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

Simultaneous 2D-Single Shot Imaging of OH Concentrations and Temperature Fields in a SI Engine Simulator

Two-dimensional (2D) temperature measurements in engines are required for the detailed understanding of the combustion process. Because of the unsteady and turbulent nature of engine combustion, these measurements must be performed on a single-shot basis to obtain cycle-resolved results. Details of the flame front structure are also important to know for the numerical modeling of internal combustion processes. Simultaneous measurements of temperature and hydroxyl radical distributions provide such data sets. The combustion of methane in a fully transparent square piston engine was studied with a combination of 2D laser-induced fluorescence of hydroxyl radicals and 2D Rayleigh scattering. A tunable KrF excimer laser at 248 nm was used for the measurementsThe wavelength of the laser was tuned to excite the P2(8) transition in the OH (3,0) band of the A-X system. Spectral filtering of the resulting fluorescence to detect solely the fluorescence from the (3,2) band significantly reduces the effect of collisional quenching imposed to the fluorescence to the predissociating v_=3 level by vibrational energy transfer (VET) to lower vibrational levels. Using a second camera, which only records the Rayleigh signals after appropriate filtering, allows the simultaneous measurement of temperature fields with a single laser. The analysis of corresponding OH and temperature images allowed the decision that the combustion conditions are in a regime where the flamelet approach for modeling is appropriate. Good agreement with model predictions has been achieved for the peak temperatures.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86753/1/Sick49.pd

3D simulations of gas puff effects on edge density and ICRF coupling in ASDEX Upgrade

In recent experiments, a local gas puff was found to be an effective way to tailor the scrape-off layer (SOL) density and improve the ion cyclotron range of frequency (ICRF) power coupling in tokamaks. In order to quantitatively reproduce these experiments, to understand the corresponding physics and to optimize the gas valve positions and rates, simulations were carried out with the 3D edge plasma transport code EMC3-EIRENE in ASDEX Upgrade. An inter-ELM phase of an H-mode discharge with a moderate gas puff rate (1.2 x 10(22) electrons s(-1)) is used in our simulations. We simulated cases with gas puff in the lower divertor, the outer mid-plane and the top of the machine while keeping other conditions the same. Compared with the lower divertor gas puff, the outer mid-plane gas puff can increase the local density in front of the antennas most effectively, while a toroidally uniform but significantly smaller enhancement is found for the top gas puff. Good agreement between our simulations and experiments is obtained. With further simulations, the mechanisms of SOL density tailoring via local gas puffing and the strategies of gas puff optimization are discussed in the paper