Stabilization of darkand vortex parametric spatial solitons
ABSTRACT We demonstrate that a weak defocusing Kerr effect in an optical medium with predominantly quadratic [or chi((2))] nonlinear response can eliminate the parametric modulational instability of plane waves, leading to the existence of stable two-wave dark and vortex spatial solitons.
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ABSTRACT: Batch processes are commonly operated in multiple phases; phase-based approaches are intuitively well suited for batch process monitoring and quality prediction. In this paper, we therefore propose a phase-based approach to online prediction of end-of-batch quality. Our framework integrates dynamic feature synchronization and dynnamic time warping (DTW) with Dynamic Partial Least Square (DPLS). The Singular Point concept  is applied to divide process trajectories into phases with similar dynamics. The challenge of unequal phase lengths is solved by using DTW to equalize the phase trajectories from different runs. A DPLS model  is subsequently built between each phase and the final quality variables. Using a well-known simulation, PenSim, we show that this phase-based DPLS (PDPLS) outperforms original DPLS in both monitoring as well as online prediction of end-of-batch quality.
Article: Chapter 4 Singular optics