A domain decomposition discretization of parabolic problems

In recent years, domain decomposition methods have attracted much attention due to their successful application to many elliptic and parabolic problems. Domain decomposition methods treat problems based on a domain substructuring, which is attractive for parallel computation, due to the independence among the subdomains. In principle, domain decomposition methods may be applied to the system resulting from a standard discretization of the parabolic problems or, directly, be carried out through a discretization of parabolic problems. In this paper, a direct domain decomposition method is introduced to discretize the parabolic problems. The stability and convergence of this algorithm are analyzed. This work was supported in part by Polish Sciences Foundation under grant 2P03A00524. This work was supported in part by the US Department of Energy under Contracts DE-FG02-92ER25127 and by the Director, Office of Science, Advanced Scientific Computing Research, U.S. Department of Energy under contract DE-AC02-05CH11231.     

Multilevel additive and multiplicative methods for orthogonal spline collocation problems

Summary. Multilevel preconditioners are proposed for the iterative solution of the discrete problems which arise when orthogonal spline collocation with piecewise Hermite bicubics is applied to the Dirichlet boundary value problem for a self-adjoint elliptic partial differential equation on a rectangle. Additive and multiplicative preconditioners are defined respectively as sums and products of independent operators on a sequence of nested subspaces of the fine partition approximation space. A general theory of additive and multiplicative Schwarz methods is used to prove that the preconditioners are spectrally equivalent to the collocation discretization of the Laplacian with the spectral constants independent of the fine partition stepsize and the number of levels. The preconditioned conjugate gradient and preconditioned Orthomin methods are considered for the solution of collocation problems. An implementation of the methods is discussed and the results of numerical experiments are presented. Received March 1, 1994 / Revised version received January 23, 1996     

Continua of interactions between pairs of atoms in molecular crystals

The electron density distributions in crystals of five previously studied DMAN complexes and five Schiff bases (two new ones) have been analysed in terms of various properties of bond critical points (BCPs) found in the pair-wise interactions in their lattices. We analysed the continua of interactions including covalent/ionic bonds as well as hydrogen bonds and all other types of weak interactions for all pairs of interacting atoms. The charge density at BCPs and local kinetic and potential energy densities vary exponentially with internuclear distance (or other measures of separation). The parameters of the dependences appear to be characteristics of particular pairs of atom types. The Laplacian and the total (sum of kinetic and potential) energy density at BCPs show similar behaviour with the dependence being of the Morse type. The components lambda1, lambda2, lambda3 of the Laplacian at BCPs vary systematically with internuclear distance according to the type of atom pair. For lambda1 and lambda2 the distribution is of the exponential type, whereas lambda3 does not seem to follow any simple functional form, consistent with previous theoretical findings. Analytical nonlinear dependences of Laplacian on charge density have been found. They agree reasonably well with those obtained by least square fit of the Laplacian to charge density data. There are four distinct regions of the [symbol: see text]2rho(BCP)/rho(BCP) space, generated by E(BCP) = 0 and G(BCP)/rho(BCP) = 1 conditions. Two regions clearly correspond to the shared-shell and closed-shell interactions and the other two to some intermediate situation.     

Description of band wings and band area measurement

Applicability of the Gaussian and Lorentzian function to spectral bands is analyzed, and some problems of band area determination are discussed.     

3‐(1‐Pyridinio)propane­sulfonate and 3‐(benzyl­dimethyl­ammonio)propane­sulfonate monohydrate

3‐(1‐Pyridinio)propane­sulfonate, C₈H₁₁NO₃S, and 3‐(benzyl­dimethyl­ammonio)propane­sulfonate monohydrate, C₁₂H₁₉NO₃S·H₂O, used as additives during protein refolding and crystallization, both crystallize in the monoclinic system in the P2₁/c space group, with one mol­ecule (or one set of mol­ecules) per asymmetric unit. The solvent water mol­ecule present in the second crystal structure results in the formation of a dimer through hydrogen bonds. The conformation of the propane­sulfonate moiety is similar in both structures.     

