![Nicolas Dirr](https://profiles-cardiff.imgix.net/attachments/166?w=200&h=200&auto=format&crop=faces&fit=crop&q=90")
Overview
Research Interests:
My interests comprise nonlinear Partial Differential Equations with stochastic coefficients and related scaling limits, in particular as mathematical models for phase transition and nucleation (often evolution equations for interface motion), and (stochastic) homogenisation of such equations and their relation to interacting particle systems and models for the brain.
More precisely:
- Interfaces in heterogeneous and random media and associated nonlinear PDEs
- Homogenization
- Interacting Stochastic Processes and their scaling limits
- Nonlinear PDEs and Stochastic Processes
Research Group:
Mathematical Analysis Research Group
Publication
2022
- Cardaliaguet, P., Dirr, N. and Souganidis, P. E. 2022. Scaling limits and stochastic homogenization for some nonlinear parabolic equations. Journal of Differential Equations 307, pp. 389-443. (10.1016/j.jde.2021.10.057)
2021
- Dirr, N., Grillmeier, H. and Grün, G. 2021. On stochastic porous-medium equations with critical-growth conservative multiplicative noise. Discrete and Continuous Dynamical Systems - Series A 41(6), pp. 2829-2871. (10.3934/dcds.2020388)
2020
- Dirr, N., Dragoni, F., Mannucci, P. and Marchi, C. 2020. Gamma-convergence and homogenisation for a class of degenerate functionals. Nonlinear Analysis 190, article number: 111618. (10.1016/j.na.2019.111618)
- Dirr, N., Dragoni, F. and Grande, R. 2020. Asymptotics for optimal controls for horizontal mean curvature flow.. [Online]. arXiv. Available at: https://arxiv.org/abs/2005.10599
2019
- Dirr, N. and Nguyen, V. D. 2019. Some new results on Lipschitz regularization for parabolic equations. Journal of Evolution Equations 19(4), pp. 1149-1166. (10.1007/s00028-019-00512-w)
- Li, X., Dirr, N., Embacher, P., Zimmer, J. and Reina, C. 2019. Harnessing fluctuations to discover dissipative evolution equations. Journal of the Mechanics and Physics of Solids 131, pp. 240-251. (10.1016/j.jmps.2019.05.017)
2018
- Dirr, N., Dragoni, F., Mannucci, P. and Marchi, C. 2018. Stochastic homogenization for functionals with anisotropic rescaling and noncoercive Hamilton--Jacobi equations. SIAM Journal on Mathematical Analysis 50(5), pp. 5198-5242. (10.1137/17M1144428)
- Embacher, P., Dirr, N., Zimmer, J. and Reina, C. 2018. Computing diffusivities from particle models out of equilibrium. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474(2212), article number: 694. (10.1098/rspa.2017.0694)
2017
- Dirr, N. P., Stamatakis, M. G. and Zimmer, J. 2017. Hydrodynamic limit of condensing two-species zero range processes with sub-critical initial profiles. Journal of Statistical Physics 168(4), pp. 794-825. (10.1007/s10955-017-1827-6)
- Birmpa, P., Dirr, N. and Tsagkarogiannis, D. 2017. Large deviations for the macroscopic motion of an interface. Journal of Statistical Physics 166, pp. 1163-1192. (10.1007/s10955-017-1720-3)
- Cesaroni, A., Dirr, N. and Novaga, M. 2017. Homogenization of a semilinear heat equation. Journal de l'École polytechnique — Mathématiques 4, pp. 633-660.
