Mathematical modelling of heat conduction in certain functionally graded composites

The aim of contribution is to formulate a certain extended version of the tolerance modelling technique for functionally graded composites. For the sake of simplicity, the considerations are restricted to the bidirectionally graded heat conductors. It is shown that the proposed approach enables to determine an entire class of mathematical models for which applications can be found in various specific problems. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic coupling between coordinates in a model for biomolecular isomerization

To understand a complex reaction, it is necessary to project the dynamics of the system onto a low-dimensional subspace of physically meaningful coordinates. We recently introduced an automatic method for identifying coordinates that relate closely to stable-state commitment probabilities and successfully applied it to a model for biomolecular isomerization, the C(7eq)-->alpha(R) transition of the alanine dipeptide [A. Ma and A. R. Dinner, J. Phys. Chem. B 109, 6769 (2005)]. Here, we explore approximate means for estimating diffusion tensors for systems subject to restraints in one and two dimensions and then use the results together with an extension of Kramers theory for unimolecular reaction rates [A. Berezhkovskii and A. Szabo, J. Chem. Phys. 122, 014503 (2005)] to show explicitly that both the potential of mean force and the diffusion tensor are essential for describing the dynamics of the alanine dipeptide quantitatively. In particular, the signficance of off-diagonal elements of the diffusion tensor suggests that the coordinates of interest are coupled by the hydrodynamic-like response of the bath of remaining degrees of freedom.     

A convenient approach for access to both carbapentofuranoses and carbahexopyranoses. Stereocontrolled synthesis of enantiopure carba-D-ribofuranoses, carba-D-arabinofuranoses and carba-L-gulopyranose

A new approach to carbasugars in enantiomerically pure form is reported. The key step involves ring-closing metathesis of dienols 6 derived from a (R)-(+)-glyceraldehyde derivative 4 to form the substituted cyclopentenol 9 and cyclohexenol 34a. Stereocontrolled addition of hydroxyl groups followed by conversion of the ketal unit to hydroxymethyl group in these intermediates led to carbapentoses and -hexoses. Stereoselectivity during introduction of hydroxyl groups arises through the steric hindrance posed by the allylic substituents. A remarkable feature of the present approach is the accessibility of both d- and l-series of carbapentoses as illustrated by the synthesis of beta-D- and beta-L-carbaribofuranoses 17 and 20, respectively. Carba-alpha-D-ribofuranose 25, the biosynthetic intermediate to the antibiotic aristeromycin, has also been synthesized from the same cyclopentenol 9. Functional group manipulation in the cyclopentenol 9a also enabled access to carbaarabinofuranose 32. The present synthetic strategy can be extended for the synthesis of carbahexopyranose, as illustrated by the synthesis of carba-alpha-L-gulopyranose 40b.     

22pi smaragdyrin molecular conjugates with aromatic phenylacetylenes and ferrocenes: Syntheses, electrochemical, and photonic properties

Syntheses, spectroscopic, electrochemical, and third-order nonlinear optical susceptibilities of a series of 22pi smaragdyrins and their corresponding Rh(I) derivatives bearing phenylacetylene substituents and ferrocene-containing substituents are reported. The synthetic strategy involved a [3 + 2] acid-catalyzed oxidative coupling reaction of the appropriate dipyrromethane and oxatripyrrane. The desired meso substituents, such as phenylacetylenylphenyl and the ferrocenes, were incorporated to the dipyrromethane unit prior to the oxidative coupling reaction. The optical absorption, emission characteristics, and the quantum yield of the smaragdyrin conjugates depends on the nature of the substituent, nature of linker group, and the spacer length. Theoretical studies at the DFT level suggest high delocalization of electrons confined to only four of the five available heterocyclic rings for the free bases. However, upon Rh(I) metalation, the pi-electron delocalization is extended to all the heterocyclic rings. The two-photon absorption cross section (TPA) values sigma(2) measured through the open aperture Z-scan method, increases linearly with enhanced pi-electron delocalization for the smaragdyrins containing phenylacetylene substituents. The meta branching of substituents decreases sigma(2) values. Introduction of Rh(I) to the smaragdyrin cavity enhances the sigma(2) values by about 3-10 orders of magnitude, attributed to the increased aromatic character upon Rh(I) insertion. The calculated molecular electrostatic potential (MESP) and harmonic oscillator model of aromaticity (HOMA) for the free bases and the Rh(I) derivatives justifies such a conclusion. A linear correlation observed for the second oxidation potential of Rh(I) derivatives and corresponding free bases also support the increased aromaticity upon Rh(I) insertion. The electrochemical data for ferrocene-containing smaragdyrins reveal easier ring oxidation by about 50-130 mV and harder ferrocene oxidation by 40-180 mV suggesting electron-donating nature of the ferrocene upon linking with the smaragdyrin system. The TPA cross section value of 88782 GM observed for 5g represents one of the highest values known for a metalloexpanded porphyrin derivative.     

