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\title{CURRICULUM VIT\AE}
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\Large{Francesco Vecil}
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\section{Curriculum vit\ae}
\subsection{Personal information}
\begin{itemize}
\item \textbf{Family name:} Vecil.
\item \textbf{Given name:} Francesco.
\item \textbf{Birth date and place:} 21 February 1978, Udine (Italy).
\item \textbf{Citizenship:} Italian.
\item \textbf{Address:} 48, rue Eug\`ene Gilbert, apt. 11, 63000 Clermont-Ferrand (France).
\item \textbf{Address 2:} via Como, 37/B, 33100 Udine, Italy.
\item \textbf{Address 3:} calle Mallorca, 494, $1^o$, $2^a$, Barcelona E08013, Spain.
\item \textbf{Professional address:} Laboratoire de Math\'ematiques,
Universit\'e Blaise Pascal (Clermont-Ferrand 2), UMR 6620 - CNRS - Campus des C\'zeaux - B.P. 80026, 63171 Aubi\`ere cedex (FRANCE).
\item \textbf{Mobile phone contact:} +33 (0)785764194 (France), +34 635924630 (Spain), +39 3291298154 (Italy).
\item \textbf{E-mail:} francesco.vecil@gmail.com
\item \textbf{Skype contact:} francesco.vecil
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Positions held}
\begin{itemize}
\item \textbf{01 October 2002-30 September 2006}: Ph.D. student at the
Universitat Aut\`onoma de Barcelona, supervisor Jos\'e
Antonio Carrillo, with Ph.D. fellowship IGSOC-IQUC
from the Catalan government.
\item \textbf{01 October 2006-30 September 2007}: Ph.D. student
at the Universit\'e de Toulouse, co-supervisor Naoufel Ben Abdallah,
with a European DEASE-Marie Curie fellowship.
\item \textbf{01 October 2007-30 November 2007}: Ph.D. student
at the Universitat Aut\`onoma de Barcelona
with a fellowship of the research group on
numerical simulation of PDEs.
\item \textbf{01 April 2008-30 September 2008}:
post-doctoral position at the Universidad de Granada
in the project ``Ingenio Mathematica''
(CSD2006-0032) in order to realize
``Deterministic quantum model for 2D MOSFETs. Comparison with Monte Carlo
and parallel implementation on a cluster of PCs'',
funded by the Spanish ministry for Education and Culture.
\item \textbf{01 October 2008-30 September 2010}:
post-doctoral position at the Radon Institute
for Computational and Applied Mathematics,
Austrian Academy of Sciences, Linz (Austria).
\item \textbf{01 October 2010-30 August 2013}:
post-doctoral position, with a Juan de la Cierva fellowship of the Spanish ministry,
at the Applied Mathematics department,
Universitat de Val\`encia (Spain).
\item \textbf{01 September 2013-}:
ma\^itre de conf\'erences (assistant professor)
at the Universit\'e Blaise Pascal, Clermont-Ferrand (France).
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Academic certificates}
\begin{itemize}
\item
\textbf{12/07/2002:} Degree in Mathematics, Universit\`a degli Studi di Padova, Italy.\\
\textbf{Degree thesis:} Asynchronous exponential growth in
age-structured populations.\\
\textbf{Supervisors:} Rosanna Bressan Villella, Lorenza Tonetto.\\
\item \textbf{2005:} Diploma de Estudios Avanzados (Master) in
Applied Mathematics, Universitat Aut\`onoma de Barcelona (Spain).\\
\textbf{Research project:} Non-oscillatory interpolation methods
applied to kinetic equations for plasmas.\\
\textbf{Supervisor:} Jos\'e Antonio Carrillo.\\
\textbf{Committee:} Llu\'is Alsed\`a, Francesc Xavier Mora,
Josep Maria Mondelo.
\item
\textbf{17/12/2007:} Ph.D. degree, Universitat Aut\`onoma de Barcelona (Spain).
\textbf{Thesis title:} A contribution to the simulation of Vlasov-based models.\\
http://www.tesisenxarxa.net/TDX-0314108-170950/\\
\textbf{Supervisors:} Jos\'e Antonio Carrillo, Naoufel Ben Abdallah.\\
\textbf{Committee:} Rosa Donat, Josep Maria Mondelo,
Mar\'ia J. C\'aceres, St\'ephane Cordier, Armando Majorana.
\item
\textbf{17/12/2007:} European Ph.D. degree, Universitat Aut\`onoma de Barcelona (Spain).
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Teaching r\'esum\'e}
\begin{itemize}
\item {\bf Numerical integration of PDEs},
30 hours, academic year 2005-06, Mathematics department,
Universitat Aut\`onoma de Barcelona (Spain).
\item {\bf Hyperbolic conservation laws}, 14 hours, academic year 2009-10,
Johannes Kepler Universit\"at, Linz (Austria).
\item {\bf Mathematics II}, 60 hours, academic year 2011-12,
Chemical Engineering, Universit\`at de Val\`encia, Burjassot - Val\`encia (Spain).
\item {\bf Mathematics II}, 60 hours, academic year 2012-13,
Chemical Engineering, Universit\`at de Val\`encia, Burjassot - Val\`encia (Spain).
\item {\bf Numerical Analysis}, 68 hours, academic year 2013/14,
L1 ISIMA, Cler\-mont-Ferrand (France).
\item {\bf Integrals and resolution of differential equations}, 28 hours (TD), academic year 2013/14,
L3 Physics, Universit\'e Blaise Pascal, Clermont-Ferrand (France).
\item {\bf Numerical Analysis}, 14 hours (TD), academic year 2013/14, Polytech, Cler\-mont-Ferrand (France).
\item {\bf Series and Differential Calculus}, 56 hours (TD), academic year 2013/14, L2 Physics, Universit\'e Blaise Pascal, Clermont-Ferrand (France).
\item {\bf General Mathematics 2}, 30 hours (TD), academic year 2013/14, L1 Mathematics, Universit\'e Blaise Pascal, Clermont-Ferrand (France).
\item {\bf Module Math\'ematiques A/B}, 85 h., academic year 2014-15, L1, Universit\'e Blaise Pascal, Clermont-Ferrand (France).
\item {\bf Math\'ematiques (21MP31)}, 30 h., academic year 2014-15, L2, Universit\'e Blaise Pascal, Clermont-Ferrand (France).
\item {\bf Int\'egrales (31MM59)}, 26 h., academic year 2014-15, L3, Universit\'e Blaise Pascal, Clermont-Ferrand (France).
\item {\bf Harmonisation 2 (41FM12)}, 16 h., academic year 2014-15, M1, Universit\'e Blaise Pascal, Clermont-Ferrand (France).
\item {\bf Math\'ematiques G\'en\'erales 2 (11MM22)}, 30 h., academic year 2014-15, L1, Universit\'e Blaise Pascal, Clermont-Ferrand (France).
\item {\bf Analyse Num\'erique (370P6NUM)}, 14 h., academic year 2014-15, Polytech, Clermont-Ferrand (France).
\item {\bf Module A ou B Math\'ematiques (11MM11)}, 85 h., academic year 2015-16, L1, Universit\'e Blaise Pascal, Clermont-Ferrand (France).
\item {\bf Math\'ematiques (21MP31)}, 30 h., academic year 2015-16, L2, Universit\'e Blaise Pascal, Clermont-Ferrand (France).
\item {\bf Int\'egrales, r\'esolution d'\'equations diff\'erentielles (31MM59)}, 26 h., academic year 2015-16, L3, Universit\'e Blaise Pascal, Clermont-Ferrand (France).
\item {\bf Harmonisation - M\'ethodes num\'eriques (41FM12)}, 16 h., academic year 2015-16, M1, Universit\'e Blaise Pascal, Clermont-Ferrand (France).
\item {\bf Math\'ematiques appliqu\'ees \`a la chimie (21MM311)}, 25 h., academic year 2015-16, L2, Universit\'e Blaise Pascal, Clermont-Ferrand (France).
\item {\bf M\'ethodes num\'eriques (31MM55)}, 14 h., academic year 2015-16, L2, Universit\'e Blaise Pascal, Clermont-Ferrand (France).
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Research r\'esum\'e}
\noindent \textbf{Main research fields:}
\begin{itemize}
\item WENO, semi-Lagrangian, Strang splitting, finite-differences Runge-Kutta,
A\-dap\-tive Mesh Refinement and discontinuous-Galerkin
methods for hyperbolic and kinetic equations;
\item realistic simulation of a nanoscaled MOSFET;
\item simulation of laser-plasma interaction models and
of the guiding-center model for plasma physics;
\item simulation of particle and kinetic models for swarming;
\item simulation of radiative transfert models.
