A characterization of Dynkin elements

We give a characterization of the Dynkin elements of a simple Lie algebra. Namely, we prove that one-half of a Dynkin element is the unique point of minimal length in its N-region. In type A_n this translates into a statement about the regions determined by the canonical left Kazhdan-Lusztig cells. Some possible generalizations are explored in the last section.Comment: 9 page

Voice Therapy Techniques in Combination with the Group Therapy Setting for Individuals with Parkinson’s Disease

This report aims to provide background information related to voicing in Parkinson’s Disease (PD), review the various therapeutic approaches used to benefit individuals diagnosed with PD, and examine how voice impairments affect the lives of individuals with PD. Specifically, therapy techniques focusing on voice and techniques applied in the group therapy setting will be reviewed. PD has a multitude of consequences on an individual’s life, and speech is an area that is greatly affected. This project will highlight some of the interventions that can positively impact the lives of those with Parkinson’s Disease and reflect on how the group therapy setting can enhance their therapy experience. Research in support of this project has been gathered through on-site evaluation and therapy observations in addition to a literature review; this permits a comparison between previous findings and what is practiced in the clinical setting. Additionally, to measure the impact of voice impairments on the quality of life of individuals with PD, an alternative version of the Voice Handicap Index was administered. Using these methods, I was able to gain valuable insight in the role of the speech-language pathologist in treating clients with PD through my observation of a diagnostic evaluation, as well as through leading multiple sessions through the Voice Clinic

Characterization of Ion Acceleration Processes in a Surface ECR Plasma Source

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76528/1/AIAA-2008-4536-812.pd

Development of a Microwave Cusp Accelerator Driven by Electron Cyclotron Resonance

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/83621/1/AIAA-2010-6518-215.pd

Nonlinear oscillations of gas bubbles submerged in water: implications for plasma breakdown

Gas bubbles submerged in a dielectric liquid and driven by an electric field can undergo dramatic changes in both shape and volume. In certain cases, this deformation can enhance the distribution of the applied field inside the bubble as well as decrease the internal gas pressure. Both effects will tend to facilitate plasma formation in the gas volume. A practical realization of these two effects could have a broad impact on the viability of liquid plasma technologies, which tend to suffer from high voltage requirements. In this experiment, bubbles of diameter 0.4–0.7 mm are suspended in the node of a 26.4 kHz underwater acoustic standing wave and excited into nonlinear shape oscillations using ac electric fields with amplitudes of 5–15 kV cm −1 . Oscillations of the deformed bubble are photographed with a high-speed camera operating at 5130 frames s −1 and the resulting images are decomposed into their axisymmetric spherical harmonic modes, ##IMG## [http://ej.iop.org/images/0022-3727/45/41/415203/jphysd431220ieqn001.gif] {$Y_l^0$ , using an edge detection algorithm. Overall, the bubble motion is dominated by the first three even modes l = 0, 2 and 4. Electrostatic simulations of the deformed bubble's internal electric field indicate that the applied field is enhanced by as much as a factor of 2.3 above the nominal applied field. Further simulation of both the pure l = 2 and l = 4 modes predicts that with additional deformation, the field enhancement factors could reach as much as 10–50.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98592/1/0022-3727_45_41_415203.pd

Hierarchical solutions of the Sherrington-Kirkpatrick model: Exact asymptotic behavior near the critical temperature

We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a spin glass. We present a general scheme for deriving an exact asymptotic behavior near the critical temperature of the solution with an arbitrary number of discrete hierarchies of the broken replica symmetry. We show that all solutions with finite-many hierarchies are unstable and only the scheme with infinite-many hierarchies becomes marginally stable. We show how the solutions from the discrete replica-symmetry-breaking scheme go over to the continuous one with increasing the number of hierarchies.Comment: REVTeX4, 11 pages, no figure