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We study the broadband emission of Mrk 501 using multi-wavelength observations from 2017 to 2020 performed with a multitude of instruments, involving, among others, MAGIC, Fermi-LAT, NuSTAR, Swift, GASP-WEBT, and OVRO. Mrk 501 showed an extremely low broadband activity, which may help to unravel its baseline emission. Nonetheless, significant flux variations are detected at all wavebands, with the highest occurring at X-rays and very-high-energy (VHE) $\gamma$-rays. A significant correlation ($>$3$\sigma$) between X-rays and VHE $\gamma$-rays is measured, supporting leptonic scenarios to explain the variable parts of the emission, also during low activity. This is further supported when we extend our data from 2008 to 2020, and identify, for the first time, significant correlations between Swift-XRT and Fermi-LAT. We additionally find correlations between high-energy $\gamma$-rays and radio, with the radio lagging by more than 100 days, placing the $\gamma$-ray emission zone upstream of the radio-bright regions in the jet. Furthermore, Mrk 501 showed a historically low activity in X-rays and VHE $\gamma$-rays from mid-2017 to mid-2019 with a stable VHE flux ($>$0.2 TeV) of 5% the emission of the Crab Nebula. The broadband spectral energy distribution (SED) of this 2-year-long low-state, the potential baseline emission of Mrk 501, can be characterized with one-zone leptonic models, and with (lepto)-hadronic models fulfilling neutrino flux constraints from IceCube. We explore the time evolution of the SED towards the low-state, revealing that the stable baseline emission may be ascribed to a standing shock, and the variable emission to an additional expanding or traveling shock., Comment: 55 pages, 30 figures, 14 tables, accepted by APJS. Corresponding authors are L. Heckmann, D. Paneque, S. Gasparyan, M. Cerruti, and N. Sahakyan

Only in the last fifteen years or so has the notion of semi-uniform stability, which lies between exponential stability and strong stability, become part of the asymptotic theory of $C_0$-semigroups. It now lies at the very heart of modern semigroup theory. After briefly reviewing the notions of exponential and strong stability, we present an overview of some of the best known (and often optimal) abstract results on semi-uniform stability. We go on to indicate briefly how these results can be applied to obtain (sometimes optimal) rates of energy decay for certain damped second-order Cauchy problems., Comment: To appear in Philosophical Transactions of the Royal Society A

This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for initial values satisfying a slightly stronger condition we obtain an optimal estimate on the rate of convergence. By establishing a connection with a related problem in continuous time, we are able to use this optimal estimate to improve the rate of convergence in the continuous setting obtained by the authors in a previous paper. We illustrate the power of the general approach by using it to study several concrete examples, both in continuous and in discrete time., Comment: To appear in J. Dyn. Differ. Equ

We present a non-technical overview of the results obtained by the authors (2015) concerning the so-called robot rendezvous problem studied by Feintuch and Francis (2012). In particular, we present a necessary and sufficient condition for convergence of the solution in terms of Ces\`aro convergence of the translates $S^k x_0$, $k\ge0$, of the sequence $x_0$ of initial positions under the right-shift operator $S$, thus shedding new light on questions left open in by Feintuch and Francis. We also formulate a stronger ergodic condition on $x_0$ which ensures that the corresponding solution converges to its limit at the rate $O(t^{-1/2})$ as $t\to\infty$. We conclude with a brief discussion of a natural two-sided variant of the robot rendezvous problem and by relating the robot rendezvous problem to a more realistic model of vehicle platoons, for which the authors' earlier general results lead to analogous statements., Comment: To appear in Automatica

We study a simple one-dimensional coupled wave-heat system and obtain a sharp estimate for the rate of energy decay of classical solutions. Our approach is based on the asymptotic theory of $C_0$-semigroups and in particular on a result due to Borichev and Tomilov (Math. Ann., 2010), which reduces the problem of estimating the rate of energy decay to finding a growth bound for the resolvent of the semigroup generator. This technique not only leads to an optimal result, it is also simpler than the methods used by other authors in similar situations., Comment: To appear in Journal of Evolution Equations

The Senior Aerospace System Design class at the University of Michigan undertook the design of a manned space transportation vehicle (STV) that would transport payloads between low earth orbit (LEO) and geosynchronous earth orbit (GEO). Designated ARGO after the ship of the Greek adventurer Jason, two different versions of an STV that would be based, refueled, and serviced at the Space Station Freedom were designed and analyzed by the class. With the same 2-man/7-day nominal mission of transporting a 10,000-kg payload up to GEO and bringing a 5000-kg payload back to LEO, the two versions of ARGO differ in the manner in which the delta V is applied to insert the vehicle into LEO upon return from GEO. The all-propulsive ARGO (or CSTV for chemical STV) uses thrust from its LH2/LOX rocket engines to produce the delta V during all phases of its mission. While the aeroassisted ARGO (or ASTV for aeroassisted STV) also uses the same engines for the majority of the mission, the final delta V used to insert the ASTV into LEO is produced by skimming the Earth's atmosphere and using the drag on the vehicle to apply the required delta V. This procedure allows for large propellant, and thus cost, savings, but creates many design problems such as the high heating rates and decelerations experienced by a vehicle moving through the atmosphere at hypersonic velocities. The design class, consisting of 43 senior aerospace engineering students, was divided into one managerial and eight technical groups. The technical groups consisted of spacecraft configuration and integration, mission analysis, atmospheric flight, propulsion, power and communications, life support and human factors, logistics and support, and systems analysis. Two committees were set up with members from each group to create the scale models of the STV's and to produce the final report.

The situation in which an operator is faced with a continuous control task plus one or more discrete information processing tasks is discussed. A modelling approach which has the capability of realistically representing both types of tasks and the resulting interactions is sought. The modelling approach utilizes discrete network models for the cognitive tasks and elements of an open-loop - closed-loop control representation for the continuous task. the approach is demonstrated through its application to a simulated Digital Avionics Information System in which subjects were required to perform retrieval and processing tasks as well as flight control. This model differs from conventional model in that system status sampling is not necessarily continuous or periodic. Rather, the pilot is assumed to read system status displays only as time permits and operate in a so-called open-loop preprogrammed fashion between sampling.

A Process Development Unit (PDU), which consisted of the four major units of the process, was designed, installed, and experimentally operated. The PDU was sized to 50MT/Yr. The deposition took place in a fluidized bed reactor. As a consequences of the experiments, improvements in the design an operation of these units were undertaken and their experimental limitations were partially established. A parallel program of experimental work demonstrated that Zinc can be vaporized for introduction into the fluidized bed reactor, by direct induction-coupled r.f. energy. Residual zinc in the product can be removed by heat treatment below the melting point of silicon. Current efficiencies of 94 percent and above, and power efficiencies around 40 percent are achievable in the laboratory-scale electrolysis of ZnCl2.

SAINT (Systems Analysis of Integrated Networks of Tasks) is a network modeling and simulation technique for design and analysis of complex man machine systems. SAINT provides the conceptual framework for representing systems that consist of discrete task elements, continuous state variables, and interactions between them. It also provides a mechanism for combining human performance models and dynamic system behaviors in a single modeling structure. The SAINT technique is described and applications of the SAINT are discussed.

Low temperature ductility and high temperature strength of pure chromium and chromium-thoria alloy prepared from vapor deposited powders