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\noindent \textbf{R\'esum\'e.} My research activity has developed around
the numerical simulation of problems having an interest for physics or
engineering, namely the simulation of semiconductors, plasmas, collective
behavior models and the radiative transfert equation.
During my Ph.D. studies I validated numerical methods based on
WENO interpolation and splitting on kinetic test cases of
increasing difficulty, from linear advection, passing
through the Vlasov-Poisson model, up to a
Boltzmann-Schr\"odinger-Poisson
system to describe the transport and the eigenstates
inside nanoscaled MOSFETs, for which quantum effects become non-neglectable.
Moreover, I afforded the simulation of problems
related to plasma physics, with a 1D model describing
the laser-plasma interaction.
During my post-doctoral positions (Granada 2008, Linz 2008-2010 and Valencia 2010-),
I have begun several research lines: the CPU and GPU parallelization of the
solver for the nanoMOSFETs; the simulation of particle and kinetic
collective behavior models; thanks to the participation
to the cemracs 2010, a Discontinuous Galerkin scheme for the guiding-center model,
involved in fusion energy models;
the implementation of a Discontinuous Galerkin method
for the radiative transfert equation, interesting
for medical purposes; application of an Adaptive Mesh Refinement
strategy to semi-Lagrangian solvers for hyperbolic conservation laws
and to the Vlasov-Maxwell system for laser-plasma interaction.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Publications}
\begin{enumerate}
\item J.A. Carrillo, F. Vecil, ``Non oscillatory interpolation methods
applied to Vlasov-based models'', {\bf SIAM Journal
on Scientific Computing} 29, 1179-1206, 2007.
\item J.A. Carrillo, A. Majorana, F. Vecil, ``A Semi-lagrangian
deterministic solver for the semiconductor Boltzmann-Poisson system'',
{\bf Communications in Co\-mpu\-ta\-tio\-nal Physics} 2, 1027-1054, 2007.
\item J.A. Carrillo, T. Goudon, P. Lafitte, F. Vecil, ``Numerical Schemes
of Diffusion Asymptotics and Moment Closures for Kinetic Equations'',
{\bf Journal of Scientific Computing}, 35, 113-149 (2008).
\item N.B. Abdallah, M.J. C\'aceres, J.A. Carrillo, F. Vecil,
``A deterministic solver for a hybrid quantum-classical
transport model in nanoMOSFETs'', {\bf Journal of Computational Physics},
vol. 228, nr. 17, 6553-6571 (2009).
\item J. A. Carrillo, M. Fornasier, G. Toscani, F. Vecil,
``Particle, Kinetic, and Hydrodynamic Models of Swarming'',
in Naldi, G., Pareschi, L., Toscani, G. (eds.)
\textbf{Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences},
Series: Modelling and Simulation in Science and Technology, Birkhauser, (2010), 297-336.
\item Pep Mulet, Francesco Vecil,
``A semi-Lagrangian AMR scheme for 1D and 2D hyperbolic conservation laws'',
\textbf{Journal of Computational Physics} vol. 237 (2013), 151--176.
\item Francesco Vecil, Pauline Lafitte, Jes\'us Rosado,
``Numerical analysis on attraction/repulsion collective behavior model'',
\textbf{Physica D Nonlinear Phenomena}, special
issue related to the BIRS meeting, vol. 260 (2013), 127--144.
\item Francesco Vecil, Jos\'e Miguel Mantas, Mar\'ia J. C\'aceres, Carlos Sampedro,
Andr\'es Godoy, Francisco G\'amiz,
``A parallel deterministic solver for the Schr\"odinger-Poisson-Boltzmann
system in ultra-short DG-MOSFETs: Comparison with Monte Carlo'',
\textbf{Computers and Mathematics with Applications} vol. 67 (2014), 1703--1721.
\item Francesco Vecil, Pep Mulet, Simon Labrunie,
``WENO schemes applied to the quasi-relativistic Vlasov-Maxwell
model for laser-plasma interaction'', accepted for publication in
{\bf Comptes Rendus de M\'ecanique} for the special issue
``Theoretical and Numerical Approaches for Vlasov-Maxwell Equations'' (2014).
\end{enumerate}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\textbf{Proceedgins. }
\begin{enumerate}
\item Fischer, M., Moriarty J., Nordhausen, K., Panov, I. and Vecil, F. (2006):
``Dynamic Traffic Control''. In Heili\"o, M. and Kauranne, T. (editors)
\textbf{Proceedings of the 18th ECMI Modelling Week 13.-21. August 2004},
39-47, Research Report 101, Lappeenranta University of Technology, Lappeenranta.
\item Nicolas Crouseilles, Michel Mehrenberger, Francesco Vecil,
``Discontinuous-Galerkin semi-Lagrangian method for
Vlasov-Poisson'', {\bf CEMRACS 2010 research achievements: numerical modeling of fusion},
ESAIM: proceedings vol. 32, (2011), 211-230.
\end{enumerate}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\textbf{Works in progress. }
\begin{enumerate}
\item Mar\'ia J. C\'aceres, Francisco G\'amiz, Andr\'es Godoy,
Jos\'e Miguel Mantas, Carlos Sampedro, Francesco Vecil,
``The impact of the surface roughness in the Schr\"dinger-Poisson-Boltzmann solver for ultra-short DG-MOSFETs''.
\item Mar\'ia J. C\'aceres, Jos\'e Miguel Mantas, Francesco Vecil,
``GPU implementation of the Schr\"dinger-Poisson-Boltzmann solver for ultra-short DG-MOSFETs''.
\item Antonio Baeza Manzanares, Simon Labrunie, Pep Mulet Mestre, Francesco Vecil,
``An electrodynamic AMR solver for the quasi-relativistic Vlasov-Amp\`ere-Maxwell model''.
\item Massimo Fornasier, Francesco Vecil,
``Numerical analysis on Cucker-Smale collective behavior models''.
\item Nicolas Crouseilles, Michel Mehrenberger, Francesco Vecil,
``A Discontinuous-Galerkin semi-Lagrangian scheme for the
guiding-center problem''.
\item Pauline Lafitte, Francesco Vecil,
``Two-dimensional continuum simulation of attraction/repulsion collective behavior models''.
\item Armando Majorana, Francesco Vecil,
``A Discontinuous-Galerkin solver for the radiative
transfer equation''.
\end{enumerate}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Seminars and talks}
\begin{itemize}
\item
\textbf{Semi-Lagrangian method for pointwise WENO interpolation}.
D\'e\-par\-te\-ment de Math\'ematiques, Universit\'e de Nancy (France).
1 June 2005.
\textbf{Seminar}.
\item
\textbf{Non oscillatory interpolation methods applied to kinetic equations for plasmas},
Journ\'ees EDPs et Applications, Communaut\'e de Travail des Pyr\'en\'ees.
Universit\'e Paul Sabatier, Toulouse (France).
30 September 2005.
\textbf{Seminar}.
\item
\textbf{A solver for a coupled quantum-clas\-si\-cal model for nanoMOSFETs},
DEASE Summer-school and Annual Meeting.
Wolfgang Pauli Institut, Vienne (Austria).
09-14 July 2007.
\textbf{Talk}.
\item
\textbf{Hybrid model for 2D quantum transport},
International Workshop in Computational Electronics.
University of Massachusetts, Amherst MA (\'Etats Unis).
08-10 October 2007.
\textbf{Poster}.
\item
\textbf{A semi-Lagrangian deterministic solver for a hybrid quantum-clas\-si\-cal nanoMOSFET},
COMSON International Summer School on Modelling and Optimization
for the Design of Electronic Circuits and Devices.
Baia Samuele, Sampieri (Italy).
14-21 June 2008.
\textbf{Talk}.
\item
\textbf{A semi-lagrangian deterministic solver for a hybrid quantum-clas\-si\-cal nanoMOSFET},
minisymposium ``M15: Mathematical Problems from Semiconductor Industry''.
SIMAI $9^{th}$ congress, Roma (Italy).
15-19 September 2008.
\textbf{Talk}.
\item
\textbf{Splitting methods for the solution of electron transport in semiconductors},
Radon Institute for Computational and Applied Mathematics, Linz (Austria).
7 October 2008.
\textbf{Seminar}.
\item
\textbf{A deterministic hybrid quantum/classical solver for a nanoscaled MOSFET device},
Quantum Systems and Semiconductor Devices: Analysis, Simulation, Applications.
Peking University (Chine).
20-24 April 2009.
\textbf{Talk}.
\item
\textbf{Simulation of a Double Gate MOSFET through a hybrid quantum/classical model},
PDEs in Engineering Nanoscience and Biology.
Hotel Le Royal, Hammamet (Tunisia).
May 2010.
\textbf{Talk}.
\item
\textbf{Simulation of a Double Gate MOSFET through a hybrid quantum-classical model},
minisymposium ``Advanced Numerical Simulations for Kinetic Equations''.