l‐Methioninium chloride and l‐seleno­methioninium chloride at 103 K

The crystal structures of the title compounds, (S)‐1‐carboxy‐3‐(methyl­sulfanyl)­propanaminium chloride, C₅H₁₂NO₂S⁺·Cl⁻, and (S)‐1‐carboxy‐3‐(methyl­selanyl)­propanaminium chloride, C₅H₁₂NO₂Se⁺·Cl⁻, are isomorphous. The proton­ated l ‐methionine and l ‐seleno­methionine mol­ecules have almost identical conformations and create very similar contacts with the Cl⁻ anions in the crystal structures of both compounds. The amino acid cations and the Cl⁻ anions are linked viaN—H⋯Cl⁻ and O—H⋯Cl⁻ hydrogen bonds.     

Potentiometric determination of equilibrium constants for Ag(I)-pyridine,Ag(I)-2,2′-bipyridine and Ag(I)-1,10-phenanthroline systems in acetonitrile

The composition and the complex formation constants of Ag(I) with pyridine, 2,2′-bipyridine, and 1,10-phenanthroline were determined by the potentiometric method. The measurement procedure can be reduced to the determination of the EMF of the concentration cell: $$\begin{gathered} Ag|c_1 AgNO_3 (AN) + 0.1 M(C_2 H_5 )_4 NClO_4 (AN)||0.1 M(C_2 H_5 )_4 NClO_4 (AN) || \hfill \\ c_2 AgNO_3 (AN) + x L(AN) + 0.1 M (C_2 H_5 )_4 NClO_4 (AN)|Ag. \hfill \\ \end{gathered}$$ All complexes have coordination number 2. The solubility product for Ag(1,10-phenanthroline)₂NO₃ in acetonitrile was also determined. In all measurements the association of AgNO₃ was considered. Differences in the stability of analogous complexes in water and acetonitrile are discussed.     

A Long Cycle‐Life High‐Voltage Spinel Lithium‐Ion Battery Electrode Achieved by Site‐Selective Doping

Spinel LiNi_0.5Mn_1.5O₄ (LNMO) is a promising cathode candidate for the next‐generation high energy‐density lithium‐ion batteries (LIBs). Unfortunately, the application of LNMO is hindered by its poor cycle stability. Now, site‐selectively doped LNMO electrode is prepared with exceptional durability. In this work, Mg is selectively doped onto both tetrahedral (8a) and octahedral (16c) sites in the Fd m structure. This site‐selective doping not only suppresses unfavorable two‐phase reactions and stabilizes the LNMO structure against structural deformation, but also mitigates the dissolution of Mn during cycling. Mg‐doped LNMOs exhibit extraordinarily stable electrochemical performance in both half‐cells and prototype full‐batteries with novel TiNb₂O₇ counter‐electrodes. This work pioneers an atomic‐doping engineering strategy for electrode materials that could be extended to other energy materials to create high‐performance devices.     

Structural Characterization of Act c 10.0101 and Pun g 1.0101—Allergens from the Non-Specific Lipid Transfer Protein Family

(1) Background: Non-specific lipid transfer proteins (nsLTPs), which belong to the prolamin superfamily, are potent allergens. While the biological role of LTPs is still not well understood, it is known that these proteins bind lipids. Allergen nsLTPs are characterized by significant stability and resistance to digestion. (2) Methods: nsLTPs from gold kiwifruit (Act c 10.0101) and pomegranate (Pun g 1.0101) were isolated from their natural sources and structurally characterized using X-ray crystallography (3) Results: Both proteins crystallized and their crystal structures were determined. The proteins have a very similar overall fold with characteristic compact, mainly α-helical structures. The C-terminal sequence of Act c 10.0101 was updated based on our structural and mass spectrometry analysis. Information on proteins’ sequences and structures was used to estimate the risk of cross-reactive reactions between Act c 10.0101 or Pun g 1.0101 and other allergens from this family of proteins. (4) Conclusions: Structural studies indicate a conformational flexibility of allergens from the nsLTP family and suggest that immunoglobulin E binding to some surface regions of these allergens may depend on ligand binding. Both Act c 10.0101 and Pun g 1.0101 are likely to be involved in cross-reactive reactions involving other proteins from the nsLTP family.