Lagrangian Data-Driven Reduced Order Modeling of Finite Time Lyapunov Exponents

There are two main strategies for improving the projection-based reduced order model (ROM) accuracy: (i) improving the ROM, i.e., adding new terms to the standard ROM; and (ii) improving the ROM basis, i.e., constructing ROM bases that yield more accurate ROMs. In this paper, we use the latter. We propose new Lagrangian inner products that we use together with Eulerian and Lagrangian data to construct new Lagrangian ROMs. We show that the new Lagrangian ROMs are orders of magnitude more accurate than the standard Eulerian ROMs, i.e., ROMs that use standard Eulerian inner product and data to construct the ROM basis. Specifically, for the quasi-geostrophic equations, we show that the new Lagrangian ROMs are more accurate than the standard Eulerian ROMs in approximating not only Lagrangian fields (e.g., the finite time Lyapunov exponent (FTLE)), but also Eulerian fields (e.g., the streamfunction). We emphasize that the new Lagrangian ROMs do not employ any closure modeling to model the effect of discarded modes (which is standard procedure for low-dimensional ROMs of complex nonlinear systems). Thus, the dramatic increase in the new Lagrangian ROMs' accuracy is entirely due to the novel Lagrangian inner products used to build the Lagrangian ROM basis

Effects of Incomplete Ionization on Beta - Ga2O3 Power Devices: Unintentional Donor with Energy 110 meV

Understanding the origin of unintentional doping in Ga2O3 is key to increasing breakdown voltages of Ga2O3 based power devices. Therefore, transport and capacitance spectroscopy studies have been performed to better understand the origin of unintentional doping in Ga2O3. Previously unobserved unintentional donors in commercially available (-201) Ga2O3 substrates have been electrically characterized via temperature dependent Hall effect measurements up to 1000 K and found to have a donor energy of 110 meV. The existence of the unintentional donor is confirmed by temperature dependent admittance spectroscopy, with an activation energy of 131 meV determined via that technique, in agreement with Hall effect measurements. With the concentration of this donor determined to be in the mid to high 10^16 cm^-3 range, elimination of this donor from the drift layer of Ga2O3 power electronics devices will be key to pushing the limits of device performance. Indeed, analytical assessment of the specific on-resistance (Ronsp) and breakdown voltage of Schottky diodes containing the 110 meV donor indicates that incomplete ionization increases Ronsp and decreases breakdown voltage as compared to Ga2O3 Schottky diodes containing only the shallow donor. The reduced performance due to incomplete ionization occurs in addition to the usual tradeoff between Ronsp and breakdown voltage. To achieve 10 kV operation in Ga2O3 Schottky diode devices, analysis indicates that the concentration of 110 meV donors must be reduced below 5x10^14 cm^-3 to limit the increase in Ronsp to one percent.Comment: 23 pages, 8 figure