Application of graph combinatorics to rational identities of type A

To a word $w$, we associate the rational function $\Psi_w = \prod (x_{w_i} - x_{w_{i+1}})^{-1}$. The main object, introduced by C. Greene to generalize identities linked to Murnaghan-Nakayama rule, is a sum of its images by certain permutations of the variables. The sets of permutations that we consider are the linear extensions of oriented graphs. We explain how to compute this rational function, using the combinatorics of the graph $G$. We also establish a link between an algebraic property of the rational function (the factorization of the numerator) and a combinatorial property of the graph (the existence of a disconnecting chain).Comment: This is the complete version of the submitted fpsac paper (2009

Modular converter system for low-cost off-grid energy storage using second life Li-ion batteries

Lithium ion batteries are promising for small off- grid energy storage applications in developing countries because of their high energy density and long life. However, costs are prohibitive. Instead, we consider 'used' Li-ion batteries for this application, finding experimentally that many discarded laptop cells, for example, still have good capacity and cycle life. In order to make safe and optimal use of such cells, we present a modular power management system using a separate power converter for every cell. This novel approach allows individual batteries to be used to their full capacity. The power converters operate in voltage droop control mode to provide easy charge balancing and implement a battery management system to estimate the capacity of each cell, as we demonstrate experimentally.Comment: Presented at IEEE GHTC Oct 10-14, 2014, Silicon Valle

Buoyancy-driven exchange flows in inclined ducts

Buoyancy-driven exchange flows arise in the natural and built environment wherever bodies of fluids at different densities are connected by a narrow constriction. In this paper we study these flows in the laboratory using the canonical stratified inclined duct experiment, which sustains an exchange flow in an inclined duct of rectangular cross-section over long time periods (Meyer & Linden, J. Fluid Mech., vol. 753, 2014). We study the behaviour of these sustained stratified shear flows by focusing on three dependent variables of particular interest: the qualitative flow regime (laminar, wavy, intermittently turbulent, or fully turbulent), the mass flux (net transport of buoyancy between reservoirs), and the interfacial thickness (thickness of the layer of intermediate density between the two counter-flowing layers). Dimensional analysis reveals five non-dimensional independent input parameters: the duct aspect ratios in the longitudinal direction $A$ and spanwise direction $B$, the tilt angle $\theta$, the Reynolds number $Re$ (based on the initial buoyancy difference driving the flow), and the Prandtl number $Pr$ (we consider both salt and temperature stratifications). After reviewing the literature and open questions on the scaling of regimes, mass flux, and interfacial thickness with $A,B,\theta,Re,Pr$, we present the first extensive, unified set of experimental data where we varied systematically all five input parameters and measured all three output variables with the same methodology. Our results in the $(\theta,Re)$ plane for five sets of $(A,B,Pr)$ reveal a variety of scaling laws, and a non-trivial dependence of all three variables on all five parameters, in addition to a sixth elusive parameter. We further develop three classes of candidate models to explain the observed scaling laws: ..

Spacecraft Autonomous Decision-Planning for Collision Avoidance: a Reinforcement Learning Approach

The space environment around the Earth is becoming increasingly populated by both active spacecraft and space debris. To avoid potential collision events, significant improvements in Space Situational Awareness (SSA) activities and Collision Avoidance (CA) technologies are allowing the tracking and maneuvering of spacecraft with increasing accuracy and reliability. However, these procedures still largely involve a high level of human intervention to make the necessary decisions. For an increasingly complex space environment, this decision-making strategy is not likely to be sustainable. Therefore, it is important to successfully introduce higher levels of automation for key Space Traffic Management (STM) processes to ensure the level of reliability needed for navigating a large number of spacecraft. These processes range from collision risk detection to the identification of the appropriate action to take and the execution of avoidance maneuvers. This work proposes an implementation of autonomous CA decision-making capabilities on spacecraft based on Reinforcement Learning (RL) techniques. A novel methodology based on a Partially Observable Markov Decision Process (POMDP) framework is developed to train the Artificial Intelligence (AI) system on board the spacecraft, considering epistemic and aleatory uncertainties. The proposed framework considers imperfect monitoring information about the status of the debris in orbit and allows the AI system to effectively learn stochastic policies to perform accurate Collision Avoidance Maneuvers (CAMs). The objective is to successfully delegate the decision-making process for autonomously implementing a CAM to the spacecraft without human intervention. This approach would allow for a faster response in the decision-making process and for highly decentralized operations.Comment: Preprint accepted in the 74th International Astronautical Congress (IAC) - Baku, Azerbaijan, 2-6 October 202

