Convective Cahn-Hilliard models: from coarsening to roughening

In this paper we demonstrate that convective Cahn-Hilliard models, describing phase separation of driven systems (e.g., faceting of growing thermodynamically unstable crystal surfaces), exhibit, with the increase of the driving force, a transition from the usual coarsening regime to a chaotic behavior without coarsening via a pattern-forming state characterized by the formation of various stationary and traveling periodic structures as well as structures with localized oscillations. Relation of this phenomenon to a kinetic roughening of thermodynamically unstable surfaces is discussed.     

Regularization of diffusion tensor MRI via local coordinates

We propose a novel framework for regularization of symmetric positive-definite (SPD) tensors (e.g., diffusion tensors). This framework is based on differential geometry. The space of SPD matrices, P_n, is described as a Riemannian manifold that is parameterized via the Iwasawa coordinate system. Then, distances on P_n are measured in terms of a natural GL (n)-invariant Riemannian metric. Using the Beltrami framework we construct a set of coupled geometric PDEs with respect to the Iwasawa coordinates. Then, by means of the gradient descent method these equations define the regularization flow over P_n. It appears to be that the local coordinate approach via that coordinate system results in very simple numerics that leads to fast convergence of the algorithm. We demonstrate the efficiency of this algorithm on real volumetric DTI datasets. Results of fibers tractography before and afterthe regularization process arepresented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Effect of varying correlation lengths on Anomalous Transport

Conventional concepts for transport in porous media assume that the heterogeneous distribution of hydraulic conductivities is the source for the contaminant temporal and spatial heavy tail. This tailing, known as anomalous or non-Fickian transport, can be captured by the β parameter in the continuous-time random walk framework. This study shows that with the increase in spatial correlation length between these heterogeneous distributions of hydraulic conductivities, the transport’s anomaly reduces; yet, the β value is unchanged, suggesting a topological component of the conductivity field, captured by the β. This finding is verified by an analysis of the solute transport, showing that the changing conductivity values have a moderate effect on the transport shape.

     

Cold Bose stars

By solving the Einstein equations coupled to a noninteracting quantum Bose field we determine the mass, density, and radius of equilibrium states of cold Bose matter localized under its own gravity. In particular we find that the maximum mass of a cold Bose star is 0.633/Gm.     

Reductive transformation of isoprenoid cyclosulfonates into linear homoallylic alcohols and amines

Conclusions Isoprene, myrcene, and ocimene sultones were converted into the corresponding linear homoallylic alcohols and amines via the stage of desulfonylation of the in situ generated allylsulfinic acids. A new synthesis of myrcenol and isogeraniol has been carried out.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 8, pp. 1820–1823, August, 1985.     

On realizing symmetric 3-polytopes

We prove the analogue of Eberhard’s Theorem for symmetric convex 3-polytopes with a 4-valent graph, and disprove a conjecture of the late T. Motzkin about realizing symmetric convex 3-polytopes so that all of their geodesics are in planes. This research was supported by the National Research Council of Canada Grant A-3999.     

Half-factorial-domains

LetR be a commutative domain with 1. We termR an HFD (Half-Factorial-Domain) provided the equality Π _i=1 ⁿ χ_i=Π{_f=1/^m}y _f impliesm=n, whenever thex’s and they’s are non-zero, non-unit and irreducible elements ofR. The purpose of this note is to study HFD’s, in particular, Krull domains that are HFD’s, and to provide examples of HFD’s, that contradict a conjecture of Narkiewicz.     

An approach to remove alpha amylase for proteomic analysis of low abundance biomarkers in human saliva

Proteomic characterization of human whole saliva for the identification of disease-specific biomarkers is guaranteed to be an easy-to-use and powerful diagnostic tool for defining the onset, progression and prognosis of human systemic diseases and, in particular, oral diseases. The high abundance of proteins, mainly alpha amylase, hampers the detection of low abundant proteins appearing in the disease state and therefore should be removed. In the present study a 2-DE was used to analyze human whole saliva following the removal of alpha amylase by affinity adsorption to potato starch. After alpha amylase removal whole saliva was analyzed by SDS-PAGE showing at least sixfold removal efficiency and by an alpha amylase activity assay showing 97% reduced activity. MS identification of the captured alpha amylase after elution demonstrated specific removal; 2-DE analysis showed the selective removal of alpha amylase and consequently increased gel resolution. MS identification of protein spots in the 60 kDa area revealed 15 proteins, which were masked before alpha amylase removal. In conclusion, treatment of human whole saliva with an alpha amylase removal device increases gel resolution and enables a higher protein sample for analysis.     

Highly efficient bismuth telluride doped p‐type Pb0.13Ge0.87Te for thermoelectric applications

Bi₂Te₃ doped p‐type Pb_0.13Ge_0.87Te samples were prepared by hot pressing. We report on very high power factor values of ～30 μW/cm K² at 500 °C, as were determined from Seebeck coefficient and electrical resistivity measurements. From dilatometric characterization, the phase transition from the low temperature rhombohedral to the high temperature cubic NaCl structures, takes place at 373 °C. This transition is accompanied by a continuous and gradual change of the lattice parameters, as was observed by hot stage XRD, suggesting a good mechanical durability upon thermal cycling and operating in large thermal gradients.

     

Levels in the toposes of simplicial sets and cubical sets

The essential subtoposes of a fixed topos form a complete lattice, which gives rise to the notion of a level in a topos. In the familiar example of simplicial sets, levels coincide with dimensions and give rise to the usual notions of n-skeletal and n-coskeletal simplicial sets. In addition to the obvious ordering, the levels provide a stricter means of comparing the complexity of objects, which is determined by the answer to the following question posed by Bill Lawvere: when does n-skeletal imply k-coskeletal? This paper, which subsumes earlier unpublished work of some of the authors, answers this question for several toposes of interest to homotopy theory and higher category theory: simplicial sets, cubical sets, and reflexive globular sets. For the latter, n-skeletal implies (n+1)-coskeletal but for the other two examples the situation is considerably more complicated: n-skeletal implies (2n−1)-coskeletal for simplicial sets and 2n-coskeletal for cubical sets, but nothing stronger. In a discussion of further applications, we prove that n-skeletal cyclic sets are necessarily (2n+1)-coskeletal.