Optimal Control in Heterogeneous Domain Decomposition Methods for Advection-Diffusion Equations

New domain decomposition methods (DDM) based on optimal control approach are introduced for the coupling of first and second order equations on overlapping subdomains. Several cost functionals and control functions are proposed. Uniqueness and existence results are proved for the coupled problem, and the convergence of iterative processes is analyzed. The work was supported by the Russian Foundation for Basic Research (04-01-00615) and it was partly carried out while the first author was visiting the IACS at EPFL.     

Unravelling the effect of the E545K mutation on PI3Kα kinase

PI3Kα controls several cellular processes and its aberrant signalling is implicated in tumorigenesis. One of its hotspot mutations, E545K, increases PI3Kα lipid kinase activity, but its mode of action is only partially understood. Here, we perform biased and unbiased molecular dynamics simulations of PI3Kα and uncover, for the first time, the free energy landscape of the E545K PI3Kα mutant. We reveal the mechanism by which E545K leads to PI3Kα activation in atomic-level detail, which is considerably more complex than previously thought.

The mechanism by which the cancer-causing E545K mutation may lead to PI3Kα activation is described in atomic-level detail.     

Synthesis and structure of a dithioether-substituted butene-2-olide-4-ylidene-4 cobalt carbonyl complex

The complex (1) has been prepared and its structure determined. Complex1 is the first stable thioether derivative of a metal carbonyl containing only cobalt as metal. It crystallizes in the monoclinic P2₁/c space group, witha = 13.975( 4 ),b = 11.363( 3 ),c = 14.686(2)A, = 112.25(2)°,V = 2158.5(7)A³.Z = 4. The solution using direct methods and the anisotropic refinement of all nonhydrogen atoms led toR = 0.039,wR = 0.041 for 3296 reflections with F> 4.0(F) Analogous but less stable complexes are formed with 1,6-diphenyl-2,5-dithiahexane and the crown thioether 1,4,7-trithiacyclonane, the latter functioning either as a bidenlate or a tridentate ligand.     

Synthesis and structure of the cluster ion pair [Ru3(CO)9[mu-P(NPri2)2]3][Ru6(CO)15(mu 6-C)[mu-P(NPri2)2]]. A theoretical overview of M3(mu-PR2)3 frameworks

The compound [Ru3(CO)9[mu-P(NPri2)2]3][Ru6(CO)15(mu 6-C)[mu-P(NPri2)2]] (1), obtained via the addition of PCl(NPri2)2 to K2[Ru4(CO)13], crystallizes in the monoclinic space group P2l/c with a = 15.537(8) A, b = 36.151(16) A, c = 19.407(5) A, beta = 91.14(2) degrees, Z = 4, and R = 0.069 for 8006 observed reflections. The unit cell is unusual in that it contains both a typical octahedral Ru6 cluster anion (1a), featuring an encapsulated carbide, and a symmetrical phosphido bridge, in addition to a 50-electron trinuclear cluster cation [Ru3(CO)9[mu-P(NPri2)2]3]+ (1c). The latter, with approximate D3h symmetry, exhibits long Ru-Ru distances (> or = 3.15 A). Among the family of clusters with M3(mu-PR2)3 cores and different numbers of both electrons (TEC) and terminal ligands (LxLyLz), 1c is unique in that it is a 333 stereotype with 50 valence electrons. MO calculations permit us to predict the existence of redox congeners of 1c clusters and related 48e Re3 clusters. This work also presents a summary of the relationships between the electronic and the geometric structures for all known M3LxLyLz(mu-PR2)3 species. The basic stereochemical features are influenced by the total-electron count and, hence, by the degree of M-M bonding, as well as the remarkable flexibility of the phosphido bridging ligands. The mu-PR2 ligands need not necessarily lie in the M3 plane, and a wide range of M-P-M angles (as small as 72 degrees or as large as 133 degrees) have been observed.     

