A characteristic based numerical method with tracking for nonlinear wave equations

Many physical problems can be modeled by scalar, first-order, nonlinear, hyperbolic, partial differential equations (PDEs). The solutions to these PDEs often contain shock and rarefaction waves, where the solution becomes discontinuous or has a discontinuous derivative. One can encounter difficulties using traditional finite difference methods to solve these equations. In this paper, we introduce a numerical method for solving first-order scalar wave equations. The method involves solving ordinary differential equations (ODEs) to advance the solution along the characteristics and to propagate the characteristics in time. Shocks are created when characteristics cross, and the shocks are then propagated by applying analytical jump conditions. New characteristics are inserted in spreading rarefaction fans. New characteristics are also inserted when values on adjacent characteristics lie on opposite sides of an inflection point of a nonconvex flux function, Solutions along characteristics are propagated using a standard fourth-order Runge-Kutta ODE solver. Shocks waves are kept perfectly sharp. In addition, shock locations and velocities are determined without analyzing smeared profiles or taking numerical derivatives. In order to test the numerical method, we study analytically a particular class of nonlinear hyperbolic PDEs, deriving closed form solutions for certain special initial data. We also find bounded, smooth, self-similar solutions using group theoretic methods. The numerical method is validated against these analytical results. In addition, we compare the errors in our method with those using the Lax-Wendroff method for both convex and nonconvex flux functions. Finally, we apply the method to solve a PDE with a convex flux function describing the development of a thin liquid film on a horizontally rotating disk and a PDE with a nonconvex flux function, arising in a problem concerning flow in an underground reservoir.

Antigenic determinants at the carboxy terminus of chicken egg white riboflavin carrier protein (RCP): Epitope mapping and antibody-mediated pregnancy curtailment in rodents

The epitopic core sequences recognized by three monoclonal antibodies raised to chicken riboflavin carrier protein (RCP) were mapped to the C-terminal tail-end of the protein using the pepscan method A 21-residue synthetic peptide corresponding to residues 200-219 of the protein and comprising the regions corresponding to the antibodies was synthesized. Administration of polyclonal antibodies specific to this peptide led to termination of early pregnancy in mice. Also, active immunization of rats with the peptide-purified protein derivative conjugate inhibited establishment of pregnancy. These results demonstrate the functional importance of the C-terminal 200-219 region of chicken RCP. Copyright (C) 1996 Elsevier Science Ltd.

Automatic identification of modal damping from Floquet analysis

A practical method is proposed to identify the mode associated with the frequency part of the eigenvalue of the Floquet transition matrix (FTM). From the FTM eigenvector, which contains the states and their derivatives, the ratio of the derivative and the state corresponding to the largest component is computed. The method exploits the fact that the imaginary part of this (complex) ratio closely approximates the frequency of the mode. It also lends itself well to automation and has been tested over a large number of FTMs of order as high as 250.

Phosphate derivatives of 123 cuprates of the formula LnSr(2)Cu(3)O(7) (Ln=Gd, Dy, Ho)

Partial substitution of Cu in the chain by the phosphate ion stabilizes LnSr(2)Cu(3)O(7) (Ln = Gd, Dy or Ho) in the 123 structure. The LnSr(2)Cu(2.8)(PO4)(0.2)O-y derivatives exhibit incommensurately modulated structures. The holmium oxy-phosphate derivative has been rendered superconducting by the partial substitution of Ho by Ca.

Potassamide induced in situ alkylation of 5,6-dihydroisoquinoline with allyl bromide and Michael acceptors

Potassamide induced in situ alkylation of 4-cyano-3-methoxy-1-methyl-5, 6-dihydroisoquinoline (1a) with allyl bromide gives the 5-allyl- and 5,9-diallyl-5,6-dihydroisoquinolines (1c and 1d), isoquinoline derivative 2 and 4-allyl-1, 2, 3, 4-tetrahydroisoquinolin-3(2H)-one (3a). However, potassamide induced in situ alkylation of In with buten-2-one, mesityl oxide and acrylonitrile results in the formation of only 5-alkylated 5,6-dihydroisoquinoline derivatives 1e-g along with fully aromatised compound 2.

