Stochastic rectification of fast oscillations on slow manifold closures

The problems of identifying the slow component (e.g., for weather forecast initialization) and of characterizing slow–fast interactions are central to geophysical fluid dynamics. In this study, the related rectification problem of slow manifold closures is addressed when breakdown of slow-to-fast scales deterministic parameterizations occurs due to explosive emergence of fast oscillations on the slow, geostrophic motion. For such regimes, it is shown on the Lorenz 80 model that if 1) the underlying manifold provides a good approximation of the optimal nonlinear parameterization that averages out the fast variables and 2) the residual dynamics off this manifold is mainly orthogonal to it, then no memory terms are required in the Mori–Zwanzig full closure. Instead, the noise term is key to resolve, and is shown to be, in this case, well modeled by a state-independent noise, obtained by means of networks of stochastic nonlinear oscillators. This stochastic parameterization allows, in turn, for rectifying the momentum-balanced slow manifold, and for accurate recovery of the multiscale dynamics. The approach is promising to be further applied to the closure of other more complex slow–fast systems, in strongly coupled regimes.

Shock induced aerobreakup of a droplet

The multiscale dynamics of a shock–droplet interaction is crucial in understanding the atomisation of droplets due to external airflow. The interaction phenomena are classified into wave dynamics (stage I) and droplet breakup dynamics (stage II). Stage I involves the formation of different wave structures after an incident shock impacts the droplet surface. These waves momentarily change the droplet's ambient conditions, while in later times they are mainly influenced by shock-induced airflow. Stage II involves induced airflow interaction with the droplet that leads to its deformation and breakup. Primarily, two modes of droplet breakup, i.e. shear-induced entrainment and Rayleigh–Taylor piercing (RTP) (based on the modes of surface instabilities) were observed for the studied range of Weber numbers $(We\sim 30\text{--}15\,000)$ . A criterion for the transition between two breakup modes is obtained, which successfully explains the observation of RTP mode of droplet breakup at high Weber numbers $(We\sim 800)$ . For $We > 1000$ , the breakup dynamics is governed by the shear-induced surface waves. After formation, the Kelvin–Helmholtz waves travel on the droplet surface and merge to form a liquid sheet near the droplet equator. Henceforth, the liquid sheet undergoes breakup processes via nucleation of several holes. The breakup process is recurrent until the complete droplet disintegrates or external drag acting on the droplet is insufficient for further disintegration. At lower Weber numbers, the droplet undergoes complete deformation like a flattened disk, and a multibag mode of breakup based on RTP is observed.

Estimation and Optimal Control of the Multiscale Dynamics of Covid-19: A Case Study From Cameroon

This work aims at a better understanding and the optimal control of the spread of the new severe acute respiratory corona virus 2 (SARS-CoV-2). We first propose a multi-scale model giving insights on the virus population dynamics, the transmission process and the infection mechanism. We consider 10 compartments in the human population in order to take into accounts the effects of different specific mitigation policies. The population of viruses is also partitioned into 10 compartments corresponding respectively to each of the first nine human population compartments and the free viruses available in the environment. We show the global stability of the disease free equilibrium if a given threshold T0 is less or equal to 1 and we provide how to compute the basic reproduction number R0. A convergence index T1 is also defined in order to estimate the speed at which the disease extincts and an upper bound to the time of extinction is given. The existence of the endemic equilibrium is conditional and its description is provided. We evaluate the sensitivity of R0, T0 and T1 to control parameters such as the maximal human density allowed per unit of surface, the rate of disinfection both for people and environment, the mobility probability, the wearing mask probability or efficiency, and the human to human contact rate which results from the previous one. According to a functional cost taking into consideration economic impacts of SARS-CoV-2, we determine and discuss optimal fighting strategies. The study is applied to available data from Cameroon.

Stellar Turbulent Convection: The Multiscale Nature of the Solar Magnetic Signature

The multiscale dynamics associated with turbulent convection present in physical systems governed by very high Rayleigh numbers still remains a vividly disputed topic in the community of astrophysicists, and in general, among physicists dealing with heat transport by convection. The Sun is a very close star for which detailed observations and estimations of physical properties on the surface, connected to the processes of the underlying convection zone, are possible. This makes the Sun a unique natural laboratory in which to investigate turbulent convection in the hard turbulence regime, a regime typical of systems characterized by high values of the Rayleigh number. In particular, it is possible to study the geometry of convection using the photospheric magnetic voids (or simply voids), the quasi-polygonal quiet regions nearly devoid of magnetic elements, which cover the whole solar surface and which form the solar magnetic network. This work presents the most extensive statistics, both in the spatial scales studied (1–80 Mm) and in the temporal duration (SC 23 and SC 24), to investigate the multiscale nature of solar magnetic patterns associated with the turbulent convection of our star. We show that the size distribution of the voids, in the 1–80 Mm range, for the 317,870 voids found in the 692 analyzed magnetograms, is basically described by an exponential function.

Multiscale dynamics underlying neocortical slow oscillations

Slow oscillations in the sleeping and anesthetized brain invariantly emerge as an alternation between Up (high firing) and Down (almost quiescent) states. In cortex, they occur simultaneously in cell assemblies in different layers and propagate as traveling waves, a concerted activity at multiple scales whose interplay and role is still under debate. Slow oscillations have been reported to start in deep layers, more specifically in layer 5. Here, we studied the laminar organization of slow oscillations in the anesthetized rat cortex and we found that the activity leading to Up states actually initiates in layer 6, then spreads towards upper layers. Layer 5 cell assemblies have a threshold-like activation that can persist after layer 6 inactivation, giving rise to hysteresis loops like in "flip-flop" computational units. We found that such hysteresis is finely tuned by the columnar circuitry depending on the recent history of the local ongoing activity. Furthermore, thalamic inactivation reduced infragranular excitability without affecting the columnar activation pattern. We propose a role for layer 6 acting as a hub unraveling a hierarchy of cortical loops.

A multiscale view of the Phanerozoic fossil record reveals the three major biotic transitions

The hypothesis of the Great Evolutionary Faunas is a foundational concept of macroevolutionary research postulating that three global mega-assemblages have dominated Phanerozoic oceans following abrupt biotic transitions. Empirical estimates of this large-scale pattern depend on several methodological decisions and are based on approaches unable to capture multiscale dynamics of the underlying Earth-Life System. Combining a multilayer network representation of fossil data with a multilevel clustering that eliminates the subjectivity inherent to distance-based approaches, we demonstrate that Phanerozoic oceans sequentially harbored four global benthic mega-assemblages. Shifts in dominance patterns among these global marine mega-assemblages were abrupt (end-Cambrian 494 Ma; end-Permian 252 Ma) or protracted (mid-Cretaceous 129 Ma), and represent the three major biotic transitions in Earth’s history. Our findings suggest that gradual ecological changes associated with the Mesozoic Marine Revolution triggered a protracted biotic transition comparable in magnitude to the end-Permian transition initiated by the most severe biotic crisis of the past 500 million years. Overall, our study supports the notion that both long-term ecological changes and major geological events have played crucial roles in shaping the mega-assemblages that dominated Phanerozoic oceans.