Dr Nicolas Dirr
Overview
Position:
Reader
Email:
DirrNP@cardiff.ac.ukTelephone: +44(0)29 208 70920
Fax: +44(0)29 208 74199
Extension: 70920
Location: M/2.16
Research Interests
Nonlinear Partial Differential Equations with stochastic coefficients and scaling limits, in particular as mathematical models for phase transition and nucleation (often evolution equations for interface motion) and their derivation from interacting particle systems.
More precisely:
- Interfaces in heterogeneous and random media and associated nonlinear PDEs
- Interacting Stochastic Processes and their scaling limits
- Stochastic nonlinear PDEs
- Nonlinear PDEs and Stochastic Processes
- Homogenization and Gamma-convergence
- Scaling limits of singularly perturbed differential equations.
Research Group
Recent Significant Publications
Non-existence of positive stationary solutions for a class of semi-linear PDEs with random coefficients.(With Jerome Coville and Stephan Luckhaus.)
Evolution by mean curvature flow in sub-Riemannian geometries: a stochastic approach. (With Federica Dragoni and Max von Renesse.) Communications on Pure and Applied Analysis 9, no. 2, (2010), pp. 307-326
Sharp-Interface Limit of a Ginzburg--Landau Functional with a Random External Field (With Enza Orlandi.) SIAM Journal on Mathematical Analysis Volume 41, Issue 2, (2009) pp. 781-824
Pulsating Wave for Mean Curvature Flow in Inhomogeneous Medium (With Georgia Karali and Aaron Nung Kwan Yip.) European Journal of Applied Mathematics 19 (2008), 661-699.
Publications
[ADPZ10] From a large deviations principle to the Wasserstein gradient flow: A new micro-macro passage (With S. Adams, M. Peletier and J. Zimmer.) Submitted.
[DDS10] Pinning of Interfaces in Random Media.(With P.W. Dondl and M. Scheutzow.) Submitted.
[DO10] Unique minimizer for a random functional with a double-well potential in dimension 1 and 2 (With E. Orlandi.) Accepted, Communications in Mathematical Sciences.
[DDGHS09] Lipschitz Percolation.(With P.W. Dondl, G.R. Grimmett, A.E. Holroyd, and M. Scheutzow.) Elect. Comm. in Probab. 15 (2010), 14–21.
[CDL09] Non-existence of positive stationary solutions for a class of semi-linear PDEs with random coefficients. (With Jerome Coville and Stephan Luckhaus.) Networks and Heterogeneous Media (NHM) 5, no 4, 2010, pp. 745 – 763.
[DDR09] Evolution by mean curvature flow in sub-Riemannian geometries: a stochastic approach. (With Federica Dragoni and Max von Renesse.) Communications on Pure and Applied Analysis 9, no. 2, (2010), pp. 307-326
[DO09] Sharp-Interface Limit of a Ginzburg--Landau Functional with a Random External Field (With Enza Orlandi.) SIAM Journal on Mathematical Analysis Volume 41, Issue 2, (2009) pp. 781-824
[DKY08] Pulsating Wave for Mean Curvature Flow in Inhomogeneous Medium (With Georgia Karali and Aaron Nung Kwan Yip.) European Journal of Applied Mathematics 19 (2008), 661-699.
[DLN08] Gradient theory of phase transitions with a rapidly oscillating forcing term (With Marcello Lucia and Matteo Novaga.) Asymptotic Analysis 60 (2008), 29-59.
[BDDP07b] Stability of invariant manifolds in one and two dimensions. (With Giovanni Bellettini, Anna De Masi and Errico Presutti.) Nonlinearity 20 (2007), 537-582. Preprint
[BDDP07a] Tunneling in two dimensions. (With Giovanni Bellettini, Anna De Masi and Errico Presutti.) Communications in Mathematical Physics 269 (2007), 715-763 Preprint
[DDP06] Interface Instability under Forced Displacements (With Anna De Masi and Errico Presutti.) Annales Henri Poincaré 7 (2006), no. 3, 471-511, Preprint
[DY06] Pinning and de-pinning phenomena in front propagation in heterogeneous media. (With Nung Kwan (Aaron) Yip.) Interfaces and Free Boundaries 8 (2006), no. 1, 79-109, Preprint
[DLN06] Gamma-convergence of the Allen-Cahn energy with an oscillating forcing term. (With Marcello Lucia and Matteo Novaga.) Interfaces and Free Boundaries 8 (2006), no. 1, 57-78, Preprint
[DS05] Large-time behavior for viscous and non-viscous Hamilton-Jacobi equations forced by additive noise. (With Panagiotis E. Souganidis.) SIAM J. Math. Anal. 37 (2005), no. 3, 777--796 .
[D04] A Stefan problem with surface tension as the sharp interface limit of a nonlocal system of phase field type. Journal of Statistical Physics 114, no 3/4, (2004), 1085-1113
[DLN01] A stochastic selection principle in case of fattening for curvature flow. (With Stephan Luckhaus and Matteo Novaga.) Calculus of Variations and Partial Differential Equations 13 (4), 405-425, 2001.
[DL01] Mesoscopic limit for non-isothermal phase transition. (With Stephan Luckhaus.) Markov Process. Relat. Fields 7, no. 3, 355-381, (2001), Preprint
Research
External Funding.
2006-2007 Member and theme leader of focus research group (Forschergruppe) "Analysis and Stochastics in Complex Physical Systems," Berlin/Leipzig, Germany
2007-2010 Royal Society and LMS travel and conference grant
Major Conference Talks
2010
Isaac Newton Institute (Stochastic Partial Differential Equations), invited programme participant.
Stochastic Processes and Applications, Osaka, invited talk in focus session.
2009
Analysis of Stochastic Surface Evolution, Leipzig, Germany, invited speaker.
Analysis of Nonlinear PDEs and Free Boundary Problems: Applications to homogenization, Vancouver, invited speaker.
2008
Free Boundary Problems 2008, Stockholm, invited speaker and organiser of focus session.
Postgraduate Students
Current
Vaios Laschos ( University of Bath, jointly with Dr. Johannes Zimmer)
Biography
Qualifications
Diploma in Mathematics: University of Bonn, Germany, 1998
PhD – University of Leipzig, Germany, 2002
Previous Positions
1998 - 2002: Research Associate, University of Leipzig and Max-Planck-Institute for Mathematics in the Sciences, Leipzig.
2002 - 2004: Lecturer, University of Texas at Austin (partially supported by a Fellowship of the German Academic Exchange Service DAAD)
2004 - 2007: Junior Research Group Leader, Max-Planck-Institute for Mathematics in the Sciences, Leipzig.
2007 - March 2011: RCUK fellow, University of Bath
April 2011 -Present: Reader in Mathematical Analysis, School of Mathematics, University of Cardiff