Joint SIAM/RSME-SCM-SEMA Meeting Emerging Topics in Dynamical Systems and Partial Differential Equations, Bar\-ce\-lo\-na (Spain).
31 May-4 June 2010.
\textbf{Talk}.
\item
\textbf{Realistic simulation of a Double Gate MOSFET through a hybrid quantum-classical model},
minisymposium ``MSP23 - Mathematical Models and Numerical Methods for Charge Transport in Semiconductors''.
Joint SIMAI/SEMA conference on Applied and Industrial Mathematics, Cagliari (Italy).
21-25 June 2010.
\textbf{Talk}.
\item
\textbf{Simulation of a Double Gate MOSFET through a hybrid quantum-classical model},
minisymposium ``MSP34 - New Trends in Kinetic Theory''.
Joint SIMAI/SEMA conference on Applied and Industrial Mathematics, Cagliari (Italy).
21-25 June 2010.
\textbf{Talk}.
\item
\textbf{Some applications of kinetic equations},
Departament de Matem\`atica Aplicada, Universitat de Val\`encia (Spain).
23 February 2011.
\textbf{Seminar}.
\item
\textbf{Simulation of sub-band model for ultra-short DG MOSFET devices},
held at the congress in memory of Naoufel Ben Abdallah
``Kinetic models of classical and quantum particle systems'',
Institut de Math\'ematiques de Toulouse (France), 14-18 March 2011.
\textbf{Talk}.
\item
\textbf{Implementaci\'on de simuladores realistas de dispositivos DG-MOS\-FET a nanoescala en plataformas de altas prestaciones}
(Implementation of a realistic solver for nanoscaled DG-MOSFET devices on high-per\-for\-mance platforms),
held at the Department of Applied Mathematics, Universidad de Granada (Spain), 12 July 2011. \textbf{Seminar}.
\item
\textbf{AP schemes for intermediate models between a kinetic equation and its diffusive limit},
held at the 9th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2011), G-Hotels, Halkidiki (Greece), 19-25 September 2011. \textbf{Talk}.
\item
\textbf{Numerical analysis of attraction/repulsion collective behavior models},
conference ``Analysis, Modeling and Simulation of Collective Dynamics from Bacteria to Crowds''
held at the CISM (International Center for Mechanical Sciences), Udine (Italy), 9-13 July 2012. \textbf{Talk}.
\item
\textbf{A semi-Lagrangian AMR scheme for 2D transport problems in conservation form},
minisymposium ``Adaptive Numerical Techniques for Partial Differential Equations'',
conference ``WONAPDE 2013, Fourth Chilean Workshop on Numerical Analysis of Partial Differential Equations''
held at the Universidad de Concepci\'on, Concepci\'on (Chile), 14-18 January 2013. \textbf{Talk}.
\item
\textbf{A semi-Lagrangian AMR scheme for 2D transport problems in conservation form},
session ``Numerical Methods for Partial Differential Equations'',
conference ``CSASC 2013'',
held at Koper/Capodistria (Slovenia), 9-13 June 2013. \textbf{Talk}.
\item
\textbf{Deterministic simulation of a DG-MOSFET through a parallel sol\-ver},
JERAA 2013, held at Saint-\'E\-tien\-ne (France), 22 November 2013. {\bf Talk}.
\item
\textbf{Semi-Lagrangian Adaptive-Mesh-Refinement method for transport problems},
journ\'ee de l'\'equipe EDPAN, Laboratoire de Math\'ematiques, UBP, 16 January 2014. {\bf Seminar}.
\item
\textbf{Deterministic simulation of a DG-MOSFET through a parallel sol\-ver},
held at Laboratoire Jean Kuntzmann, Grenoble (France), 7 February 2014. {\bf Seminar}.
\item
\textbf{Deterministic simulation of a DG-MOSFET through a parallel solver},
held at the 2014 ECMI congress, Taormina (Italy), 13 June 2014. {\bf Talk}.
\item
\textbf{A parallel deterministic solver for a DG-MOSFET device},
held at the Department of Applied Mathematics, Universitat de Val\`encia, Burjassot (Spain), 24 July 2014. {\bf Seminar}.
\item
\textbf{A parallel deterministic solver for DG-MOSFETs},
held at the Workshop on PDEs: Modelling, Analysis and Numerical Simulations,
Granada (Spain), 18 September 2014. {\bf Talk}.
\item
\textbf{Simulaci\'on determinista de un MOSFET de doble puerta. Implementaci\'on paralela},
Granada (Spain), 19 June 2015. {\bf Seminar}.
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Administrative activities and other competences}
\subsubsection{Referee activity}
Activity of refereeing for the following journals:
\begin{itemize}
\item Communications in Computationl Physics.
\item Journal of Computational and Applied Mathematics.
\item Journal of Scientific Computing.
\item Journal of Computational and Theoretical Transport.
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Conference and workshop organisation}
\begin{itemize}
\item
\textbf{Minisymposium ``Advanced Numerical Simulations for Kinetic E\-qua\-tions'',
Joint SIAM/RSME-SCM-SEMA Meeting Emerging Topics in Dynamical Systems and
Partial Differential Equations. Bar\-ce\-lo\-na (Spain), 31 May-4 June 2010.}\\
This minisymposium was organized by Jingmei Qiu and myself.
The organization consisted in inviting the participants,
writing the program and chair the sessions.
\item
\textbf{Special session ``Numerical techniques for the description of charged particles transport'',
10th AIMS International Conference. Madrid (Spain). 7-11 July 2014.}\\
I am the only organizer of this special session. The organization consists in inviting
the participants, writing the program and chair the sessions.
\end{itemize}
\subsubsection{Languages and informatic skills}
{\bf Languages:}
\begin{itemize}
\item Italian (native);
\item English (Certificate of Proficiency in English, Cambridge, corresponding to C2, the
highest level of the Common European Framework of Reference);
\item French (DALF C2, the highest level of the Common European Framework of Reference);
\item Spanish (Diploma de Espa\~{n}ol como Lengua Extranjera, nivel superior, Instituto Cervantes, corresponding
to C2, the highest level of the Common European Framework of Reference);
\item Catalan (EOI Barcelona Drassanes, C2, the highest level of the Common European Framework of Reference);
\item Arabic (beginner);
\item German (beginner).
\end{itemize}
{\bf Informatics skills:}
\begin{itemize}
\item Environments: Linux (Ubuntu) and Windows.
\item Software: LaTeX, Gnuplot, Office, Mathematica (beginner), Xfig.
\item Languages: C++, C, Fortran 77 (beginner) et 90 (beginner), Bash.
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Teaching activity}
\subsection{General comments}
During my Ph.D. studies I did not acquire much
teaching experience, as I gave only one course. I have
been responsible for the practical work of the course
on ``Numerical integration of PDEs'', of the final year
of the degree in Mathematics at the
Universitat Aut\`onoma de Barcelona.
During my staying in Austria I gave the practical work
of the course ``Hyperbolic Conservation Laws'' at the
Johannes Kepler Universit\"at Linz, open to
degree, master and Ph.D. students.
During the Juan de la Cierva post-doctoral position,
I gave the course ``Mathematics II'' of the first year
of the degree in Chemical Engineering, in the
Universitat de Val\`encia.