2016
- Dirr, N., Stamatakis, M. and Zimmer, J. 2016. Entropic and gradient flow formulations for nonlinear diffusion. Journal of Mathematical Physics 57, article number: 81505. (10.1063/1.4960748)
- Cesaroni, A., Dirr, N. and Marchi, C. 2016. Homogenization of a mean field game system in the small noise limit. SIAM Journal on Mathematical Analysis 48(4), pp. 2701-2729. (10.1137/16M1063459)
2015
- Dirr, N. and Orlandi, E. 2015. Uniqueness of the minimizer for a random non-local functional with double-well potential in d⩽2. Annales de l'Institut Henri Poincare (C) Non Linear Analysis 32(3), pp. 593-622. (10.1016/j.anihpc.2014.02.002)
2013
- Adams, S., Dirr, N. P., Peletier, M. and Zimmer, J. 2013. Large deviations and gradient flows. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371(2005), article number: 20120341. (10.1098/rsta.2012.0341)
2012
- Dirr, N., Laschos, V. and Zimmer, J. 2012. Upscaling from particle models to entropic gradient flows. Journal of Mathematical Physics 53(6), article number: 63704. (10.1063/1.4726509)
2011
- Dirr, N. P. and Orlandi, E. 2011. Unique minimizer for a random functional with double-well potential in dimension 1 and 2. Communications in Mathematical Sciences 9(2), pp. 331-351. (10.4310/CMS.2011.v9.n2.a1)
- Dirr, N. P., Dondl, P. and Scheutzow, M. 2011. Pinning of interfaces in random media. Interfaces and Free Boundaries 13(3), pp. 411-421. (10.4171/IFB/265)
- Adams, S., Dirr, N. P., Peletier, M. A. and Zimmer, J. 2011. From a large-deviations principle to the Wasserstein Gradient Flow: a new micro-macro passage. Communications in Mathematical Physics 307(3), pp. 791-815. (10.1007/s00220-011-1328-4)
2010
- Dirr, N. P., Dragoni, F. and Von Renesse, M. 2010. Evolution by mean curvature flow in sub-Riemannian geometries: a stochastic approach. Communications on Pure and Applied Analysis 9(2), pp. 307-326. (10.3934/cpaa.2010.9.307)
- Coville, J., Dirr, N. P. and Luckhaus, S. 2010. Non-existence of positive stationary solutions for a class of semi-linear PDEs with random coefficients. Networks and Heterogeneous Media 5(4), pp. 745-763. (10.3934/nhm.2010.5.745)
- Dirr, N. P., Dondl, P. W., Grimmett, G. R., Holroyd, A. E. and Scheutzowv, M. V. 2010. Lipschitz percolation. Electronic Communications in Probability 15(2), pp. 14-21.
2009
- Dirr, N. P. and Orlandi, E. 2009. Sharp-interface limit of a Ginzburg-Landau functional with a random external field. SIAM Journal on Mathematical Analysis 41(2), pp. 781-824. (10.1137/070684100)
2008
- Dirr, N. P. 2008. Switching paths for Ising models with long-range interaction. In: Mörters, P. et al. eds. Analysis and stochastics of growth processes and interface models. Oxford Scholarship Online, pp. 244-265., (10.1093/acprof:oso/9780199239252.003.0011)
- Dirr, N. P., Marcello, L. and Matteo, N. 2008. Gradient theory of phase transitions with a rapidly oscillating forcing term. Asymptotic Analysis 60(1-2), pp. 29-59. (10.3233/ASY-2008-0897)
- Dirr, N. P., Karali, G. and Yip, N. K. 2008. Pulsating wave for mean curvature flow in inhomogeneous medium. European Journal of Applied Mathematics 19(6), pp. 661-699. (10.1017/S095679250800764X)
2007
- Bellettini, G., De Masi, A., Dirr, N. P. and Presutti, E. 2007. Stability of invariant manifolds in one and two dimensions. Nonlinearity 20(3), pp. 537-582. (10.1088/0951-7715/20/3/002)
2006
- Dirr, N. P. and Yip, N. K. 2006. Pinning and de-pinning phenomena in front propagation in heterogeneous media. Interfaces and Free Boundaries 8(1), pp. 79-109. (10.4171/IFB/136)
- Dirr, N. P., Lucia, M. and Novaga, M. 2006. Gamma--convergence of the Allen-Cahn energy with an oscillating forcing term. Interfaces and Free Boundaries 8(1), pp. 47-78. (10.4171/IFB/135)
- De Masi, A., Dirr, N. P. and Presutti, E. 2006. Interface Instability under Forced Displacements. Annales Henri Poincaré 7(3), pp. 471-511. (10.1007/s00023-005-0257-1)
- Bellettini, G., De Masi, A., Dirr, N. P. and Presutti, E. 2006. Tunneling in Two Dimensions. Communications in Mathematical Physics 269(3), pp. 715-763. (10.1007/s00220-006-0143-9)
2005
- Dirr, N. and Souganidis, P. E. 2005. Large-time behavior for viscous and nonviscous Hamilton-Jacobi equations forced by additive noise. SIAM Journal on Mathematical Analysis 37(3), pp. 777-796. (10.1137/040611896)
2004
- Dirr, N. 2004. A Stefan problem with surface tension as the sharp interface limit of a nonlocal system of phase-field type. Journal of statistical physics 114(3-4), pp. 1085-1113. (10.1023/B:JOSS.0000012517.33719.9f)
2001
- Dirr, N. and Luckhaus, S. 2001. Mesoscopic limit for non-isothermal phase transition. Markov processes and related fields 7(3), pp. 355-381.
