A Multiscale Kinetic-Fluid Solver with Dynamic Localization of Kinetic Effects

This paper collects the efforts done in our previous works [P. Degond, S. Jin, L. Mieussens, A Smooth Transition Between Kinetic and Hydrodynamic Equations, J. Comp. Phys., 209 (2005) 665--694.],[P.Degond, G. Dimarco, L. Mieussens, A Moving Interface Method for Dynamic Kinetic-fluid Coupling, J. Comp. Phys., Vol. 227, pp. 1176-1208, (2007).],[P. Degond, J.G. Liu, L. Mieussens, Macroscopic Fluid Model with Localized Kinetic Upscaling Effects, SIAM Multi. Model. Sim. 5(3), 940--979 (2006)] to build a robust multiscale kinetic-fluid solver. Our scope is to efficiently solve fluid dynamic problems which present non equilibrium localized regions that can move, merge, appear or disappear in time. The main ingredients of the present work are the followings ones: a fluid model is solved in the whole domain together with a localized kinetic upscaling term that corrects the fluid model wherever it is necessary; this multiscale description of the flow is obtained by using a micro-macro decomposition of the distribution function [P. Degond, J.G. Liu, L. Mieussens, Macroscopic Fluid Model with Localized Kinetic Upscaling Effects, SIAM Multi. Model. Sim. 5(3), 940--979 (2006)]; the dynamic transition between fluid and kinetic descriptions is obtained by using a time and space dependent transition function; to efficiently define the breakdown conditions of fluid models we propose a new criterion based on the distribution function itself. Several numerical examples are presented to validate the method and measure its computational efficiency.Comment: 34 page

On derivation of Euler-Lagrange Equations for incompressible energy-minimizers

We prove that any distribution $q$ satisfying the equation $\nabla q=\div{\bf f}$ for some tensor ${\bf f}=(f^i_j), f^i_j\in h^r(U)$ ($1\leq r<\infty$) -the {\it local Hardy space}, $q$ is in $h^r$, and is locally represented by the sum of singular integrals of $f^i_j$ with Calder\'on-Zygmund kernel. As a consequence, we prove the existence and the local representation of the hydrostatic pressure $p$ (modulo constant) associated with incompressible elastic energy-minimizing deformation ${\bf u}$ satisfying $|\nabla {\bf u}|^2, |{\rm cof}\nabla{\bf u}|^2\in h^1$. We also derive the system of Euler-Lagrange equations for incompressible local minimizers ${\bf u}$ that are in the space $K^{1,3}_{\rm loc}$; partially resolving a long standing problem. For H\"older continuous pressure $p$, we obtain partial regularity of area-preserving minimizers.Comment: 23 page

Hormonally mediated effects of artificial light at night on behavior and fitness: linking endocrine mechanisms with function.

Alternation between day and night is a predictable environmental fluctuation that organisms use to time their activities. Since the invention of artificial lighting, this predictability has been disrupted and continues to change in a unidirectional fashion with increasing urbanization. As hormones mediate individual responses to changing environments, endocrine systems might be one of the first systems affected, as well as being the first line of defense to ameliorate any negative health impacts. In this Review, we first highlight how light can influence endocrine function in vertebrates. We then focus on four endocrine axes that might be affected by artificial light at night (ALAN): pineal, reproductive, adrenal and thyroid. Throughout, we highlight key findings, rather than performing an exhaustive review, in order to emphasize knowledge gaps that are hindering progress on proposing impactful and concrete plans to ameliorate the negative effects of ALAN. We discuss these findings with respect to impacts on human and animal health, with a focus on the consequences of anthropogenic modification of the night-time environment for non-human organisms. Lastly, we stress the need for the integration of field and lab experiments as well as the need for long-term integrative eco-physiological studies in the rapidly expanding field of light pollution

The solution of the nonlinear Boltzmann equation: A survey of analytic and computational methods

AbstractThis paper provides a survey and a critical overview of the mathematical results, analytic and computational, on the solution of the nonlinear Boltzmann equation. The topics dealt with in this paper are the following: mathematical formulation of initial and/or boundary value problems, existence theorems, computational treatment of fluid dynamical problems

Convergence analysis of domain decomposition algorithms with full overlapping for the advectiondi usion problems

The aim of this paper is to study the convergence properties of a Time Marching Algorithm solving Advection-Di usion problems on two domains using incompatible discretizations. The basic algorithm is rst presented, and theoretical or numerical results illustrate its convergence properties. This work has been supported by the Hermes Research program under grant numbe

Maximum Principles and Application to the Analysis of an Explicit Time Marching Algorithm

In this paper we develop local and global estimates for the solution of advection-di usion problems. We then study the convergence properties of a Time Marching Algorithm solving advection-di usion problems on two domains using incompatible discretizations. This study is based on a De-Giorgi-Nash maximum principle. This work has been supported by the Hermes Research program under grant numbe