arXiv subjects

Kevin D. Smith

Publications and source records attributed to Kevin D. Smith.

8 recordsLinked to original sources

arXiv2026

High CO/H2 ratios supports an exocometary origin for a CO-rich debris disk

Over 20 exocometary belts host detectable circumstellar gas, mostly in the form of CO. Two competing theories for its origin have emerged, positing the gas to be primordial or secondary. Primordial gas survives from the belt's parent protoplanetary disk and is therefore H$_2$-rich. Secondary gas is outgassed \textit{in-situ} by exocomets and is relatively H$_2$-poor. Discriminating between these scenarios has not been possible for belts hosting unexpectedly large quantities of CO. We aim to break this gas origin dichotomy \textit{via} direct measurement of H$_2$ column densities in two edge-on CO-rich exocometary belts around $\sim$15 Myr-old A-type stars, constraining the $\frac{\text{CO}}{\text{H}_2}$ ratio and CO gas lifetimes. Observing edge-on belts enables rovibrational absorption spectroscopy against the stellar background. We present near-IR CRIRES+ spectra of HD 110058 and HD 131488 which provide the first direct probe of H$_2$ gas in CO-rich exocometary belts. We target the H$_2$ (v=1-0 S(0)) line at 2223.3 nm and and the $^{12}$CO $v=2\rightarrow0$ rovibrational lines in the range 2333.8-2335.5 nm and derive constraints on column densities along the line-of-sight to the stars. We strongly detect $^{12}$CO but not H$_2$ in the CRIRES+ spectra. This allows us to place $3σ$ lower limits on the $\frac{\text{CO}}{\text{H}_2}$ ratios of $> 1.35 \times 10^{-3}$ and $> 3.09 \times 10^{-5}$ for HD 110058 and HD 131488 respectively. These constraints demonstrate that at least for HD 110058, the exocometary gas is compositionally distinct and significantly H$_2$-poor, compared to the $<10^{-4}$ $\frac{\text{CO}}{\text{H}_2}$ ratios typical of protoplanetary disks. We also find H$_2$ alone is unlikely to shield CO over the lifetime of the systems. Overall this suggests that the gas in CO-rich belts is most likely not primordial in origin, supporting the presence of exocometary gas.

astro-ph.EP↗

arXiv2022

Dual Seminorms, Ergodic Coefficients and Semicontraction Theory

Dynamical systems that are contracting on a subspace are said to be semicontracting. Semicontraction theory is a useful tool in the study of consensus algorithms and dynamical flow systems such as Markov chains. To develop a comprehensive theory of semicontracting systems, we investigate seminorms on vector spaces and define two canonical notions: projection and distance semi-norms. We show that the well-known lp ergodic coefficients are induced matrix seminorms and play a central role in stability problems. In particular, we formulate a duality theorem that explains why the Markov-Dobrushin coefficient is the rate of contraction for both averaging and conservation flows in discrete time. Moreover, we obtain parallel results for induced matrix log seminorms. Finally, we propose comprehensive theorems for strong semicontractivity of linear and non-linear time-varying dynamical systems with invariance and conservation properties both in discrete and continuous time.

math.PR↗

arXiv2022

Contractivity of the Method of Successive Approximations for Optimal Control

Strongly contracting dynamical systems have numerous properties (e.g., incremental ISS), find widespread applications (e.g., in controls and learning), and their study is receiving increasing attention. This work starts with the simple observation that, given a strongly contracting system, its adjoint dynamical system is also strongly contracting, with the same rate, with respect to the dual norm, under time reversal. As main implication of this dual contractivity, we show that the classic Method of Successive Approximations (MSA), an indirect method in optimal control, is a contraction mapping for short optimization intervals or large contraction rates. Consequently, we establish new convergence conditions for the MSA algorithm, which further imply uniqueness of the optimal control and sufficiency of Pontryagin's minimum principle under additional assumptions.

math.OC↗

arXiv2022

Convex Optimization of the Basic Reproduction Number

The basic reproduction number $R_0$ is a fundamental quantity in epidemiological modeling, reflecting the typical number of secondary infections that arise from a single infected individual. While $R_0$ is widely known to scientists, policymakers, and the general public, it has received comparatively little attention in the controls community. This note provides two novel characterizations of $R_0$: a stability characterization and a geometric program characterization. The geometric program characterization allows us to write $R_0$-constrained and budget-constrained optimal resource allocation problems as geometric programs, which are easily transformed into convex optimization problems. We apply these programs to allocating vaccines and antidotes in numerical examples, finding that targeting $R_0$ instead of the spectral abscissa of the Jacobian matrix (a common target in the controls literature) leads to qualitatively different solutions.