- Dirr, N., Luckhaus, S. and Novaga, M. 2001. A stochastic selection principle in case of fattening for curvature flow. Calculus of Variations and Partial Differential Equations 13(4), pp. 405-425. (10.1007/s005260100080)
Articles
- Cardaliaguet, P., Dirr, N. and Souganidis, P. E. 2022. Scaling limits and stochastic homogenization for some nonlinear parabolic equations. Journal of Differential Equations 307, pp. 389-443. (10.1016/j.jde.2021.10.057)
- Dirr, N., Grillmeier, H. and Grün, G. 2021. On stochastic porous-medium equations with critical-growth conservative multiplicative noise. Discrete and Continuous Dynamical Systems - Series A 41(6), pp. 2829-2871. (10.3934/dcds.2020388)
- Dirr, N., Dragoni, F., Mannucci, P. and Marchi, C. 2020. Gamma-convergence and homogenisation for a class of degenerate functionals. Nonlinear Analysis 190, article number: 111618. (10.1016/j.na.2019.111618)
- Dirr, N. and Nguyen, V. D. 2019. Some new results on Lipschitz regularization for parabolic equations. Journal of Evolution Equations 19(4), pp. 1149-1166. (10.1007/s00028-019-00512-w)
- Li, X., Dirr, N., Embacher, P., Zimmer, J. and Reina, C. 2019. Harnessing fluctuations to discover dissipative evolution equations. Journal of the Mechanics and Physics of Solids 131, pp. 240-251. (10.1016/j.jmps.2019.05.017)
- Dirr, N., Dragoni, F., Mannucci, P. and Marchi, C. 2018. Stochastic homogenization for functionals with anisotropic rescaling and noncoercive Hamilton--Jacobi equations. SIAM Journal on Mathematical Analysis 50(5), pp. 5198-5242. (10.1137/17M1144428)
- Embacher, P., Dirr, N., Zimmer, J. and Reina, C. 2018. Computing diffusivities from particle models out of equilibrium. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474(2212), article number: 694. (10.1098/rspa.2017.0694)
- Dirr, N. P., Stamatakis, M. G. and Zimmer, J. 2017. Hydrodynamic limit of condensing two-species zero range processes with sub-critical initial profiles. Journal of Statistical Physics 168(4), pp. 794-825. (10.1007/s10955-017-1827-6)
- Birmpa, P., Dirr, N. and Tsagkarogiannis, D. 2017. Large deviations for the macroscopic motion of an interface. Journal of Statistical Physics 166, pp. 1163-1192. (10.1007/s10955-017-1720-3)
- Cesaroni, A., Dirr, N. and Novaga, M. 2017. Homogenization of a semilinear heat equation. Journal de l'École polytechnique — Mathématiques 4, pp. 633-660.
