![Nicolas Dirr](https://profiles-cardiff.imgix.net/attachments/166?w=200&h=200&auto=format&crop=faces&fit=crop&q=90")
Trosolwyg
Diddordebau Ymchwil:
Mae fy niddordebau yn cynnwys Hafaliadau Differol Rhannol aflinol gyda chyfnodau stochastig a therfynau graddio cysylltiedig, yn enwedig fel modelau mathemategol ar gyfer pontio cam a cnewyllyn (yn aml yn esblygu hafaliadau ar gyfer symudiad rhyngwyneb), a homogeneiddio (stochastig) hafaliadau o'r fath a'u perthynas â systemau a modelau gronynnau rhyngweithio ar gyfer yr ymennydd.
Yn fwy penodol:
- Rhyngwynebau mewn cyfryngau heterogenaidd ac ar hap a PDE nonlinear cysylltiedig
- Homogenization
- Rhyngweithio Prosesau Stochastic a'u terfynau graddio
- PDEs Nonlinear a Phrosesau Stochastic
Grŵp Ymchwil:
Grŵp Ymchwil Dadansoddi Mathemategol
Cyhoeddiad
2025
- Huang, S., Zequn, Z., Dirr, N., Zimmer, J. and Reina, C. 2025. Statistical-Physics-Informed Neural Networks (Stat-PINNs): A machine learning strategy for coarse-graining dissipative dynamics. Journal of the Mechanics and Physics of Solids 194, article number: 105908. (10.1016/j.jmps.2024.105908)
2024
- Citti, G., Dirr, N., Dragoni, F. and Grande, R. 2024. Horizontal mean curvature flow as a scaling limit of a mean field equation in the Heisenberg group. [Online]. arXiv: Cornell University.
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)
- 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., 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)
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)
- 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.
- 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)
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
- 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)
- 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)
- 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
- Huang, S., Zequn, Z., Dirr, N., Zimmer, J. and Reina, C. 2025. Statistical-Physics-Informed Neural Networks (Stat-PINNs): A machine learning strategy for coarse-graining dissipative dynamics. Journal of the Mechanics and Physics of Solids 194, article number: 105908. (10.1016/j.jmps.2024.105908)
- 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)
- 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., 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)
- 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)
- 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.
- 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., 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)
- 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)
- 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)
- 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
- Citti, G., Dirr, N., Dragoni, F. and Grande, R. 2024. Horizontal mean curvature flow as a scaling limit of a mean field equation in the Heisenberg group. [Online]. arXiv: Cornell University.
- 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
- 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., 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)
- 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)
Ymchwil
Diddordebau Ymchwil:
Mae fy niddordebau yn cynnwys Hafaliadau Differol Rhannol aflinol gyda chyfnodau stochastig a therfynau graddio cysylltiedig, yn enwedig fel modelau mathemategol ar gyfer pontio cam a cnewyllyn (yn aml yn esblygu hafaliadau ar gyfer symudiad rhyngwyneb), a homogeneiddio (stochastig) hafaliadau o'r fath a'u perthynas â systemau a modelau gronynnau rhyngweithio ar gyfer yr ymennydd.
Yn fwy penodol:
- Rhyngwynebau mewn cyfryngau heterogenaidd ac ar hap a PDEs dirywiol cysylltiedig
- Homogenization
- Rhyngweithio Prosesau Stochastic a'u terfynau graddio
- PDEs Nonlinear a Phrosesau Stochastic
Cyllid: Leverhulme, LMS, EPSRC
Prosiectau PhD: Cysylltwch â mi'n uniongyrchol ar gyfer prosiectau PhD cyfredol
Addysgu
Modiwlau:
- Cydlynydd Prosiect Blwyddyn 3/4
- Theori Mesur (Blwyddyn 3)
Cyn-fyfyrwyr PhD
- Vaios Laschos (Prifysgol Caerfaddon, ar y cyd â Dr. Johannes Zimmer)
- Peter Embacher (ar y cyd â Johannes Zimmer)
Prosiectau PhD cyfredol: Os oes gennych ddiddordeb mewn gwneud PhD mewn maes sy'n agos at fy ymchwil, cysylltwch â mi yn uniongyrchol.
Bywgraffiad
Addysg
- Tystysgrif Astudio Ymlaen Llaw mewn Mathemateg, Caergrawnt, 1996
- Diploma mewn Mathemateg: Prifysgol Bonn, yr Almaen, 1998
- Prifysgol PhD Leipzig, yr Almaen, 2002
Trosolwg Gyrfa
- 1998 - 2002: Cydymaith Ymchwil, Prifysgol Leipzig a Max-Planck-Sefydliad Mathemateg yn y Gwyddorau, Leipzig.
- 2002 - 2004: Darlithydd, Prifysgol Texas yn Austin (a gefnogir yn rhannol gan Gymrodoriaeth y Gwasanaeth Cyfnewid Academaidd Almaeneg DAAD)
- 2004 - 2007: Arweinydd Grŵp Ymchwil Iau, Max-Planck-Sefydliad Mathemateg yn y Gwyddorau, Leipzig.
- 2007 - Mawrth 2011: Cymrawd RCUK, Prifysgol Caerfaddon
- 2011 -2016: Darllenydd mewn Dadansoddi Mathemategol, Ysgol Mathemateg, Prifysgol Caerdydd
- 2016- presennol: Athro mewn Mathemateg, Prifysgol Caerdydd (Athro Llawn)
Meysydd goruchwyliaeth
- Nonlinear Partial Differential Equations
- Scaling limits of interacting particle systems
