A well-posedness theory in measures for some kinetic models of collective motion

We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the behavior of large groups of animals, such as flocks of birds, swarms, or schools of fish. Our aim is to give a well-posedness theory for general models which possibly include a variety of effects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging effect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and self-propulsion effects, which take into account effects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models

Singular Cucker-Smale Dynamics

The existing state of the art for singular models of flocking is overviewed, starting from microscopic model of Cucker and Smale with singular communication weight, through its mesoscopic mean-filed limit, up to the corresponding macroscopic regime. For the microscopic Cucker-Smale (CS) model, the collision-avoidance phenomenon is discussed, also in the presence of bonding forces and the decentralized control. For the kinetic mean-field model, the existence of global-in-time measure-valued solutions, with a special emphasis on a weak atomic uniqueness of solutions is sketched. Ultimately, for the macroscopic singular model, the summary of the existence results for the Euler-type alignment system is provided, including existence of strong solutions on one-dimensional torus, and the extension of this result to higher dimensions upon restriction on the smallness of initial data. Additionally, the pressureless Navier-Stokes-type system corresponding to particular choice of alignment kernel is presented, and compared - analytically and numerically - to the porous medium equation

Collective behavior of animals: swarming and complex patterns

En esta nota repasamos algunos modelos basados en individuos para describir el movimiento colectivo de agentes, a lo que nos referimos usando la voz inglesa swarming. Estos modelos se basan en EDOs (ecuaciones diferenciales ordinarias) y muestran un comportamiento asintótico complejo y rico en patrones, que mostramos numéricamente. Además, comentamos cómo se conectan estos modelos de partículas con las ecuaciones en derivadas parciales para describir la evolución de densidades de individuos de forma continua. Las cuestiones matemáticas relacionadas con la estabilidad de de estos modelos de EDP's (ecuaciones en derivadas parciales) despiertan gran interés en la investigación en biología matemáticaIn this short note we review some of the individual based models of the collective motion of agents, called swarming. These models based on ODEs (ordinary differential equations) exhibit a complex rich asymptotic behavior in terms of patterns, that we show numerically. Moreover, we comment on how these particle models are connected to partial differential equations to describe the evolution of densities of individuals in a continuum manner. The mathematical questions behind the stability issues of these PDE (partial differential equations) models are questions of actual interest in mathematical biology researc

Uncertainty quantification for kinetic models in socio-economic and life sciences

Kinetic equations play a major rule in modeling large systems of interacting particles. Recently the legacy of classical kinetic theory found novel applications in socio-economic and life sciences, where processes characterized by large groups of agents exhibit spontaneous emergence of social structures. Well-known examples are the formation of clusters in opinion dynamics, the appearance of inequalities in wealth distributions, flocking and milling behaviors in swarming models, synchronization phenomena in biological systems and lane formation in pedestrian traffic. The construction of kinetic models describing the above processes, however, has to face the difficulty of the lack of fundamental principles since physical forces are replaced by empirical social forces. These empirical forces are typically constructed with the aim to reproduce qualitatively the observed system behaviors, like the emergence of social structures, and are at best known in terms of statistical information of the modeling parameters. For this reason the presence of random inputs characterizing the parameters uncertainty should be considered as an essential feature in the modeling process. In this survey we introduce several examples of such kinetic models, that are mathematically described by nonlinear Vlasov and Fokker--Planck equations, and present different numerical approaches for uncertainty quantification which preserve the main features of the kinetic solution.Comment: To appear in "Uncertainty Quantification for Hyperbolic and Kinetic Equations

Sensor Network Architectures for Monitoring Underwater Pipelines

This paper develops and compares different sensor network architecture designs that can be used for monitoring underwater pipeline infrastructures. These architectures are underwater wired sensor networks, underwater acoustic wireless sensor networks, RF (Radio Frequency) wireless sensor networks, integrated wired/acoustic wireless sensor networks, and integrated wired/RF wireless sensor networks. The paper also discusses the reliability challenges and enhancement approaches for these network architectures. The reliability evaluation, characteristics, advantages, and disadvantages among these architectures are discussed and compared. Three reliability factors are used for the discussion and comparison: the network connectivity, the continuity of power supply for the network, and the physical network security. In addition, the paper also develops and evaluates a hierarchical sensor network framework for underwater pipeline monitoring