Phase-shifting interferometry in the presence of nonlinear phase steps, harmonics, and noise

A phase-shifting piezo device commonly employed in phase-shifting interferometry exhibits a nonlinear response to applied voltage. Hence, a method for estimation of phase distribution in the presence of nonlinear phase steps is presented. The proposed method compensates for the harmonics present in the intensity fringe, allows the use of arbitrary phase-step values between 0 and tau rad, and does not impose constraints on the selection of particular phase-step values for minimizing nonlinearity and compensating for the harmonics. The comparison of the proposed method with other well-known benchmarking algorithms shows that our method is highly efficient and also works well in the presence of noise.     

Chirp estimation in phase-shifting interferometry

We propose a new approach for estimating the phase in the presence of a nonlinear response of a phase-shifting device: a piezoelectric transducer (PZT). The method is complemented well by the high resolution and the maximum likelihood estimation techniques in the estimation of the phase step and the nonlinear coefficient. The advantage of the proposed method is that it can be extended to the extraction of multiple phases in configurations involving multiple PZTs in the presence of nonlinearity. Symmetricity in the phase steps is not required in this method. Hence hysteresis of the PZT does not have any influence on the accuracy of the phase estimation. The effectiveness of the method is shown by experimental results.     

Osmium assisted C-H activation and CN cleavage of N-(2′-hydroxyphenyl) benzaldimines. Synthesis, structure and electrochemical properties of some organoosmium complexes

Reaction of N-(2′-hydroxyphenyl)-4-R-benzaldimines (L-R, R = OCH₃, CH₃, H, Cl and NO₂) with [Os(PPh₃)₃Br₂] in refluxing 2-methoxyethanol in the presence of triethylamine affords two families of organoosmium complexes (1-R and 2-R). In both 1-R and 2-R complexes a benzaldimine ligand is coordinated to the metal center as tridentate C,N,O-donor. In the 1-R complexes, a bidentate N,O-donor imionsemiquinonate ligand, derived from the hydrolysis of another benzaldimine, and a PPh₃ ligand are also coordinated to osmium. In the 2-R complexes, a carbonyl, derived from decarbonylation of 4-R-benzaldehyde (derived from the same hydrolysis stated above), and two PPh₃ ligands take up the remaining coordination sites on osmium. Structures of the 1-Cl and 2-OCH₃ complexes have been determined by X-ray crystallography. All the 1-R and 2-R complexes are diamagnetic, and show characteristic ¹H NMR signals and intense MLCT transitions in the visible region. Cyclic voltammetry on the 1-R complexes shows a reversible Os(III)-Os(IV) oxidation within 0.47-0.67 V (vs SCE), followed by an irreversible oxidation of the imionsemiquinonate ligand within 1.10-1.36 V. An irreversible Os(III)-Os(II) reduction is also displayed by the 1-R complexes within −1.02 to −1.14 V. Cyclic voltammetry on the 2-R complexes shows a reversible Os(II)-Os(III) oxidation within 0.29-0.51 V, followed by a quasi-reversible oxidation within 1.04-1.29 V, and an irreversible reduction of the coordinated benzaldimine ligand within −1.16 to −1.31 V.     

Kernel ideals and cokernel filters of a p-algebra

We discuss congruences of p-algebras. We characterize kernel ideals of a p-algebra. Indeed, we show that an ideal of a p-algebra is a p-ideal if and only if it is a kernel ideal. We study cokernel filters of a p-algebra. We construct a class of p-algebras in which every cokernel filter is a p-filter. We also give some characterizations of Boolean congruences of a p-algebra.     

Blue light emitting graphene-based materials and their use in generating white light

It has been demonstrated that acid-treated graphene samples as well as reduced graphene oxide show fairly intense blue emission centered around 440 nm. Reduction of graphene oxide can be carried out either chemically or by using different types of radiations. Blue emission from graphene-based materials can be combined with the yellow emission from materials like ZnO to produce white light sources.     

Rare earth trisoxalatocobaltates(III) a precursor for rare earth cobaltites(III)

Rare earth cobalties, LnCoO₃, can be conveniently prepared by the thermal decomposition of the precursor LnCo(C₂O₄)₃·nH₂O (La, Ce, n=9; Pr, Nd, n=8). CeCo(C₂O₄)₃·8H₂O, unlike the other oxalato compounds thermally decompose to a mixture of CeO₂ and Co₃O₄. Although LnCoO₃are formed from the precursors at a temperature lower than 800°C, thermal analysis of a mixture of La₂(C₂O₄)₃·10H₂O and CoC₂O₄·2H₂O at 900·C shows the residue containing mainly La₂O₃ and Co₃O₄ with a small amount of LaCoO₃.