Numerical Analysis of the Allen-Cahn Equation with Coarse Meshes

In this paper, we consider the finite difference semi-discretization of the Allen-Cahn equation with the diffuse interface parameter $\varepsilon$. While it is natural to make the mesh size parameter $h$ smaller than $\varepsilon$, it is desirable that $h$ is as big as possible in view of computational costs. In fact, when $h$ is bigger than $\varepsilon$ (i.e., the mesh is relatively coarse), it is observed that the numerical solution does not move at all. The purpose of this paper is to clarify the mechanism of this phenomenon. We will prove that the numerical solution converges to that of the ordinary equation without the diffusion term if $h$ is bigger than $\varepsilon$. Numerical examples are presented to support the result.     

Diffusion Coefficients of Tris(<Emphasis Type="Italic">β</Emphasis>-diketonato)ruthenium Complexes of Different Charge Numbers in Acetonitrile Solutions,Measured by Chronoamperometry

The diffusion coefficients of several tris(β-diketonato) ruthenium complexes in acetonitrile solutions containing a supporting electrolyte were determined by chronoamperometry. The diffusion coefficients of the charged complexes, which were produced by electrochemical oxidation or reduction, were also determined by double potential step chronoamperometry. Two kinds of radii of the complexes were evaluated. One was the Van der Waals radius and the other was the geometric distance from the center of the complex to the outer surface of the farthest atom. The latter quantity was determined from X-ray diffractometric data. The diffusion coefficients of the neutral complexes were discussed on the basis of the Stokes-Einstein equation. Those of charged complexes could not be explained by the theoretical equation presented by Hubbard and Onsager.     

Synthesis and photoluminescence study of anthracene based dendrimer and dendron

A new type of polyaromatic dendrimer composed of six anthracene groups was synthesized, which showed a monomeric fluorescence feature with a diminished quantum yield due to intramolecular self-quenching processes in the dendritic framework.     

Preparation of chiral 5-deazaflavin derivatives and their asymmetric reduction of ethyl benzoylformate

1,5-Dihydro-5-deazaflavin derivatives possessing a chiral substituent at N(3) position were synthesized, with which moderate asymmetric induction was observed in the reduction of ethyl benzoylformate.     

Study on the effect of diand trifluoromethyl groups on the baeyer-villiger reaction

Case studies of the Baeyer-Villiger reaction applied to diand trifluoromethylketone derivatives and the effect of the fluoromethyl groups on the Baeyer-Villiger reaction, are described.     

Synthetic studies on cell surface glycans 3: Branching pentasaccharides of glycoprotein

Synthetic routes for the branching pentasaccharides 4 and 5 of glycoproteins are described in a regio- and stereo- controlled way.     

Synthesis and optical resolution of 2-aryl-2-fluoropropionic acids, fluorinated analogues of non-steroidal anti-inflammatory drugs (NSAIDs)

We report the synthesis of optically active 2-aryl-2-fluoropropionic acids 2 as non-epimerizable mimics of 2-arylpropionic acids 1, a class of compounds which have been widely used as non-steroidal anti-inflammatory drugs (NSAIDs). This is a continuation of our research involving the design, synthesis, and evaluation of chiral fluorine-containing organic molecules as effective analogues of pharmacologically important compounds.     

Synthesis of functionalized asymmetric star polymers containing conductive polyacetylene segments by living anionic polymerization

Novel 3-arm ABC, 4-arm ABCD, and 5-arm ABCDE asymmetric star polymers comprising the conductive polyacetylene precursor, poly(4-methylphenyl vinyl sulfoxide) (PMePVSO), and other segments, such as polystyrene, poly(alpha-methylstyrene), poly(4-methoxystyrene), poly(4-trimethylsilylstyrene), and poly(4-methylstyrene), were synthesized by the methodology based on living anionic polymerization using DPE-functionalized polymers. This methodology involves the addition reaction of a DPE-functionalized polymer to a living anionic polymer followed by the living anionic polymerization of MePVSO initiated from the in situ formed polymer anion with two, three, or four polymer segments. The resultant asymmetric star polymers possessed predetermined molecular weights, narrow molecular weight distributions (Mw/Mn < 1.03), and desired compositions as confirmed by SEC, 1H NMR, SLS, and elemental analysis. After thermal treatment, the PMePVSO segment in the star polymer could be completely converted into a conductive polyacetylene segment, evident from TGA and elemental analysis. These asymmetric star polymers are expected to exhibit interesting solution properties and unique microphase-separated morphological suprastructures with potential applications in nanoscopic conductive materials. Moreover, this methodology can afford the target asymmetric star polymers with arm segments varying in a wide range and enables the synthesis of more complex macromolecular architectures.