\subsection{Details of teaching activity}
\subsubsection{Numerical integration of PDEs (practical work)}
{\bf Degree:} mathematics, Universitat Aut\`onoma de Barcelona (Spain).\\
{\bf Year:} $4^{\mbox{th}}$ year (BAC+4).\\
{\bf Academic year:} 2005-06.\\
{\bf Hours:} 30.\\
{\bf Program:} the course was dedicated to the analysis and
implementation in language C of a solver for the heat equation in 1D.\\
{\bf Persons in charge:} Josep Maria Modelo for the theoretical part,
Francesco Vecil for the practical work.\\
{\bf Personal task:} I was the sole responsible for the practical
work of the course, of which I have decided the program and
the final examination.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Hyperbolic conservation laws (practical work)}
{\bf Degree:} mathematics, Johannes Kepler Universit\"at Linz (Austria).\\
{\bf Year:} degree, master, Ph.D.\\
{\bf Academic year:} 2009-10.\\
{\bf Hours:} 14.\\
{\bf Program:} the course has as a goal the analysis
of consistency, convergence and stability, and the
implementation in language C++ of the simplest finite differences schemele
to solve the test case of linear advection.\\
{\bf Persons in charge:} Massimo Fonte for the theoretical part,
Francesco Vecil for the practical work.\\
{\bf Personal task:} I have been the sole responsible for the
practical work of the course, of which I have decided the program.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Mathematics II (theory and practical work)}
{\bf Degree:} chemical engineering, Universitat de Val\`encia (Spain).\\
{\bf Year:} $1^{\mbox{st}}$ (BAC+1).\\
{\bf Academic years:} 2011-12, 2012-13.\\
{\bf Hours:} 60.\\
{\bf Program:} the course has as goals the teaching of partial derivatives,
integration in two and three dimensions, methods for solving ODEs,
series, Fourier series, complex variable functions.\\
{\bf Persons in charge:} Francesco Vecil for the theory and the practical work.\\
{\bf Personal task:} I have been the sole responsible for the
course, of which I have decided the program and the examinations.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Numerical Analysis}
\noindent {\bf Degree:} ISIMA, Clermont-Ferrand (France).\\
{\bf Year:} BAC+3.\\
{\bf Academic years:} 2013-14.\\
{\bf Hours:} 68 \'equiv. TD.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Integrals and solution of differential equations}
\noindent {\bf Degree:} Universit\'e Blaise Pascal, Clermont-Ferrand (France).\\
{\bf Year:} L3 (Physics).\\
{\bf Academic year:} 2013-14, 2014-15, 2015-16.\\
{\bf Hours:} 26.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Numerical analysis}
\noindent {\bf Degree:} Polytech, Clermont-Ferrand (France).\\
{\bf Year:} L2.\\
{\bf Academic year:} 2013-14, 2014-15.\\
{\bf Hours:} 14.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Series}
\noindent {\bf Degree:} Universit\'e Blaise Pascal, Clermont-Ferrand (France).\\
{\bf Year:} L2 (Physique).\\
{\bf Academic year:} 2013-14.\\
{\bf Hours:} 28.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Math\'ematiques G\'en\'erales 2 (11MM22)}
\noindent {\bf Degree:} Universit\'e Blaise Pascal, Clermont-Ferrand (France).\\
{\bf Year:} L1.\\
{\bf Academic year:} 2013-14, 2014-15.\\
{\bf Hours:} 30.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Module A ou B Math\'ematiques (11MM11)}
\noindent {\bf Degree:} Universit\'e Blaise Pascal, Clermont-Ferrand (France).\\
{\bf Year:} L1.\\
{\bf Academic year:} 2014-15, 2015-16.\\
{\bf Hours:} 85.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Math\'ematiques (21MP31)}
\noindent {\bf Degree:} Universit\'e Blaise Pascal, Clermont-Ferrand (France).\\
{\bf Year:} L2 (Physique).\\
{\bf Academic year:} 2014-15, 2015-16.\\
{\bf Hours:} 30.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Harmonisation - M\'ethodes Num\'eriques (41FM12)}
\noindent {\bf Degree:} Universit\'e Blaise Pascal, Clermont-Ferrand (France).\\
{\bf Year:} M1.\\
{\bf Academic year:} 2014-15, 2015-16.\\
{\bf Hours:} 16.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Mathematics applied to chemistry (21MM311)}
\noindent {\bf Degree:} Universit\'e Blaise Pascal, Clermont-Ferrand (France).\\
{\bf Year:} L2.\\
{\bf Academic year:} 2015-16.\\
{\bf Hours:} 25.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsubsection{Numerical methods (31MM55)}
\noindent {\bf Degree:} Universit\'e Blaise Pascal, Clermont-Ferrand (France).\\
{\bf Year:} L2.\\
{\bf Academic year:} 2015-16.\\
{\bf Hours:} 14.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Research activity}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Participation to schools and conferences}
\begin{itemize}
\item \textbf{1-5 September 2003:}
New challanges in applied mathematics, Castro Urdiales (Spain).
%% \\
%% \textbf{Speakers:}
%% I. Alonso (Valladolid, Spain),
%% J.D. Benamou (INRIA, France),
%% F. Brezzi (Pavia, Italy),
%% G. Buttazzo (Pisa, Italy),
%% J.A. Carrillo (Barcelona, Spain),
%% V. Caselles (Barcelona, Spain),
%% L. Escauriaza (Bilbao, Spain),
%% M.J. Esteban (Ceremade, France),
%% I. Fonseca (USA),
%% R. Glowinski (Hoiston, USA),
%% F. Guillen (Sevilla, Spain),
%% M. Jaoua (Tunis, Tunisia),
%% A. Jorba (Barcelona, Spain),
%% I. Losada (Santander, Spain),
%% N. Masmoudi (USA),
%% J.P. Puel (Versailles, France),
%% J.P. Raymond (Toulouse, France),
%% J. Soler (Granada, Spain),
%% F. Tr\"oltzsch (Berlin, Allemagne),
%% J.L. V\'azquez (Madrid, Spain).
\item {\bf 13-21 August 2004:} ECMI Modelling Week,
Lappeenranta, Finland, summer 2004.
\item \textbf{29 September - 1 October 2005:}
Journ\'ees EDPs et Applications, Communaut\'e de Travail
des Pyr\'en\'ees, Universit\'e Paul Sabatier, Toulouse (France).
\item {\bf 11-17 September 2006:} Quantum transport: modelling,
analysis and a\-sym\-pto\-tics, CIME 2006, Cetraro (Italy).
%% \\
%% {\bf Speakers:} Tom Hou, Gregoire Allaire, Pierre Degond, Anton Arnold.
\item \textbf{09-14 July 2007:}
DEASE Summer-school and Annual Meeting, Wolfgang Pauli Institut, Vienne (Austria).
\item \textbf{08-10 October 2007:}
International Workshop in Computational Electronics,
University of Massachusetts, Amherst MA (USA).
%% \\
%% \textbf{Main speakers:} Roberto Car (Princeton University, USA),
%% Massimiliano Di Ventra (University of California-San Diego, USA),
%% David Di Vincenzo (IBM Research, USA),
%% Wilfried Haensch (IBM Research, USA),
%% Yoshinari Kamakura (Osaka University, Japan),
%% Bob Keyes (IBM Research, USA),
%% Craig Lent (University of Notre Dame, USA),
%% Mathieu Luisier (ETH, Zurich, Swit\-zer\-land),
%% Alessandro Pecchia (Universit\`a di Roma-Tor Vergata, Italy),
%% B. Montgomery Pettitt (University of Houston, USA).
\item \textbf{15-21 November 2007}: Advanced school on numerical solution of partial differential
equations. Barcelona (Spain).
%% \\
%% \textbf{Main speakers:}
%% Silvia Bertoluzza, (CNR - Pavia, Italy),
%% Jaume Peraire, (Massachusetts Institute of Technology, USA),
%% Giovanni Russo, (Universit\`a di Catania, Italy),
%% Chi-Wang Shu, (Brown University, USA).
\item \textbf{14-21 June 2008:} COMSON International Summer School on Modelling and Optimization
for the Design of Electronic Circuits and Devices, Baia Samuele, Sampieri (Italy).
%% \\
%% {\bf Speakers:}
%% N. B. Abdallah (Universit\'e Paul Sabatier, France),
%% A. Ferron (Silvaco, France),
%% M. Fischetti (University of Massachusetts, USA),
%% A. Juengel (University of Vienna, Austria),
%% O. Muscato (Universit\`a di Catania, Italy),
%% A. Nannipieri (Synopsys, Switzerland),
%% F. Bufler (Synopsys, Switzerland),
%% G. Mascali (Universit\`a di Cosenza, Italy),
%% G. Al\'i (Universit\`a di Cosenza, Italy),
%% C. Drago (Universit\`a di Catania, Italy).
\item \textbf{15-19 September 2008:}
SIMAI $9^{th}$ congress, Roma (Italy).
%% \\
%% {\bf Main speakers:}
%% Antonio Ambrosetti (SISSA, Trieste),
%% Douglas N. Arnold (University of Minnesota, USA),
%% Nicola Bellomo (Politecnico di Torino),
%% Giovanni Ciccotti (Universit\`a di Roma La Sapienza, Italy),
%% Nicholas J. Higham (University of Manchester, United Kingdom),
%% Alfio Quarteroni.
\item \textbf{20-24 April 2009:}
Quantum Systems and Semiconductor Devices: Analysis,
Simulation, Applications, Peking University (Chine).
