Asymptotic analysis of a second-order singular perturbation model for phase transitions

We study the asymptotic behavior, as ${\varepsilon}$ tends to zero, of the functionals ${F^k_\varepsilon}$ introduced by Coleman and Mizel in the theory of nonlinear second-order materials; i.e., $$F^k_\varepsilon(u):=\int\limits_{I} \left(\frac{W(u)}{\varepsilon}-k\,\varepsilon\,(u')^2+\varepsilon^3(u'')^2\right)\,dx,\quad u\in W^{2,2}(I),$$ where k?>?0 and ${W:\mathbb{R}\to[0,+\infty)}$ is a double-well potential with two potential wells of level zero at ${a,b\in\mathbb{R}}$ . By proving a new nonlinear interpolation inequality, we show that there exists a positive constant k ₀ such that, for k?<?k ₀, and for a class of potentials W, ${(F^k_\varepsilon)}$ ??(L ¹)-converges to $$F^k(u):={\bf m}_k \, \#(S(u)),\quad u\in BV(I;\{a,b\}),$$ where m _k is a constant depending on W and k. Moreover, in the special case of the classical potential ${W(s)=\frac{(s^2-1)^2}{2}}$ , we provide an upper bound on the values of k such that the minimizers of ${F_\varepsilon^k}$ cannot develop oscillations on some fine scale and a lower bound on the values for which oscillations occur, the latter improving a previous estimate by Mizel, Peletier and Troy.     

Doped CeO2-LaFeO3 composite oxide as an active anode for direct hydrocarbon-type solid oxide fuel cells

Direct utilization of hydrocarbon and other renewable fuels is one of the most important issues concerning solid oxide fuel cells (SOFCs). Mixed ionic and electronic conductors (MIECs) have been explored as anode materials for direct hydrocarbon-type SOFCs. However, electrical conductivity of the most often reported MIEC oxide electrodes is still not satisfactory. As a result, mixed-conducting oxides with high electrical conductivity and catalytic activity are attracting considerable interest as an alternative anode material for noncoke depositing anodes. In this study, we examine the oxide composite Ce(Mn,Fe)O(2)-La(Sr)Fe(Mn)O(3) for use as an oxide anode in direct hydrocarbon-type SOFCs. High performance was demonstrated for this composite oxide anode in direct hydrocarbon-type SOFCs, showing high maximum power density of approximately 1 W cm(-2) at 1073 K when propane and butane were used as fuel. The high power density of the cell results from the high electrical conductivity of the composite oxide in hydrocarbon and the high surface activity in relation to direct hydrocarbon oxidation.     

Characterization of Supramolecular Hidden Chirality of Hydrogen‐Bonded Networks by Advanced Graph Set Analysis

Supramolecular hidden chirality of hydrogen‐bonded (HB) networks of primary ammonium carboxylates was exposed by advanced graph set analysis from a symmetric viewpoint in topology. The ring‐type HB (R‐HB) networks are topologically regarded as faces, and therefore exhibit prochirality and positional isomerism due to substituents attached on the faces. To describe the symmetric properties of the faces, additional symbols, Re (right‐handed or clockwise), Si (left‐handed or anticlockwise), and m (mirror), were proposed. According to the symbols, various kinds of faces were classified based on the symmetry. This symmetry consideration of the faces enables us to precisely evaluate supramolecular chirality, especially its handedness, of 0D‐cubic, 1D‐ladder and 2D‐sheet HB networks that are composed of the faces. The 1D‐ladder and 2D‐sheet HB networks generate chirality by accumulating the chiral faces in 1D and 2D manners, respectively, whereas 0D‐cubic HB networks generate chirality based on combinations of eight kinds of faces, similar to the chirality of dice.     

Synchronization and functional central limit theorems for interacting reinforced random walks

We obtain Central Limit Theorems in Functional form for a class of time-inhomogeneous interacting random walks. Due to a reinforcement mechanism and interaction, the walks are strongly correlated and converge almost surely to the same, possibly random, limit. We study random walks interacting through a mean-field rule and compare the rate they converge to their limit with the rate of synchronization, i.e. the rate at which their mutual distances converge to zero. We show that, under certain conditions, synchronization is faster than convergence. Even if our focus is on theoretical results, we propose as main motivations two contexts in which such results could directly apply: urn models and opinion dynamics in a random network evolving via preferential attachment.     