Structural variants of hyperbranched polyesters

Hyperbranched polyesters based on 3,5-dihydroxybenzoic acid and its derivatives were prepared by self-condensation of the corresponding ester under standard trans-esterification conditions. The spacer segment length that connects the branching points was systematically varied by starting from the appropriate ethyl 3,5-bis(omega-hydroxyoligo(ethyleneoxy))benzoate. The thermal properties of the hyperbranched polyesters were studied using DSC, and they have been compared with those of the linear analogues prepared from the corresponding p-hydroxybenzoic acid derivatives and also with the molecularly ''kinked'' analogues prepared from the meta isomers. These hyperbranched polyesters were also terminally functionalized by using a potentially mesogenic 4-butoxybiphenylcarboxylic acid derivative in an attempt to prepare novel hyperbranched liquid crystalline polyesters. This was achieved by copolymerization of the AB(2) monomer with the mesogenic A-type capping unit. These polymers were found to be amorphous and did not exhibit any liquid crystalline phases, probably due to the random distribution of the mesogenic segments on the polymer framework, making it difficult to both crystallize and form mesophases.

Synthesis Based on Cyclohexadienes. 5. A New Approach to the Synthesis of a-Ring Aromatic Steroids - a Formal Total Synthesis of (+/-)-Estrone

A new strategy for the construction of A-ring aromatic steroids which resulted in the formal total synthesis of estrone is described. Thus reaction of the adduct (9), obtained from 1-methoxy-4-methylcyclohexa-1,4-diene and acrolein, with 3-(m-methoxyphenyl)propylmagnesium bromide followed by oxidation afforded the bicyclo[2.2.2]octene derivative (14). Acid-catalysed rearrangement of (14) followed by an intramolecular Michael addition resulted in the cis tetraenone (18) which was dehydrogenated with palladium chloride to the pentaenone (22). Li/NH3 reduction of (22) gave 3-methoxy-D-homoestra-1,3,5(10)-trien-16-one (31) which has been converted into the methyl ether (37) of marrianolic acid, and its methyl ester (38).

Synthesis based on cyclohexadienes. Part 17. Total synthesis of the sesquiterpenes of Eremophila georgei diels

The first stereoselective total synthesis of the novel sesquiterpenes 1 and 2 is described. The preparation of the key intermediate 27 involved a rearrangement of a bicyclo[3.2.1] octane framework to an isomeric bicyclo[3.2.1]octane skeleton via a bicyclo[2.2.2]octane derivative.

Uniform algebras generated by holomorphic and close-to-harmonic functions

The initial motivation for this paper is to discuss a more concrete approach to an approximation theorem of Axler and Shields, which says that the uniform algebra on the closed unit disc (D) over bar generated by z and h, where h is a nowhere-holomorphic harmonic function on D that is continuous up to partial derivative D, equals C((D) over bar). The abstract tools used by Axler and Shields make harmonicity of h an essential condition for their result. We use the concepts of plurisubharmonicity and polynomial convexity to show that, in fact, the same conclusion is reached if h is replaced by h + R, where R is a non-harmonic perturbation whose Laplacian is ``small'' in a certain sense.

Nonequilibrium-phase transition and 'specific-heat' singularity in the kinetic Ising model: A Monte Carlo study

The nonequilibrium-phase transition has been studied by Monte Carlo simulation in a ferromagnetically interacting (nearest-neighbour) kinetic Ising model in presence of a sinusoidally oscillating magnetic field. The ('specific-heat') temperature derivative of energies (averaged over a full cycle of the oscillating field) diverge near the dynamic transition point.

