Global solution branches for a nonlocal Allen–Cahn equation

We consider the Neumann problem of a 1D stationary Allen–Cahn equation with nonlocal term. Our previous paper [4] obtained a local branch of asymmetric solutions which bifurcates from a point on the branch of odd-symmetric solutions. This paper derives the global behavior of the branch of asymmetric solutions, and moreover, determines the set of all solutions to the nonlocal Allen–Cahn equation. Our proof is based on a level set analysis for an integral map associated with the nonlocal term.     

Finite deformation analysis of COD,J-integral and crack tip intense strain region in plane strain large-scale yielding

A finite element analysis was performed to simulate crack tip blunting and the development of the intense strain region in a small compact tension specimen (0.4 T CT) of SA533B-1 under plane strain large-scale yielding, with the condition of large-geometry change around the crack tip taken into consideration. The region where the equivalent plastic strain $\text{}\text{?}$g3_p is greater than 0.15 was defined as the intense strain region, which corresponded to the recrystallized-etched zone delineated experimentally around the blunting crack tip. The development of the intense strain region was discussed as a function of the J-integral and the crack opening displacement. A linear relationship was obtained between the plastic work W_p dissipated within the intense strain region and (J/σ_y)² or b², where b is the crack opening displacement, defined as the separation of the two points at which the boundary of the intense strain region surrounding the crack tip intersects with the free surfaces of the crack.     

Approximating Solutions of Maximal Monotone Operators in Hilbert Spaces

Let H be a real Hilbert space and let T: H→2^H be a maximal monotone operator. In this paper, we first introduce two algorithms of approximating solutions of maximal monotone operators. One of them is to generate a strongly convergent sequence with limit vT⁻¹0. The other is to discuss the weak convergence of the proximal point algorithm. Next, using these results, we consider the problem of finding a minimizer of a convex function. Our methods are motivated by Halpern's iteration and Mann's iteration.     

Conformity and precision of CO2 densimetry in CO2 inclusions: microthermometry versus Raman microspectroscopic densimetry

To assess the ability of densimetry for CO₂ fluid in CO₂ inclusions, we compare two methods, microthermometry and Raman microspectroscopic densimetry for CO₂. The comparative experiment was performed for nine CO₂ inclusions in three mantle xenoliths. The results are as follows: (1) microthermometry precisely determines CO₂ density with the range of 0.65 to 1.18 g/cm³ compared with Raman microspectroscopic densimetry; (2) CO₂ density obtained by Raman microspectroscopic densimetry is fairly consistent with that by microthermometry; (3) it is hard to determine CO₂ density in CO₂ inclusion with diameter of less than around 3 µm using microthermometry; and (4) microthermometry can be applied only to the CO₂ inclusion whose CO₂ density ranges from around 0.65 to 1.18 g/cm³, whereas the Raman microspectroscopic densimetry is applicable to CO₂ density ranging from 0.1 to 1.24 g/cm³. The above features carry the potential for estimation of depth origin of mantle‐derived rocks. The depth where the rocks were trapped by host magma can be estimated using both geothermometric data and CO₂ fluid density in CO₂ inclusions in the rocks. Typical precisions of density of CO₂ in CO₂ inclusions obtained by the Raman microspectroscopic densimetry (~0.01 g/cm³) and by the microthermometry (< 0.001 g/cm³) correspond to uncertainties in the depth origin of 2.4 km and < 1.7 km, respectively, at 1000 ± 50 °C. In case of the mantle under 750–1250 °C and 1 GPa, the CO₂ fluid has a density ranging from 1.06 g/cm³ to 1.21 g/cm³, which are well measured by the Raman microspectroscopic densimetry. Combination of both densimetries for CO₂ in mantle minerals elucidates the deep structure of the Earth. Copyright © 2012 John Wiley & Sons, Ltd.     

Angle-resolved photoemission study of CoSi2 nanofilms grown on Si(111) substrates

We have carried out an angle-resolved photoemission study for CoSi₂ nanofilms grown on the Si(111)-7×7 substrates. The surface of CoSi₂(111) nanofilm changes from the bulk-truncated surface to the surface with additional Si-bilayer by annealing at higher temperature above 825 K. The angle-resolved photoemission spectra of the CoSi₂ nanofilm annealed at 853 K show the spectral features originated from the surface resonance state on the CoSi₂ surface terminated by Si-bilayer. From the detailed photoemission study, we discuss the surface electronic structure in CoSi₂(111) nanofilms grown on Si(111) substrates.     