%% \\
%% {\bf Speakers:}
%% Massimo FISCHETTI (University of Massachusetts),
%% Shimin HOU (Peking University),
%% Walter P\"OTZ (Graz University),
%% Hans KOSINA (TU Wien),
%% Yuhui HE (Peking University),
%% Shaoqiang TANG (Peking University),
%% Lukas NEUMANN (TU Wien),
%% Jan SPRENGER (TU Wien),
%% Tong YANG (City University),
%% Li CHEN (Tsinghua University),
%% Joachim REH\-BERG (WI\-AS-Ber\-lin),
%% Daniel MATTHES (TU Wien),
%% Othmar KOCH (TU Wien),
%% Isabelle CATTO (Universit\'e, Paris-Dauphine),
%% Vittorio ROMANO (Universit\`a di Catania),
%% Martin VASICEK (TU Wien),
%% Claudia Ambrosch-Draxl (Leoben University),
%% Anton ARNOLD (TU Wien),
%% Weizhu BAO (National University of Singapore),
%% Christophe BESSE (Universit\'e de Lille 1),
%% Richard SHARP (Carnegie Mellon University),
%% Sihong SHAO (Peking University),
%% Gang DU (Peking University),
%% Francesco VECIL (RICAM Linz),
%% Jan HASKOVEC (TU Wien),
%% Shu WANG (Beijing University of Technology),
%% Hailiang LI (Capital Normal University),
%% Kaijun ZHANG (North-Eastern Normal University),
%% Zhiping YU (Tsinghua University),
%% Wei ZHANG (Peking University),
%% Ke Zong/Xuan ZENG (Fudan University),
%% Tiao LU (Peking University).
\item \textbf{1-5 September 2009:} Comson International
School for Modeling and Optimization in Micro- and
Nano-electronics, Cetraro (Italy).
%% \\
%% {\bf Main speakers:}
%% Martin Arnold (Martin-Luther-Universitat Halle, Ger\-ma\-ny),
%% Andreas Bartel (Bergische Universitat Wuppertal, Germany),
%% Luis Bonilla (Universidad Carlos III, Madrid, Spain),
%% Luca Daniel, MIT (USA).
\item \textbf{15-18 September 2009:} Summer School 2009:
Modelling and simulation for magnetic fusion, Strasbourg (France).
%% \\
%% \textbf{Speakers:} P. Beyer (Marseille),
%% J.-P. Boeuf (Toulouse),
%% M. Bostan (Besan\c{c}on),
%% S. Br\'emond (DEA),
%% W. Dorland (Maryland, USA),
%% V. Grandgirard (Cadarache),
%% S Jaouen (CEA),
%% S Jin (Madison, USA),
%% G. Manfredi (Strasbourg),
%% F. Rapetti (Nice),
%% K. Schneider (Marseille),
%% P. Strand (Chalmers, Sweden).
\item \textbf{17-21 May 2010:}
PDEs in Engineering Nanoscience and Biology,
Hammamet (Tunisia).
\item \textbf{31 May-4 June 2010:}
Joint SIAM/RSME-SCM-SEMA Meeting
Emerging Topics in Dynamical Systems and
Partial Differential Equations
DSPDEs'10, Barcelona (Spain).
%% \\
%% \textbf{Main speakers: }
%% C\'edric Villani,
%% Rosa Donat,
%% Amadeu Delshams,
%% Dwight Barkley,
%% Jos\'e Valero,
%% Alexis Vasseur,
%% Andrea Bertozzi,
%% Amy Novick-Cohen,
%% Marco A. Fontelos,
%% Manuel Doblar\'e,
%% Kenneth M. Golden,
%% Ingrid Daubechies,
%% Douglas N. Arnold,
%% Arnd Scheel,
%% Jean Dolbeault,
%% Mary Silber,
%% Clarence Eugene Wayne,
%% Jes\'us Sanz-Serna,
%% Carles Sim\'o,
%% Andrew Stuart,
%% Xavier Cabr\'e.
\item \textbf{21-25 June 2010:}
Joint SIMAI/SEMA conference on Applied and Industrial Mathematics,
Cagliari (Italy).
%% \\
%% \textbf{Main speakers: }
%% Luca Formaggia,
%% Carlos Par\'es,
%% Benedetto Piccoli,
%% Luigi Preziosi,
%% Peregrina Quintela,
%% Anna Tramontano,
%% Juan Luis V\'azquez,
%% Enrike Zuazua.
\item {\bf 19 July - 27 August 2010:} CEMRACS (Centre d'\'et\'e de math\'ematiques et de recherche
avanc\'ee en calcul scientifique) 2010: ``Numerical models for fusion'',
Marseille (France).
%% \\
%% {\bf Main speakers:}
%% Pierre Degond (CNRS, IMT Toulouse),
%% Bruno Despr\'es (Paris 6),
%% Xavier Blanc (CEA),
%% Virginie Grandgirard (CEA Cadarache),
%% Ste\-phen C. Jardin (PPPL),
%% C\'edric Villani (ENS Lyon).
\item \textbf{8-12 October 2010:}
PDEs in kinetic theories: kinetic description of biological models,
Edinburgh (Scotland, United Kingdom).
%% \\
%% \textbf{Speakers: }
%% Pierre Degond (Universit\'e de Toulouse et CNRS),
%% Mohammed Lemou (IRMAR, CNRS et Univestit\'e Rennes 1),
%% Raffaele Esposito (Universit\`a dell'Aquila),
%% Rosanna Marra (Universit\`a di Roma Tor Vergata),
%% Sebastien Motsch (University of Maryland),
%% Jos\'e Alfredo Ca\~nizo (Universitat Aut\`onoma de Barcelona),
%% Jos\'e Antonio Carrillo (Universitat Aut\`onoma de Barcelona),
%% Beno\^it Perthame (Universit\'e Pierre et Marie Curie),
%% Timothy Pedley (University of Cambridge),
%% Massimo Fornasier (RICAM),
%% Eitan Tadmor (University of Maryland),
%% Jorge Zubelli (Instituto Nacional de Matem\'atica Pura e Aplicada),
%% Adrien Blanchet (Universit\'e de Toulouse),
%% Zhongyi Huang (Tsinghua University),
%% Klemens Fellner (University of Cambridge),
%% Piotr Gwiazda (University of Warsaw),
%% Clement Mouhot (University of Cambridge),
%% Francesco Salvarani (Universit\`a degli Studi di Pavia),
%% Thierry Paul (CNRS et CMLS, \'Ecole Polytechnique),
%% Laurent Desvillettes (\'Ecole Normale Sup\'erieure de Cachan),
%% Alexander Lorz (University of Cambridge),
%% Athanasios Tzavaras (University of Crete),
%% Clemens Heitzinger (University of Cambridge),
%% Armando Majorana (Universit\`a degli Studi di Catania),
%% Pierre-Emmanuel Jabin (University of Nice),
%% Kevin Painter (Heriot-Watt University),
%% Anne Nouri (CMI, Universit\'e de Provence).
\item \textbf{14-18 March 2011:}
Kinetic models of classical and quantum particle systems,
held in memory of Naoufel Ben Abdallah at the
Institut de Ma\-th\'e\-ma\-ti\-ques de Toulouse (France).
\item
\textbf{19-25 September 2011:} 9th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2011),
held at G-Hotels, Halkidiki (Greece).
\item
\textbf{9-13 July 2012:}
Analysis, Modeling and Simulation of Collective Dynamics from Bacteria to Crowds,
International Center for Mechanical Sciences (CISM), Udine (Italy).
\item
\textbf{14-18 January 2013:},
WONAPDE 2013, Fourth Chilean Workshop on Numerical Analysis of Partial Differential Equations,
Universidad de Concepci\'on, Concepci\'on (Chile).
\item
\textbf{9-13 June 2013},
CSASC 2013, held at Koper/Capodistria (Slovenia).
\item
\textbf{21-22 November 2013},
JERAA 2013, held at Saint-\'Etienne (France).
\item
\textbf{9-13 June 2014},
ECMI 2014, held in Taormina (Italy).
\item
\textbf{8-12 July 2014},
AIMS 2014, The 10th AIMS Conference on Dynamical Systems,
Differential Equations and Applications, held in Madrid (Espagne).
\item
\textbf{15-19 September 2014},
PDE-MANS 2014, Workshop on PDEs: Modelling, Analysis and Numerical Simulation,
held in Granada (Spain).
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Collaborations with other institutions}
\begin{itemize}
\item
Center: Laboratoire MIP (Math\'ematiques pour l'Industrie et la Physique),
Institut de Math\'ematiques de Toulouse,
Universit\'e Paul Sabatier, Toulouse (France).\\
Duration: 3 weeks.\\
Year: 2004.\\
Topic: solvers for kinetic equations.\\
Collaborators: Naoufel Ben Abdallah.
\item
Center: D\'epartement de Math\'ematiques, Universit\'e de Nancy (France).\\
Duration: 1 week.\\
Year: 2005.\\
Topic: implementation of a time-splitting WENO schem for laser-plasma interaction.\\
Collaborators: Simon Labrunie.
\item
Center: Dipartimento di Matematica e Informatica,
Universit\`a di Catania (Italy).\\
Duration: 1 week.\\
Year: 2006.\\
Topic: implementation of a time-splitting WENO method for
the Boltzmann-Poisson system for semiconductors.\\
Collaborators: Armando Majorana.