Synthesis and biological evaluation of novel 2-aralkyl-5-substituted-6-(4 `-fluorophenyl)-imidazo2,1-b]1,3,4]thiadiazole derivatives as potent anticancer agents

Levamisole, the imidazo2,1-b]thiazole derivative has been reported as a potential antitumor agent. In the present study, we synthesized, characterized and evaluated biological activity of its novel analogues with substitution in the aralkyl group and on imidazothiadiazole molecules with same chemical backbone but different side chains namely 2-aralkyl-6-(4'-fluorophenyl)-imidazo2,1-b]1,3,4]thiadiazoles (SCR1), 2-aralkyl-5-bromo-6-(4'-fluorophenyl)-imidazo2,1-b]1,3,4]-thiadiaz oles (SCR2), 2-aralkyl-5-formyl-6-(4'-fluorophenyl)-imidazo2,1-b]1,3,4]-thiadia zoles (SCR3) and 2-aralkyl-5-thiocyanato-6-(4'-fluorophenyl)-imidazo2,1-b]1,3,4]-th iadiazoles (SCR4) on leukemia cells. The cytotoxic studies showed that 3a, 4a, and 4c exhibited strong cytotoxicity while others had moderate cytotoxicity. Among these we chose 4a (IC50, 8 mu M) for understanding its mechanism of cytotoxicity. FACS analysis in conjunction with mitochondrial membrane potential and DNA fragmentation studies indicated that 4a induced apoptosis without cell cycle arrest suggesting that it could be used as a potential chemotherapeutic agent. (C) 2011 Elsevier Masson SAS. All rights reserved.

Synthesis based on cyclohexadienes .23. Total synthesis of 5-epi-pupukean-2-one

A new strategy for the construction of the isotwistane skeleton is reported from easily available cyclohexadienes which involves stereoselective alkylation of a bicyclooctenone derivative and a decarboxylative 5-exo-trig radical cyclisation as the key steps in the total synthesis of 5-epi-pupukean-2-one.

Time-resolved resonance Raman spectroscopic studies on the triplet excited state of fluoranil

Perfluoro substituted organic compounds have attracted attention owing to their unique structure and reactivity induced by the perfluoro effect. Fluoranil, a perfluoro derivative of p-benzoquinone, is the subject of this paper. Although the perfluoro effect in the ground state seems to have been well understood there is no information available about such effects on the excited state. Here, the time-resolved resonance Raman spectra of the triplet excited state of fluoranil are reported along with the Raman excitation profiles (REPs) of the various vibrational modes. The vibrational spectral analyses have been carried out by analogy with the fluoranil ground state, triplet benzoquinone, and triplet chloranil vibrational spectral assignments. Also, the assignments are further supported by the calculated frequencies using ab initio theoretical methods. It is observed that for fluoranil in the triplet excited state, due to the perfluoro effect, the structure is considerably less distorted than benzoquinone and also the electron delocalization in the pi* antibonding orbital is less than that of triplet excited state of benzoquinone.

Enzymatic resolution of dioxygenated dicyclopentadienes: Enantiopure hydrindanes, hydroisoquinolones, diquinanes and application to a synthesis of (+)-coronafacic acid

A 5, 10-dioxygenated-tricyclo[5.2.1.0(2,6)]decane derivative 6 has yielded to efficient enzymatic resolution to provide a range of chiral building blocks, whose absolute configuration has been determined through a total synthesis of naturally occuring (+)-coronafacic acid. (C) 1999 Elsevier Science Ltd. All rights reserved.

Orthometalation in calixarenes: Synthesis and structural characterization of a novel orthopalladated calix[4]arene bisphosphite

The treatment of a symmetrically bridged p-Bu-t-calix[4] arene bisphosphite with PdCl2(NCPh)(2) yields a novel orthopalladated derivative by a C-C bond scission of a t-butyl group attached to an aryl ring. The structure of this orthopalladated calix[4]arene derivative has been established by X-ray crystallography.