C1natural neighbor interpolant for partial differential equations

Natural neighbor coordinates [20] are optimum weighted‐average measures for an irregular arrangement of nodes in ℝⁿ. [26] used the notion of Bézier simplices in natural neighbor coordinates Φ to propose a C¹ interpolant. The C¹ interpolant has quadratic precision in Ω ⊂ ℝ², and reduces to a cubic polynomial between adjacent nodes on the boundary ∂Ω. We present the C¹ formulation and propose a computational methodology for its numerical implementation (Natural Element Method) for the solution of partial differential equations (PDEs). The approach involves the transformation of the original Bernstein basis functions B(Φ) to new shape functions Ψ (Φ), such that the shape functions ψ_3I−2(Φ), ψ_3I−1(Φ), and ψ_3I(Φ) for node I are directly associated with the three nodal degrees of freedom w_I, , respectively. The C¹ shape functions interpolate to nodal function and nodal gradient values, which renders the interpolant amenable to application in a Galerkin scheme for the solution of fourth‐order elliptic PDEs. Results for the biharmonic equation with Dirichlet boundary conditions are presented. The generalized eigenproblem is studied to establish the ellipticity of the discrete biharmonic operator, and consequently the stability of the numerical method. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 417–447, 1999     

Presence of pseudo‐peptide bond in the crystal structure of n‐(t‐butoxycarbonyl)‐ε‐n′‐benzyloxycarbony‐l‐lysyl‐l‐isoleucine (boc‐lys(obzl)‐ile)

The dipeptide Boc‐Lys(OBzl)‐Ile crystallizes in monoclinic space group P2₁ with cell parameters a = 5.003(1), b = 19.199(3), c = 15.270(2)Å, β =93.42(1)°, V = 1464.1(3)ų, Z = 2, D_cal = 1.117 Mg/m³ at T = 293 K. The structure was solved by direct methods and refined by full‐matrix least‐squares procedure to a final R = 0.096 and wR = 0.101 using 1379 reflections. The peptide unit is in trans conformation and the molecule takes up an extended conformation. In the lysine side chain, delocalization of electrons and pseudo peptide bond formation is observed at the interaction site of benzyloxycarbonyl group. Both N‐H…O and main chain C‐H…O hydrogen bonds stabilize the molecules in the unit cell in a parallel β‐sheet fashion. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Donor electron in a quantum well under the influence of an electric field

The ionization energies and the polarizabilities of a donor in an isolated well of a quasi two dimensional (Q2D) GaAs/Ga_1−x Al _x As heterostructure have been obtained for different well widths including electron-lattice coupling. A wave function that properly reduces to the hydrogenic function in the limiting case has been used. For fields of the order of 10⁵ V/m, the ionization energies decrease slightly with electric fields for all well widths (10 nm to 50 nm) studied. Also for a given electric field, as the well width increases, the ionization energy decreases. For fields of the order of 10⁷ V/m and for smaller well widths (<10 nm), the ionization energy generally increases with electric field. The results also show that for electric fields of this order, no donor bound state associated with the lowest subband is possible for well widths greater than 20 nm. The polarizabilities estimated using the expression for the dipole operator show that as the well width increases, the polarizability values also increase and do not show any abnormal behaviour.     

Analysis of thermo-hydraulic performance and entropy generation characteristics for laminar flow through triangular corrugated channel

Journal of Thermal Analysis and Calorimetry - We analyse the thermo-hydraulic performance and entropy-generation characteristics for laminar flow through triangular corrugated channel. Results are...     

Numerical study of thermo-hydraulic characteristics for forced convective flow through wavy channel at different Prandtl numbers

Journal of Thermal Analysis and Calorimetry - The present work numerically investigates the thermo-fluidic and entropy generation characteristics for laminar forced convective flow through wavy...     

α-Oxoketene dithioacetal mediated aromatic annulation: highly efficient and concise synthetic routes to potentially carcinogenic polycyclic aromatic hydrocarbons

Highly efficient regiospecific routes to potentially carcinogenic polycyclic aromatic hydrocarbons such as substituted benzo[c]phenanthrenes, benzo[c]fluorenes, 16,17-dihydro-11-methyl-15[H]cyclopenta[a]phenanthrene, 5-methyl-7,8,9,10-tetrahydrochrysene and 1,4-dimethylphenanthrene have been developed. The overall strategy involves our aromatic annulation protocol through base induced conjugate addition-elimination on the cyclic and acyclic α-oxoketene dithioacetals with the appropriate arylacetonitriles followed by acid induced cyclodehydration of the resulting conjugate adducts. Subsequent reductive dethiomethylation (Raney Ni) and dehydrogenation (DDQ) of the cyclized products affords the methyl substituted PAHs in high yields.     

Layer-by-layer electrostatic assembly with a control over orientation of molecules: anisotropy of electrical conductivity and dielectric properties

While forming layer-by-layer (LbL) electrostatic assembly of a magnetic organic molecule, namely, nickel phthalocyanine (NiPc), we apply a magnetic field. The field orients the magnetic moment of the molecules on a monolayer along the direction of magnetic field. Such an orientation of the molecules is then electrostatically immobilized with a monolayer of a polycation. By repeating the dipping cycle, we form LbL films with planar NiPc molecules facing a particular direction. With NiPc's moment perpendicular to the molecular plane, two types of LbL films were formed: (a) NiPc's molecular plane parallel to the substrate (moment is perpendicular) and (b) molecules perpendicular to the substrate and facing one particular direction, the direction of magnetic field. Such films, with the molecules lying either (a) parallel or (b) perpendicular to the substrate, provide unique systems to study anisotropy of optical, dielectric, and electrical characteristics in these planar organic molecules. The latter film responds to the polarization of incident beam in electronic absorption spectroscopy. Here we show methods to obtain an orientation of molecules in LbL films and study anisotropy of dielectric constant and conductivity of the molecules in ultrathin films.