Conference Item records
https://feeds.library.caltech.edu/people/Tropp-J-A/conference_item.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 00:22:16 +0000On effectiveness of a rank-1 model of turbulent channels for representing the velocity spectra
https://resolver.caltech.edu/CaltechAUTHORS:20150218-094025300
Authors: {'items': [{'id': 'Moarref-R', 'name': {'family': 'Moarref', 'given': 'Rashad'}}, {'id': 'Sharma-A-S', 'name': {'family': 'Sharma', 'given': 'Ati S.'}, 'orcid': '0000-0002-7170-1627'}, {'id': 'Tropp-J-A', 'name': {'family': 'Tropp', 'given': 'Joel A.'}, 'orcid': '0000-0003-1024-1791'}, {'id': 'McKeon-B-J', 'name': {'family': 'McKeon', 'given': 'Beverley J.'}, 'orcid': '0000-0003-4220-1583'}]}
Year: 2013
DOI: 10.2514/6.2013-2480
We evaluate the efficacy of a gain-based rank-1 model, developed by McKeon & Sharma (J. Fluid Mech., 2010), for representing the energy spectra and the streamwise/wall-normal co-spectrum in a turbulent channel. This is motivated by our previous observation that the streamwise turbulent energy intensity is well approximated by the rank-1 model subject to a broadband forcing in the wall-parallel directions and a properly selected temporal intensity. In the present study, the evaluation is based on finding the optimal forcing spectrum that
minimizes the deviation between the two-dimensional velocity spectra at different wall-normal locations obtained from direct numerical simulations at friction Reynolds number
2003 (Hoyas & Jiminénez, Phys. Fluids, 2006) and from the rank-1 model at equal Reynolds number. It is shown that the optimally forced rank-1 model captures the streamwise
energy spectrum for streamwise wavelengths smaller than approximately 1000 viscous units throughout the channel. For larger wavelengths, the streamwise spectrum is matched in the outer region of the channel, i.e. wall-normal distances larger than approximately 0.15 times the channel half-height, and the mismatch close to the wall results in less than 5 percent error in the inner-scaled peak of the streamwise energy intensity. In addition, we show that the rank-1 model with optimal forcing captures the essential features of the wall-normal and spanwise spectra and the streamwise/wall-normal co-spectrum. We observe that the predicted magnitudes of the latter three spectra are smaller in the rank-1 model compared to the simulation results suggesting that a higher-order or different rank-1 model may be necessary for accurate representation of these spectra.https://authors.library.caltech.edu/records/2hsw0-afr39Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data
https://resolver.caltech.edu/CaltechAUTHORS:20180829-073029156
Authors: {'items': [{'id': 'Tropp-J-A', 'name': {'family': 'Tropp', 'given': 'Joel A.'}, 'orcid': '0000-0003-1024-1791'}, {'id': 'Yurtsever-A', 'name': {'family': 'Yurtsever', 'given': 'Alp'}}, {'id': 'Udell-M', 'name': {'family': 'Udell', 'given': 'Madeleine'}, 'orcid': '0000-0002-3985-915X'}, {'id': 'Cevher-V', 'name': {'family': 'Cevher', 'given': 'Volkan'}}]}
Year: 2017
DOI: 10.48550/arXiv.1706.05736
Several important applications, such as streaming PCA and semidefinite programming, involve a large-scale positive-semidefinite (psd) matrix that is presented as a sequence of linear updates. Because of storage limitations, it may only be possible to retain a sketch of the psd matrix. This paper develops a new algorithm for fixed-rank psd approximation from a sketch. The approach combines the Nyström approximation with a novel mechanism for rank truncation. Theoretical analysis establishes that the proposed method can achieve any prescribed relative error in
the Schatten 1-norm and that it exploits the spectral decay of the input matrix. Computer experiments show that the proposed method dominates alternative techniques for fixed-rank psd matrix approximation across a wide range of examples.https://authors.library.caltech.edu/records/h2qre-xhg74