Surface-plasmon-polariton wave propagation guided by a metal slab in a sculptured nematic thin film

Surface-plasmon-polariton~(SPP) wave propagation guided by a metal slab in a periodically nonhomogeneous sculptured nematic thin film~(SNTF) was studied theoretically. The morphologically significant planes of the SNTF on both sides of the metal slab could either be aligned or twisted with respect to each other. The canonical boundary-value problem was formulated, solved for SPP-wave propagation, and examined to determine the effect of slab thickness on the multiplicity and the spatial profiles of SPP waves. Decrease in slab thickness was found to result in more intense coupling of two metal/SNTF interfaces. But when the metal slab becomes thicker, the coupling between the two interfaces reduces and SPP waves localize to one of the two interfaces. The greater the coupling between the two metal/SNTF interfaces, the smaller is the phase speed.Comment: 17 page

Grating-coupled excitation of multiple surface plasmon-polariton waves

The excitation of multiple surface-plasmon-polariton (SPP) waves of different linear polarization states and phase speeds by a surface-relief grating formed by a metal and a rugate filter, both of finite thickness, was studied theoretically, using rigorous coupled-wave-analysis. The incident plane wave can be either p or s polarized. The excitation of SPP waves is indicated by the presence of those peaks in the plots of absorbance vs. the incidence angle that are independent of the thickness of the rugate filter. The absorbance peaks representing the excitation of s-polarized SPP waves are narrower than those representing p-polarized SPP waves. Two incident plane waves propagating in different directions may excite the same SPP wave. A line source could excite several SPP waves simultaneously

Computing ?-Stretch Paths in Drawings of Graphs

Let f be a drawing in the Euclidean plane of a graph G, which is understood to be a 1-dimensional simplicial complex. We assume that every edge of G is drawn by f as a curve of constant algebraic complexity, and the ratio of the length of the longest simple path to the the length of the shortest edge is poly(n). In the drawing f, a path P of G, or its image in the drawing ?=f(P), is ?-stretch if ? is a simple (non-self-intersecting) curve, and for every pair of distinct points p?P and q?P, the length of the sub-curve of ? connecting f(p) with f(q) is at most ?||f(p)-f(q)?, where ?.? denotes the Euclidean distance. We introduce and study the ?-stretch Path Problem (?SP for short), in which we are given a pair of vertices s and t of G, and we are to decide whether in the given drawing of G there exists a ?-stretch path P connecting s and t. The ?SP also asks that we output P if it exists. The ?SP quantifies a notion of "near straightness" for paths in a graph G, motivated by gerrymandering regions in a map, where edges of G represent natural geographical/political boundaries that may be chosen to bound election districts. The notion of a ?-stretch path naturally extends to cycles, and the extension gives a measure of how gerrymandered a district is. Furthermore, we show that the extension is closely related to several studied measures of local fatness of geometric shapes. We prove that ?SP is strongly NP-complete. We complement this result by giving a quasi-polynomial time algorithm, that for a given ?>0, ??O(poly(log |V(G)|)), and s,t?V(G), outputs a ?-stretch path between s and t, if a (1-?)?-stretch path between s and t exists in the drawing

Biologically Informed Individual-Based Network Model for Rift Valley Fever in the US and Evaluation of Mitigation Strategies

Citation: Scoglio, C. M., Bosca, C., Riad, M. H., Sahneh, F. D., Britch, S. C., Cohnstaedt, L. W., & Linthicum, K. J. (2016). Biologically Informed Individual-Based Network Model for Rift Valley Fever in the US and Evaluation of Mitigation Strategies. Plos One, 11(9), 26. doi:10.1371/journal.pone.0162759Rift Valley fever (RVF) is a zoonotic disease endemic in sub-Saharan Africa with periodic outbreaks in human and animal populations. Mosquitoes are the primary disease vectors; however, Rift Valley fever virus (RVFV) can also spread by direct contact with infected tissues. The transmission cycle is complex, involving humans, livestock, and multiple species of mosquitoes. The epidemiology of RVFV in endemic areas is strongly affected by climatic conditions and environmental variables. In this research, we adapt and use a network-based modeling framework to simulate the transmission of RVFV among hypothetical cattle operations in Kansas, US. Our model considers geo-located livestock populations at the individual level while incorporating the role of mosquito populations and the environment at a coarse resolution. Extensive simulations show the flexibility of our modeling framework when applied to specific scenarios to quantitatively evaluate the efficacy of mosquito control and livestock movement regulations in reducing the extent and intensity of RVF outbreaks in the United States

Towards the Formalization of Fractional Calculus in Higher-Order Logic

Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to analyze a wide class of physical systems in various fields of science and engineering. In this paper, we describe an ongoing project which aims at formalizing the basic theories of fractional calculus in the HOL Light theorem prover. Mainly, we present the motivation and application of such formalization efforts, a roadmap to achieve our goals, current status of the project and future milestones.Comment: 9 page

Very low-grade metamorphism of sedimentary rocks of the Meliata unit; Western Carpathians, Slovakia: implications of phyllosilicate characteristics.

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