Geometry of Warped Product Semi-Invariant Submanifolds of a Locally Riemannian Product Manifold

2000 Mathematics Subject Classification: 53C42, 53C15.

Next generation high density three-dimensional magnetic recording systems

This work is the first work using patterned soft underlayers in multilevel three-dimensional vertical magnetic data storage systems. The motivation stems from an exponentially growing information stockpile, and a corresponding need for more efficient storage devices with higher density. The world information stockpile currently exceeds 150EB (ExaByte=1x1018Bytes); most of which is in analog form. Among the storage technologies (semiconductor, optical and magnetic), magnetic hard disk drives are posed to occupy a big role in personal, network as well as corporate storage. However; this mode suffers from a limit known as the Superparamagnetic limit; which limits achievable areal density due to fundamental quantum mechanical stability requirements. There are many viable techniques considered to defer superparamagnetism into the 100's of Gbit/in2 such as: patterned media, Heat-Assisted Magnetic Recording (HAMR), Self Organized Magnetic Arrays (SOMA), antiferromagnetically coupled structures (AFC), and perpendicular magnetic recording. Nonetheless, these techniques utilize a single magnetic layer; and can thusly be viewed as two-dimensional in nature. In this work a novel three-dimensional vertical magnetic recording approach is proposed. This approach utilizes the entire thickness of a magnetic multilayer structure to store information; with potential areal density well into the Tbit/in2 regime. ^ There are several possible implementations for 3D magnetic recording; each presenting its own set of requirements, merits and challenges. The issues and considerations pertaining to the development of such systems will be examined, and analyzed using empirical and numerical analysis techniques. Two novel key approaches are proposed and developed: (1) Patterned soft underlayer (SUL) which allows for enhanced recording of thicker media, (2) A combinatorial approach for 3D media development that facilitates concurrent investigation of various film parameters on a predefined performance metric. A case study is presented using combinatorial overcoats of Tantalum and Zirconium Oxides for corrosion protection in magnetic media. ^ Feasibility of 3D recording is demonstrated, and an emphasis on 3D media development is emphasized as a key prerequisite. Patterned SUL shows significant enhancement over conventional "un-patterned" SUL, and shows that geometry can be used as a design tool to achieve favorable field distribution where magnetic storage and magnetic phenomena are involved. ^

Music of Today: 80 and 90 Stuart Dempster William O. "Bill" Smith October 26, 2016

Concert Program

John Frazer

John Frazer, Professor, trained at the Architectural Association, taught first at Cambridge University and then the AA in the 1970s and again in the '90s. He was Head of School of Design Research History and Criticism at the University of Ulster in the 1980s, he also ran a systems and design consultancy with his wife Julia (including projects for Cedric Price and Walter Segal) and was founder and chairman of Autographics software. He is currently Swire Chair Professor and Head of School of Design in Hong Kong.----- This is a very personal perspective on a concept of universal and future significance. It is personal, both is the sense that it is an unashamedly biased view of both the significance of the project, and the nature of that significance and because the author was personally involved as one of the consultants on GENERATOR and subsequently involved Cedric Price in its educational application at the Architectural Association. GENERATOR is still very much alive and was still developing whilst this chapter was being written.

Tangible interfaces to explain Gaudi's use of ruled-surface geometries

This paper summarises the development of a machine-readable model series for explaining Gaudi's use of ruled surface geometry in the Sagrada Familia in Barcelona, Spain. The first part discusses the modeling methods underlying the columns of the cathedral and the techniques required to translate them into built structures. The second part discusses the design and development of a tangible machine-readable model to explain column-modeling methods interactively in educational contexts such as art exhibitions. It is designed to explain the principles underlying the column design by means of physical interaction without using mathematical terms or language.

