Search for: All records

The Loewner framework is extended to compute reduced order models (ROMs) for systems governed by the incompressible Navier-Stokes (NS) equations. For quadratic ordinary differential equations (ODEs) it constructs a ROM directly from measurements of transfer function components derived from an expansion of the system’s input-to-output map. Given measurements, no explicit access to the system is required to construct the ROM. To extend the Loewner framework, the NS equations are transformed into ODEs by projecting onto the subspace defined by the incompressibility condition. This projection is used theoretically, but avoided computationally. This paper presents the overall approach. Currently, transfer function measurements are obtained via computational simulations; obtaining them from experiments is an open issue. Numerical results show the potential of the Loewner framework, but also reveal possible lack of stability of the ROM. A possible approach, which currently requires access to the NS system, to deal with these instabilities is outlined. 

The isoperimetric problem with a density or weighting seeks to enclose prescribed weighted volume with minimum weighted perimeter. According to Chambers' recent proof of the log-convex density conjecture, for many densities on Rn the answer is a sphere about the origin. We seek to generalize his results to some other spaces of revolution or to two dierent densities for volume and perimeter. We provide general results on existence and boundedness and a new approach to proving circles about the origin isoperimetric. 

Abstract The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in ℝ N is the standard double bubble. We seek the optimal double bubble in ℝ N with density, which we assume to be strictly log-convex. For N = 1 we show that the solution is sometimes two contiguous intervals and sometimes three contiguous intervals. In higher dimensions we think that the solution is sometimes a standard double bubble and sometimes concentric spheres (e.g. for one volume small and the other large). 

The IceCube Neutrino Observatory at the South Pole has measured the diffuse astrophysical neutrino flux up to ~PeV energies and is starting to identify first point source candidates. The next generation facility, IceCube-Gen2, aims at extending the accessible energy range to EeV in order to measure the continuation of the astrophysical spectrum, to identify neutrino sources, and to search for a cosmogenic neutrino flux. As part of IceCube-Gen2, a radio array is foreseen that is sensitive to detect Askaryan emission of neutrinos beyond ~30 PeV. Surface and deep antenna stations have different benefits in terms of effective area, resolution, and the capability to reject backgrounds from cosmic-ray air showers and may be combined to reach the best sensitivity. The optimal detector configuration is still to be identified. This contribution presents the full-array simulation efforts for a combination of deep and surface antennas, and compares different design options with respect to their sensitivity to fulfill the science goals of IceCube-Gen2.