- Dirr, N., Stamatakis, M. and Zimmer, J. 2016. Entropic and gradient flow formulations for nonlinear diffusion. Journal of Mathematical Physics 57, article number: 81505. (10.1063/1.4960748)
- Cesaroni, A., Dirr, N. and Marchi, C. 2016. Homogenization of a mean field game system in the small noise limit. SIAM Journal on Mathematical Analysis 48(4), pp. 2701-2729. (10.1137/16M1063459)
- Dirr, N. and Orlandi, E. 2015. Uniqueness of the minimizer for a random non-local functional with double-well potential in d⩽2. Annales de l'Institut Henri Poincare (C) Non Linear Analysis 32(3), pp. 593-622. (10.1016/j.anihpc.2014.02.002)
- Adams, S., Dirr, N. P., Peletier, M. and Zimmer, J. 2013. Large deviations and gradient flows. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371(2005), article number: 20120341. (10.1098/rsta.2012.0341)
- Dirr, N., Laschos, V. and Zimmer, J. 2012. Upscaling from particle models to entropic gradient flows. Journal of Mathematical Physics 53(6), article number: 63704. (10.1063/1.4726509)
- Dirr, N. P. and Orlandi, E. 2011. Unique minimizer for a random functional with double-well potential in dimension 1 and 2. Communications in Mathematical Sciences 9(2), pp. 331-351. (10.4310/CMS.2011.v9.n2.a1)
- Dirr, N. P., Dondl, P. and Scheutzow, M. 2011. Pinning of interfaces in random media. Interfaces and Free Boundaries 13(3), pp. 411-421. (10.4171/IFB/265)
- Adams, S., Dirr, N. P., Peletier, M. A. and Zimmer, J. 2011. From a large-deviations principle to the Wasserstein Gradient Flow: a new micro-macro passage. Communications in Mathematical Physics 307(3), pp. 791-815. (10.1007/s00220-011-1328-4)
- Dirr, N. P., Dragoni, F. and Von Renesse, M. 2010. Evolution by mean curvature flow in sub-Riemannian geometries: a stochastic approach. Communications on Pure and Applied Analysis 9(2), pp. 307-326. (10.3934/cpaa.2010.9.307)
- Coville, J., Dirr, N. P. and Luckhaus, S. 2010. Non-existence of positive stationary solutions for a class of semi-linear PDEs with random coefficients. Networks and Heterogeneous Media 5(4), pp. 745-763. (10.3934/nhm.2010.5.745)
- Dirr, N. P., Dondl, P. W., Grimmett, G. R., Holroyd, A. E. and Scheutzowv, M. V. 2010. Lipschitz percolation. Electronic Communications in Probability 15(2), pp. 14-21.
- Dirr, N. P. and Orlandi, E. 2009. Sharp-interface limit of a Ginzburg-Landau functional with a random external field. SIAM Journal on Mathematical Analysis 41(2), pp. 781-824. (10.1137/070684100)
- Dirr, N. P., Marcello, L. and Matteo, N. 2008. Gradient theory of phase transitions with a rapidly oscillating forcing term. Asymptotic Analysis 60(1-2), pp. 29-59. (10.3233/ASY-2008-0897)
- Dirr, N. P., Karali, G. and Yip, N. K. 2008. Pulsating wave for mean curvature flow in inhomogeneous medium. European Journal of Applied Mathematics 19(6), pp. 661-699. (10.1017/S095679250800764X)
- Bellettini, G., De Masi, A., Dirr, N. P. and Presutti, E. 2007. Stability of invariant manifolds in one and two dimensions. Nonlinearity 20(3), pp. 537-582. (10.1088/0951-7715/20/3/002)
- Dirr, N. P. and Yip, N. K. 2006. Pinning and de-pinning phenomena in front propagation in heterogeneous media. Interfaces and Free Boundaries 8(1), pp. 79-109. (10.4171/IFB/136)
- Dirr, N. P., Lucia, M. and Novaga, M. 2006. Gamma--convergence of the Allen-Cahn energy with an oscillating forcing term. Interfaces and Free Boundaries 8(1), pp. 47-78. (10.4171/IFB/135)
- De Masi, A., Dirr, N. P. and Presutti, E. 2006. Interface Instability under Forced Displacements. Annales Henri Poincaré 7(3), pp. 471-511. (10.1007/s00023-005-0257-1)
- Bellettini, G., De Masi, A., Dirr, N. P. and Presutti, E. 2006. Tunneling in Two Dimensions. Communications in Mathematical Physics 269(3), pp. 715-763. (10.1007/s00220-006-0143-9)
- Dirr, N. and Souganidis, P. E. 2005. Large-time behavior for viscous and nonviscous Hamilton-Jacobi equations forced by additive noise. SIAM Journal on Mathematical Analysis 37(3), pp. 777-796. (10.1137/040611896)
- Dirr, N. 2004. A Stefan problem with surface tension as the sharp interface limit of a nonlocal system of phase-field type. Journal of statistical physics 114(3-4), pp. 1085-1113. (10.1023/B:JOSS.0000012517.33719.9f)
- Dirr, N. and Luckhaus, S. 2001. Mesoscopic limit for non-isothermal phase transition. Markov processes and related fields 7(3), pp. 355-381.
