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2014

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Articles 991 - 994 of 994

Full-Text Articles in Mathematics

Krein-Langer Factorization And Related Topics In The Slice Hyperholomorphic Setting, Daniel Alpay, Fabrizio Colombo, Irene Sabadini Jan 2014

Krein-Langer Factorization And Related Topics In The Slice Hyperholomorphic Setting, Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

We study various aspects of Schur analysis in the slice hyperholomorphic setting. We present two sets of results: first, we give new results on the functional calculus for slice hyperholomorphic functions. In particular, we introduce and study some properties of the Riesz projectors. Then we prove a Beurling-Lax type theorem, the so-called structure theorem. A crucial fact which allows to prove our results, is the fact that the right spectrum of a quaternionic linear operator and the point S-spectrum coincide. Finally, we study the Krein-Langer factorization for slice hyperholomorphic generalized Schur functions. Both the Beurling-Lax type theorem and the Krein-Langer …

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Network-Based Assessments Of Percolation-Induced Current Distributions In Sheared Rod Macromolecular Dispersions, Feng Shi, Simi Wang, M. Gregory Forest, Peter J. Mucha, Ruhai Zhou Jan 2014

Network-Based Assessments Of Percolation-Induced Current Distributions In Sheared Rod Macromolecular Dispersions, Feng Shi, Simi Wang, M. Gregory Forest, Peter J. Mucha, Ruhai Zhou

Mathematics & Statistics Faculty Publications

Conducting high-aspect-ratio rods with 1-10 nm-scale diameters dispersed in poorly conducting matrices at extremely low, O(1%), volume fractions induce dramatic gains in bulk conductivity at rod percolation threshold. Experimentally [Nan, Shen, and Ma, Annu. Rev. Mater. Res., 40 (2010), pp. 131-151], bulk conductivity abandons the prepercolation, linear scaling with volume fraction that follows from homogenization theory [Zheng et al., Adv. Funct. Mater., 15 (2005), pp. 627-638], and then postpercolation jumps orders of magnitude to approach that of the pure rod macromolecular phase as predicted by classical percolation theory [Stauffer and Aharony, Introduction to Percolation Theory, CRC …

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Scalar Wave Scattering By Two-Layer Radial Inhomogeneities, Umaporn Nuntaplook, John Adam Jan 2014

Scalar Wave Scattering By Two-Layer Radial Inhomogeneities, Umaporn Nuntaplook, John Adam

Mathematics & Statistics Faculty Publications

It is shown that the iteration technique gives a better approximation for the problem with long wavelengths.

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Rheological Signatures In Limit Cycle Behaviour Of Dilute, Active, Polar Liquid Crystalline Polymers In Steady Shear, M. Gregory Forest, Panon Phuworawong, Qi Wang, Ruhai Zhou Jan 2014

Rheological Signatures In Limit Cycle Behaviour Of Dilute, Active, Polar Liquid Crystalline Polymers In Steady Shear, M. Gregory Forest, Panon Phuworawong, Qi Wang, Ruhai Zhou

Mathematics & Statistics Faculty Publications

We consider the dilute regime of active suspensions of liquid crystalline polymers (LCPs), addressing issues motivated by our kinetic model and simulations in Forest et al. (Forest et al. 2013 Soft Matter 9, 5207-5222 (doi:10.1039/c3sm27736d)). In particular, we report unsteady two-dimensional heterogeneous flow-orientation attractors for pusher nanorod swimmers at dilute concentrations where passive LCP equilibria are isotropic. These numerical limit cycles are analogous to longwave (homogeneous) tumbling and kayaking limit cycles and two-dimensional heterogeneous unsteady attractors of passive LCPs in weak imposed shear, yet these states arise exclusively at semi-dilute concentrations where stable equilibria are nematic. The results in Forest …

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