We prove a local existence theorem for the free boundary problem for a relativistic fluid in a fixed spacetime. Our proof involves an a priori estimate which only requires control of derivatives tangential to the boun...
We investigate an inverse problem in time-frequency localization: the approximation of the symbol of a time-frequency localization operator from partial spectral information by the method of accumulated spectrograms (...
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A local artificial neural network (LANN) framework is developed for turbulence modeling. The Reynolds-averaged Navier-Stokes (RANS) unclosed terms are reconstructed by artificial neural network (ANN) based on the loca...
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Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By di...
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MSC Codes 94A15, 62B10We analyze the problem of estimating a signal from multiple measurements on a group action channel that linearly transforms a signal by a random group action followed by a fixed projection and ad...
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In the multireference alignment model, a signal is observed by the action of a random circular translation and the addition of Gaussian noise. The goal is to recover the signal's orbit by accessing multiple indepe...
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To fill the gap between accurate (and expensive) ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials, a new class of descriptions of atomic interactions has emerged and...
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Accurate prediction for the electronic structure properties of halide perovskites plays a significant role in the design of highly efficient and stable solar cells. While density functional theory (DFT) within the gen...
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This paper concerns the convergence of empirical measures in high dimensions. We propose a new class of probability metrics and show that under such metrics, the convergence is free of the curse of dimensionality (CoD...
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To date, all experiments in nonlinear statistical optics have relied on beams whose transverse spatial statistics were Gaussian. Here, we present a new technique to generalize these studies by using a spatial light mo...
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To date, all experiments in nonlinear statistical optics have relied on beams whose transverse spatial statistics were Gaussian. Here, we present a new technique to generalize these studies by using a spatial light modulator to create spatially incoherent beams with arbitrary spectral distributions. As a specific example of the new dynamics possible, we consider the spatial modulation instability of a partially coherent beam. We show that, for statistical beams of uniform intensity and equal correlation length, the underlying spectral shape determines the threshold and visibility of intensity modulations as well as the spectral profile of the growing sidebands. We demonstrate the behavior using statistical light, but the results will hold for any wave-kinetic system, such as plasma, ultracold gases, and turbulent acoustic waves.
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