Sensitivity of proximal femoral stiffness and areal bone mineral density to changes in bone geometry and density

Areal bone mineral density (aBMD) is the most common surrogate measurement for assessing the bone strength of the proximal femur associated with osteoporosis. Additional factors, however, contribute to the overall strength of the proximal femur, primarily the anatomical geometry. Finite element analysis (FEA) is an effective and widely used computerbased simulation technique for modeling mechanical loading of various engineering structures, providing predictions of displacement and induced stress distribution due to the applied load. FEA is therefore inherently dependent upon both density and anatomical geometry. FEA may be performed on both three-dimensional and two-dimensional models of the proximal femur derived from radiographic images, from which the mechanical stiffness may be redicted. It is examined whether the outcome measures of two-dimensional FEA, two-dimensional, finite element analysis of X-ray images (FEXI), and three-dimensional FEA computed stiffness of the proximal femur were more sensitive than aBMD to changes in trabecular bone density and femur geometry. It is assumed that if an outcome measure follows known trends with changes in density and geometric parameters, then an increased sensitivity will be indicative of an improved prediction of bone strength. All three outcome measures increased non-linearly with trabecular bone density, increased linearly with cortical shell thickness and neck width, decreased linearly with neck length, and were relatively insensitive to neck-shaft angle. For femoral head radius, aBMD was relatively insensitive, with two-dimensional FEXI and threedimensional FEA demonstrating a non-linear increase and decrease in sensitivity, respectively. For neck anteversion, aBMD decreased non-linearly, whereas both two-dimensional FEXI and three dimensional FEA demonstrated a parabolic-type relationship, with maximum stiffness achieved at an angle of approximately 15o. Multi-parameter analysis showed that all three outcome measures demonstrated their highest sensitivity to a change in cortical thickness. When changes in all input parameters were considered simultaneously, three and twodimensional FEA had statistically equal sensitivities (0.41±0.20 and 0.42±0.16 respectively, p = ns) that were significantly higher than the sensitivity of aBMD (0.24±0.07; p = 0.014 and 0.002 for three-dimensional and two-dimensional FEA respectively). This simulation study suggests that since mechanical integrity and FEA are inherently dependent upon anatomical geometry, FEXI stiffness, being derived from conventional two-dimensional radiographic images, may provide an improvement in the prediction of bone strength of the proximal femur than currently provided by aBMD.

Bubble geometry and chaotic pricing behaviour

This paper is a deductive theoretical enquiry into the flow of effects from the geometry of price bubbles/busts, to price indices, to pricing behaviours of sellers and buyers, and back to price bubbles/busts. The intent of the analysis is to suggest analytical approaches to identify the presence, maturity, and/or sustainability of a price bubble. We present a pricing model to emulate market behaviour, including numeric examples and charts of the interaction of supply and demand. The model extends into dynamic market solutions myopic (single- and multi-period) backward looking rational expectations to demonstrate how buyers and sellers interact to affect supply and demand and to show how capital gain expectations can be a destabilising influence – i.e. the lagged effects of past price gains can drive the market price away from long-run market-worth. Investing based on the outputs of past price-based valuation models appear to be more of a game-of-chance than a sound investment strategy.

Relentless patterns the immersive interior

What happens when patterns become all pervasive? When pattern contagiously corrupts and saturates adjacent objects, artefacts and surfaces; blurring internal and external environment and dissolving any single point of perspective or static conception of space. Mark Taylor ruminates on the possibilities of relentless patterning in interior space in both a historic and a contemporary context.

Application of bag sampling technique for particle size distribution measurements

Bag sampling techniques can be used to temporarily store an aerosol and therefore provide sufficient time to utilize sensitive but slow instrumental techniques for recording detailed particle size distributions. Laboratory based assessment of the method were conducted to examine size dependant deposition loss coefficients for aerosols held in VelostatTM bags conforming to a horizontal cylindrical geometry. Deposition losses of NaCl particles in the range of 10 nm to 160 nm were analysed in relation to the bag size, storage time, and sampling flow rate. Results of this study suggest that the bag sampling method is most useful for moderately short sampling periods of about 5 minutes.