\item
Center: Mathematics department,
Johannes Gutenberg Universit\"at, Mainz (Germany).\\
Duration: 2 weeks.\\
Year: 2006.\\
Topic: Energy Transport models applied to transport problems.\\
Collaborators: Stefan Holst.
\item
Center: D\'epartement de Math\'ematiques,
Universit\'e de Lille (France).\\
Duration: 1 week.\\
Year: November 2006.\\
Topic: numerical methods for macroscopic limits of kinetic equations.\\
Collaborators: Thierry Goudon, Pauline Lafitte, Jos\'e Antonio Carrillo.
\item
Center: Center of mathematical Sciences,
Universit\'e de Cambridge (UK).\\
Duration: 2 weeks.\\
Year: 17/11/2008 - 29/11/2008.\\
Topic: solvrs for chemotaxis problems.\\
Collaborators: Peter Markowich, Klemens Fellner, Massimo Fornasier.
\item
Center: Institut de Math\'ematiques de Toulouse,
Universit\'e de Toulouse (Fran\-ce).\\
Duration: 3 days.\\
Year: January 2009.\\
Topic: solver for a coupled quantum/classical model for nanoMOSFETs.\\
Collaborators: Naoufel Ben Abdallah, Jos\'e Antonio Carrillo.
\item
Center: Departament de Matem\`atiques,
Universitat Aut\`onoma de Barcelona (Spain).\\
Duration: 3 weeks.\\
Year: January 2009.\\
Topic: kinetic solvers for swarming, flocking et milling problems.\\
Collaborators: Jos\'e Antonio Carrillo, Jos\'e Alfredo Ca\~nizo,
Jes\'us Rosado.
\item
Center: Departamento de Matem\'aticas,
Universidad de Granada (Spain).\\
Duration: 1 month.\\
Year: July 2009.\\
Topic: parallel implementation of a deterministic solver for
the sub-band Boltzmann-Schroedinger-Poisson model
for nanoMOSFETs.\\
Collaborators: Mar\'ia J. C\'aceres, Jos\'e Miguel Mantas, Carlos Sampedro, An\-dr\'es Godoy.
\item
Center: D\'epartament de Matem\`atiques,
Universitat Aut\`onoma de Barcelona (Spain).\\
Duration: 1 week.\\
Year: November 2009.\\
Topic: numerical simulation of collective behavior models.\\
Collaborators: Jos\'e Antonio Carrillo.
\item
Center: Laboratoire de Math\'ematiques de Toulouse,
Universit\'e Paul Sabatier, Toulouse (France).\\
Duration: 1 week.\\
Year: November 2009.\\
Topic: an AP (asymptotic-preserving) scheme for the simulation of
sub-band models for nanoMOSFETs.\\
Collaborators: Naoufel Ben Abdallah, Marie-H\'el\`ene Vignal.
\item
Center: Centre International de Rencontres Math\'emqtiques, Luminy, Marseille (France).\\
Duration: 6 weeks.\\
Year: 19 July-27 August 2010.\\
Topic: CEMRACS 2010: numerical models for fusion.\\
Organizers: N. Crouseilles (INRIA Nancy-Grand-Est),
H. Guillard (INRIA-Sophia Antipolis M\'editerran\'ee),
B. Nkonga (Universit\'e de Nice et INRIA),
E. Sonnendr\"ucker (Universit\'e de Strasbourg et INRIA).
\item
Center: Newton Institute for Mathematical Sciences,
University of Cambridge.\\
Duration: 2 months.\\
Year: 1 November 2010-22 December 2010.\\
Topic: Partial Differential Equations in Kinetic Theories.\\
Organizers: J.A. Carrillo (Barcelona), S. Jin (Wisconsin) et P.A. Markowich (Cambridge).
\item
Center: IRMA (Institut de Recherche Math\'ematique Avanc\'ee), Universit\'e de Strasbourg.\\
Duration: 1 week.\\
Period: 28 February 2011-4 March 2011.\\
Topic: Implementation of a Discontinuous Galerkin scheme for the guiding-center model.\\
Collaborators: Nicolas Crouseilles (INRIA Strasbourg), Michel Mehrenberger (Strasbourg).
\item
Center: Departamento de Matem\'aticas,
Universidad de Granada (Spain).\\
Duration: 1 month.\\
Year: July 2011.\\
Topic: implementation of a deterministic Boltzmann-Schroedinger-Poisson sub-band model
for nanoMOSFETs on a high-performance platform.\\
Collaborators: Mar\'ia J. C\'aceres, Jos\'e Miguel Mantas, Carlos Sampedro, An\-dr\'es Godoy.
\item
Center: Departamento de Matem\'aticas,
Universidad de Granada (Spain).\\
Duration: 1 month.\\
Year: June 2012.\\
Topic: GPU version of the deterministic solver for partially-confined DG-MOSFETs.\\
Collaborators: Mar\'ia J. C\'aceres, Jos\'e Miguel Mantas, Carlos Sampedro, An\-dr\'es Godoy.
\item
Center: Department of Applied Mathematics, Technical University of Munich, Garching-Munich (Germany).\\
Duration: 1 week (17-21 December 2012).\\
Year: December 2012.\\
Topic: numerical analysis of the Cucker-Smale collective behavior model.\\
Collaborator: Massimo Fornasier.
\item
Center: \'Ecole Centrale Paris, Ch\^ateney-Malabry (France).\\
Duration: 1 week (11-15 february 2013).\\
Year: February 2013.\\
Topic: Implementation of the 2D kinetic solver for an attractive/repulsive collective behavior model.\\
Collaborator: Pauline Lafitte.
\item
Center: Universidad de Granada (Spain).\\
Duration: 2 week.\\
Year: June 2013.\\
Topic: GPU version of the deterministic solver for partially-confined DG-MOSFETs.\\
Collaborator: Mar\'ia J. C\'aceres, Jos\'e Miguel Mantas, Carlos Sampedro, An\-dr\'es Godoy.
\item
Center: Departamento de Matem\'aticas, Universitad de Granada (Spain).\\
Duration: 20 June-8 July 2014.\\
Topic: parallelization on GPU of the subband solver for the Boltzmann-Schr\"o\-din\-ger-Poisson system for nanoMOSFETs, and
implementation of the surface roughness scattering phenomenon.\\
Collaborators: Jos\'e Miguel Mantas (Universidad de Gra\-na\-da), Mar\'ia J. C\'aceres (Universidad de Gra\-na\-da),
Carlos Sampedro (Universidad de Gra\-na\-da), Andr\'es Godoy (Universidad de Gra\-na\-da).
\item
Center: Departament de Matem\`atica Aplicada,
Universitat de Val\`encia (\-Es\-pa\-gne).\\
Duration: 14-25 July 2014.\\
Topic: electrodynamic solver for the quasi-relativistic Vlasov-Maxwell solver.\\
Collaborators: Pep Mulet Mestre, Antonio Baeza Manzanares.
\item
Center: Departamento de Matem\'aticas, Universitad de Granada (Spain).\\
Duration: 2 weeks, 2015.\\
Topic: parallelization on GPU of the subband solver for the Boltzmann-Schr\"o\-din\-ger-Poisson system for nanoMOSFETs.\\
Collaborators: Jos\'e Miguel Mantas, Mar\'ia J. C\'aceres.
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Participation to research projects}
\begin{itemize}
\item Qualitative properties of PDEs and diffusion equations.\\
Funded by: DGI-MEC (Ministry for education and culture).\\
Reference: MTM2005-08024.\\
Period: 2005-2008.\\
Main researcher: Jos\'e Antonio Carrillo.
\item Deterministic kinetic model for 2D MOSFET.
Comparaison with Monte Carlo and parallel implementation on a cluster of PCs.\\
Reference: CSD2006-0032 / FUT-C2-0041.\\
Period: 01/12/2007-30/11/08.\\
Main researcher: Mar\'ia J. C\'aceres.
\item Alta resoluci\'on y adaptatividad en modelos hiperb\'olicos y procesamiento de im\'agenes
(High resolution and adaptivity in hyperbolic models and image processing).
Reference : MINECO MTM2011-22741 (Spanish Ministry of Economic Affairs and Competitiveness).\\
Period : 2012-2014.\\
Main researchers : Pep Mulet, Rosa Donat.
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{R\'esum\'e of the results}
%% My research activity has developed around the numerical simulation
%% of problems which are interesting from the point of view of physics and
%% engineering, in particular the simulation of semiconductors, of plasmas,
%% of collective behaviour models and recently of the radiative transfert
%% equation. During my Ph.D. studies I worked to validate numerical techniques
%% based on WENO interpolation and splitting on some kinetic test cases of
%% increasing complexity, from linear advection, passing through the
%% Vlasov-Poisson model, to a system of Boltzmann equations coupled to a
%% Schr\"odinger-Poisson system to describe the eigenstates of nanoscaled
%% semiconductors, where the quantum effects cannot be neglected anymore.
