A systematic study of spiral waves in a realistic reaction-diffusion model describing the isothermal CO oxidation on Pt ( 1 IO) is carried out. Spirals exist under oscillatory, excitable, and bistable (doubly metastable) conditions. In the excitable region, two separate meandering transitions occur, both when the time scales become strongly different and when they become comparable. By the assumption of surface defects of the order of 10 pm, to which the spirals can be pinned, the continuous distribution of wavelengths observed experimentally can be explained. An external periodic perturbation generally causes a meandering motion of a free spiral, while a straight drift results, if the period of the perturbation divided by the rotation period is a natural number.
Scatterometry is frequently used as a non-imaging indirect optical method to reconstruct the critical dimensions (CD) of periodic nanostructures. A particular promising direction is EUV scatterometry with wavelengths in the range of 13 - 14 nm. The conventional approach to determine CDs is the minimization of a least squares function (LSQ). In this paper, we introduce an alternative method based on the maximum likelihood estimation (MLE) that determines the statistical error model parameters directly from measurement data. By using simulation data, we show that the MLE method is able to correct the systematic errors present in LSQ results and improves the accuracy of scatterometry. In a second step, the MLE approach is applied to measurement data from both extreme ultraviolet (EUV) and deep ultraviolet (DUV) scatterometry. Using MLE removes the systematic disagreement of EUV with other methods such as scanning electron microscopy and gives consistent results for DUV.
We show that the parametrically driven nonlinear Schrödinger equation has wide classes of travelling soliton solutions, some of which are stable. For small driving strengths stable nonpropagating and moving solitons co-exist while strongly forced solitons can only be stable when moving sufficiently fast. PACS number(s): 05.45.Yv, 05.45.Xt
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