Theory of chemical bonds in metalloenzymes XXII: a concerted bond-switching mechanism for the oxygen–oxygen bond formation coupled with one electron transfer for water oxidation in the oxygen-evolving complex of photosystem II

ABSTRACT

QM(UB3LYP)/MM(AMBER) calculations were performed for the locations of the transition structure (TS) of the oxygen–oxygen (O–O) bond formation in the S₄ state of the oxygen-evolving complex (OEC) of photosystem II (PSII). The natural orbital (NO) analysis of the broken-symmetry (BS) solutions was also performed to elucidate the nature of the chemical bonds at TS on the basis of several chemical indices defined by the occupation numbers of NO. The computational results revealed a concerted bond switching (CBS) mechanism for the oxygen–oxygen bond formation coupled with the one-electron transfer (OET) for water oxidation in OEC of PSII. The orbital interaction between the σ-HOMO of the Mn(IV)₄–O₍₅₎ bond and the π*-LUMO of the Mn(V)₁=O₍₆₎ bond plays an important role for the concerted O–O bond formation for water oxidation in the CaMn₄O₆ cluster of OEC of PSII. One electron transfer (OET) from the π-HOMO of the Mn(V)₁=O₍₆₎ bond to the σ*-LUMO of the Mn(IV)₄–O₍₅₎ bond occurs for the formation of electron transfer diradical, where the generated anion radical [Mn(IV)₄–O₍₅₎]^-? part is relaxed to the ?Mn(III)₄?…?O₍₅₎^- structure and the cation radical [O₍₆₎=Mn(V)₁]⁺ ? part is relaxed to the ⁺O₍₆₎–Mn(IV)₁? structure because of the charge-spin separation for the electron-and hole-doped Mn–oxo bonds. Therefore, the local spins are responsible for the one-electron reductions of Mn(IV)₄->Mn(III)₄ and Mn(V)₁->Mn(IV)₁. On the other hand, the O₍₅₎^- and O₍₆₎⁺ sites generated undergo the O–O bond formation in the CaMn₄O₆ cluster. The Ca(II) ion in the cubane- skeleton of the CaMn₄O₆ cluster assists the above orbital interactions by the lowering of the orbital energy levels of π*-LUMO of Mn(V)₁=O₍₆₎ and σ*-LUMO of Mn(IV)₄–O₍₅₎, indicating an important role of its Lewis acidity. Present CBS mechanism for the O–O bond formation coupled with one electron reductions of the high-valent Mn ions is different from the conventional radical coupling (RC) and acid-base (AB) mechanisms for water oxidation in artificial and native photosynthesis systems. The proton-coupled electron transfer (PC-OET) mechanism for the O–O bond formation is also touched in relation to the CBS-OET mechanism.     

Luminance-Type Additive Mechanism Produces Shading

It has been reported that the luminance mechanism mediates shadow perception of binary images. We evaluated the luminance additivity law to determine whether shading, which is produced by gradual intensity changes, is mediated by luminance or brightness using pictures with tones: two still lives and a painting. They were depicted by two colors-a reference color and a test color. The reference color was white with a constant luminance profile, and the test color was a mixture of red and green in various proportions. The observer’s task was to adjust the luminance of the test color in order that the impression of depth due to shading just disappeared (shading disappearance setting), where the intensity that produced the shading supposed to be equated between the test and the reference colors. The results show that the luminance additivity law holds for shading disappearance settings. This suggests that shading perception is based on luminance or a luminance-type additive mechanism as well as shadow.     

Self-oscillation of polymer chains with rhythmical soluble-insoluble changes

Self-oscillation of polymer chains in an aqueous solution has been achieved. The ruthenium catalyst for the Belousov-Zhabotinsky reaction was polymerized by using N-isopropylacrylamide and dissolved into the solution containing the BZ substrates. Periodical soluble-insoluble changes of the polymer chain were spontaneously induced by the BZ reaction. The conformational oscillations of the polymer were measured as the optical transmittance changes of the solution. This is the first report that rhythmical and reversible soluble-insoluble changes of polymer chains are realized under constant and homogeneous conditions. The transducing system from chemical energy of the BZ reaction to optical information has been constructed.