PD Dr. Flavius Guias

 
z.Zt. Lehre an der FH Dortmund

Sprechstunde: n.V.

Frühere Lehrveranstaltungen

Curriculum Vitae:

• Since April 2008 * Position of Akademischer Oberrat, Dortmund University of Technology.

• February 2007 * Habilitation (Title of Privatdozent). Professorial dissertation (Habilitationsschrift): "Elements of a Stochastic Numerical Method for Transport and Reaction Problems".

  • Habilitationsvortrag (7.02.2007) Algorithmen zur optimalen Quantisierung von Signalen

  • Antrittsvorlesung (19.04.2007) Einführung in die Boltzmann-Gleichung

• May 2001 - March 2008  * Scientific position at the University of Dortmund.

• July 2000 - April 2001  * Scientific position in the SFB 359 , Heidelberg.

• July 1998 - June 2000  * Postdoc position in the Graduate College at IWR Heidelberg.

• July 1998  * Ph.D. degree. Title of the thesis:  "Coagulation-Fragmentation Processes: Relations Between Finite Particle Systems and Differential Equations ".

• October 1994 - July 1998   * Ph.D. student at the Heidelberg University under the guidance of Prof. Dr. Dr. h.c. mult. Willi Jäger.

• October 1992 - March 1994   * visiting student at the Heidelberg University in frame of the TEMPUS program.

• 1989-1994 * Faculty of Mathematics of the Timisoara University, Romania.

Scientific interests:

• Mathematical modeling by deterministic or stochastic particle systems (particle methods), approximation of solutions of partial differential equations by stochastic processes. Stochastic algorithms, Monte Carlo Methods, agent-based modeling.

• Stochastics, stochastic processes and their characterization by infinitesimal operators, martingale problems or stochastic differential equations, convergence properties of stochastic processes, applications in finance and insurance.

• Applied analysis, applications of semigroup theory in partial differential equations, harmonic analysis, optimal mass transportation.

Publications:

• 1. F.G., Lydia Olszewski:   A model for herd behaviour of agents in financial markets: analysis and simulation (submitted)

• 2.   Direct simulation of the infinitesimal dynamics of semi-discrete approximations for convection-diffusion- reaction problems, Math. Comput. Simulation, 81 (2010), (820-836) doi:10.1016/j.matcom.2010.09.005

• 3. A stochastic approach for simulating spatially inhomogeneous coagulation dynamics in the gelation regime, Comm. Nonlinear Sci. Numer. Simulat.  14 No.1 (2009), (204-222), doi:10.1016/j.cnsns.2007.07.015

• 4.  Generalized Becker-Döring equations modeling the time evolution of a process of preferential attachment with fitness, Monte Carlo Meth.Appl. (MCMA) 14 No.2 (2008), (151-170), doi: 10.1515/MCMA.2008.008

• 5.  An improved implementation of stochastic particle methods and applications to coagulation equations,  in Monte Carlo and Quasi-Monte Carlo Methods 2006, A.Keller, S. Heinrich, H.Niederreiter (eds.)  Springer, 2007 (383-395)

• 6.  Elements of a Stochastic Numerical Method for Transport and Reaction Problems (Habilitationsschrift, University of Dortmund, 2006)

• 7.  A Stochastic Numerical Method for Diffusion Equations and Applications to Spatially Inhomogeneous Coagulation Processes,  in Monte Carlo and Quasi-Monte Carlo Methods 2004, H.Niederreiter, D.Talay (eds.)  Springer, 2006 (147-162)

• 8.  Stochastic Models for Population Dynamics with Nonlinear Interaction and their Deterministic Limits, in Mathematical Modeling and Computing in Biology and Medicine, 5th ESMTB Conference , V.Capasso (editor), Miriam Research Centre for Industrial and Applied Mathematics, Milano, 2003 (579-586)

• 9. Mesoscopic models of reaction-diffusion processes with exclusion mechanism, in Multiscale Problems in Science and Technology - Challenges to Mathematical Analysis and Perpectives, N.Antonic, C.J.van Duijn, W.Jäger, A.Mikelic (eds.) Springer, 2002 (161-173)

• 10. Convergence Properties of a Stochastic Model for Coagulation-Fragmentation Processes with Diffusion, Stochastic Anal.Appl. 19 No.2 (2001) (245-278)

• 11. On Existence and Uniqueness of Solutions for a Class of Infinite-Dimensional Systems of Differential Equations, Mathematica, 42 (65) No.2 (2000), (137-152)

• 12. A Direct Simulation Method for the Coagulation-Fragmentation Equations with Multiplicative Coagulation Kernels ,Monte Carlo Meth.Appl. (MCMA)  5 No.4 (1999), (287-309)

• 13. Stochastic Models for Coagulation-Fragmentation Processes,in ECMI - Activity Report, edited by MIRIAM (Milan Research Center for Industrial and Applied Mathematics), (1999)

• 14. Coagulation-Fragmentation Processes: Relations Between Finite Particle Systems and Differential Equations (Ph.D. Thesis), Preprint 41/1998,  SFB 359, Heidelberg

• 15. A Monte Carlo Approach to the Smoluchowski Equations,Monte Carlo Meth.Appl. (MCMA) 3 No.4 (1997), (313-326)

•  16. Stochastic approximation of the solution of a coagulation-fragmentation equation with diffusion, Proceedings of the International Conference on Approximation and Optimization (Romania) - ICAOR Cluj-Napoca,  July 29 - August 1, 1996, Volume II, pp. 127-134.

Technische Universität Dortmund, Fakultät für Mathematik
Vogelpothsweg 87 (Mathematikgebäude) R.644, 44221 Dortmund
tel:++49-(0)231- 755 3058
E-mail: Flavius.Guias at math.uni-dortmund.de