The Crossover Regime for the Weakly Asymmetric Simple Exclusion Process

We consider the asymmetric simple exclusion process in one dimension with weak asymmetry (WASEP) and 0–1 step initial condition. Our interest are the fluctuations of the time-integrated particle current at some prescribed spatial location. One expects a crossover from Gaussian to Tracy-Widom distributed fluctuations. The appropriate crossover scale is an asymmetry of order \(\sqrt{\varepsilon}\), times of order ε ^?2, and a spatial location of order ε ^?3/2. For this parameter window we obtain the limiting distribution function of the integrated current in terms of an integral over the difference of two Fredholm determinants. For large times, on the scale ε ^?2, this distribution function converges to the one of Tracy-Widom.     

Control of release properties of guest molecules by the type of benzoheterocyclic ring in supramolecular host complexes

Three types of supramolecular benzoheterocyclic host complexes were successfully prepared using (1R,2S)-2-amino-1,2-diphenylethanol and three types of benzoheterocyclic (benzothiophene, benzofuran, and benzopyrrole) acid derivatives. The host complexes had one-dimensional (1D) channel-like cavities that were formed by the assembly of two-component 2₁-helical columnar network structures, which included guest alcohol molecules. The release behavior of the guest molecules could be tuned by the type of heterocyclic ring in the supramolecular host complex.     

Dense coordination network capable of selective CO2 capture from C1 and C2 hydrocarbons

We elucidated the specific adsorption property of CO(2) for a densely interpenetrated coordination polymer which was a nonporous structure and observed gas separation properties of CO(2) over CH(4), C(2)H(4), and C(2)H(6), studied under both equilibrium and kinetic conditions of gases at ambient temperature and pressure.     

Supramolecularly engineered perylene bisimide assemblies exhibiting thermal transition from columnar to multilamellar structures

Perylene 3,4:9,10-tetracarboxylic acid bisimide (PBI) was functionalized with ditopic cyanuric acid to organize it into complex columnar architectures through the formation of hydrogen-bonded supermacrocycles (rosette) by complexing with ditopic melamines possessing solubilizing alkoxyphenyl substituents. The aggregation study in solution using UV-vis and NMR spectroscopies showed the formation of extended aggregates through hydrogen-bonding and π-π stacking interactions. The cylindrical fibrillar nanostructures were visualized by microscopic techniques (AFM, TEM), and the formation of lyotropic mesophase was confirmed by polarized optical microscopy and SEM. X-ray diffraction study revealed that a well-defined hexagonal columnar (Col(h)) structure was formed by solution-casting of fibrillar assemblies. All of these results are consistent with the formation of hydrogen-bonded PBI rosettes that spontaneously organize into the Col(h) structure. Upon heating the Col(h) structure in the bulk state, a structural transition to a highly ordered lamellar (Lam) structure was observed by variable-temperature X-ray diffraction, differential scanning calorimetry, and AFM studies. IR study showed that the rearrangement of the hydrogen-bonding motifs occurs during the structural transition. These results suggest that such a striking structural transition is aided by the reorganization in the lowest level of self-organization, i.e., the rearrangement of hydrogen-bonded motifs from rosette to linear tape. A remarkable increase in the transient photoconductivity was observed by the flash-photolysis time-resolved microwave conductivity (FP-TRMC) measurements upon converting the Col(h) structure to the Lam structure. Transient absorption spectroscopy revealed that electron transfer from electron-donating alkoxyphenyl groups of melamine components to electron-deficient PBI moieties takes place, resulting in a higher probability of charge carrier generation in the Lam structure compared to the Col(h) structure.     

Permeability retrieval in InP-based waveguide optical device combined with metamaterial

An InP-based Mach-Zehnder interferometer combined with a metamaterial layer consisting of a split-ring resonator array was constructed to measure the complex permeability of the metamaterial. At a wavelength of 1.5 μm, the metamaterial showed non-unity relative permeability induced by magnetic interaction with propagating light in the device. This method of measurement would be useful to determine constitutive parameters in such waveguide-based photonic devices, allowing us to design photonic integrated circuits that make use of metamaterials.     