- Dirr, N., Luckhaus, S. and Novaga, M. 2001. A stochastic selection principle in case of fattening for curvature flow. Calculus of Variations and Partial Differential Equations 13(4), pp. 405-425. (10.1007/s005260100080)
Book sections
- Dirr, N. P. 2008. Switching paths for Ising models with long-range interaction. In: Mörters, P. et al. eds. Analysis and stochastics of growth processes and interface models. Oxford Scholarship Online, pp. 244-265., (10.1093/acprof:oso/9780199239252.003.0011)
Websites
- Dirr, N., Dragoni, F. and Grande, R. 2020. Asymptotics for optimal controls for horizontal mean curvature flow.. [Online]. arXiv. Available at: https://arxiv.org/abs/2005.10599
- Dirr, N. P., Dondl, P. and Scheutzow, M. 2011. Pinning of interfaces in random media. Interfaces and Free Boundaries 13(3), pp. 411-421. (10.4171/IFB/265)
- Adams, S., Dirr, N. P., Peletier, M. A. and Zimmer, J. 2011. From a large-deviations principle to the Wasserstein Gradient Flow: a new micro-macro passage. Communications in Mathematical Physics 307(3), pp. 791-815. (10.1007/s00220-011-1328-4)
- Dirr, N. P., Dragoni, F. and Von Renesse, M. 2010. Evolution by mean curvature flow in sub-Riemannian geometries: a stochastic approach. Communications on Pure and Applied Analysis 9(2), pp. 307-326. (10.3934/cpaa.2010.9.307)
- Coville, J., Dirr, N. P. and Luckhaus, S. 2010. Non-existence of positive stationary solutions for a class of semi-linear PDEs with random coefficients. Networks and Heterogeneous Media 5(4), pp. 745-763. (10.3934/nhm.2010.5.745)
- Dirr, N. P. and Orlandi, E. 2009. Sharp-interface limit of a Ginzburg-Landau functional with a random external field. SIAM Journal on Mathematical Analysis 41(2), pp. 781-824. (10.1137/070684100)
- Dirr, N. P. 2008. Switching paths for Ising models with long-range interaction. In: Mörters, P. et al. eds. Analysis and stochastics of growth processes and interface models. Oxford Scholarship Online, pp. 244-265., (10.1093/acprof:oso/9780199239252.003.0011)
- Dirr, N. P., Karali, G. and Yip, N. K. 2008. Pulsating wave for mean curvature flow in inhomogeneous medium. European Journal of Applied Mathematics 19(6), pp. 661-699. (10.1017/S095679250800764X)
Research
Research Interests:
My interests comprise nonlinear Partial Differential Equations with stochastic coefficients and related scaling limits, in particular as mathematical models for phase transition and nucleation (often evolution equations for interface motion), and (stochastic) homogenisation of such equations and their relation to interacting particle systems and models for the brain.
More precisely:
- Interfaces in heterogeneous and random media and associated nonlinear degenerate PDEs
- Homogenization
- Interacting Stochastic Processes and their scaling limits
- Nonlinear PDEs and Stochastic Processes
Funding: Leverhulme, LMS, EPSRC
PhD projects: Please contact me directly for current PhD projects
Teaching
Modules:
- Year 3/4 project coordinator
- Measure Theory (Year 3)
Past PhD students
- Vaios Laschos (University of Bath, jointly with Dr. Johannes Zimmer)
- Peter Embacher (jointly with Johannes Zimmer)
Current PhD projects: If you are interested in doing a PhD in an area close to my research please contact me directly.
Biography
Education
- Certificate of Advance Study in Mathematics, Cambridge, 1996
- Diploma in Mathematics: University of Bonn, Germany, 1998
- PhD University of Leipzig, Germany, 2002
Career Overview
- 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
- 2011 -2016: Reader in Mathematical Analysis, School of Mathematics, University of Cardiff
- 2016- present: Professor in Mathematics, Cardiff University (Full Professor)
Supervisions
- Nonlinear Partial Differential Equations
- Scaling limits of interacting particle systems
