Uniaxial and biaxial soft deformations of nematic elastomers

We give a geometric interpretation of the soft elastic deformation modes of nematic elastomers, with explicit examples, for both uniaxial and biaxial nematic order. We show the importance of body rotations in this non-classical elasticity and how the invariance under rotations of the reference and target states gives soft elasticity (the Golubovic and Lubensky theorem). The role of rotations makes the Polar Decomposition Theorem vital for decomposing general deformations into body rotations and symmetric strains. The role of the square roots of tensors is discussed in this context and that of finding explicit forms for soft deformations (the approach of Olmsted).Comment: 10 pages, 10 figures, RevTex, AmsTe

My Angeline

https://digitalcommons.library.umaine.edu/mmb-vp/4756/thumbnail.jp

Spin bearing retainer design optimization

The dynamics behavior of spin bearings for momentum wheels (control-moment gyroscope, reaction wheel assembly) is critical to satellite stability and life. Repeated bearing retainer instabilities hasten lubricant deterioration and can lead to premature bearing failure and/or unacceptable vibration. These instabilities are typically distinguished by increases in torque, temperature, audible noise, and vibration induced by increases into the bearing cartridge. Ball retainer design can be optimized to minimize these occurrences. A retainer was designed using a previously successful smaller retainer as an example. Analytical methods were then employed to predict its behavior and optimize its configuration

Development of an hp-version finite element method for computational optimal control

The purpose of this research effort was to begin the study of the application of hp-version finite elements to the numerical solution of optimal control problems. Under NAG-939, the hybrid MACSYMA/FORTRAN code GENCODE was developed which utilized h-version finite elements to successfully approximate solutions to a wide class of optimal control problems. In that code the means for improvement of the solution was the refinement of the time-discretization mesh. With the extension to hp-version finite elements, the degrees of freedom include both nodal values and extra interior values associated with the unknown states, co-states, and controls, the number of which depends on the order of the shape functions in each element. One possible drawback is the increased computational effort within each element required in implementing hp-version finite elements. We are trying to determine whether this computational effort is sufficiently offset by the reduction in the number of time elements used and improved Newton-Raphson convergence so as to be useful in solving optimal control problems in real time. Because certain of the element interior unknowns can be eliminated at the element level by solving a small set of nonlinear algebraic equations in which the nodal values are taken as given, the scheme may turn out to be especially powerful in a parallel computing environment. A different processor could be assigned to each element. The number of processors, strictly speaking, is not required to be any larger than the number of sub-regions which are free of discontinuities of any kind

Pathways: Augmenting interoperability across scholarly repositories

In the emerging eScience environment, repositories of papers, datasets, software, etc., should be the foundation of a global and natively-digital scholarly communications system. The current infrastructure falls far short of this goal. Cross-repository interoperability must be augmented to support the many workflows and value-chains involved in scholarly communication. This will not be achieved through the promotion of single repository architecture or content representation, but instead requires an interoperability framework to connect the many heterogeneous systems that will exist. We present a simple data model and service architecture that augments repository interoperability to enable scholarly value-chains to be implemented. We describe an experiment that demonstrates how the proposed infrastructure can be deployed to implement the workflow involved in the creation of an overlay journal over several different repository systems (Fedora, aDORe, DSpace and arXiv).Comment: 18 pages. Accepted for International Journal on Digital Libraries special issue on Digital Libraries and eScienc