Concentration under scaling limits for weakly pinned Gaussian random walks

We study scaling limits for d-dimensional Gaussian random walks perturbed by an attractive force toward a certain subspace of $\mathbb {R}^d$ , especially under the critical situation that the rate functional of the corresponding large deviation principle admits two minimizers. We obtain different type of limits, in a positive recurrent regime, depending on the co-dimension of the subspace and the conditions imposed at the final time under the presence or absence of a wall. The motivation comes from the study of polymers or (1 + 1)-dimensional interfaces with δ-pinning.     

A stochastic heat equation with the distributions of Lévy processes as its invariant measures

We consider a linear heat equation on a half line with an additive noise chosen properly in such a manner that its invariant measures are a class of distributions of Lévy processes. Our assumption on the corresponding Lévy measure is, in general, mild except that we need its integrability to show that the distributions of Lévy processes are the only invariant measures of the stochastic heat equation.     

Hydrodynamic limit for ∇φ interface model on a wall

 We consider random evolution of an interface on a hard wall under periodic boundary conditions. The dynamics are governed by a system of stochastic differential equations of Skorohod type, which is Langevin equation associated with massless Hamiltonian added a strong repelling force for the interface to stay over the wall. We study its macroscopic behavior under a suitable large scale space-time limit and derive a nonlinear partial differential equation, which describes the mean curvature motion except for some anisotropy effects, with reflection at the wall. Such equation is characterized by an evolutionary variational inequality. Received: 10 January 2002 / Revised version: 18 August 2002 / Published online: 15 April 2003 Mathematics Subject Classification (2000): 60K35, 82C24, 35K55, 35K85 Key words or phrases: Hydrodynamic limit – Effective interfaces – Hard wall – Skorohod's stochastic differential equation – Evolutionary variational inequality     

Derivation of the hydrodynamical equation for one-dimensional Ginzburg-Landau model

Summary The hydrodynamical behavior of one-dimensional scalar Ginzburg-Landau model with conservation law is investigated. The dynamics of the system is given by solving a stochastic partial differential equation. Under appropriate space-time scaling, a deterministic limit is obtained and the limit is described by a certain nonlinear diffusion equation.Dedicated to Professor Takeyuki Hida on his 60th birthday     

Synthesis and complexing properties of [2.n](2,6)pyridinocrownophanes

[2.n](2,6)Pyridinocrownophanes (3a-e) were efficiently prepared by intramolecular [2 + 2] photocycloaddition of vinylpyridine derivatives under irradiation using a 400-W high-pressure mercury lamp through a Pyrex filter. They were of cis-configuration with respect to the cyclobutane ring, which was proven by the specific methine proton NMR resonances at delta 3.98-4.08. From ESI-MS analysis 3a-e were found to form 1:1 complexes with Ag+ cation. In a liquid-liquid extraction, 3 showed the highest affinity toward Ag+ cation among several heavy metal nitrates. In this series, 3c possessing four ethereal oxygen atoms was found to show the highest Ag+ affinity, according to the liquid-liquid extraction and determination of stability constant with the cation. The photoreactivity of precursor vinylpyridines is discussed by the predictor gamma(r(c)) proposed by Caldwell.     

Crystal structures and vibrational spectra of racemic and chiral 4-phenyl-1,3-oxazolidine-2-thione

The crystal structures of (rac)- and (R)-4-phenyl-1,3-oxazolidine-2-thione (4-POT) have been determined by X-ray diffraction. The structure of (rac)-4-POT is monoclinic P2₁/n with a = 11.9096(9) Å, b = 5.9523(6) Å, c = 12.3563(8) Å, = 91.054(6)°, V = 875.8(1) ų, and Z = 4. The structure of (R)-4-POT is orthorhombic P2₁2₁2₁ with a = 7.7197(6) Å, b = 21.603(2) Å, c = 5.4613(9) Å, V = 910.8(2) ų, and Z = 4. (rac)-4-POT and (R)-4-POT crystals are shown to have different hydrogen-bonding patterns. In the racemic crystals, the enantiomeric (R)- and (S)-4-POT molecules are connected to form a cyclic dimer via the N–H S hydrogen bond of the cis thioamide moiety [N Sⁱ 3.438(2) Å, N–H Sⁱ 176(2)° symmetry code: (i) 1 – x, 1 – y, 1 – z]. In the chiral (R)-4-POT crystals, the N–H S intermolecular hydrogen bond forms a zigzag chain around the twofold screw axis [N Sⁱⁱ 3.347(3) Å, N–H Sⁱⁱ 161(3)° symmetry code: (ii) 1/2 + x, 1/2 – y, 2 – z]. Observed difference of 46°C in the melting points between the (rac)-4-POT and (R)-4-POT crystals is correlated with difference in the crystal packing. Vibrational spectra of (rac)- and (R)-4-POT crystals are discussed both in the solid state and in solution.     

Lyophilized hemoglobin‐albumin cluster with disaccharides: Long‐term storable powder of artificial O2‐carrier

Core‐shell protein cluster comprising a hemoglobin (Hb) in the center and human serum albumins (HSA) at the exterior, Hb‐HSA ₃ cluster, is an artificial O₂‐carrier designed for use as a red blood cell (RBC) substitute. Lyophilization of the Hb‐HSA ₃ cluster solution ([Hb unit] = 5 g/dL) with sucrose and trehalose yielded stable pink powder, which can be stored for 2 years at 4°C. Addition of pure water to the powder regenerated the homogeneous solution. The O₂‐binding properties and oxyHb rate have been unaltered during the storage period. Infrared spectroscopic studies revealed that the hydrogen bond between protein and sugar stabilizes three‐dimensional structure of the cluster.     

Synthesis and Photovoltaic Properties of Boron β‐Ketoiminate Dyes Forming a Linear Donor‐π‐Acceptor Structure

Organoboron complexes are of interest as chromophores for dye sensitizers owing to their light‐harvesting and carrier‐transporting properties. In this study, compounds containing boron β‐ketoiminate (BKI) as a chromophore were synthesized and used as dye sensitizers in dye‐sensitized solar cells. The new dyes were orange or red crystals and showed maximum absorptions in the 410–450 nm wavelength region on titanium dioxide substrates. These electrodes exhibited maximum efficiencies of over 80% in incident photon‐to‐current conversion efficiency spectra, suggesting that the continuous process of light absorption‐excitation‐electron injection was effectively performed. Open‐circuit photovoltages were relatively high owing to the large dipole moments of the BKI dyes with a linear molecular structure. Thus, a maximum power conversion efficiency of 5.3% was successfully observed. Comparison of BKI dyes with boron β‐diketonate dyes revealed certain differences in solution stability, spectral properties, and photovoltaic characteristics.     

Resonance States and Alpha Condensation in 12C and 16O

Low density states near the 3α and 4α breakup thresholds in ¹²C and ¹⁶O, respectively, are discussed in terms of the α-particle condensation. Calculations are performed in Orthogonality Condition Model and Tohsaki–Horiuchi–Schuck–Röpke approaches. The ${0_2^+}$ state in ¹²C and the ${0_6^+}$ state in ¹⁶O are shown to have dilute density structures and give strong enhancement of the occupation of the S-state c.o.m. orbital of the α-particles. The possibility of the existence of α-particle condensed states in heavier nα nuclei is also discussed.