Uniform asymptotics of the coefficients of unitary moment polynomials

Keating and Snaith showed that the $2k^{th}$ absolute moment of the characteristic polynomial of a random unitary matrix evaluated on the unit circle is given by a polynomial of degree $k^2$. In this article, uniform asymptotics for the coefficients of that polynomial are derived, and a maximal coefficient is located. Some of the asymptotics are given in explicit form. Numerical data to support these calculations are presented. Some apparent connections between random matrix theory and the Riemann zeta function are discussed.Comment: 31 pages, 1 figure, 2 tables. A few minor misprints fixe

Powder Forming Using Dynamic Magnetic Compaction

Conventional powder forming of metals, ceramics and composites uses room temperature pressing approaches such as static uniaxial pressing, isotropic pressing - cold isostatic pressing (CIP) or elevated temperature hot isostatic pressing (HIP) methods. In this paper, description of a unique dynamic pressing approach for powder materials will be presented where very high pulse pressures (of GPa range) are applied for a short duration (of < 1 millisecond) on powders. Such a dynamic pressing offers the ability to form uniformly high density net shape parts with fine microstructures. The method can be applied to wide range of materials such as metals, ceramics, composites and soft and hard magnetic materials. A broad range of powder particle size distributions, from coarse micron size to fine nano size powders, can be used in the process. The principles of dynamic pressing method along with the summary of results on various powder material systems will be presented. The performance of parts made with dynamic method will be compared with conventional processes

Distribution of periodic torus orbits and Duke's theorem for cubic fields

We study periodic torus orbits on spaces of lattices. Using the action of the group of adelic points of the underlying tori, we define a natural equivalence relation on these orbits, and show that the equivalence classes become uniformly distributed. This is a cubic analogue of Duke's theorem about the distribution of closed geodesics on the modular surface: suitably interpreted, the ideal classes of a cubic totally real field are equidistributed in the modular 5-fold SL_3(Z)\SL_3(R)/SO_3(R). In particular, this proves (a stronger form of) the folklore conjecture that the collection of maximal compact flats in SL_3(Z)\SL_3(R)/SO_3(R) of volume less than V becomes equidistributed as V goes to infinity. The proof combines subconvexity estimates, measure classification, and local harmonic analysis.Comment: Annals of Maths. (to appear) typos corrected; references update

Processing and Characterization of Porous Alumina Ceramics with Wide Porosity Range

In recent years, porous ceramics with tailored microstructure has received wide attention in the research communities for its specialized properties. To have a customized microstructure suitable for different applications, several fabrication methods have also been developed during the last decades to manipulate porosity, pore size distribution and pore interconnectivity in the porous ceramics. In the present study, an attempt has been made to develop porous alumina ceramics with wide porosity (10-80%) using three different fabrication methods. The three methods are starch consolidation casting (SCC), polymeric sponge replica technique (SRT) as well as the combination of the two methods (SCC+SRT). A theoretical model has also been developed and validated with the experimental data to predict the porosity of the samples prepared by SCC theoretically. Alumina loading, starch content, starch types are used as the tools to develop different porosity in the samples made by starch consolidation casting. TiO2 has been used as sintering additives to improve high strength in the starch consolidated samples without compromising the porosity. The viscosity of the slurry in the range 0.05-1.19 Pa.s was found to be optimum to fabricate defect free samples by starch consolidation casting. The porosity of the samples could be varied from 20-70% in this technique. TiO2 as sintering aid was able to reduce the sintering temperature of the samples in the tune of 300oC without compromising the strength and porosity of the samples fabricated by this technique. It was observed that 10% porous samples could be developed through this technique. Particle loading of the slurry was found as an important parameter to develop different pore morphology when the samples prepared using sponge replica technique. The porosity of the samples could be varied from 75- 80% of strength 0.31-2.46 MPa by this technique. An attempt has also been made to develop hierarchical porosity in the samples while fabricated by the combination of the above two techniques. The microstructural study revealed the formation of hierarchical porosity in the samples fabricated by the combination technique. Thus, porous ceramics with porosity in the range these techniques could achieve 10-80%

