Fingering instability in particle systems

In many multiphase systems, material interfaces can be destabilized by shocks. Small disturbances at these interfaces can grow in size to form large-scale fingers. We consider a shock propagating through a system that consists of two types of particles, of different mass, that are initially separated by an interface, but are free to mix. In the classical case of immiscible fluids, the finger of heavy fluid propagating into the light fluid grows faster and becomes much thinner than the finger of light fluid propagating into the heavy fluid. We show that collisions between particles of different types lead to shock focusing that causes a secondary flow that is initially similar to the fluid case. However, the particle system can exhibit completely different qualitative behavior in the nonlinear-growth phase and can give rise to the situation where the finger of heavy material is actually wider than the finger of the light material. We show that this qualitative change is due to a strong decompression that occurs in the heavy material. We also show that microscopic mixing can have an important impact on finger growth.     

Effects of individual and family functioning on interest in genetic testing

OBJECTIVE: The present study reports on the important issue of how family communication and support regarding breast cancer risk affects interest in genetic testing and mental health. METHODS: Participants (n = 221) were women aged 18-74 who had at least one relative of Ashkenazi Jewish descent, no personal history of breast or ovarian cancer, and lived within 60 miles of Seattle, Wash. RESULTS: Communication about breast cancer risk was reported with very low frequency across all types of relatives. Women talked with their mothers and sisters more often than their fathers, brothers, or children. The only significant predictor of interest in genetic testing was the individual level variable of seeking social support. CONCLUSION: Social support needs might be a part of the genetic testing process.     

Noncompact manifolds with nonnegative Ricci curvature

Let (M, d) be a metric space. For 0 < r < R, let G(p, r, R) be the group obtained by considering all loops based at a point p ∈ M whose image is contained in the closed ball of radius r and identifying two loops if there is a homotopy between them that is contained in the open ball of radius R. In this article we study the asymptotic behavior of the G(p, r, R) groups of complete open manifolds of nonnegative Ricci curvature. We also find relationships between the G(p, r, R) groups and tangent cones at infinity of a metric space and show that any tangent cone at infinity of a complete open manifold of nonnegative Ricci curvature and small linear diameter growth is its own universal cover.     

On regularity of block triangular fuzzy matrices

Necessary and sufficient conditions are given for the regularity of block triangular fuzzy matrices. This leads to characterization of idempotency of a class of triangular Toeplitz matrices. As an application, the existence of group inverse of a block triangular fuzzy matrix is discussed. Equivalent conditions for a regular block triangular fuzzy matrix to be expressed as a sum of regular block fuzzy matrices is derived. Further, fuzzy relational equations consistency is studied.     

Effect of chelating ring size in catalytic ketone hydrogenation: facile synthesis of ruthenium(II) precatalysts containing an N-heterocyclic carbene with a primary amine donor for ketone hydrogenation and a DFT study of mechanisms

A half-sandwich ruthenium(II) complex, [Ru(η(6)-p-cymene)(C-NH(2))Cl]PF(6) (4·PF(6)), containing an N-heterocyclic carbene (NHC) with a primary amine donor (C-NH(2)) which chelates through the carbene carbon and the amine nitrogen to form a 6-membered ring was synthesized in a one-pot reaction starting from a primary-amine functionalized imidazolium salt 2. Complex 4·PF(6) catalyzed the hydrogenation of ketones using 2-propanol or H(2) as the reductant. A maximum turnover frequency of 1062 h(-1) and a turnover number of 1140 at 5 h were achieved for the transfer hydrogenation of 3'-chloroacetophenone in 2-propanol at 75 °C. A cationic hydride-amine complex 5, [Ru(η(6)-p-cymene)(C-NH(2))H]PF(6), was synthesized, and this reacted very slowly with acetophenone unless first activated by an alkoxide base. Computational studies by DFT methods suggested that the poor reactivity of the hydride-amine complex 5 was attributed to a large barrier for the transfer of its H(+)/H(-) couple to a ketone for bifunctional catalysis. An inner-sphere mechanism, which involves a decoordinated amine group of the C-NH(2) ligand, was computed to be a feasible energetic pathway in comparison to the computed outer-sphere bifunctional mechanism. This explains the catalytic activity and selectivity that is observed for the newly synthesized ruthenium(II) catalysts.     

Probabilistic Inductive Classes of Graphs

A unifying framework—probabilistic inductive classes of graphs (PICGs)—is defined by imposing a probability space on the rules and their left elements from the standard notion of inductive class of graphs. The rules can model the processes creating real-world social networks, such as spread of knowledge, dynamics of acquaintanceships or sexual contacts, and emergence of clusters. We demonstrate the characteristics of PICGs by casting some well-known models of growing networks in this framework. Results regarding expected size and order are derived. For PICG models of connected and 2-connected graphs order, size and asymptotic degree distribution are presented. The approaches used represent analytic alternative to computer simulation, which is mostly used to obtain the properties of evolving graphs.