On the stability of periodic orbits in delay equations with large delay

We prove a necessary and sufficient criterion for the exponential stability of periodic solutions of delay differential equations with large delay. We show that for sufficiently large delay the Floquet spectrum near criticality is characterized by a set of curves, which we call asymptotic continuous spectrum, that is independent on the delay.Comment: postprint versio

Meereswirtschaft in Europa : rechtliche und ökonomische Rahmenbedingungen für deutsche Unternehmen.

Meeresnutzung; Meeresboden; Meeresbergbau; Seerecht; Erdgasvorkommen; Fischerei; EU-Staaten; Norwegen; Deutschland;

Optimization of double pulse pumping for Ni-like Sm x-ray lasers

We report a systematic study of double pulse pumping of the Ni-like Sm x-ray laser at 73 Angstrom, currently the shortest wavelength saturated x-ray laser. It is found that the Sm x-ray laser output can change by orders of magnitude when the intensity ratio of the pumping pulses and their relative delay are varied. Optimum pumping conditions are found and interpreted in terms of a simple model. (C) 1999 American Institute of Physics. [S0021-8979(99)07102-9]

Phase sensitive excitability of a limit cycle

The classical notion of excitability refers to an equilibrium state that shows under the influence of perturbations a nonlinear threshold-like behavior. Here, we extend this concept by demonstrating how periodic orbits can exhibit a specific form of excitable behavior where the nonlinear threshold-like response appears only after perturbations applied within a certain part of the periodic orbit, i.e the excitability happens to be phase sensitive. As a paradigmatic example of this concept we employ the classical FitzHugh-Nagumo system. The relaxation oscillations, appearing in the oscillatory regime of this system, turn out to exhibit a phase sensitive nonlinear threshold-like response to perturbations, which can be explained by the nonlinear behavior in the vicinity of the canard trajectory. Triggering the phase sensitive excitability of the relaxation oscillations by noise we find a characteristic non-monotone dependence of the mean spiking rate of the relaxation oscillation on the noise level. We explain this non-monotone dependence as a result of an interplay of two competing effects of the increasing noise: the growing efficiency of the excitation and the degradation of the nonlinear response

Compositional Analysis of Lignocellulosic Feedstocks. 2. Method Uncertainties

The most common procedures for characterizing the chemical components of lignocellulosic feedstocks use a two-stage sulfuric acid hydrolysis to fractionate biomass for gravimetric and instrumental analyses. The uncertainty (i.e., dispersion of values from repeated measurement) in the primary data is of general interest to those with technical or financial interests in biomass conversion technology. The composition of a homogenized corn stover feedstock (154 replicate samples in 13 batches, by 7 analysts in 2 laboratories) was measured along with a National Institute of Standards and Technology (NIST) reference sugar cane bagasse, as a control, using this laboratory's suite of laboratory analytical procedures (LAPs). The uncertainty was evaluated by the statistical analysis of these data and is reported as the standard deviation of each component measurement. Censored and uncensored versions of these data sets are reported, as evidence was found for intermittent instrumental and equipment problems. The censored data are believed to represent the “best case” results of these analyses, whereas the uncensored data show how small method changes can strongly affect the uncertainties of these empirical methods. Relative standard deviations (RSD) of 1−3% are reported for glucan, xylan, lignin, extractives, and total component closure with the other minor components showing 4−10% RSD. The standard deviations seen with the corn stover and NIST bagasse materials were similar, which suggests that the uncertainties reported here are due more to the analytical method used than to the specific feedstock type being analyzed