Nicholas DeFilippis | Searcharxiv

arXiv2026

Frequency spreading of internal wave energy by balanced flows in two dimensions

Interactions between inertia-gravity waves and balanced flows lead to a spectral diffusion of wave action. Prior work has established that this diffusion is weak across constant frequency surfaces in three-dimensional settings, but can be significant in two dimensions with a non-stationary balanced flow. We investigate the two-dimensional setting through numerical simulations that simultaneously evolve a turbulent quasigeostrophic balanced flow and advect rotating shallow water wave packets. In contrast to earlier predictions based on the synthetic flows used by Dong et al. (J. Fluid Mech., 2020, vol. 905, R3), we find that frequency spreading from wave mean-flow interactions is weaker for realistic turbulent flows. We derive a timescale for frequency diffusion and show that frequency spreading with a realistic background flow is an order of magnitude smaller than with the synthetic flow. We narrow the discrepancy between the two- and three-dimensional induced diffusion theories, which suggests other mechanisms are responsible for the broadband frequency spectra seen in the atmosphere and ocean.

physics.flu-dyn↗

arXiv2025

Procurement Auctions with Predictions: Improved Frugality for Facility Location

We study the problem of designing procurement auctions for the strategic uncapacitated facility location problem: a company needs to procure a set of facility locations in order to serve its customers and each facility location is owned by a strategic agent. Each owner has a private cost for providing access to their facility (e.g., renting it or selling it to the company) and needs to be compensated accordingly. The goal is to design truthful auctions that decide which facilities the company should procure and how much to pay the corresponding owners, aiming to minimize the total cost, i.e., the monetary cost paid to the owners and the connection cost suffered by the customers (their distance to the nearest facility). We evaluate the performance of these auctions using the \emph{frugality ratio}. We first analyze the performance of the classic VCG auction in this context and prove that its frugality ratio is exactly $3$. We then leverage the learning-augmented framework and design auctions that are augmented with predictions regarding the owners' private costs. Specifically, we propose a family of learning-augmented auctions that achieve significant payment reductions when the predictions are accurate, leading to much better frugality ratios. At the same time, we demonstrate that these auctions remain robust even if the predictions are arbitrarily inaccurate, and maintain reasonable frugality ratios even under adversarially chosen predictions. We finally provide a family of ``error-tolerant'' auctions that maintain improved frugality ratios even if the predictions are only approximately accurate, and we provide upper bounds on their frugality ratio as a function of the prediction error.

cs.GT↗