Computational Study of Turbulent-Laminar Patterns in Couette Flow

Turbulent-laminar patterns near transition are simulated in plane Couette flow using an extension of the minimal flow unit methodology. Computational domains are of minimal size in two directions but large in the third. The long direction can be tilted at any prescribed angle to the streamwise direction. Three types of patterned states are found and studied: periodic, localized, and intermittent. These correspond closely to observations in large aspect ratio experiments.Comment: 4 pages, 5 figure

Absolute integral closure in positive characteristic

Let R be a local Noetherian domain of positive characteristic. A theorem of Hochster and Huneke (1992) states that if R is excellent, then the absolute integral closure of R is a big Cohen-Macaulay algebra. We prove that if R is the homomorphic image of a Gorenstein local ring, then all the local cohomology (below the dimension) of such a ring maps to zero in a finite extension of the ring. There results an extension of the original result of Hochster and Huneke to the case in which R is a homomorphic image of a Gorenstein local ring, and a considerably simpler proof of this result in the cases where the assumptions overlap, e.g., for complete Noetherian local domains

Hypermatter : properties and formation in relativistic nuclear collisions

The extension of the Periodic System into hitherto unexplored domains - anti- matter and hypermatter - is discussed. Starting from an analysis of hyperon and single hypernuclear properties we investigate the structure of multi-hyperon objects (MEMOs) using an extended relativistic meson field theory. These are contrasted with multi-strange quark states (strangelets). Their production mechanism is stud- ied for relativistic collisions of heavy ions from present day experiments at AGS and SPS to future opportunities at RHIC and LHC. It is pointed out that abso- lutely stable hypermatter is unlikely to be produced in heavy ion collisions. New attention should be focused on short lived metastable hyperclusters ( / 10 10s) and on intensity interferometry of multi-strange-baryon correlations

Assessing New England Family Forest Owners\u27 Invasive Insect Awareness

Family forest owners in the United States have underscored the need for forest insect pest (FIP) information, and numerous Extension programs have been developed to meet pest information needs. We developed the Pest Awareness Index to illustrate the heterogeneity of familiarity, knowledge, and experience regarding three FIPs (hemlock woolly adelgid, emerald ash borer, Asian long-horned beetle) in four New England states. Using mail survey data of family forest owners, we calculated an index from three components and provided comparisons based on region and actual insect presence. The differences in the index across these domains have implications for measurement and delivery of Extension programs

Heat kernel for reflected diffusion and extension property on uniform domains

We study reflected diffusion on uniform domains where the underlying space admits a symmetric diffusion that satisfies sub-Gaussian heat kernel estimates. A celebrated theorem of Jones (Acta Math. 1981) states that uniform domains in Euclidean space are extension domains for Sobolev spaces. In this work, we obtain a similar extension property for metric spaces equipped with a Dirichlet form whose heat kernel satisfies a sub-Gaussian estimate. We introduce a scale-invariant version of this extension property and apply it to show that the reflected diffusion process on such a uniform domain inherits various properties from the ambient space, such as Harnack inequalities, cutoff energy inequality, and sub-Gaussian heat kernel bounds. In particular, our work extends Neumann heat kernel estimates of Gyrya and Saloff-Coste (Ast\'erisque 2011) beyond the Gaussian space-time scaling. Furthermore, our estimates on the extension operator imply that the energy measure of the boundary of a uniform domain is always zero. This property of the energy measure is a broad generalization of Hino's result (PTRF 2013) that proves the vanishing of the energy measure on the outer square boundary of the standard Sierpi\'nski carpet equipped with the self-similar Dirichlet form.Comment: 56 pages; comments welcom

A Scoping Study of United States Extension Professional Competencies

This scoping study aimed to answer the question: What is known from existing research studies about the major competencies required of Extension professionals? Scoping studies are characterized by searching the literature to summarize major concepts on a research topic, and they are valuable as they show evidence for the major concepts. This study was limited to research studies of United States’ Extension professionals. The major conclusion from the scoping study is that existing research studies have yielded a rich literature base regarding Extension professional competencies. This scoping study identified 15 Extension professional competency domains: communication, diversity and cultural competence, flexibility, interpersonal relations, knowledge of Extension, leadership, professionalism, program planning and evaluation, resource management, subject matter competence, teaching methodology and delivery, technology, thinking and problem-solving, understanding community needs, and volunteer management. It is recommended that the results inform Extension professional job descriptions and professional learning programs

Symmetry properties of stable solutions of semilinear elliptic equations in unbounded domains

We consider stable solutions of a semilinear elliptic equation with homogeneous Neumann boundary conditions. A classical result of Casten, Holland [20] and Matano [44] states that all stable solutions are constant in convex bounded domains. In this paper, we examine whether this result extends to unbounded convex domains. We give a positive answer for stable non-degenerate solutions, and for stable solutions if the domain Ω further satisfies Ω ∩ {|x| ≤ R} = O(R^2), when R → +∞. If the domain is a straight cylinder, an additional natural assumption is needed. These results can be seen as an extension to more general domains of some results on De Giorgi’s conjecture.As an application, we establish asymptotic symmetries for stable solutions when the domain satisfies a geometric property asymptotically