We will focus on recent developments of approximation methods and implementation schemes associated to the Boltzmann and Landau models for linear and binary collisional kinetic flows couple to mean field forces. These problems appear in several frameworks associated to mesoscales modeling of collisional plasma dynamics. Applications  focus on hot-electron ion (or vacancies) transport interactions in highly anisotropic spacial regimes generated by double layer potential formation due to large potential bias. The proposed conservative schemes  are given by  splitting spectral and Galerkin approaches for the flow dynamics. Examples will be discussed, first by exhibiting benchmarks simulations of relative entropy  decay rates and  spectral gaps calculation in admissible regimes,  and then calculating stable  Non-Equilibrium Statistical States (NESS) configurations due to  the effect of rough boundary conditions in the flow dynamics as much as the inverse reconstruction of the double potential layers for very high mean velocity due to strong field advection.



BIO
Irene M. Gamba is Professor of Mathematics and leader of the ICES Applied Mathematics Group. She holds the W.A. “Tex” Moncrief, Jr. Chair in Computational Engineering and Sciences III.

She earned her Ph.D. in mathematics at the University of Chicago in 1989 and held a National Science Foundation (NSF) postdoctoral fellowship at the Courant Institute at New York University, where she later became assistant and associate professor before coming to The University of Texas at Austin in 1997.

Gamba
 has held invited visiting positions at many universities and institutes, both nationally and internationally, including, Stanford and Columbia University, The University of Chicago, Ecole Normale Superiere at Paris, the Newton Institute at Cambridge University, UK; The Institute for Advanced Studies at Princeton; Kyoto University, Japan, Paul Sabatier University, Toulouse, France, and the Nice Sophia Antipolis University, France. She has been an organizer of long term programs for IPAM at 
UCLA in 2009 and the inaugural one for ICERM at Brown University in 2011.

In addition to being in the inaugural class of Fellows of the American Mathematical Society (2013), Gamba is also a Fellow of the Society for Industrial and Applied Mathematics (2012).

Gamba has served in the Scientific Advisory Board of IPAM and SAMSI Mathematics NSF Institutes.   She has been Chair and Program Director of the SIAM Activity Group
 on the Analysis of Partial Differential Equations (APDE). Gamba currently serves on the editorial board of several journals and is currently an editor for the Bulletin of the American Mathematical Society, the Journal of Mathematical Fluid Dynamics, and SIAM Journal in Applied Mathematics, and has been a member of Advisory Board member for Springer Graduate Texts in Mathematics (GTM) Series, among others. In addition, she has authored more than 120 research articles and her work has been and currently is  funded by NSF and U.S. Department of Energy programs.
 
She has delivered an invited address at The SIAM Conference on Analysis of Partial Differential Equation in December 2019, the SIAM-AWM invited address at the JMM 2017 meetings, received and delivered The Sonia Kowalesvka Lecture award at the SIAM annual Meeting 2014,  the  XV David Alcaraz Spinola Lecture Award, Universidad Autonoma de Mexico (2006), and the Matheon Distinguished Lecture at WIAS Berlin (2005) and AMS invited address at the CR meeting (2004).

Personal Page:  https://www.ma.utexas.edu/users/gamba/