math.OC↗

arXiv2021

Topology Inference with Multivariate Cumulants: The Möbius Inference Algorithm

Many tasks regarding the monitoring, management, and design of communication networks rely on knowledge of the routing topology. However, the standard approach to topology mapping--namely, active probing with traceroutes--relies on cooperation from increasingly non-cooperative routers, leading to missing information. Network tomography, which uses end-to-end measurements of additive link metrics (like delays or log packet loss rates) across monitor paths, is a possible remedy. Network tomography does not require that routers cooperate with traceroute probes, and it has already been used to infer the structure of multicast trees. This paper goes a step further. We provide a tomographic method to infer the underlying routing topology of an arbitrary set of monitor paths using the joint distribution of end-to-end measurements, without making any assumptions on routing behavior. Our approach, called the Möbius Inference Algorithm (MIA), uses cumulants of this distribution to quantify high-order interactions among monitor paths, and it applies Möbius inversion to "disentangle" these interactions. In addition to MIA, we provide a more practical variant called Sparse Möbius Inference, which uses various sparsity heuristics to reduce the number and order of cumulants required to be estimated. We show the viability of our approach using synthetic case studies based on real-world ISP topologies.

eess.SP↗

arXiv2020

Flow and Elastic Networks on the $n$-torus: Geometry, Analysis, and Computation

Networks with phase-valued nodal variables are central in modeling several important societal and physical systems, including power grids, biological systems, and coupled oscillator networks. One of the distinctive features of phase-valued networks is the existence of multiple operating conditions corresponding to critical points of an energy function or feasible flows of a balance equation. For networks with phase-valued states, it is not yet fully understood how many operating conditions exist, how to characterize them, and how to compute them efficiently. A deeper understanding of feasible operating conditions, including their dependence upon network structures, may lead to more reliable and efficient network systems. This paper introduces flow and elastic network problems on the $n$-torus and provides a rigorous and comprehensive framework for their study. Based on a monotonicity assumption, this framework localizes the solutions, bounds their number, and leads to an algorithm to compute them. Our analysis is based on a novel winding partition of the $n$-torus into winding cells, induced by Kirchhoff's angle law for undirected graphs. The winding partition has several useful properties, including notably that, each winding cell contains at most one solution. The proposed algorithm is based on a novel contraction mapping and is guaranteed to compute all solutions. Finally, we apply our results to numerically study the active power flow equations in several test cases and estimate power capacity and congestion of a power network.

math.OC↗

arXiv2020

Transient Stability of Droop-Controlled Inverter Networks with Operating Constraints

Due to the rise of distributed energy resources, the control of networks of grid-forming inverters is now a pressing issue for power system operation. Droop control is a popular control strategy in the literature for frequency control of these inverters. In this paper, we analyze transient stability in droop-controlled inverter networks that are subject to multiple operating constraints. Using a physically-meaningful Lyapunov-like function, we provide two sets of criteria (one mathematical and one computational) to certify that a post-fault trajectory achieves frequency synchronization while respecting operating constraints. We show how to obtain less-conservative transient stability conditions by incorporating information from loop flows, i.e., net flows of active power around cycles in the network. Finally, we use these conditions to quantify the scale of parameter disturbances to which the network is robust. We illustrate our results with numerical case studies of the IEEE 24-bus system.

eess.SY↗

arXiv2020

A Tutorial on Multivariate $k$-Statistics and their Computation

This document aims to provide an accessible tutorial on the unbiased estimation of multivariate cumulants, using $k$-statistics. We offer an explicit and general formula for multivariate $k$-statistics of arbitrary order. We also prove that the $k$-statistics are unbiased, using Möbius inversion and rudimentary combinatorics. Many detailed examples are considered throughout the paper. We conclude with a discussion of $k$-statistics computation, including the challenge of time complexity, and we examine a couple of possible avenues to improve the efficiency of this computation. The purpose of this document is threefold: to provide a clear introduction to $k$-statistics without relying on specialized tools like the umbral calculus; to construct an explicit formula for $k$-statistics that might facilitate future approximations and faster algorithms; and to serve as a companion paper to our Python library PyMoments, which implements this formula.

stat.ME↗