A weight-function approach for determining watershed initial conditions for combustion waves

In many generic combustion models, one finds that a combustionwave will develop with a specific wave speed. However, thereare possible initial temperature profiles which do not evolveinto such waves, but rather die out to the ambient temperature.There can exist, in some models, a clear distinction betweenthose initial conditions that do evolve into combustion wavesand those that do not; this is sometimes referred to as thewatershed initial condition. When fuel consumption is consideredto be negligible, analytical methods can be used to obtain theexact watershed. In this paper, we consider the problem of determiningpseudo-watersheds and ascertaining the relationship betweenthese pseudo-watersheds and the exact watersheds. In the processa novel weight-function approach for infinite spatial domainsis developed.     

Chlorination-methylation of the hydrogen-terminated silicon(111) surface can induce a stacking fault in the presence of etch pits

Recently, we reported STM images of the methylated Si(111) surface [prepared through chlorination-alkylation of the Si(111)-H surface] taken at 4.7 K, indicating that the torsion angle of the methyl group with respect to the subsurface silicon layer is phi = 23 +/- 3 degrees . Repulsions between H atoms in adjacent methyl groups are minimized at 30 degrees , while repulsions between H atoms and second layer Si atoms are minimized at 60 degrees . The experimental result of 23 degrees is surprising because it suggests a tendency of the methyl group toward the eclipsed configuration (0 degrees ) rather than staggered (60 degrees ). In contrast, extensive fully periodic quantum mechanical Density Functional Theory studies of this surface give an equilibrium torsion angle of 37.5 degrees , indicating a tendency toward the staggered configuration. This discrepancy can be resolved by showing that the CH3 on the step edges and etch pits interacts repulsively with the CH3 on the surface terraces unless a stacking fault is introduced between the first and second silicon layers of the Si(111)-CH3 surface terraces. We propose that this could occur during the chlorination-alkylation of the Si(111)-H surface. This stacking fault model predicted phi = 22.5 degrees measured with respect to the bulk (corresponding to phi = 37.5 degrees with respect to the second layer Si atoms). This model can be tested by measuring the orientation of the CH3 within the etch pits, which should have phi = 37.5 degrees , or by making a surface without etch pits, which should have phi = 37.5 degrees .     

Theoretical investigation of the structure and coverage of the Si(111)-OCH3 surface

The surface structure, strain energy, and charge profile of the methoxylated Si(111) surface, Si(111)-OCH3, has been studied using quantum mechanics, and the results are compared to those obtained previously for Si(111)-CH3 and Si(111)-C2H5. The calculations indicate that 100% coverage is feasible for Si(111)-OCH3 (similar to the methylated surface), as compared to only approximately 80% coverage for the ethylated surface. These differences can be understood in terms of nearest-neighbor steric and electrostatic interactions. Enthalpy and free energy calculations indicate that the formation of the Si(111)-OCH3 surface from Si(111)-H and methanol is favorable at 300 K. The calculations have also indicated the conditions under which stacking faults can emerge on Si(111)-OCH3, and such conditions are contrasted with the behavior of Si(111)-CH3 and Si(111)-CH2CH3 surfaces, for which stacking faults are calculated to be energetically feasible when etch pits with sufficiently long edges are present on the surface.     

Scanning tunneling microscopy of ethylated Si(111) surfaces prepared by a chlorination/alkylation process

Scanning tunneling microscopy (STM) and computational modeling have been used to study the structure of ethyl-terminated Si(111) surfaces. The ethyl-terminated surface was prepared by treating the H-terminated Si(111) surface with PCl5 to form a Cl-terminated Si(111) surface with subsequent exposure to C(2)H(5)MgCl in tetrahydrofuran to produce an alkylated Si(111) surface. The STM data at 77 K revealed local, close-packed, and relatively ordered regions with a nearest-neighbor spacing of 0.38 nm as well as disordered regions. The average spot density corresponded to approximately 85% of the density of Si atop sites on an unreconstructed Si(111) surface. Molecular dynamics simulations of a Si(111) surface randomly populated with ethyl groups to a total coverage of approximately 80% confirmed that the ethyl-terminated Si(111) surface, in theory, can assume reasonable packing arrangements to accommodate such a high surface coverage, which could be produced by an exoergic surface functionalization route such as the two-step chlorination/alkylation process. Hence, it is possible to consistently interpret the STM data within a model suggested by recent X-ray photoelectron spectroscopic data and infrared absorption data, which indicate that the two-step halogenation/alkylation method can provide a relatively high coverage of ethyl groups on Si(111) surfaces.     