Phytochemical Analysis and Molecular Identification of Green Macroalgae Caulerpa spp. from Bali,Indonesia

The studies of the Bulung Boni and Bulung Anggur (Caulerpa spp.) species and secondary metabolites are still very limited. Proper identification will support various aspects, such as cultivation, utilization, and economic interests. Moreover, understanding the secondary metabolites will assist in developing algae-based products. This study aimed to identify these indigenous Caulerpa algae and analyze their bioactive components. The tufA sequence was employed as a molecular marker in DNA barcoding, and its bioactive components were identified using the GC-MS method. The phylogenetic tree was generated in MEGA 11 using the maximum likelihood method, and the robustness of the tree was evaluated using bootstrapping with 1000 replicates. This study revealed that Bulung Boni is strongly connected to Caulerpa cylindracea. However, Bulung Anggur shows no close relationship to other Caulerpa species. GC-MS analysis of ethanolic extracts of Bulung Boni and Bulung Anggur showed the presence of 11 and 13 compounds, respectively. The majority of the compounds found in these algae have been shown to possess biological properties, such as antioxidant, antibacterial, anticancer, anti-inflammation, and antidiabetic. Further study is necessary to compare the data obtained using different molecular markers in DNA barcoding, and to elucidate other undisclosed compounds in these Caulerpa algae.     

Pair distribution function and 71Ga NMR study of aqueous Ga3+ complexes

The atomic structures, and thereby the coordination chemistry, of metal ions in aqueous solution represent a cornerstone of chemistry, since they provide first steps in rationalizing generally observed chemical information. However, accurate structural information about metal ion solution species is often surprisingly scarce. Here, the atomic structures of Ga³⁺ ion complexes were determined directly in aqueous solutions across a wide range of pH, counter anions and concentrations by X-ray pair distribution function analysis and ⁷¹Ga NMR. At low pH (<2) octahedrally coordinated gallium dominates as either monomers with a high degree of solvent ordering or as Ga-dimers. At slightly higher pH (pH ≈ 2–3) a polyoxogallate structure is identified as either Ga₃₀ or Ga₃₂ in contradiction with the previously proposed Ga₁₃ Keggin structures. At neutral and slightly higher pH nanosized GaOOH particles form, whereas for pH > 12 tetrahedrally coordinated gallium ions surrounded by ordered solvent are observed. The effects of varying either the concentration or counter anion were minimal. The present study provides the first comprehensive structural exploration of the aqueous chemistry of Ga³⁺ ions with atomic resolution, which is relevant for both semiconductor fabrication and medical applications.

With changing pH four different structural regions in Ga³⁺ aqueous solutions are observed. In contrast the effects of different anions and concentrations are minimal.     

Halogenzahlen der Fette

Ohne Zusammenfassung     

Dynamical structure of α-Ag0.99Cu0.01I crystal by Cu NMR chemical shift, spin-lattice relaxation time and molecular dynamics simulation

Solid ⁶³Cu NMR and Molecular Dynamics (MD) methods have been used to investigate the dynamical structure of Ag_0.99Cu_0.01I crystal, through the viewpoint of the chemical shift and the spin-lattice relaxation. In the superionic phase (α-phase), we obtained the temperature variation of the chemical shift as −0.2 ppm/K, and the activation energy of the Cu⁺ ion diffusion as 11 kJ/mol. The temperature dependence of the chemical shift was explained by the calculated chemical shielding surface based on ab initio MO calculation, and by the probability density of Cu⁺ ion estimated by MD simulation. The spin-lattice relaxation was also analyzed by using the MD method in which we assumed two jumping models as the diffusion process of the mobile cations. It is concluded that the temperature dependence of the chemical shift is dominated by the shielding in the vicinity of the 24(h) site, and the observed activation energy is due to the diffusion process of the mobile cations jumping from the 6(b) intrasub-lattice to the nearest-neighbor 6(b) sub-lattice.