Expansion of a singularly perturbed equation with a two-scale converging convection term

In many physical contexts, evolution convection equations may present some very large amplitude convective terms. As an example, in the context of magnetic confinement fusion, the distribution function that describes the plasma satisfies the Vlasov equation in which some terms are of the same order as $\epsilon^{-1}$, $\epsilon \ll 1$ being the characteristic gyrokinetic period of the particles around the magnetic lines. In this paper, we aim to present a model hierarchy for modeling the distribution function for any value of $\epsilon$ by using some two-scale convergence tools. Following Fr\'enod \\& Sonnendr\"ucker's recent work, we choose the framework of a singularly perturbed convection equation where the convective terms admit either a high amplitude part or a an oscillating part with high frequency $\epsilon^{-1} \gg 1$. In this abstract framework, we derive an expansion with respect to the small parameter $\epsilon$ and we recursively identify each term of this expansion. Finally, we apply this new model hierarchy to the context of a linear Vlasov equation in three physical contexts linked to the magnetic confinement fusion and the evolution of charged particle beams

Two-dimensional Finite Larmor Radius approximation in canonical gyrokinetic coordinates

In this paper, we present some new results about the approximation of the Vlasov-Poisson system with a strong external magnetic field by the 2D finite Larmor radius model. The proofs within the present work are built by using two-scale convergence tools, and can be viewed as a new slant on previous works of Fr\'enod and Sonnendr\"ucker and Bostan on the 2D finite Larmor Radius model. In a first part, we recall the physical and mathematical contexts. We also recall two main results from previous papers of Fr\'enod and Sonnendr\"ucker and Bostan. Then, we introduce a set of variables which are so-called canonical gyrokinetic coordinates, and we write the Vlasov equation in these new variables. Then, we establish some two-scale convergence and weak-* convergence results

Two-scale semi-lagrangian simulation of a charged particle beam in a periodic focusing channel

This paper is devoted to numerical simulation of a charged particle beam submitted to a strong oscillating electric field. For that, we consider a two-scale numerical approach as follows: we first recall the two-scale model which is obtained by using two-scale convergence techniques; then, we numerically solve this limit model by using a backward semi-lagrangian method and we propose a new mesh of the phase space which allows us to simplify the solution of the Poisson's equation. Finally, we present some numerical results which have been obtained by the new method, and we validate its efficiency through long time simulations

Asymptotic-Preserving scheme for a bi-fluid Euler-Lorentz model

The present work is devoted to the simulation of a strongly magnetized plasma considered as a mixture of an ion fluid and an electron fluid. For the sake of simplicity, we assume that the model is isothermal and described by Euler equations coupled with a term representing the Lorentz force. Moreover we assume that both Euler systems are coupled through a quasi-neutrality constraint. The numerical method which is described in the present document is based on an Asymptotic-Preserving semi-discretization in time of a variant of this two-fluid Euler-Lorentz model with a small perturbation of the quasi-neutrality constraint. Firstly, we present the two-fluid model and the motivations for introducing a small perturbation into the quasi-neutrality equation, then we describe the time semi-discretization of the perturbed model and a fully-discrete finite volume scheme based on it. Finally, we present some numerical results which have been obtained with this method

Efficacy of a web-based, center-based or combined physical activity intervention among older adults

peer reviewedWith more social support and environment-centered interventions being recommended in web-based interventions, this study examined the efficacy of three intervention conditions aimed at promoting physical activity (PA) in older adults. The efficacy analyses included the self-reported PA level, stage of change for PA and awareness about PA among participants. Eligible participants (N = 149; M = 65 years old, SD = 6), recruited in a unique Belgian French-speaking municipality, were randomized in four research arms for a 3-month intervention: (i) web-based; (ii) center-based; (iii) mixed (combination of web- and center-based); and (iv) control (no intervention). Web-based condition included a PA website and monthly tailored emails whereas center-based condition comprised 12 sessions (1 per week) of group exercising. With a significant increase in PA, the PA stage of change and the PA awareness at 12 months, the mixed intervention condition seemed to include the key social and motivating elements for sustainable behavior change. Center-based intervention was more likely to produce significant improvements of the PA level and the stage of change for PA change whereas web-based intervention was more likely to extend the awareness about PA

Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field

In this paper, we build a Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field. This consists in writing the solution of this equation as a sum of two oscillating functions with circonscribed oscillations. The first of these functions has a shape which is close to the shape of the Two-Scale limit of the solution and the second one is a correction built to offset this imposed shape. The aim of such a decomposition is to be the starting point for the construction of Two-Scale Asymptotic-Preserving Schemes.Comment: Mathematical Models and Methods in Applied Sciences 00, 00 (2012) 1 --

Numerical resolution of an anisotropic non-linear diffusion problem

International audienceThis paper is devoted to the numerical resolution of an anisotropic non-linear diffusion problem involving a small parameter ε, defined as the anisotropy strength reciprocal. In this work, the anisotropy is carried by a variable vector function b. The equation being supplemented with Neumann boundary conditions, the limit ε → 0 is demonstrated to be a singular perturbation of the original diffusion equation. To address efficiently this problem, an Asymptotic-Preserving scheme is derived. This numerical method does not require the use of coordinates adapted to the anisotropy direction and exhibits an accuracy as well as a computational cost independent of the anisotropy strength

A “start to swim” program for health-enhancement purpose: a Delphi study

Introduction Popularity of “start to run” or “start to cycle” programs increases with the evidence that regular physical activity contributes to the prevention and management of a wide range of chronic diseases (Rippe and Angelopoulos, 2010). Nevertheless, start to swim programs could lead to even more health-enhancing outcomes (Chase et al., 2008). The aim of this study was to obtain a “start to swim” model program by means of a two-round Delphi study. Methods In the first round, 10 key-experts in sport physiology (n=4) or in swimming coaching (n=6) outlined possible relevant components of the “start to swim” program in a semi-structured interview. Initial exclusion criterion, program set-up, program key principles, program progression and final goals were interrogated. Then, a facilitator provided an anonymous summary of the experts’ suggestions from the previous round as well as the arguments they provided for their choice. In the second round, experts were asked to comment on this summary before providing a final form to this program. Results After two rounds, the experts agreed on a collective and coached intervention with 2 sessions per week and a progressive replacing of the coach by a group leader during a 4 months program. People without medical contraindication and able to swim 25 meters could take part to this program. The final goal-setting is personal and based on each individual progression and motivation. Sessions are endurance-oriented and divided between traditional swimming sessions and diversified aquatic activities. In order to support this active lifestyle in a long-term basis, referring to swimming clubs or other aquatic activities associations are performed by the coach at the end of the program. Discussion The start to swim program take into consideration behavioural and social aspects necessary for a successful adoption and maintenance of physical activity (Khan et al, 2002). Consistent with previous findings, a group-based program (Cox et al., 2008) with individually adapted-goals (Marcus and Forsyth, 2003) could lead to a long-term adherence to exercise. Future studies should include systematic evaluation of the “start to swim” program before translation into the community