Structural studies of apatite-type oxide ion conductors doped with cobalt

A series of Co doped lanthanum silicate apatite-type phases, La9.83Si4.5Co1.5O26, La9.66Si5CoO26, La10Si5CoO26.5 and La8BaCoSi6O26, have been synthesised, and neutron diffraction, EXAFS and XANES used to investigate their structures in detail. All compositions were shown to possess the hexagonal apatite structure, and the results confirmed that cobalt can be doped onto both the La and Si sites within the structure depending on the starting composition. The Co doping is shown to cause considerable local distortions within the apatite structure. In the case of Si site doping two compositions showed anisotropic peak broadening, which has been attributed to incommensurate ordering of oxygen within the apatite channels.     

Many triangulated 3-spheres

We construct combinatorial types of triangulated 3-spheres on n vertices. Since by a result of Goodman and Pollack (1986) there are no more than 2^{O(n log n)} combinatorial types of simplicial 4-polytopes, this proves that asymptotically there are far more combinatorial types of triangulated 3-spheres than of simplicial 4-polytopes on n vertices. This complements results of Kalai (1988), who had proved a similar statement about d-spheres and (d+1)-polytopes for fixed d4.Mathematics Subject Classification (1991): 52B11, 52B70, 57Q15Supported by the Deutsche Forschungsgemeinschaft within the European graduate program Combinatorics, Geometry, and Computation (GRK 588/1) and an MSRI post-doctoral fellowship.Partially supported by Deutsche Forschungs-Gemeinschaft (DFG), via the DFG Research Center Mathematics in the Key Technologies (FZT86), the Research Group Algorithms, Structure, Randomness (Project ZI 475/3), and a Leibniz grant (ZI 475/4).     

Large-Scale Production of 3D Bioactive Glass Macroporous Scaffolds for Tissue Engineering

For tissue engineering applications, a scaffold is required that can act as a template and guide for cell proliferation, cell differentiation and tissue growth. Interconnected pores with diameters greater than 100 m are required for tissue ingrowth, vascularisation and nutrient delivery to the centre of the scaffold. 3D bioactive glass scaffolds have been produced, by foaming sol-gel derived bioactive glasses. The method to produce foams with a modal macropore diameter of 100 m, and a handling strength suitable for cell culture, was to foam 50 ml batches of sol with the aid of a surfactant and gelling agent. In vitro and in vivo tests show that the scaffolds have high potential to be used in bone tissue engineering applications. Larger batches are required to produce scaffolds commercially. The aim of this work was to investigate how the process could be up-scaled for commercial use. This study shows that foaming larger aliquots of sol decreased the scaffold porosity and interconnectivity and investigates methods of modifying the process to obtain large quantities of foam scaffolds with pores in excess of 100 m. The optimum method to produce foams of similar pore structure from 200 ml sol to those produced from 50 ml sol comprised of adding 3 ml surfactant and 12 ml dionised water to the sol to start foaming and injecting a gas mixture (70% helium, 30% nitrogen) at 0.2 bar while applying vigorous agitation.     

Effects of ultraviolet B exposure on the expression of proliferating cell nuclear antigen in murine skin

Proliferating cell nuclear antigen (PCNA) is an active nuclear protein involved in DNA replication, recombination and repair. PCNA is found throughout the basal layer in normal skin and in all layers of the epidermis in malignancy. This study evaluates PCNA's expression after acute and chronic UV-B irradiation. Skh-1 hairless mice exposed to 1.5 and 4.5 kJ/m2 of UV-B were sacrificed at 6, 12, 24, 48, 72 and 168 h. Immunohistochemical analysis revealed PCNA expression throughout the basal layer of untreated skin, with diminished expression at 6 h, indicative of immediate UV damage, and evidenced by the observable upregulation in pyrimidine dimer formation early on. Subsequently, PCNA immunoreactivity progressively increased, demonstrating an aberrant upward epidermal migratory pattern in association with chronic exposure. The 4.5 kJ/m2 group exhibited prolonged recovery in staining and also demonstrated this altered migratory pattern with chronic exposure. Progressive reactivation of PCNA expression occurs with repair. PCNA migration to upper layers of the epidermis indicates proliferation and possibly a subsequent increased malignant potential. We conclude that PCNA can serve as a marker of DNA repair and indirectly as an indicator of UV-B-induced damage, expression being time dependent and dose related. Specific immunoreactivity patterns and the observable atypia in keratinocytes are relevant in elucidating malignant potentiation.     

