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The spatially varying intensity in a standing wave resonator leads to spatial hole burning in the gain medium of a laser. The spatial hole burning changes the gain of different longitudinal modes and can thus determine the optical spectrum of the laser. We simulate this longitudinal mode competition in standing wave resonators of thin-disk lasers. The resulting optical spectra of the laser are compared to measured optical spectra. We examine two types of resonators: I-resonators and V-resonators with different angles of incidence. In V-resonators, the non-normal incidence of the laser beam on the disk lifts the degeneracy of the polarization. Experiments show that the slight gain advantage for the p-polarization does not lead to polarized emission. For both types of resonators, the measured spectra are in good agreement with the simulated ones. The simulations allow to study the influence of spectral intra-cavity losses on the optical spectrum of a thin-disk laser.
Different model structures were compared to simulate the characteristic process variables of the anaerobic digestion of maize, sugar beet and grain silage. Depending on the type and number of the required components, it can be shown that in comparison to the complex Anaerobic Digestion Model No. 1 (ADM1) different simplified model structures can describe the gas production rate, ammonia nitrogen and acetate concentration or pH value equally well. Since the reduction of the predominantly fast kinetics of the methanogenesis, acetogenesis or acidogenesis will only have little effect on the simulation of the specific gas production, it can be proven that the hydrolysis is the rate-limiting step during the uninhibited anaerobic digestion of complex particulate substrates. However, the stoichiometric comparison reveals that the model protein gelatine is not suitable for a representative characterization of agricultural energy crops.