulvalene. The resistance is found to show characteristic dip structures in the superconducting state. The results are consistent with pinning interactions between the vortices penetrating the insulating layers and the order parameter of the FFLO state. This gives strong evidence for an oscillating order parameter in real space.     

Combined Theoretical and Experimental Studies of Sodium Battery Materials

Owing to developments in theoretical chemistry and computer power, the combination of calculations and experiments is now standard practice in understanding and developing new materials for battery systems. Here, we briefly review our recent combined studies based on density functional theory and molecular dynamics calculations for electrode and electrolyte materials for sodium‐ion batteries. These findings represent case studies of successful combinations of experimental and theoretical methods.     

Impurity effects at hydrophobic surfaces

The effective charge of hydrophobic surfaces and in particular of the air–water interface is a crucial parameter for electrochemistry, colloidal chemistry and interfacial science, but different experiments give conflicting estimates. Zeta-potential and disjoining-pressure measurements point to a strongly negative surface charge, often interpreted as being due to adsorbing hydroxide ions. In contrast, surface tension measurements of acids and bases suggest the hydronium ion to be surface active, in agreement with some surface-specific non-linear spectroscopy results. The air–electrolyte interfacial tension exhibits a characteristic minimum at millimolar electrolyte concentration for all salts, the so-called Jones–Ray effect, which points to competitive adsorption mechanisms present in dilute electrolyte solutions. We show that all these puzzling experimental findings can be explained by the presence of trace amounts of surface-active charged impurities, most likely anionic surfactants.     

Stereospecific polymerization of o-methoxystyrene by anionic initiators

o-Methoxystyrene was polymerized with n-butyllithium (n-BuLi), Na naphthalene, and K dispersion as initiators in tetrahydrofuran (THF) and toluene. The stereoregularity of the polymer was investigated by means of the NMR spectroscopy. The methoxy resonance of the spectrum split into ten components due to the tactic pentads. It was found by x-ray examination that the polymer obtained by n-BuLi in toluene at ?45°C was crystalline and highly isotactic. In THF, the stereospecificity of the polymerization was independent of the initiator, and the isotacticity of the polymer increased with increasing reaction temperature. In toluene, the stereospecificity depended on the initiator; i.e., n-BuLi gave a polymer with higher isotacticity than that given by phenylsodium. The fraction of isotactic triad of the polymer obtained by n-BuLi in toluene at ?78°C was more than 90%, but 50% at 50°C. The presence of ca. 1% THF in toluene led to a steep decrease in the isotacticity even at ?78°C. The tacticity of the polymer given by Na naphthalene was not affected by the existence of NaB(C₆H₅)₄ in THF. The polymerization in THF could be explained by Bovey's “single σ” process, while a penultimate effect was observed in the polymerization by n-BuLi in toluene.     

Observation of three-dimensional fermi surfaces in a single-component molecular metal, [Ni(tmdt)2

Rigorous evidence of metallicity of a molecular crystal consisting of single-component neutral molecules is disclosed by observing the Fermi surface through magnetic quantum oscillations. Torque magnetometry measurements of de Haas-van Alphen oscillatory signals in a single crystal of [Ni(tmdt)2] molecules (tmdt = trimethylenetetrathiafulvalenedithiolate) were performed by using a sensitive microcantilever at low temperatures in high magnetic fields to 45 T. The observed signals for all directions of magnetic field revealed unambiguously the presence of three-dimensional Fermi surfaces for both holes and electrons. The results are consistent with electronic band structure calculations for [Ni(tmdt)2].     

Enhanced electron-capture decay rate of 7Be encapsulated in C60 cages

The decay rate of 7Be electron capture was measured in C60 and Be metal with a reference method. The half-life of 7Be endohedral C60 ((7)Be@C(60)) and 7Be in Be metal (Be metal (7Be)) is found to be 52.68+/-0.05 and 53.12+/-0.05 days, respectively. This amounts to a 0.83% difference in electron-capture decay half-life between (7)Be@C(60) and Be metal (7Be). Our result is a reflection of the different electron wave functions for (7)Be@C(60) inside C60 compared to the situation when 7Be is in a Be metal.     

STM observation of surface phases of Sn/Cu(0 0 1)

Geometrical structures of the Sn-adsorbed Cu(0 0 1) surfaces are studied with scanning tunneling microscopy. There are four phases in the Sn coverage range between 0.2 and 0.5 mono-atomic layer (ML). On the basis of the observed atomic images in this range, we propose structural models for the phases with 0.33 and 0.375 ML of Sn. All the phases consist of embedded Sn atoms in the Cu surface, forming two-dimensional surface alloy structures. On the surface with ∼0.4 ML of Sn, a novel one-dimensional structure is observed.     

Anionic copolymerization of 1,1-diphenylethylene and 2,3-dimethylbutadiene

1,1-Diphenylethylene (M₂) and 2,3-dimethylbutadiene (M₁) were copolymerized with n-butyllithium in tetrahydrofuran. The rate of consumption of each monomer was followed by the change of high resolution NMR spectra of the reaction mixture. The copolymerization proceeded alternately, if the ratio of initial monomer concentrations, [M₂]₀/[M₁]₀, was sufficiently larger than unity. By assuming the rate constant k₂₂ to be zero, the constants k₂₁ were obtained from the consumption rates of the monomers. In the alternating copolymerization, 2,3-dimethylbutadiene was incorporated into the copolymer only as the 1,4-structure, while the 1,2-structure was predominant in homopolymerization.