%% Before the defence of my thesis, I have also started working of problems
%% related to plasma physics, with a one-dimensional model describing the
%% laser-plasma interaction. More recently, thanks to the participation to
%% cemracs 2010, I have afforded the simulation of the guiding-center model
%% through a Discontinuous Galerkin scheme. During my post-doctoral stage
%% in Austria I have started working on swarming models, which find an
%% application in many domains. Very recently I began a new research
%% line by testing a Discontinuous Galerkin method for the radiative
%% transfert equation, which is relevant for medical clinics.
\subsection{During the Ph.D. thesis}
My main research activity developed with Jos\'e Antonio Carrillo of the
Universitat Aut\`onoma de Barcelona (Spain). Under his supervision
I developed numerical methods for the simulation of evolution problems
described through hyperbolic and kinetic PDEs. This category of problems
is traditionally treated through a Runge-Kutta time discretisation,
coupled to finite differences or Galerkin discretisations for the
phase-space, e.g. WENO (Weighted Essentially Non Oscillatory) methods
for flux reconstruction. This strategy is robust and quite precise,
but the constraint on the time-step, CFL condition, forces a large
number of iterations, and increasingly larger proportionally to the
grid refinement. It is with the aim of avoiding this constraint on the
time-step that Strang splitting schemes become
attractive. In exchange of a loss in the order-in-space (usually a
second-order splitting is used instead of the third-order
Total Variation Diminishing Runge-Kutta) and of some additional
difficulties to a proper description of the asymptotic state,
splitting methods allow for faster simulations, and are very
effective for the description of transient states. Another advantage is the
possibility of decomposing a complex problem into simpler problems, solving these
last ones for separate and recombining them to approximate the solution of the
complete problem. In particular, in the case of kinetic problems, the fundamental
block is the solution of a one-dimensional advection problem, either linar or nonlinear.
The first step of my work of thesis has, therefore, been the implementation and
validation of a method for the one-dimensional linear advection, namely a
semi-Lagrangian method based on reconstruction at the foot of characteristics.
As interpolation we have chosen the PWENO (Pointwise WENO) scheme, a method
which we have implemented at an arbitrary precision; nevertheless, for
practical purpose, some routines have been optimized in order to minimise the
computational times. The results have been validated through other methods
in the literature and through the analysis of the scheme and comparisons with analytic solutions.
Once the method has been validated in the simplest test case, it has been
involved in increasingly complicated problems: first of all a two-dimensional
test of a Boltzmann equation with a relaxation operator and a given potential,
where the transport part is split from the collisional part (time splitting),
the phase-space is split (dimensional splitting) and advections are linear.
After that, the second test case has been a Vlasov-Fokker-Planck system,
where the advection is nonlinear. The third test case has been a non-collisional
Vlasov-Poisson system, where the advection stages have to be coupled to a
solver for the electric field: we have implemented the classical test case
of Landau damping, both linear and nonlinear, and the two-stream instability.
The fourth and last test case used to validate the method has been a simple
one-dimensional diode with collisions described through a relaxation operator.
The results have been publushed in the \textbf{SIAM Journal on Scientific Computing}.
During my Ph.D. thesis I went to Nancy to implement with Simon Labrunie a
splitting method for a Vlasov-Maxwell system which describes the effect
of a laser penetrating into a plasma. The code has given good results,
but this work has not been published yet.
During my Ph.D. we have, together with Armando Majorana of Catania,
implemented a splitting method for a semiconductor in which the collisional
operator described the scattering due to acoustic and optical phonons with
multiple frequencies, after a one-week visit in Sicily. This work has given
satisfactory results and has been published
in \textbf{Communications in Computational Physics}. With the method we have proposed,
adding as many scattering phenomena as we wanted has been easy.
A work slightly separated from the line of the other ones in my thesis has
been a collaboration we had with Thierry Goudon and Pauline Lafitte
in Lille: we have worked on intermediate models between a simple kinetic
equation with relaxation to a Gaussian and its diffusive limit the heat
equation. First-order and second-order closures of the moment equations
have been written and schemes for all these regimes have been written and
implemented. The methods have been validated on typical test cases of this
domain (the Su-Olson test) and the results have been published
in the \textbf{Journal of Scientific Computing}.
Before the defence of my Ph.D. thesis I obtained a pre-doctoral DEASE-Marie
Curie fellowship to spend one year in Toulouse under the co-supervision of
Naoufel Ben Abdallah: there, I have begun the implementation of a kinetic
solver for the sub-band model describing a nanoscaled partially-confined
Double Gate MOSFET: quantum effects are not neglectable anymore, stationary
Schr\"odinger equations have to be solved in the confinement direction.
\subsection{After the Ph.D. thesis}
The research activity developed during my Ph.D. studies has been carried on
after my Ph.D. defence.
With Mar\'ia J. C\'aceres I have worked with a six-month
post-doctoral position in Granada. There, I finished the first part of the work
begun in Toulouse: an article with the methods for the computation of the
eigenstates of the nanoscaled MOSFET, and simulations in the simplified case
of one-valley band structure and relaxation as scatterings. This work has
been published on the \textbf{Journal of Computational Physics}.
Once the numerical schemes have been prepared in a simplified case, I have
implemented a realistic model of interest for engineering, with
three-valley silicon band-structure, non-parabolic bands, and a scattering
operator with seven electron-phonon interaction phenomena.
The goal of our code is to be a reference result for other less accurate but less costly models.
In Granada works Jos\'e Miguel Mantas, an informatic engineer specialist in parallel
computing: with him we have reduced the computational times thanks
to the parallelization on a cluster of CPUs.
This work will be sent soon to the Journal of Scientific Computing.
The parallelization on GPUs and adding the roughness as scattering phenomenon are works \textbf{in progress}.
Between October 2008 and September 2010 I had a post-doctoral position in
Austria (RICAM, Linz): there, I started working with Massimo Fornasier on the simulation
of swarming models, both at particle and kinetic level, this last one being
its mesoscopic limit, needed when the number of agents is too large, like e.g.
the migration of fish schools. In particular, with Massimo Fornasier we have
focused on the Cucker-Smale model, which is a simple orientation model:
the agents try to correct their velocities by observing their neighbours.
These models have an interest in several domains in which a set of individuals converge
to a uniform behaviour even if there is no leader. The paper concerning the numerical
study of this model is being revised after the first reply from Physica D.
On similar topics I also work
with other people, namely Jes\'us Rosado and Pauline Lafitte: in this case
the reference model tries to describe another characteristic of the behaviour of animal species, the
fact of being social and wanting to stay close, but not too much, to other
similars; this is modeled by an attraction/repulsion potential. This work
has been accepted for publication in \textbf{Physica D}. The extension to the
continuum 2D setting is \textbf{in progress}.
During summer 2010 I participated to the cemracs, in Luminy (Marseille), where with
Nicolas Crouseilles and Michel Mehrenberger we have implemented a
semi-Lagrangian Discontinuous Galerkin scheme for the simulation of the guiding-center
model: the first part of the work describes how we solve
the one-dimensional linear advection and how we pass to the two-dimensional case through
a Strang splitting; the solver has then been validated with the classical test cases
of Landau damping and bump-on-tail (published as a peer-reviewed \textbf{proceeding});
the second part of the work describes how
we solve the 1D and 2D nonlinear advection, and the coupling to a Poisson solver
in order to simulate the guiding-center model (\textbf{in progress}).
In end 2010 I started working with Armando Majorana of the University of Catania on the
implementation of a Discontinuous Galerkin solver for the radiative transfert
equation. He had the idea of treating separately the velocity-space and the
position-space; the first one is treated by a low-order Discontinuous Galerkin
method, which gives a system of PDEs in the other variables, system which, a
priori, can be solved by any other method. This work is \textbf{in progress}.
Since 2011, with Pep Mulet of the
University of Valencia, we are affording the application of an Adaptive Mesh Refinement
(AMR) strategy to 1D and 2D semi-Lagrangian solvers for hyperbolic conservation laws: the
idea is to use different resolution levels in the domain, depending on the features of the
distribution function, thus using many discretization points only where needed
and avoiding unnecessary time integrations. Our schemes have been
successfully tested on the test cases of linear and nonlinear advection,
nonlinear Landau damping, two-stream instability, swirling deformation flow
and Kelvin-Helmholtz instabilities. The results have been published in the \textbf{Journal of Computational Physics}.
We now aim at applying this solver to the simulation of laser-plasma interaction
through the quasi-relativistic 1D Vlasov-Maxwell system (with Pep Mulet, Simon Labrunie,
\textbf{in progress}).