Outcomes Associated With Delirium in Older Patients in Surgical ICUs

BACKGROUND: We previously noted that older adults admitted to surgical ICUs (SICUs) are at high risk for delirium. In the current study, we describe the association between the presence of delirium and complications in older SICU patients, and describe the association between delirium occurring in the SICU and functional ability and discharge placement for older patients. METHODS: Secondary analysis of prospective, observational, cohort study. Subjects were 114 consecutive patients \u3eor= 65 years old admitted to a surgical critical care service. All subjects underwent daily delirium and sedation/agitation screening during hospitalization. Outcomes prospectively recorded included SICU complication development, discharge location, and functional ability (as measured by the Katz activities of daily living instrument). RESULTS: Nearly one third of older adults (31.6%) admitted to an SICU had a complication during ICU stay. There was a strong association between SICU delirium and complication occurrence (p = 0.001). Complication occurrence preceded delirium diagnosis for 16 of 20 subjects. Subjects with delirium in the SICU were more likely to be discharged to a place other than home (61.3% vs 20.5%, p \u3c 0.0001) and have greater functional decline (67.7% vs 43.6%, p = 0.023) than nondelirious subjects. After adjusting for covariates including severity of illness and mechanical ventilation use, delirium was found to be strongly and independently associated with greater odds of being discharged to a place other than home (odds ratio, 7.20; 95% confidence interval, 1.93 to 26.82). CONCLUSIONS: Delirium in older surgical ICU patients is associated with complications and an increased likelihood of discharge to a place other than home

Advanced Motors

Project Summary Transportation energy usage is predicted to increase substantially by 2020. Hybrid vehicles and fuel cell powered vehicles are destined to become more prominent as fuel prices rise with the demand. Hybrid and fuel cell vehicle platforms are both dependent on high performance electric motors. Electric motors for transportation duty will require sizeable low-speed torque to accelerate the vehicle. As motor speed increases, the torque requirement decreases which results in a nearly constant power motor output. Interior permanent magnet synchronous motors (IPMSM) are well suited for this duty. , , These rotor geometries are configured in straight lines and semi circular arc shapes. These designs are of limited configurations because of the lack of availability of permanent magnets of any other shapes at present. We propose to fabricate rotors via a novel processing approach where we start with magnet powders and compact them into a net shape rotor in a single step. Using this approach, widely different rotor designs can be implemented for efficiency. The current limitation on magnet shape and thickness will be eliminated. This is accomplished by co-filling magnet and soft iron powders at specified locations in intricate shapes using specially designed dies and automatic powder filling station. The process fundamentals for accomplishing occurred under a previous Applied Technology Program titled, ÃÂÃÂÃÂÃÂÃÂÃÂÃÂâÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂMotors and Generators for the 21st CenturyÃÂÃÂÃÂÃÂÃÂÃÂÃÂâÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂÃÂ. New efficient motor designs that are not currently possible (or cost prohibitive) can be accomplished by this approach. Such an approach to motor fabrication opens up a new dimension in motor design. Feasibility Results We were able to optimize a IPMSM rotor to take advantage of the powder co-filling and DMC compaction processing methods. The minimum low speed torque requirement of 5 N-m can be met through an optimized design with magnet material having a Br capability of 0.2 T. This level of magnetic performance can be met with a variety of bonded magnet compositions. The torque ripple was found to drop significantly by using thinner magnet segments. The powder co-filling and subsequent compaction processing allow for thinner magnet structures to be formed. Torque ripple can be further reduced by using skewing and pole shaping techniques. The techniques can be incorporated into the rotor during the powder co-filling process

Lightweight Aluminum/Nano composites for Automotive Drive Train Applications

During Phase I, we successfully processed air atomized aluminum powders via Dynamic Magnetic Compaction (DMC) pressing and subsequent sintering to produce parts with properties similar to wrought aluminum. We have also showed for the first time that aluminum powders can be processed without lubes via press and sintering to 100 % density. This will preclude a delube cycle in sintering and promote environmentally friendly P/M processing. Processing aluminum powders via press and sintering with minimum shrinkage will enable net shape fabrication. Aluminum powders processed via a conventional powder metallurgy process produce too large a shrinkage. Because of this, sinter parts have to be machined into specific net shape. This results in increased scrap and cost. Fully sintered aluminum alloy under this Phase I project has shown good particle-to-particle bonding and mechanical properties. We have also shown the feasibility of preparing nano composite powders and processing via pressing and sintering. This was accomplished by dispersing nano silicon carbide (SiC) powders into aluminum matrix comprising micron-sized powders (<100 microns) using a proprietary process. These composite powders of Al with nano SiC were processed using DMC press and sinter process to sinter density of 85-90%. The process optimization along with sintering needs to be carried out to produce full density composites