Cauchy-Born Rule and the Stability of Crystalline Solids： Dynamic Problems

We study continuum and atomistic models for the elastodynamics of crystalline solids at zerotemperature.We establish sharp criterion for the regime of validity of the nonlinear elastic wave equationsderived from the well-known Cauchy-Born rule.     

Trace element concentrations from São Francisco River - PR analyzed with PIXE technique

Summary Kulcsszavak (angolul, ha nem azonos az elozovel)     

A new approach towards peptidosulfonamides: synthesis of potential inhibitors of bacterial peptidoglycan biosynthesis enzymes MurD and MurE

Peptidosulfonamides are an emerging group of peptidomimetics with a variety of applications in medicinal chemistry. We present a novel approach to the synthesis of peptidosulfonamides, and apply it to a series of new potential inhibitors of the bacterial peptidoglycan biosynthesis enzymes MurD and MurE. The synthesis was conducted via N-phthalimido β-aminoethanesulfonyl chlorides, which are new building blocks for the synthesis of peptidosulfonamides. In the most crucial step, sulfonic acids or their sodium salts were converted into the corresponding sulfonyl chlorides using an excess of either SOCl₂ or SOCl₂/DMF, and then coupled to the C-protected amino acid. None of the compounds significantly inhibited MurD, however, some inhibited MurE; one had an IC₅₀ below 200 μM, which constitutes a promising starting point for further development. Molecular modelling simulations were performed on two analogues to investigate the absence of inhibitory activity of the sulfonamide compounds on MurD.     

Regioselectivity in the ene-reaction of singlet oxygen with cyclic alkenes: photooxygenation of methyl-substituted 1,4-cyclohexadiene derivatives

The photooxygenation of the 1-methyl-, 2,3-dimethyl-, and 1,4-dimethylcyclohexa-1,4-dienes, which are readily available through Birch reduction, yielded the corresponding ene-products. The formed endocyclic dienes were trapped by the addition of singlet oxygen to give the corresponding bicyclic endoperoxy hydroperoxides. In the case of 1-methylcyclohexa-1,4-diene and 1,4-dimethylcyclohexa-1,4,-diene, the cis-effect determined the product distribution. Photooxygenation of 2,3-dimethylcyclohexa-1,4-dienes gave mainly exocyclic olefin, which was attributed to the lowered rotational barrier of the methyl group and increased reactivity of the methyl groups.     

Structural studies of Cr-doped mullite derived from single-phase precursors

Cr-doped mullites were prepared from single-phase precursors containing up to 9.60 wt% Cr₂O₃ using a sol-gel technique followed by thermal treatment. Particle induced X-ray emission spectroscopy and X-ray powder diffraction were used to characterize the samples. Mullites were orthorhombic, space group Pbam. Cr doping caused the increase of unit-cell parameters. Strongest expansion was noticed along c-axis followed by a and b (Δc/c=0.089, Δa/a=0.061, Δb/b=0.045% per mole Cr₂O₃). A second phase, namely θ-(Al,Cr)₂O₃, was revealed by XRD in the sample containing 9.60 wt% Cr₂O₃. The structure of mullites was refined by the Rietveld method, location of Cr³⁺ was performed by the EPR spectroscopy. At low chromium doping level (Cr₂O₃ content less than ∼5 wt%) Cr³⁺ ions were substituted for Al³⁺ in the AlO₆ octahedra of the mullite structure (M1 site). For higher doping level, Cr³⁺ ions were additionally substituted for Al³⁺ in the AlO₆ octahedra of the second phase [θ-(Al,Cr)₂O₃ at 1400 °C, or α-(Al,Cr)₂O₃ at 1600 °C] which segregated in the system. Substitution of Cr³⁺ for Al³⁺ on M1 site in the mullite structure resulted in increase of average distances in (M1)O₆ octahedron and decrease of average distances in T*O₄ tetrahedron, while average distances in TO₄ tetrahedron stayed almost constant.     

Extension of a combined analytical/numerical initial value problem solver for unsteady periodic flow

Here we describe analytical and numerical modifications that extend the Differential Reduced Ejector/ mixer Analysis (DREA), a combined analytical/numerical, multiple species ejector/mixing code developed for preliminary design applications, to apply to periodic unsteady flow. An unsteady periodic flow modelling capability opens a range of pertinent simulation problems including pulse detonation engines (PDE), internal combustion engine ICE applications, mixing enhancement and more fundamental fluid dynamic unsteadiness, e.g. fan instability/vortex shedding problems. Although mapping between steady and periodic forms for a scalar equation is a classical problem in applied mathematics, we will show that extension to systems of equations and, moreover, problems with complex initial conditions are more challenging. Additionally, the inherent large gradient initial condition singularities that are characteristic of mixing flows and that have greatly influenced the DREA code formulation, place considerable limitations on the use of numerical solution methods. Fortunately, using the combined analytical–numerical form of the DREA formulation, a successful formulation is developed and described. Comparison of this method with experimental measurements for jet flows with excitation shows reasonable agreement with the simulation. Other flow fields are presented to demonstrate the capabilities of the model. As such, we demonstrate that unsteady periodic effects can be included within the simple, efficient, coarse grid DREA implementation that has been the original intent of the DREA development effort, namely, to provide a viable tool where more complex and expensive models are inappropriate. Copyright © 2002 John Wiley & Sons, Ltd.