High-pressure droplet combustion studies

This is a joint research program, pursued by investigators at the University of Tokyo, UCSD, and NASA Lewis Research Center. The focus is on high-pressure combustion of miscible binary fuel droplets. It involves construction of an experimental apparatus in Tokyo, mating of the apparatus to a NASA-Lewis 2.2-second drop-tower frame in San Diego, and performing experiments in the 2.2-second tower in Cleveland, with experimental results analyzed jointly by the Tokyo, UCSD, and NASA investigators. The project was initiated in December, 1990 and has now involved three periods of drop-tower testing by Mikami at Lewis. The research accomplished thus far concerns the combustion of individual fiber-supported droplets of mixtures of n-heptane and n-hexadecane, initially about 1 mm diameter, under free-fall microgravity conditions. Ambient pressures ranged up to 3.0 MPa, extending above the critical pressures of both pure fuels, in room-temperature nitrogen-oxygen atmospheres having oxygen mole fractions X of 0.12 and 0.13. The general objective is to study near-critical and super-critical combustion of these droplets and to see whether three-stage burning, observed at normal gravity, persists at high pressures in microgravity. Results of these investigations will be summarized here; a more complete account soon will be published

Discriminating different classes of biological networks by analyzing the graphs spectra distribution

The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world topology. Recent studies indicate that some pathologies present topological network alterations relative to norms seen in the general population. Therefore, methods to discriminate the processes that generate the different classes of networks (e.g., normal and disease) might be crucial for the diagnosis, prognosis, and treatment of the disease. It is known that several topological properties of a network (graph) can be described by the distribution of the spectrum of its adjacency matrix. Moreover, large networks generated by the same random process have the same spectrum distribution, allowing us to use it as a "fingerprint". Based on this relationship, we introduce and propose the entropy of a graph spectrum to measure the "uncertainty" of a random graph and the Kullback-Leibler and Jensen-Shannon divergences between graph spectra to compare networks. We also introduce general methods for model selection and network model parameter estimation, as well as a statistical procedure to test the nullity of divergence between two classes of complex networks. Finally, we demonstrate the usefulness of the proposed methods by applying them on (1) protein-protein interaction networks of different species and (2) on networks derived from children diagnosed with Attention Deficit Hyperactivity Disorder (ADHD) and typically developing children. We conclude that scale-free networks best describe all the protein-protein interactions. Also, we show that our proposed measures succeeded in the identification of topological changes in the network while other commonly used measures (number of edges, clustering coefficient, average path length) failed

From Discrete Hopping to Continuum Modeling on Vicinal Surfaces with Applications to Si(001) Electromigration

Coarse-grained modeling of dynamics on vicinal surfaces concentrates on the diffusion of adatoms on terraces with boundary conditions at sharp steps, as first studied by Burton, Cabrera and Frank (BCF). Recent electromigration experiments on vicinal Si surfaces suggest the need for more general boundary conditions in a BCF approach. We study a discrete 1D hopping model that takes into account asymmetry in the hopping rates in the region around a step and the finite probability of incorporation into the solid at the step site. By expanding the continuous concentration field in a Taylor series evaluated at discrete sites near the step, we relate the kinetic coefficients and permeability rate in general sharp step models to the physically suggestive parameters of the hopping models. In particular we find that both the kinetic coefficients and permeability rate can be negative when diffusion is faster near the step than on terraces. These ideas are used to provide an understanding of recent electromigration experiment on Si(001) surfaces where step bunching is induced by an electric field directed at various angles to the steps.Comment: 10 pages, 4 figure

Deformations of Lie Algebras using σ\sigma-derivations

In this article we develop an approach to deformations of the Witt and Virasoro algebras based on $\sigma$-derivations. We show that $\sigma$-twisted Jacobi type identity holds for generators of such deformations. For the $\sigma$-twisted generalization of Lie algebras modeled by this construction, we develop a theory of central extensions. We show that our approach can be used to construct new deformations of Lie algebras and their central extensions, which in particular include naturally the $q$-deformations of the Witt and Virasoro algebras associated to $q$-difference operators, providing also corresponding q-deformed Jacobi identities.Comment: 52 page