Non-local kinetic and macroscopic models for self-organised animal aggregations

The last two decades have seen a surge in kinetic and macroscopic models derived to investigate the multi-scale aspects of self-organised biological aggregations. Because the individual-level details incorporated into the kinetic models (e.g., individual speeds and turning rates) make them somewhat difficult to investigate, one is interested in transforming these models into simpler macroscopic models, by using various scaling techniques that are imposed by the biological assumptions of the models. However, not many studies investigate how the dynamics of the initial models are preserved via these scalings. Here, we consider two scaling approaches (parabolic and grazing collision limits) that can be used to reduce a class of non-local 1D and 2D models for biological aggregations to simpler models existent in the literature. Then, we investigate how some of the spatio-temporal patterns exhibited by the original kinetic models are preserved via these scalings. To this end, we focus on the parabolic scaling for non-local 1D models and apply asymptotic preserving numerical methods, which allow us to analyse changes in the patterns as the scaling coefficient ϵ is varied from ϵ=1 (for 1D transport models) to ϵ=0 (for 1D parabolic models). We show that some patterns (describing stationary aggregations) are preserved in the limit ϵ→0, while other patterns (describing moving aggregations) are lost. To understand the loss of these patterns, we construct bifurcation diagrams

Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics

International audienceWe provide a complete and rigorous description of phase transitions for kinetic models of self-propelled particles interacting through alignment. These models exhibit a competition between alignment and noise. Both the alignment frequency and noise intensity depend on a measure of the local alignment. We show that, in the spatially homogeneous case, the phase transition features (number and nature of equilibria, stability, convergence rate, phase diagram, hysteresis) are totally encoded in how the ratio between the alignment and noise intensities depend on the local alignment. In the spatially inhomogeneous case, we derive the macroscopic models associated to the stable equilibria and classify their hyperbolicity according to the same function

Isolation of a wide range of minerals from a thermally treated plant: Equisetum arvense, a Mare’s tale

Silica is the second most abundant biomineral being exceeded in nature only by biogenic CaCO3. Many land plants (such as rice, cereals, cucumber, etc.) deposit silica in significant amounts to reinforce their tissues and as a systematic response to pathogen attack. One of the most ancient species of living vascular plants, Equisetum arvense is also able to take up and accumulate silica in all parts of the plant. Numerous methods have been developed for elimination of the organic material and/or metal ions present in plant material to isolate biogenic silica. However, depending on the chemical and/or physical treatment applied to branch or stem from Equisetum arvense; other mineral forms such glass-type materials (i.e. CaSiO3), salts (i.e. KCl) or luminescent materials can also be isolated from the plant material. In the current contribution, we show the chemical and/or thermal routes that lead to the formation of a number of different mineral types in addition to biogenic silica

Thermal characterization testing of a robust and reliable thermal knife HDRM (Hold Down and Release Mechanism) for CubeSat deployables

Thermal knife HDRMs (Hold Down and Release Mechanisms) are commonly used in CubeSats and other small satellites. However, detailed information on proven designs is difficult to find. Design of a robust and reliable mechanism can present technical challenges which may only become apparent during testing, and often only when tested in a space representative environment. A custom thermal knife HDRM was designed and built for the antenna deployment module of EIRSAT-1 to deploy four coil spring antenna elements, but the same or a similar design could be repurposed quite easily to release a wide range of CubeSat deployables. In this design resistors are used to cut dyneema lines. For robustness and reliability, the thermal response of the mechanism must be well understood. To reach the melting point of the dyneema (150C) the power dissipated in the resistors must often exceed the maximum rated value. Therefore, choosing the operating current and the burn time is a careful trade-off between ensuring that the resistor reliably cuts the dyneema line and ensuring that the resistor, solder joints, PCB and nearby components are not damaged by the high temperatures. These choices are further complicated by the requirement that the mechanism operates over a range of temperatures. A thermal vacuum test campaign was carried out to better understand and characterise the thermal behaviour of the EIRSAT-1 mechanism. For the test a model of the mechanism was built with several temperature sensors installed. Two of these sensors were installed directly on the body of the resistors using a thermally conductive epoxy. Burn tests were performed in vacuum at temperatures between -37C and +56C. The test shows many interesting results including the effect of the dyneema lines on the thermal response, the possibility of desoldering the burn resistors and a comparison between the performance at ambient and vacuum conditions. Finally, a summary is given of the key technical challenges associated with this type of mechanism along with some recommendations to help make future designs more robust and reliable