Search Results
EDP-convergence for nonlinear fast–slow reaction systems with detailed balance*
2021, Mielke, Alexander, Peletier, Mark A., Stephan, Artur
We consider nonlinear reaction systems satisfying mass-action kinetics with slow and fast reactions. It is known that the fast-reaction-rate limit can be described by an ODE with Lagrange multipliers and a set of nonlinear constraints that ask the fast reactions to be in equilibrium. Our aim is to study the limiting gradient structure which is available if the reaction system satisfies the detailed-balance condition. The gradient structure on the set of concentration vectors is given in terms of the relative Boltzmann entropy and a cosh-type dissipation potential. We show that a limiting or effective gradient structure can be rigorously derived via EDP-convergence, i.e. convergence in the sense of the energy-dissipation principle for gradient flows. In general, the effective entropy will no longer be of Boltzmann type and the reactions will no longer satisfy mass-action kinetics.
Mode competition in broad-ridge-waveguide lasers
2020, Koester, J.-P., Putz, A., Wenzel, H., Wünsche, H.-J., Radziunas, M., Stephan, H., Wilkens, M., Zeghuzi, A., Knigge, A.
The lateral brightness achievable with high-power GaAs-based laser diodes having long and broad waveguides is commonly regarded to be limited by the onset of higher-order lateral modes. For the study of the lateral-mode competition two complementary simulation tools are applied, representing different classes of approximations. The first tool bases on a completely incoherent superposition of mode intensities and disregards longitudinal effects like spatial hole burning, whereas the second tool relies on a simplified carrier transport and current flow. Both tools yield agreeing power-current characteristics that fit the data measured for 5-23 µm wide ridges. Also, a similarly good qualitative conformance of the near and far fields is found. However, the threshold of individual modes, the partition of power between them at a given current, and details of the near and far fields show differences. These differences are the consequence of a high sensitivity of the mode competition to details of the models and of the device structure. Nevertheless, it can be concluded concordantly that the brightness rises with increasing ridge width irrespective of the onset of more and more lateral modes. The lateral brightness W mm-1at 10 MW cm-2 power density on the front facet of the investigated laser with widest ridge (23 µm) is comparable with best values known from much wider broad-area lasers. In addition, we show that one of the simulation tools is able to predict beam steering and coherent beam coupling without introducing any phenomenological coupling coefficient or asymmetries. © 2020 The Author(s). Published by IOP Publishing Ltd.