On algebraic damping close to inhomogeneous Vlasov equilibria in multi-dimensional spaces

We investigate the asymptotic damping of a perturbation around inhomogeneous stable stationary states of the Vlasov equation in spatially multi-dimensional systems. We show that branch singularities of the Fourier-Laplace transform of the perturbation yield algebraic dampings. In two spatial dimensions, we classify the singularities and compute the associated damping rate and frequency. This 2D setting also applies to spherically symmetric self-gravitating systems. We validate the theory using a toy model and an advection equation associated with the isochrone model, a model of spherical self-gravitating systems.Comment: 37 pages, 10 figure

Motility-induced phase separation of active particles in the presence of velocity alignment

Self-propelled particle (SPP) systems are intrinsically out of equilibrium systems, where each individual particle converts energy into work to move in a dissipative medium. When interacting through a velocity alignment mechanism, and the medium acts as a momentum sink, even momentum is not conserved. In this scenario, a mapping into an equilibrium system seems unlikely. Here, we show that an entropy functional can be derived for SPPs with velocity alignment and density-dependent speed, at least in the (orientationally) disordered phase. This non-trivial result has important physical consequences. The study of the entropy functional reveals that the system can undergo phase separation before the orientational-order phase transition known to occur in SPP systems with velocity alignment.Moreover, we indicate that the spinodal line is a function of the alignment sensitivity and show that density fluctuations as well as the critical spatial diffusion, that leads to phase separation, dramatically increase as the orientational-order transition is approached.Comment: Published in J. Stat. Phy

Multi-physic system simplification method applied to a helicopter flight axis active control

A helicopter flight axis control, which is a complex multi-physic system, is modelled using an energetic based graphical tool: the Energetic Macroscopic Representation. Elements of the system are mainly composed of passive technologies and their number tends to increase year after year to improve the pilots comfort by adding new functions. A new methodology is proposed to transform the system into a new active one by replacing some hydro-mechanical elements by a new controllable active mechanical source. The challenge is to simplify the flight control architecture while preserving the global behaviour of the system

Modeling Stiffness and Damping in Rotational Degrees of Freedom Using Multibond Graphs

A contribution is proposed for the modeling of mechanical systems using multibond graphs. When modeling a physical system, it may be needed to catch the dynamic behavior contribution of the joints between bodies of the system and therefore to characterize the stiffness and damping of the links between them. The visibility of where dissipative or capacitive elements need to be implemented to represent stiffness and damping in multibond graphs is not obvious and will be explained. A multibond graph architecture is then proposed to add stiffness and damping in hree rotational degrees of freedom. The resulting joint combines the spherical joint multibond graph relaxed causal constraints while physically representing three concatenated revolute joints. The mathematical foundations are presented, and then illustrated through the modeling and simulation of an inertial navigation system; in which stiffness and damping between the gimbals are taken into account. This method is particularly useful when modeling and simulating multibody systems using Newton-Euler formalism in multibond graphs. Future work will show how this method can be extended to more complex systems such as rotorcraft blades' connections with its rotor hub.Fondation Airbus Grou

Statistical mechanics: contributions to rigidity percolation and long range interacting systems

This dissertation presents my scientific activities since the end of my PhD in 2003. During this period, I spent two years as a post doc at the Los Alamos National Laboratory (USA), in the Center for Non Linear Studies (CNLS) and the Condensed Matter group. Then, in Fall 2005, I was recruited as a ”Maˆıtre de Conf ́erences” at the Nice-Sophia Antipolis University, in the Mathematics Department.At first glance, my activity can be divided in two rather distinct themes: rigidity percolation on one side, and long range interacting systems on the other side, the latter regrouping a rather diverse body of works. However, my works in these two directions have several features in common. First, at the level of methods. In both cases, the problem is usually to understand some macroscopic properties starting from a microscopic modeling, using probabilistic tools: this might be a definition of the statistical mechanics endeavor in general. More precisely, tools from large deviation theory play an important role in many of the works presented here, both for rigidity percolation and long range interacting systems. Second, there are similarities in the strategies to attack the problems: I have often concentrated first on simple models, on which a detailed study is possible, before trying to extract a generic behavior.Although the statistical mechanics of long range interacting systems was already the subject of my PhD thesis, done under the joint supervision of Thierry Dauxois and Stefano Ruffo, my research on the subject has followed new directions since 2003: my position in a mathematics department gave me the opportunity to start a mathematically oriented research project on ki- netic limits for systems of interacting particles, with Pierre-Emmanuel Jabin and Maxime Hauray; at the same time, I started a collaboration with an experimental team on cold atoms in INLN (Institut Non Lin ́eaire de Nice).The dissertation is organized in two chapters: the first one is devoted to rigidity percolation, and the second one to long range interacting systems. In each case, I have tried to give a detailed and non technical introduction to the subject, to emphasize the motivations and questions behind my works, andto present and summarize my contributions. I then append to each chapter a few articles which I consider to best illustrate my scientific activity since 2003.There is one bibliography at the end of each chapter. Citations of the type [B*] refer to works of which I am a coauthor. These references are gathered at the end of the document for clarity.The works presented in this dissertation owe much to my numerous col- laborators during these years; I take this opportunity to warmly thank all of them

Multi-physic system simplification method applied to a helicopter flight axis active control

International audienceA helicopter flight axis control, which is a complex multi-physic system, is modelled using an energetic based graphical tool: the Energetic Macroscopic Representation. Elements of the system are mainly composed of passive technologies and their number tends to increase year after year to improve the pilots comfort by adding new functions. A new methodology is proposed to transform the system into a new active one by replacing some hydro-mechanical elements by a new controllable active mechanical source. The challenge is to simplify the flight control architecture while preserving the global behaviour of the system

Modelling and Control of an Effort Feedback Actuator in Helicopter Flight Control Using Energetic Macroscopic Representation

In helicopter field, electromechanical devices controllers are usually designed and tuned from global analysis with transfer functions calculations. This leads to control architectures with a reduced number of controllers. Their regulating loops are usually global PID controllers where parameters are directly set up on dedicated test benches. Energetic representation tools such as Energetic Macroscopic Representation (EMR) aim at simplifying systems analysis and control providing model and control structuring method. In this paper, a simplified helicopter flight axis control is modelled with the intention of controlling the helicopter stick force feedback. Performances of both global PID and energetic model based inversion controllers are discussed through simulation results

Complementary use of BG and EMR formalisms for multiphysics systems analysis and control

In this paper, a complex multiphysics system is modeled using two different energy-based graphical techniques: Bond Graph and Energetic Macroscopic Representation. These formalisms can be used together to analyze, model and control a system. The BG is used to support physical, lumped-parameter modeling and analysis processes, and then EMR is used to facilitate definition of a control structure through inversion-based methodology. This complementarity between both of these tools is set out through a helicopter flight control subsystem

Modelling and Control of an Effort Feedback Actuator in Helicopter Flight Control Using Energetic Macroscopic Representation

In helicopter field, electromechanical devices controllers are usually designed and tuned from global analysis with transfer functions calculations. This leads to control architectures with a reduced number of controllers. Their regulating loops are usually global PID controllers where parameters are directly set up on dedicated test benches. Energetic representation tools such as Energetic Macroscopic Representation (EMR) aim at simplifying systems analysis and control providing model and control structuring method. In this paper, a simplified helicopter flight axis control is modelled with the intention of controlling the helicopter stick force feedback. Performances of both global PID and energetic model based inversion controllers are discussed through simulation results