Tricyclic-isoxazolidine analogues via intramolecular 1,3-dipolar cycloaddition reactions of nitrones

The tricyclic-isoxazolidine analogues tetrahydrothiochromenoisoxazoles, hexahydroisoxazolequinolines and tetrahydroisoxazolepyranopyridines were prepared by an intramolecular 1,3-dipolar cycloaddition reaction of a nitrone with an alkene. For N-alkylated hexahydroisoxazolequinolines, reduction of the reaction time from two days to 40 min was achieved using microwave heating. The cyclization to form tetrahydroisoxazolepyranopyridines only proceeded when the alkene was substituted with an electron withdrawing group.     

Isospectral surfaces with distinct covering spectra via Cayley graphs

The covering spectrum is a geometric invariant of a Riemannian manifold, more generally of a metric space, that measures the size of its one-dimensional holes by isolating a portion of the length spectrum. In a previous paper we demonstrated that the covering spectrum is not a spectral invariant of a manifold in dimensions three and higher. In this article we give an example of two isospectral Cayley graphs that admit length space structures with distinct covering spectra. From this we deduce the existence of infinitely many pairs of Sunada-isospectral surfaces with unequal covering spectra.     

An experimental and numerical investigation of the dynamics of microconfined droplets in systems with one viscoelastic phase

The dynamics of single droplets in a bounded shear flow is experimentally and numerically investigated for blends that contain one viscoelastic component. Results are presented for systems with a viscosity ratio of 1.5 and a Deborah number for the viscoelastic phase of 1. The numerical algorithm is a volume-of-fluid method for tracking the placement of the two liquids. First, we demonstrate the validation of the code with an existing boundary integral method and with experimental data for confined systems containing Newtonian components. This is followed by numerical simulations and experimental data for the combined effect of geometrical confinement and component viscoelasticity on the droplet dynamics after startup of shear flow at a moderate capillary number. The viscoelastic liquids are Boger fluids, which are modeled with the Oldroyd-B constitutive model and the Giesekus model. Confinement substantially increases the viscoelastic stresses and the elongation rates in and around the droplet. We show that the latter can be dramatic for the use of the Oldroyd-B model in confined systems with viscoelastic components. A sensitivity analysis for the choice of the model parameters in the Giesekus constitutive equation is presented.     

Chemical shift assignment and conformational analysis of monoalkylated acylguanidines

Monoalkylated acylguanidines are important functional groups in many biologically active compounds and additionally applied in coordination chemistry. Yet a straightforward assignment of the individual NH chemical shifts and the acylguanidine conformations is still missing. Therefore, in this study, NMR spectroscopic approaches for the chemical and especially the conformational assignment of protonated monoalkylated acylguanidines are presented. While NOESY and ³J_{H, H} scalar couplings cannot be applied successfully for the assignment of acylguanidines, ⁴J_{H, H} scalar couplings in ¹H,¹H COSY spectra allow for an unambiguous chemical shift and conformational assignment. It is shown that these ⁴J_{H, H} long‐range couplings between individual acylguanidinium NH resonances are observed solely across all‐trans (w) pathways. Already one cis orientation in the magnetisation transfer pathway leads to signal intensities below the actual detection limit and significantly lower than cross‐peaks from ²J_{NH, NH} couplings or chemical exchange. However, it should be noted that also in the case of conformational exchange being fast on the NMR time scale, averaged cross‐peaks from all‐trans ⁴J_{H, H} scalar couplings are detected, which may lead at first glance to an incomplete or even wrong conformational analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

Packing and covering the plane with translates of a convex polygon

A covering of the Euclidean plane by a polygon P is a system of translated copies of P whose union is the plane, and a packing of P in the plane is a system of translated copies of P whose interiors are disjoint. A lattice covering is a covering in which the translates are defined by the points of a lattice, and a lattice packing is defined similarly. We show that, given a convex polygon P with n vertices, the densest lattice packing of P in the plane can be found in O(n) time. We also show that the sparsest lattice covering of the plane by a centrally symmetric convex polygon can be solved in O(n) time. Our approach utilizes results from classical geometry that reduce these packing and covering problems to the problems of finding certain extremal enclosed figures within the polygon.     

Entangled Porphyrins in Cyclodextrin Vesicles

The entanglement process between porphyrins and some amphiphiliccyclodextrins and the occurrence of different species have been proved by the combination of UV-Visabsorption, fluorescence anisotropy, resonance light scattering and ¹H NMR spectroscopy.     

Chemical stability at noble metal M/YBa2Cu3O6.8 interfaces (M = Pt, Ag, Au)

The chemical compatibility between YBa₂Cu₃O_6.8 (Y123) and Pt, Ag or Au was studied using quasi-infinite diffusion couples which were encapsulated and annealed at 650 to 800°C for 5 to 80 h. The phase formation at the interface was analyzed in cross sections of these couples using optical and scanning electron microscopy together with energy- and wavelength dispersive X-ray microanalysis. In addition, bulk powder mixtures of Y123 with Pt, Ag or Au were annealed at 800°C for 100 h and phase analysis was performed using X-ray diffraction.

At the Pt/Y123 interface a reaction zone grows slowly but decisively at 800°C. Its microstructure is multiphase with Y---Cu-oxides and a fine-grained dispersion of Y₂BaCuO₅ (Y211) with Ba---Cu-oxides. Additional Ba---Pt oxides and other phases are seen in powder mixtures annealed for longer times. Barium is suspected to diffuse out from the superconductor along grain boundaries from as deep as 1 mm, causing the decomposition of Y123 into Y---Cu-oxides in the depleted regions. Ag and Au form a stable contact at the interface to Y123 with no reaction zone or new phases. Interdiffusion at the Ag/Y123 interface at 800°C was too low to be clearly detected. In contrast, Au diffuses very fast into Y123 and at 800°C the solubility is 4.2 mass% Au. Yttrium and barium diffuse much slower into the (Au) phase, Cu diffusion was not detected. Weak traces of decomposition products, mostly Y211 and Ba---Cu-oxides, were observed in bulk powder mixtures of Y123 with Ag or Au annealed at 800°C for 100 h in closed capsules. These decomposition products are considered to be due to the high oxygen pressure in the closed capsule, exceeding the stability limit of Y123, and not due to the reduction of Y123. Both Ag and Au are virtually non-reactive with Y123.     

An Approximate Analytical Solution for Counter-Current Spontaneous Imbibition

An approximate analytical solution is provided for one-dimensional, counter- current, spontaneous imbibition of a wetting phase (water) into a semi-infinite porous medium. The solution is based on the assumption that a similarity solution exists for the displacement process. This assumption, in turn, rests on the assumption that the set of relative permeability and capillary pressures curves are unique functions of saturation and do not depend on the nature of the displacement. It further rests on the assumption that the saturation at the imbibition face does not vary with time. It is demonstrated that the solution is in agreement with results obtained from experiments and also numerical analyses of these experiments. The experiments utilize cylindrical samples with the radial surface and one end-face sealed, and with counter-current imbibition occurring at the open end-face. The stage of the experiment that is modeled by the present solution is the period before the imbibition front contacts the sealed end-face. An important finding of the present analysis is that the pressure upstream of the advancing invasion front is a constant. A second, improved solution is also presented; this solution is an iterative, series solution of an integral-differential equation. It converges to a stable solution in very few terms.