An approach to developing a force field for molecular simulation of martensitic phase transitions between phases with subtle differences in energy and structure

d,l-Norleucine is one of only a few molecules whose crystals exhibit a martensitic or displacive-type phase transformation where the emerging phase shows a topotaxial relationship with the parent phase. The molecular mechanism for such phase transformations, particularly in molecular crystals, is not well understood. Crystalline phases that exhibit displacive phase transitions tend to be very similar in structure and energy. Consequently, the development of a force field for such phases is challenging as the phase behavior is determined by subtle differences in their lattice energies and entropies. We report an approach for developing a force field for such phases with an application to d,l-norleucine. The proposed procedure includes calculation of the phase diagram of the crystalline phases as a function of temperature to identify the best force field. d,l-Norleucine also presents an additional problem since in the solid state it exists as a zwitterion that is unstable in vacuo and therefore cannot be characterized using high-level ab initio calculations in the gas phase. However, a stable zwitterion could be obtained using Onsager's reaction-field continuum model for a solvent (SCRF) using both Hartree-Fock and density functional theory. A number of force fields and the various sets of partial charges obtained from the SCRF calculations were screened for their ability to reproduce the crystal structures of the two known phases, alpha and beta, of d,l-norleucine. Selected parameter sets were then employed in free energy minimizations to identify the best set on the basis of a correct prediction of the alpha-beta phase transition. The Williams' nonbonded parameters combined with partial charges from SCRF-Polarized Continuum Model calculation were found to reproduce the structures of the phases accurately and also maintained their stability in extended molecular dynamics simulations in the Parrinello-Rahman constant stress ensemble. Moreover, we were also able to successfully simulate the phase transformation of the beta- to the alpha-phase. The identified force field should enable detailed studies of the phase transformations exhibited by crystals of d,l-norleucine and hence enhance our understanding of martensitic-type transformations in molecular crystals.     

Generalized frequency selection in multifrequency interferometry

We present a generalized frequency selection method for N-frequency interferometry to form an optimum geometric series at synthetic wavelengths. The absolute range that is measurable is bounded by the number of beat frequency operations, phase noise, and the number of wavelengths used to form the geometric series of synthetic wavelengths. Theoretical predictions are compared with experimental results from a full-field fringe projector. A comparison of this technique with the method of excess fractions shows orders-of-magnitude faster processing with similar measurement reliability.     

Inverse scattering problem for optical coherence tomography

We deal with the imaging problem of determining the internal structure of a body from backscattered laser light and low-coherence interferometry. Specifically, using the interference fringes that result when the backscattering of low-coherence light is made to interfere with the reference beam, we obtain maps detailing the values of the refractive index within the sample. Our approach accounts fully for the statistical nature of the coherence phenomenon; the numerical experiments that we present, which show image reconstructions of high quality, were obtained under noise floors exceeding those present for various experimental setups reported in the literature.     

Salt bridge stabilization of charged zwitterionic arginine aggregates in the gas phase

The discovery of several new unusually stable aggregates of arginine that are intermolecularly bound by salt bridges is reported. Quadrupole ion-trap mass spectrometry provides evidence for the stability of arginine in the zwitterionic state, where the protonated guanidinium group of one arginine interacts strongly with the carboxylate of another to form stable noncovalent complexes, coordinated to either a cation or anion. Clusters of arginine with itself, sodium, potassium, lithium, magnesium, chloride, fluoride, bromide, iodide, and nitrate are observed. DFT calculations at the B3LYP/6-31G level are used to assess the structures and energetics of particularly prominent clusters. An examination of mixtures of D-arginine with isotopically labeled L-arginine indicates that the stability of these clusters does not depend on arginine enantiomeric purity. The cyclic trimers of arginine, capped with either Cl(-) or NO(3)(-), possess exceptional stability.     

Pseudotwistors

We deal with the Hermitian Hurwitz pairs of signature (, s), + s = 5 + 4, | + 1 – s| = 2 + 4m;, m = 0, 1,.... We introduce the Hurwitz twistors for signature (3, 2) and its dual (1, 4) and we indicate the relationship between Hurwitz and Penrose twistors. The signatures (1, 8) and (7, 6) give rise to pseudotwistors and bitwistors, respectively. For pseudotwistors, we prove a counterpart of the Penrose theorem in the local version, on real analytic solutions of the related spinor equations versus harmonic forms, and in the semiglobal version, on holomorphic solutions of those equations versus Dolbeault cohomology groups. We prove an atomization theorem: There exist complex structures on isometric embeddings for the Hermitian Hurwitz pairs so that the embeddings are real parts of holomorphic mappings.     

On Nonlinear Integro-differential Operators in Generalized Orlicz–Sobolev Spaces

A nonlinear integral operator T of the form (Tf)(s)=∫_G K(t, f (σ(s, t))) dμ(t), for sG, is defined and investigated in the measure space (G, Σ, μ), where f and K are vector-valued functions with values in normed linear spaces E and F, respectively. The results are applied to the case of integro-differential operators in generalized Orlicz–Sobolev spaces. There are studied problems of existence, embeddings, and approximation by means of T.