Comment on "Floquet non-Abelian topological insulator and multifold bulk-edge correspondence"

We comment on the recent paper ``Floquet non-Abelian topological insulator and multifold bulk-edge correspondence" by Tianyu Li and Haiping Hu, Nat. Comm. {\bf 14}, 6418 (2023). Apart from the fact that the authors unjustly imply to study multi-gap topology in Floquet systems for the first time, only known homotopic relations are presented. While such insights are used to present interesting Floquet phenomena and phases, which is an attractive result in itself, they cannot be used to deduce the total bulk characterization in the dynamical context without further proof. In fact, the authors essentially rephrase a Zak phase description. These results should in particular be contrasted to earlier results, arXiv:2208.12824, in which static-compatible Zak phases {\it and} dynamical Dirac strings were shown to be able to {\it distinguish} rather similar non-Abelian Floquet phases in $2+1$ dimensional systems. As a result, the claim of a sharp multifold bulk-edge correspondence cannot be concluded from the given arguments

Corrosion behaviour of mechanically polished AA7075-T6 aluminium alloy

In the present study, the effects of mechanical polishing on the microstructure and corrosion behaviour of AA7075 aluminium alloy are investigated. It was found that a nano-grained, near-surface deformed layer, up to 400 nm thickness, is developed due to significant surface shear stress during mechanically polishing. Within the near-surface deformed layer, the alloying elements have been redistributed and the microstructure of the alloy is modified; in particular, the normal MgZn2 particles for T6 are absent. However, segregation bands, approximately 10-nm thick, containing mainly zinc, are found at the grain boundaries within the near-surface deformed layer. The presence of such segregation bands promoted localised corrosion along the grain boundaries within the near-surface deformed layer due to microgalvanic action. During anodic polarisation of mechanically polished alloy in sodium chloride solution, two breakdown potentials were observed at −750 mV and −700 mV, respectively. The first breakdown potential is associated with an increased electrochemical activity of the near-surface deformed layer, and the second breakdown potential is associated with typical pitting of the bulk alloy

Genomic evidence of functional diversity in DPANN archaea, from oxic species to anoxic vampiristic consortia

DPANN archaea account for half of the archaeal diversity of the biosphere, but with few cultivated representatives, their metabolic potential and environmental functions are poorly understood. The extreme geochemical and environmental conditions in meromictic ice-capped Lake A, in the Canadian High Arctic, provided an isolated, stratified model ecosystem to resolve the distribution and metabolism of uncultured aquatic DPANN archaea living across extreme redox and salinity gradients, from freshwater oxygenated conditions, to saline, anoxic, sulfidic waters. We recovered 28 metagenome-assembled genomes (MAGs) of DPANN archaea that provided genetic insights into their ecological function. Thiosulfate oxidation potential was detected in aerobic Woesearchaeota, whereas diverse metabolic functions were identified in anaerobic DPANN archaea, including degradation and fermentation of cellular compounds, and sulfide and polysulfide reduction. We also found evidence for “vampiristic” metabolism in several MAGs, with genes coding for pore-forming toxins, peptidoglycan degradation, and RNA scavenging. The vampiristic MAGs co-occurred with other DPANNs having complementary metabolic capacities, leading to the possibility that DPANN form interspecific consortia that recycle microbial carbon, nutrients and complex molecules through a DPANN archaeal shunt, adding hidden novel complexity to anaerobic microbial food webs