Some graphs with small second eigenvalue

For any prime,p, we construct a Cayley graph on the group,G, of affine linear transformations ofℤ/pℤ of degree 2(p−1) and second eigenvalue with the following special property: the adjacency matrix of the graph is supported on the “blocks” associated to the trivial representation and the irreducible representation of sizep−1. SinceG is of orderp(p−1), the correspondingt-uniform Cayley hypergraph has essentially optimal second eigenvalue for this degree and size of the graph (see [2] for definitions). En route we give, for any integerk>1, a simple Cayley graph onp ^k nodes of degreep of second eigenvalue . The author wishes to acknowledge the National Science Foundation for supporting this research in part under Grant CCR-8858788, and the Office of Naval Research under Grant N00014-87-K-0467.     

Thermal multifragmentation in p + Au interactions at 2.16, 3.6 and 8.1 GeV incident energies

Multiple emission of intermediate-mass fragments has been studied for the collisions p + Au at 2.16, 3.6 and 8.1 GeV with the FASA setup. The mean IMF multiplicities for events with at least one IMF are equal to 1.7, 1.9 and 2.1 (±0.2) respectively. The multiplicity, charge distributions and kinetic energy spectra of IMF are described in the framework of a intranuclear cascade model followed by the statistical multifragmentation model. However, between the two parts of the calculation the excitation energies and the residual masses and charges are modified to take into account the losses during expansion. The results support a scenario of true thermal multifragmentation of a hot and expanded target spectator. Received: 15 December 1997 / Revised version: 24 April 1998     

Rank one lightly mixing

A rank one transformationT was constructed by Chacón that is weakly mixing but not mixing. We will show thatT is lightly mixing, not partially mixing, and not lightly 2-mixing. Partially supported by an NSF Postdoctoral Research Fellowship.     

Floating Electrode Dielectric Barrier Discharge Plasma in Air Promoting Apoptotic Behavior in Melanoma Skin Cancer Cell Lines

Initiation of apoptosis, or programmed cell death, is an important issue in cancer treatment as cancer cells frequently have acquired the ability to block apoptosis and thus are more resistant to chemotherapeutic drugs. Targeted and perhaps selective destruction of cancerous tissue is desirable for many reasons, ranging from the enhancement of or aid to current medical methods to problems currently lacking a solution, i.e., lung cancer. Demonstrated in this publication is the inactivation (killing) of human Melanoma skin cancer cell lines, in vitro, by Floating Electrode Dielectric Barrier Discharge (FE-DBD) plasma. Not only are these cells shown to be killed immediately by high doses of plasma treatment, but low doses are shown to promote apoptotic behavior as detected by TUNEL staining and subsequent flow cytometry. It is shown that plasma acts on the cells directly and not by “poisoning” the solution surrounding the cells, even through a layer of such solution. Potential mechanisms of interaction of plasma with cells are discussed and further steps are proposed to develop an understanding of such systems.     

Optimal design of an optical lens

We wish to construct an optimal optical lens, in the sense that it focuses all rays from a given source onto a given focal point. The construction can be reduced mathematically to a global study of a system of two nonlinear functional differential equations. We prove that this system has precisely two analytic solutions.     

Reconstruction of large coherent structures from SPIV measurements in a forced turbulent mixing layer

A procedure is suggested here for reconstructing the time variation of a three-dimensional (3D) coherent velocity field, based on applying Least Square Method to a very limited number of phase-locked measurements. The measurements are performed in a spanwise plane of a forced turbulent mixing layer by employing the stereo particle image velocimetry system. The forcing is produced by oscillating two- and three-dimensional (3D) flappers placed at the edge of the splitter plate. The feasibility and validity of the procedure for velocity field reconstruction are checked by using Hot Wire Measurements. Very clear patterns are observed of two types of coherent structures: spanwise K-H billows (rolls) and streamwise vortices. These are due to primary and secondary instabilities and their time evolution is presented.