k‐Version of finite element method in 2‐D polymer flows: Oldroyd‐B constitutive model

In this paper, a new mathematical framework based on h, p, k and variational consistency (VC) of the integral forms is utilized to develop a finite element computational process of two‐dimensional polymer flows utilizing Oldroyd‐B constitutive model. Alternate forms of the choices of dependent variables in the governing differential equations (GDEs) are considered and is concluded that u, v, p, τ choice yielding strong form of the GDEs is meritorious over others. It is shown that: (a) since, the differential operator in the GDEs is non‐linear, Galerkin method and Galerkin method with weak form are variationally inconsistent (VIC). The coefficient matrices in these processes are non‐symmetric and hence may have partial or completely complex basis and thus the resulting computational processes may be spurious. (b) Since the VC of the VIC integral forms cannot be restored through any mathematically justifiable means, the computational processes in these approaches always have possibility of spurious solutions. (c) Least squares process utilizing GDEs in u, v, p, τ (strong form of the GDEs) variables (as well as others) is variationally consistent. The coefficient matrices are always symmetric and positive definite and hence always have a real basis and thus naturally yield computational processes that are free of spurious solutions. (d) The theoretical solution of the GDEs are generally of higher order global differentiability. Numerical simulations of such solutions in which higher order global differentiability characteristics of the theoretical solution are preserved, undoubtedly requires local approximations in higher order scalar product spaces . (e) LSP with local approximations in spaces provide an incomparable mathematical and computational framework in which it is possible to preserve desired characteristics of the theoretical solution in the computational process. Numerical studies are presented for fully developed flow between parallel plates and a lid driven square cavity. M1 fluid is used in all numerical studies. The range of applicability of the Oldroyd‐B model or lack of it is examined for both model problems for increasing De. A mathematical idealization of the corners where stationary wall meets the lid is presented and is shown to simulate the real physics when the local approximations are in higher order spaces and when h_d→0. For both model problems shear rate is examined in the flow domain to establish validity of the Oldroyd‐B constitutive model. Copyright © 2006 John Wiley & Sons, Ltd.     

Strange star surface: a crust with nuggets

We reexamine the surface composition of strange stars. Strange quark stars are hypothetical compact stars which could exist if strange quark matter was absolutely stable. It is widely accepted that they are characterized by an enormous density gradient (10(26) g/cm4) and large electric fields at the surface. By investigating the possibility of realizing a heterogeneous crust, comprised of nuggets of strange quark matter embedded in an uniform electron background, we find that the strange star surface has a much reduced density gradient and negligible electric field. We comment on how our findings will impact various proposed observable signatures for strange stars.     

P[N(i-Bu)CH(2)CH(2)](3)N: nonionic Lewis base for promoting the room-temperature synthesis of α,β-unsaturated esters, fluorides, ketones, and nitriles using Wadsworth-Emmons phosphonates

The bicyclic triaminophosphine P(RNCH(2)CH(2))(3)N (R = i-Bu, 1c) serves as an effective promoter for the room-temperature stereoselective synthesis of α,β-unsaturated esters, fluorides, and nitriles from a wide array of aromatic, aliphatic, heterocyclic, and cyclic aldehydes and ketones, using a range of Wadsworth-Emmons (WE) phosphonates. Among the analogues of 1c [R = Me (1a), i-Pr (1b), Bn (1d)], 1a and 1b performed well, although longer reaction times were involved, and 1d led to poorer yields than 1c. Functionalities such as cyano, chloro, bromo, methoxy, amino, ester, and nitro were well tolerated. We were able to isolate and characterize (by X-ray means; see above) the reactive WE intermediate species formed from 2b and 1c.     

Sc(OTf)3-catalyzed one-pot ene-Prins cyclization: a novel synthesis of octahydro-2H-chromen-4-ols

(R)-Citronellal undergoes initial ene reaction followed by Prins cyclization with aldehydes in the presence of 5 mol % of scandium triflate at ambient temperature to furnish octahydro-2H-chromen-4-ols in good yields and with high cis-selectivity. The use of scandium triflate makes this procedure simple, more convenient, and practical.     

Synthesis and antimicrobial study of linked heterocyclics containing Pyrazole-pyrimidine-thiazolidin-4-one

A new series of linked heterocyclics, 3-[4-(4-chlorophenyl)-6-(3,5-dimethyl-1-phenyl-1H-4-pyrazolyl)-2-pyrimidinyl]-2-(aryl/heteryl)-1,3-thiazolan-4-ones (6a-j), has been synthesized by the one-pot cyclo-condensation of 4-(4-chlorophenyl)-6-(3,5-dimethyl-1-phenyl-1H-4-pyrazolyl)-2-pyrimidinamine (5), aryl/heteroaryl aldehyde and thioglycolic acid. The structures of the synthesized compounds have been confirmed via IR, (1)H-NMR, (13)C-NMR, MS and elemental analyses. Further, all the newly synthesized compounds 6a-j have been assayed for their antimicrobial activity against Gram-positive and Gram-negative bacteria and fungi. The compounds containing moieties like 4-nitrophenyl (6c), 3-nitrophenyl (6d), 4-dimethylaminophenyl (6g), 2-furyl (6i) and 1,3-benzodioxole (6j), at 2-position of thiazolidin-4-one ring exhibited good inhibitory activity against all the tested organisms.     

Stereoselective formal synthesis of aspergillide A

The stereoselective formal synthesis of aspergillide A (1), a cytotoxic 14-membered macrolide, is disclosed. The key intermediate, a trisubstituted tetrahydropyran core is prepared by SmI₂-induced intramolecular reductive cyclization as well as by using sequential α-aminooxylation, Horner-Wadsworth-Emmons olefination, and followed by Oxa-Michael cyclization. Other notable transformations in the synthesis include the use of Jacobsen’s hydrolytic kinetic resolution, esterification, ring-closing metathesis (RCM), and cross-metathesis (CM) reactions.     

Total synthesis of cryptopyranmoscatone B1 from 3,4,6-tri-O-acetyl-d-glucal

The first stereoselective total synthesis of the natural cryptopyranmoscatone B1 has been accomplished from 3,4,6-tri-O-acetyl-d-glucal. In addition to the double cross-metathesis reaction, a tandem nucleophilic addition-diastereoselective reduction of an in situ generated oxocarbenium cation have been used as key steps to assemble the glycoside moiety of the target molecule.     

The silylalkyne-Prins cyclization: a novel synthesis of 4-iododihydropyrans

The silylated secondary homopropargylic alcohols undergo smooth coupling with aldehydes in the presence of molecular iodine under mild reaction conditions to produce 4-iododihydropyrans in good yields. This method is highly stereoselective, affording cis-dihydropyrans exclusively.