Relationships between the anisotropy of longitudinal wave velocity and hydroxyapatite crystallite orientation in bovine cortical bone

Quantitative ultrasound (QUS) is now widely used for evaluating bone in vivo, because obtained ultrasonic wave properties directly reflect the visco-elasticity. Bone tissue is composed of minerals like hydroxyapatite (HAp) and a collagen matrix. HAp crystallites orientation is thus one parameter of bone elasticity. In this study, we experimentally investigated the anisotropy of ultrasonic wave velocity and the HAp crystallites orientation in the axial-radial and axial-tangential planes in detail, using cylindrical specimens obtained from the cortical bone of three bovine femurs. Longitudinal bulk wave propagation was investigated by using a conventional ultrasonic pulse system. We used the one cycle of sinusoidal pulse which was emitted from wide band transmitter. The nominal frequency of the pulse was 1 MHz. First, we investigated the anisotropy of longitudinal wave velocity, measuring the anisotropy of velocity in two planes using cylindrical specimens obtained from identical bone areas. The wave velocity changed due to the rotation angle, showing the maximum value in the direction a little off the bone axis. Moreover, X-ray pole figure measurements also indicated that there were small tilts in the HAp crystallites orientation from the bone axis. The tilt angles were similar to those of the highest velocity direction. There were good correlations between velocity and HAp crystallites orientation obtained in different directions. However, a comparatively low correlation was found in posterior bone areas, which shows the stronger effects of bone microstructure. In the radial-tangential plane, where the HAp crystallites hardly ever align, weak anisotropy of velocity was found which seemed to depend on the bone microstructure.     

Large-aperture focusing of x rays with micropore optics using dry etching of silicon wafers

Large-aperture focusing of Al K(α) 1.49 keV x-ray photons using micropore optics made from a dry-etched 4 in. (100 mm) silicon wafer is demonstrated. Sidewalls of the micropores are smoothed with high-temperature annealing to work as x-ray mirrors. The wafer is bent to a spherical shape to collect parallel x rays into a focus. Our result supports that this new type of optics allows for the manufacturing of ultralight-weight and high-performance x-ray imaging optics with large apertures at low cost.     

Complete reducibility,Külshammer’s question,conjugacy classes: A D4 example

Let k be a nonperfect separably closed field. Let G be a connected reductive algebraic group defined over k. We study rationality problems for Serre’s notion of complete reducibility of subgroups of G. In particular, we present a new example of subgroup H of G of type D₄ in characteristic 2 such that H is G-completely reducible but not G-completely reducible over k (or vice versa). This is new: all known such examples are for G of exceptional type. We also find a new counterexample for Külshammer’s question on representations of finite groups for G of type D₄. A problem concerning the number of conjugacy classes is also considered. The notion of nonseparable subgroups plays a crucial role in all our constructions.     

Gas-phase chlorine-initiated photooxidation of methanol and isopropanol

The photolysis of CH₃OH/Cl₂/air, CH₃OH/Cl₂/NO₂/air, and (CH₃)₂CHOH/Cl₂/NO₂/air at 28 ± 2°C was studied using the long-path FTIR method. The primary reactions of methanol and isopropanol with Cl atoms were α-hydrogen abstraction (100%), and α hydrogen (85%), and α-hydrogen abstraction (15%), respectively. The failure to detect hydroxyalkyl-peroxy nitrates suggested that the oxygen addition to α-hydroxy radicals is not important. From the product distribution an upper limit of the ratio of oxygen addition to CH₂OH and CH₃CHOH was estimated to be about 6 and 7%, respectively. The oxygen addition ratio to (CH₃)₂COH was very low. The reaction mechanism is also discussed.