74 research outputs found
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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