Reaction of Ru3(CO)12 with but-2-yn-1,4-diol in CH3OH/KOH solution. Crystal structure of (μ-Cl)Ru3(CO)9[μ3-η-H2CCC(H)CH2]

The reaction of Ru₃(CO)₁₂ with but-2-yn-1,4-diol (HOCH₂CCCH₂OH, BUD) in CH₃OH/KOH followed by acidification with HCl leads to four products, one of which has been identified as the title complex (μ-Cl)Ru₃(CO)₉[μ₃-η⁴-H₂CCC(H)CH₂]. This is an open cluster containing a bridging Cl atom on the open side and a C₄H₅ moiety bound to all the metals. The structure of the complex has been determined by X-ray analysis.The thermal reaction of Ru₃(CO)₁₂ with BUD has been revisited for a comparison with the results in alkaline solution. The main product is the allylic derivative HRu₃(CO)₉[HCCHCCHO].     

Solvent effects on charge spatial extent in DNA and implications for transfer

To clarify the role played by water in facilitating long-range DNA charge transport, carefully designed, state-of-the-art, self-interaction corrected density-functional quantum mechanical and molecular mechanical (SIC-QM/MM) simulations are performed for the first time on two ionized adenine:thymine bridge models in explicit water solvent at finite temperature. For random solvent configurations, the charge is partially delocalized. However, a charge localization on different, well-separated adenines can be induced and is correlated with a restructuring of their first solvation shells. Thus, the importance of water in the mechanism of long-range charge transport is explicitly demonstrated, and the microscopic conditions for a charge localization are revealed.     

Binary inorganic salt mixtures as high conductivity liquid electrolytes for >100 degrees C fuel cells

We report the successful application of low-melting inorganic salts with protonated cations (e.g. ammonium) as electrolytes in fuel cells operating in the temperature range 100-200 degrees C, where even with unoptimized electrodes, cell performance is comparable to that of the phosphoric acid fuel cell operating with optimized electrodes in the same temperature range, while open circuit voltages, and efficiencies at low current densities, can be much better--and there is no need for humidification or pressure to sustain performance.     

Complete hypersurfaces with constant scalar curvature in spheres

To a given immersion ${i:M^n\to \mathbb S^{n+1}}$ with constant scalar curvature R, we associate the supremum of the squared norm of the second fundamental form sup |A|². We prove the existence of a constant C _n (R) depending on R and n so that R ≥ 1 and sup |A|² = C _n (R) imply that the hypersurface is a H(r)-torus ${\mathbb S^1(\sqrt{1-r^2})\times\mathbb S^{n-1} (r)}$ . For R > (n ? 2)/n we use rotation hypersurfaces to show that for each value C > C _n (R) there is a complete hypersurface in ${\mathbb S^{n+1}}$ with constant scalar curvature R and sup |A|² = C, answering questions raised by Q. M. Cheng.     

Crystal structure of Co4(CO)10S2 and Co4(CO)10Se2; v(CO) vibrations of a model cluster molecule: Co4(CO)10S2

The crystal structure of Co₄(CO)₁₀S₂ has been redetermined and that of Co₄(CO)₁₀Se₂ obtained by X-ray analysis. The compounds are monoclinic and isomorphous, space groupP2₁/n,Z=2, with (S compound)a=10.42(2)Å,b=6.794(1)Å,c=12.421(2)Å,=97.27(1) and (Se compound)a=10.110(2)Å,b=6.747(2)Å,c=12.592(4)Å,=96.37(2); finalR(S)=0.029,R _w =0.032 for 1414 reflections and finalR (Se)=0.052,R _w =0.054 for 1264 reflections. The molecules, which lie on a crystallographic center of symmetry, consist of a rectangle with Co atoms at the corners, each face of the rectangle being capped by a chalcogen atom. Each Co atom is bonded to two terminal CO groups; there are two bridging CO groups, one on each member of a pair of opposite sides of the rectangle. The vibrational spectra of the sulfur compound are considered in detail. A study of the crystal structure, and recognition of an approximate spectroscopic space group, are shown to be essential for an understanding of thev(CO) infrared spectrum of polycrystalline Co₄(CO)₁₀S₂. In this molecule, intramolecular vibrational coupling in the crystal leads to extensive modifications of the infrared-activev(CO) molecular coordinates.