A method to construct refracting profiles

We propose an original method for determining suitable refracting profiles between two media to solve two related problems: to produce a given wave front from a single point source after refraction at the refracting profile, and to focus a given wave front in a fixed point. These profiles are obtained as envelopes of specific families of Cartesian ovals. We study the singularities of these profiles and give a method to construct them from the data of the associated caustic.Comment: 12 pages, 5 figure

The Rich Globular Cluster System of Abell 1689 and the Radial Dependence of the Globular Cluster Formation Efficiency

We study the rich globular cluster (GC) system in the center of the massive cluster of galaxies Abell 1689 (z=0.18), one of the most powerful gravitational lenses known. With 28 HST/ACS orbits in the F814W bandpass, we reach magnitude I_814=29 with >90% completeness and sample the brightest ~5% of the GC system. Assuming the well-known Gaussian form of the GC luminosity function (GCLF), we estimate a total population of N(GC_total) = 162,850 GCs within a projected radius of 400kpc. As many as half may comprise an intracluster component. Even with the sizable uncertainties, which mainly result from the uncertain GCLF parameters, this is by far the largest GC system studied to date. The specific frequency S_N is high, but not uncommon for central galaxies in massive clusters, rising from S_N~5 near the center to ~12 at large radii. Passive galaxy fading would increase S_N by ~20% at z=0. We construct the radial mass profiles of the GCs, stars, intracluster gas, and lensing-derived total mass, and we compare the mass fractions as a function of radius. The estimated mass in GCs, M(GC_total)=3.9x10^10 Msun, is comparable to ~80% of the total stellar mass of the Milky Way. The shape of the GC mass profile appears intermediate between those of the stellar light and total cluster mass. Despite the extreme nature of this system, the ratios of the GC mass to the baryonic and total masses, and thus the GC formation efficiency, are typical of those in other rich clusters when comparing at the same physical radii. The GC formation efficiency is not constant, but varies with radius, in a manner that appears similar for different clusters; we speculate on the reasons for this similarity in profile.Comment: 13 pages, 11 figures; accepted for publication in Ap

Phase Behavior of Blends of Linear and Branched Polyethylenes on Micron-Length Scales via Ultra-Small-Angle Neutron Scattering (USANS)

SANS experiments on blends of linear, high density (HD) and long chain branched, low density (LD) polyethylenes indicate that these systems form a one-phase mixture in the melt. However, the maximum spatial resolution of pinhole cameras is approximately equal to 103Å and it has therefore been suggested that data might also be interpreted as arising from a bi-phasic melt with large a particle size (~ 1 µm), because most of the scattering from the different phases would not be resolved. We have addressed this hypothesis by means of USANS experiments, which confirm that HDPEILDPE blends are homogenous in the melt on length scales up to 20 µm. We have also studied blends of HDPE and short-chain branched linear low density polyethylenes (LLDPEs), which phase separate when the branch content is sufficiently high. LLDPEs prepared with Ziegler-Natta catalysts exhibit a wide distribution of compositions, and may therefore be thought of as a �blend� of different species. When the composition distribution is broad enough, a fraction of highly branched chains may phase separate on µm-length scales, and USANS has also been used to quantify this phenomenon

Mesoscopic effects in tunneling between parallel quantum wires

We consider a phase-coherent system of two parallel quantum wires that are coupled via a tunneling barrier of finite length. The usual perturbative treatment of tunneling fails in this case, even in the diffusive limit, once the length L of the coupling region exceeds a characteristic length scale L_t set by tunneling. Exact solution of the scattering problem posed by the extended tunneling barrier allows us to compute tunneling conductances as a function of applied voltage and magnetic field. We take into account charging effects in the quantum wires due to applied voltages and find that these are important for 1D-to-1D tunneling transport.Comment: 8 pages, 7 figures, improved Figs., added Refs. and appendix, to appear in Phys. Rev.

High-Frequency (> 100 GHz) Electronic Devices

Contains reports on four research projects, the research facility and a list of publications.Defense Advanced Research Projects Agency Contract MDA972-90-C-0021National Aeronautics and Space Administration Grant NAG2-693National Science Foundation Grant ECS 91-0933

Parameter identification problems in the modelling of cell motility

We present a novel parameter identification algorithm for the estimation of parameters in models of cell motility using imaging data of migrating cells. Two alternative formulations of the objective functional that measures the difference between the computed and observed data are proposed and the parameter identification problem is formulated as a minimisation problem of nonlinear least squares type. A Levenberg–Marquardt based optimisation method is applied to the solution of the minimisation problem and the details of the implementation are discussed. A number of numerical experiments are presented which illustrate the robustness of the algorithm to parameter identification in the presence of large deformations and noisy data and parameter identification in three dimensional models of cell motility. An application to experimental data is also presented in which we seek to identify parameters in a model for the monopolar growth of fission yeast cells using experimental imaging data. Our numerical tests allow us to compare the method with the two different formulations of the objective functional and we conclude that the results with both objective functionals seem to agree

High-Frequency (> 100 GHz) Electronic Devices

Contains reports on five research projects and a list of publications.MIT Lincoln LaboratoryNational Aeronautics and Space Administration Grant NAG2-693National Science Foundation Grant ECS 91-09330Defense Advanced Research Projects Agency Contract MDA972-90-C-0021U.S. Army - Research Office Grant DAAL03-92-G-025

High-Frequency (> 100 GHz) and High-Speed (< 1 ps) Electronic Devices

Contains reports on six research projects and a list of publications.MIT Research Laboratory of Electronics Postdoctoral FellowshipNational Science Foundation Grant DMR 90-22933MIT Lincoln Laboratory Advanced Concept ProgramAdvanced Research Projects Agency Contract MDA972-90-C-0021MIT Lincoln LaboratoryNational Aeronautics and Space Administration Grant NAG2-693U.S. Army Research Office Grant DAAL03-92-G-025

Campus Mental Health: Implications for Instructors Supporting Students

The recent escalation in student suicides due to mental health problems has encouraged higher education institutions to not only modify their overall support structures, but to also (re)define the role of faculty and staff. Despite the increased attention given to student mental health in Canadian higher education institutions, little is known and understood about how instructors view their role as supporters or promoters of student mental health. The purpose of this study was to explore the role of college instructors in supporting students with mental health problems or illnesses. Participants were 42 instructors between the ages of 25 to 64 from Molize College in Toronto, Ontario. Qualitative ethnography was employed to gather data from participants, specifically through a survey questionnaire and interviews. A constructivist framework was adopted to analyze and understand the values, perceptions, meanings, and practices post-secondary instructors carry around notions of student mental health and intervention. Findings revealed that instructors were generally aware of student mental health concerns in post-secondary institutions, but that greater awareness was still warranted, namely in the areas of instructor mental health and location of support services. Findings also demonstrated that most instructors evaluated their knowledge and confidence in relation to student mental health as poor, which was often credited to limited relevant professional development and training. Additionally, data indicated that instructors carried skepticism towards the role of some student support services departments, as well as towards their own role when supporting the mental health and well-being of students. On a final note, findings revealed that instructors commonly employed four practices to support the mental health and well-being of students: conversation, referral, accommodations, and curricular inclusion and instruction. Future studies are encouraged to acknowledge the narratives of instructors through ethnographic inquiry, to allow for greater insights into their awareness, knowledge/confidence, responsibilities, and practices when it comes to supporting the mental health and well-being of students in higher education settings. Incorporating the instructor may not be a panacea for the shortcomings of current mental health policies and practices in higher education settings, but it can certainly represent a colossal step in that direction. KEYWORDS: student mental health, higher education, instructor