After summer 2012, I have gone back to a work which has long been suspended,
namely the simulation of a Vlasov-Maxwell model to describe the effect of a laser
penetrating into a plasma; our goal is to test several novelties at the same
time: a semi-Lagrangian splitting scheme for the quasi-relativistic problem,
its coupling to an AMR strategy, and the transformation into AMR of a classical
finite-differences Runge-Kutta scheme. This work is \textbf{in progress}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Future plans}
\begin{itemize}
%% \item Implementation of a semi-Lagrangian Discontinuous Galerkin scheme
%% for the guiding-center model.
%% The guiding-center model is interesting in the domain of nuclear fusion.
%% The Discontinuous Galerkin schemes are attractive because they allow
%% a better resolution of the density thanks to a local refinement of the
%% meshes, thus avoiding the constraint on the time step; moreover,
%% it is a good starting point for the parallelization of the code.
%% During the cemracs 2010 we have, with Nicolas Crouseilles et
%% Michel Mehrenberger, started implementing this kind of solver,
%% and we have tested these methods for the Vlasov-Poisson model,
%% with a Strang splitting in the phase-space. The difference
%% in the guiding-center case is that the advection is nonlinear
%% and the force field is 2D. The state of the art is the following: we
%% are able to solve the 2D Poisson equation on a Discontinuous
%% Galerkin discretization, we are able to solve the nonlinear advection
%% for a given advection field, but we have not found yet a good
%% strategy to couple transport and Poisson, because the Galerkin basis
%% is Discontinuous and we cannot just advect through a
%% discontinous field.
\item \emph{Simulation of the quasi-relativistic Vlasov-Maxwell model
for laser-plasma interaction, through a semi-Lagrangian Strang-split AMR scheme.}
Adaptive Mesh Refinement (AMR) strategies can be used to speed up
simulations in which there are zones of the domain that do not
carry essential information and that can be thus given less resolution than others.
By now, with Pep Mulet of
the University of Valencia, we have implemented a 1D semi-Lagrangian solver,
extended to 2D thanks to the Strang splitting, we have coupled it
to a fast solver (FFTW) for the Poisson equation, and we have tested it against
classical, academic test cases (results published on the \textbf{Journal of Computational Physics}).
Several features of this solver can still be improved:
the use of resolution-adapted time steps;
the use of a different solver for the advection, namely in order to improve the conservation properties;
improve the approximation of Jacobian by higher-order schemes inside the characteristic-based
formula for the the time integration.
We wish now to apply our solver to a problem of interest in the field of fusion research:
the laser-plasma interaction, described by a 1D Vlasov-Maxwell model.
Fixed-mesh schemes based on finite differences and a Runge-Kutta time integration
have already been implemented by Simon Labrunie. We wish now to
provide three novelties: coupling the \emph{leap-frog} Yee scheme for the computation of the
Maxwell part to a semi-Lagrangian Strang-split WENO scheme for the transport part,
so as to be allowed to use larger time steps; coupling this method
to an AMR strategy; using the AMR strategy also for the finite-differences scheme.
At the end we aim at an empirical hint about the most effective way of integrating
the quasi-relativistic Vlasov-Maxwell system.
This work is \textbf{in progress} (with Simon Labrunie and Pep Mulet).
\item \emph{Deterministic simulation for a partially-confined DG-MOSFET
through the Boltzmann-Schr\"odinger-Poisson model.}
The MOSFET is the fundamental block of any electronic device.
The technological development produces smaller and smaller transistors,
and now sizes have been reached for which quantum effects cannot be
neglected anymore, most of all because of the confinement in the
transversal direction. Nowadays' solvers are usually Monte Carlo,
which is noisy and provides unreliable information in the zones
with a low electron density, or macroscopic, which lack precision.
This is why it is interesting to have a deterministic solver,
whose goal is to provide reference results even if it is
computationally costlier than other methods.
In 2006 I have started working on this topic in Toulouse with Naoufel Ben Abdallah
(my thesis' co-supervisor). The numerical methods for the computation
of the confinement have been written
(the results are published on the \textbf{Journal of Computational Physics}),
and a big implementation effort has been made. In this first stage
we have used Cartesian coordinates for the wave vector and a semi-Lagrangian splitting scheme
for the time integration.
We have now improved the solver in several directions:
seven electron-phonon interaction phenomena;
ellipsoidal coordinates for the wave vector in order to better integrate the scattering operator;
Runge-Kutta time discretization coupled to a finite-differences WENO scheme,
which is better suitable for ellipsoidal coordinates for the wave vector;
MPI-parallel code on a cluster of CPUs;
comparison to Monte Carlo.
The work up to here is going to be sent soon to the \textbf{Journal of Scientific Computing}.
Apart from that, we are also improving the model by
taking into account the surface roughness phenomenon
and we are developing a parallel code on the GPU (through CUDA libraries),
with the ultimate goal of developing an open computational platform (\textbf{in progress}).
This work is being developed with
Mar\'ia J. C\'aceres (mathematician),
Jos\'e Miguel Mantas (informatic engineer),
Carlos Sampedro, Andr\'es Godoy et Francisco G\'amiz (electronic engineers),
all of them from the University of Granada.
\item \emph{Implementation of a semi-Lagrangian discontinuous-Galerkin (DG) scheme
for the guiding-center model.}
The guiding-center model is of interest in the field of nuclear fusion.
DG schemes allow for an improvement of the resolution
thanks to a local refinement, which gives no constraint on the time stepping
and allows for a parallelization of the code.
During cemracs 2010 we have, with Nicolas Crouseilles and Michel
Mehrenberger, started implementing this kind of solvers, and we have tested
these methods for the Vlasov-Poisson model, with a Strang-split phase space.
These results are published as (peer-reviewed) \textbf{proceeding}.
The difference in the case of the guiding-center model is that the advection
is non-constant (with respect to the advected variable)
and that the field is 2D. The state-of-the-art is the following:
we can solve the 2D Poisson equation on a DG discretization,
we can solve the non-constant advections and therefore we can simulate
the guiding-center model. Still, our strategy should be compared to those
in the litterature and the \emph{divergence-free} condition should be numerically imposed.
This work is \textbf{in progress}.
\item \emph{Numerical analysis of collective-behavior models.}
Collective-behavior models aim at describing situations in which a certain
amount of agents achieve a uniform behavior even if there is no leader,
like e.g. bird flocks, the development of languages in primitive societies,
the averaging of prices in stock exchanges.
With Massimo Fornasier, we have worked on the numerical analysis of the Cucker-Smale
model, which is a simple orientation model: the ``birds'' modify their velocities
by copying the direction of their neighbors. The paper with the results is
being revised at \textbf{Physica D}. Our work up to now mainly concerns the results
in the discrete context; still, we wish to perform an exaustive
numerical study in the continuum setting, a work which is \textbf{in progress}.
With Pauline Lafitte and Jes\'us Rosado, we have worked on a different kind
of model, of the attractive/repulsive category; the numerical study on
the 3D discrete case and the 1D continuum case has been published in \textbf{Physica D},
and the extension to the 2D continuum setting is \textbf{in progress}.
\item \emph{Developement and implementation of a Discontinuous Galerkin scheme
for the radiative transfert equation.}
The radiative transfert equation has arisen to a new interest
in the field of medical analyses. Armando Majorana had the idea
of treating the kinetic equations in a quite simple way: first of all
we integrate in velocity through a first order Discontinuous Galerkin discretization,
then a set of kinetic equations has to be solved, which can
be realized with any method, for instance with a Discontinuous
Galerkin method coupled to a Runge-Kutta time discretization
for the sake of coherence. We obtain a quite simple scheme which
we want to implement and test on benchmarks in the literature.
This work is \textbf{in progress}.
\item \emph{Spectral methods for the integration of
scattering phenomena for the Boltzmann equation.}
When, in the Boltzmann equation, the scattering operator
is essentially given by a sum of Dirac masses,
a spectral method could be used. Mar\'ia J.
C\'aceres and Cl\'ement Mouhot started writing the numerical scheme
some years ago. The idea seems interesting because no numerical
cost would be added to the traditional schemes, nevertheless
improving their precision.
\item \emph{Analysis and numerical study of the plasma oscillations.}
When a bias is applied to a positive-doped transistor, the holes try to
oppose the electrons' displacement. This leads to oscillations (before
the system stabilizes towards an equilibrium) which are all the more
evident as the device's size becomes smaller and the applied bias large.
This phenomenon, in principle, does not depend
on the quantum effects nor on the scattering operator,
but essentially on the self-consistent electric field given by the Poisson equation.
With Mar\'ia J. C\'aceres, we wish for a better understanding of this
aspect of the diodes by developing an analysis and a numerical study
of different models of increasing complexity: 1D Vlasov-Poisson,
1D Boltzmann-Poisson with plain relaxation, etc., up to partially-confined devices
taking into account electron-phonon interaction and surface roughness.
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}