Quantum mechanics calculations of the thermodynamically controlled coverage and structure of alkyl monolayers on Si(111) surfaces

The heat of formation, Delta E, for silicon (111) surfaces terminated with increasing densities of the alkyl groups CH3- (methyl), C2H5- (ethyl), (CH3)2CH- (isopropyl), (CH3)3C- (tert-butyl), CH3(CH2)5- (hexyl), CH3(CH2)7- (octyl), and C6H5- (phenyl) was calculated using quantum mechanics (QM) methods, with unalkylated sites being H-terminated. The free energy, Delta G, for the formation of both Si-C and Si-H bonds from Si-Cl model compounds was also calculated using QM, with four separate Si-H formation mechanisms proposed, to give overall Delta G(S) values for the formation of alkylated Si(111) surfaces through a two step chlorination/alkylation method. The data are in good agreement with measurements of the packing densities for alkylated surfaces formed through this technique, for Si-H free energies of formation, Delta G(H), corresponding to a reaction mechanism including the elimination of two H atoms and the formation of a C=C double bond in either unreacted alkyl Grignard groups or tetrahydrofuran solvent.     

Biocatalytic preparation of enantioenriched 3,4-dihydroxypiperidines and theoretical study of Candida antarctica lipase B enantioselectivity

Enzymatic acetylations of N-substituted cis- and trans-3,4-dihydroxypiperidine and hydrolysis of their diacetylated derivatives have been studied. High enantioselectivities are obtained with Pseudomonas cepacia lipase and Candida antarctica lipase B for the hydrolysis of the trans-derivative, while the cis-derivatives are not adequate substrates in the same biocatalytic conditions. The enantiopreference of these processes can be rationalized by means of a molecular modelling study.     

Density functional theory study of the geometry, energetics, and reconstruction process of Si111 surfaces

We report the structures and energies from first principles density functional calculations of 12 different reconstructed (111) surfaces of silicon, including the 3x3 to 9x9 dimer-adatom-stacking fault (DAS) structures. These calculations used the Perdew-Burke-Ernzerhof generalized gradient approximation of density functional theory and Gaussian basis functions. We considered fully periodic slabs of various thicknesses. We find that the most stable surface is the DAS 7x7 structure, with a surface energy of 1.044 eV/1x1 cell (1310 dyn/cm). To analyze the origins of the stability of these systems and to predict energetics for more complex, less-ordered systems, we develop a model in which the surface energy is partitioned into contributions from seven different types of atom environments. This analysis is used to predict the surface energy of larger DAS structures (including their asymptotic behavior for very large unit cells) and to study the energetics of the sequential size change (SSC) model proposed by Shimada and Tochihara for the observed dynamical reconstruction of the Si(111) 1x1 structure. We obtain an energy barrier at the 2x2 cell size and confirm that the 7x7 regular stage of the SSC model (corresponding to the DAS 7x7 reconstruction) provides the highest energy reduction per unit cell with respect to the unreconstructed Si111 1x1 surface.     

Synthesis of cytotoxic cyanobactin,Wewakazole B

We report herein the synthesis of cytotoxic cyanobactin, Wewakazole B through an efficient solution-phase approach. The key steps of the synthesis are the macrocyclic lactamization of linear dodecapeptide and construction of two hexapeptides with three different substituted oxazole rings.     

Interpreting linear systems of equalities and inequalities. Application to the water supply problem

This paper shows how the mathematical and the engineering points of view are complementary and help to model real problems that can be stated as systems of linear equations and inequalities. The paper is devoted to point out these relations and making them explicit for the readers to realize about the new possibilities that arise when contemplating the compatibility conditions or the set of general solutions from the dual perspective. After reviewing an orthogonally based powerful algorithm to analyse the compatibility of linear systems of equations and solving them, a water supply problem is used to illustrate its mathematical and engineering multiple aspects, including the optimal statement of the problem in terms of an adequate selection and numbering of equations and unknowns, an analysis of the compatibility conditions and a physical interpretation of the general solution, together with that of each individual generators of the affine space. The possibilities of removing unknowns without altering the compatibility of the problem is also analysed. Next, the Γ‐algorithm to analyse the compatibility of linear systems of inequalities and solving them is described and then, the water supply problem is revisited adding some constraints, such as capacity limits for the pipes and retention valves, and discussed as to how they affect the resulting general solution and other aspects. Finally, some conclusions are derived. Copyright © 2005 John Wiley & Sons, Ltd.