

1996  PhD in Mathematics, University of Bonn  1996  1997  Postdoc, Courant Institute, New York University, NY, USA  1997  2003  Research Assistant (C1), University of Bonn  2001  Guest scientist, Max Planck Institute for Mathematics in the Sciences, Leipzig  2002  Habilitation in Mathematics, University of Bonn  2003  2007  Professor (C4), HU Berlin  2007  2012  Professor in the Mathematical Institute and Tutorial Fellow of St Edmund Hall, University of Oxford, England, UK  Since 2012  Professor (W3), University of Bonn 


My research interests are in applied mathematics and include the analysis of problems with multiple scales, dynamics in highdimensional dynamical systems and universal scaling behaviour in models of mass aggregation and coarsening.
A focus of my earlier research was Ostwald ripening, a fundamental process in the aging of materials, where small solid particles immersed in a liquid interact to reduce their total surface energy. The classical LSW theory suggests a meanfield equation for the size distribution of particles and predicts universal longtime behaviour of solutions. I have been working on a clarification of the range of validity of the LSW model [10,11] as well as on the analysis of the longtime behaviour of its solutions. Surprisingly, it turned out that the latter is not universal as predicted by LSW, but rather depends sensitively on the initial data [12]. A central issue in Ostwald ripening and many other problems where particles interact through a field is the understanding of screening effects, which means that interactions between particles that are in principle longrange are screened by neighbouring particles [13]. Subsequently I investigated further meanfield type equations for various coarsening mechanisms [14,15,16] and recently obtained some new results for Smoluchowski's coagulation equation [1] for which, apart from some exactly solvable models, only few results had been available.
In many coarsening systems that are relevant in applications, such as grain growth in polycrystals for example, the particle statistics cannot be described by a meanfield equation. A future goal is to develop methods to characterize initial configurations that exhibit a universal scaling behaviour. First steps in this direction for a onedimensional toy model can be found in [6].
I am also interested in the reduction of highdimensional dynamical systems with small parameters to lowdimensional evolution equations. On example arises in the description of manyparticle storage systems. The corresponding mathematical problem involves nonlocal FokkerPlanck equations with multiple scales that can be reduced in certain regimes to rate independent systems that exhibit hysteresis [9].


Project in DFG Research Center MATHEON on “Precipitation in crystalline solids”
2004  2008
DFG Research Group FOR 718 “Analysis and Stochastics in Complex Physical Systems”
Member, 2005  2007
DFG Graduate School on “Analysis, Numerics and Optimization of Multiphase Problems”
Member, 2005  2008
International Joint Project, Royal Society and CNRS, “Kinetic models with mass transport and coalescence”
2010  2012
Project “Selfsimilarity in Smoluchowski's coagulation equation”
within Collaborative Research Center SFB 1060 “The Mathematics of Emergent Effects”, 2013  2020
Project “Screening effects in interacting particle systems”
within Collaborative Research Center SFB 1060 “The Mathematics of Emergent Effects”, 2017  2020
“Bonn International Graduate School of Mathematics”
Director, since 2017


Research Area B
The classical coagulation equation by Smoluchowski describes binary coagulation of a homogeneous system of clusters. The mathematical model is a nonlocal integral equation for the number density of clusters of a given size and it involves a rate kernel in which the microscopic details of the coagulation process are subsumed. Of particular interest is to understand whether the longtime behaviour of solutions to this model is described by selfsimilar solutions. This issue is however only understood for the solvable kernels such as the constant one, while for the other nonsolvable kernels much less is understood. We have contributed to the understanding of selfsimilar solutions with fat tails for such kernels [1,2,3,4] and have also identified via formal mathematical analysis and numerical simulations specific types of kernels for which we do not expect selfsimilar longtime behaviour [5]. In contrast to applications that can be described by Smoluchowski's equation, some relevant examples from applications, such as grain growth, cannot be described by a meanfield model. A first step into the direction to understand the phenomena in such systems can be found in [6].
I have also been interested in FokkerPlanck equations with nonlocal forcing term that arises in the description of manyparticle storage systems [7]. Due to an interaction of a nonconvex energy, entropic terms and the forcing, the model involves several time scales. We have identified critical parameter regimes [8] and rigorously derived in a certain scaling regime a rateindependent model exhibiting hysteresis [9]. 


[ 1] B. Niethammer, J. J. L. Velázquez
Selfsimilar solutions with fat tails for Smoluchowski's coagulation equation with locally bounded kernels Comm. Math. Phys. , 318: (2): 505532 2013[ 2] B. Niethammer, S. Throm, J. J. L. Velázquez
Selfsimilar solutions with fat tails for Smoluchowski's coagulation equation with singular kernels Ann. Inst. H. Poincaré Anal. Non Linéaire , 33: (5): 12231257 2016[ 3] Marco; Niethammer, Barbara; Velázquez, Juan J. L. Bonacini
Selfsimilar solutions to coagulation equations with timedependent tails: the case of homogeneity one eprint, arXiv:1612.06610 2016[5] Michael Herrmann, Barbara Niethammer, Juan J. L. Velázquez
Instabilities and oscillations in coagulation equations with kernels of homogeneity one Quart. Appl. Math. , 75: (1): 105130 2017 [ 6] Michael Helmers, Barbara Niethammer, Juan J. L. Velázquez
Mathematical analysis of a coarsening model with local interactions J. Nonlinear Sci. , 26: (5): 12271291 2016[ 8] Michael Herrmann, Barbara Niethammer, Juan J. L. Velázquez
Kramers and nonKramers phase transitions in manyparticle systems with dynamical constraint Multiscale Model. Simul. , 10: (3): 818852 2012[ 9] Michael Herrmann, Barbara Niethammer, Juan J. L. Velázquez
Rateindependent dynamics and Kramerstype phase transitions in nonlocal FokkerPlanck equations with dynamical control Arch. Ration. Mech. Anal. , 214: (3): 803866 2014[ 13] B. Niethammer, J. J. L. Velázquez
Screening in interacting particle systems Arch. Ration. Mech. Anal. , 180: (3): 493506 2006





• SIAM Multiscale Modeling and Simulation
• Kinetic and Related Models
• Research in Mathematical Sciences


2003  Richard von Mises Prize, GAMM  2011  Whitehead Prize, London Mathematical Society 


2009  Annual Meeting of GAMM, Gdansk, Poland  2011  Equadiff, Loughborough, England, UK  2013  SIAM, Mathematical Aspects of Materials Science, Philadelphia, PA, USA  2014  International Congress of Mathematicians, Seoul, South Korea  2015  Dynamics Days Europe, Exeter, England, UK 


Reiner Henseler (2007): “A Kinetic Model for Grain Growth”
Dirk Peschka (2008): “SelfSimilar Rupture of Thin Liquid Films with Slippage” (joint with Andreas Münch),
now Assistant, Weierstrass Institute, Berlin
SvenJoachim Kimmerle (2009): “Macroscopic Diffusion Models for Precipitation in Crystalline Gallium Arsenide  Modelling, Analysis and Simulation”,
now Substitute Professor (“Vertretungsprofessor”), Bundeswehr University Munich
Michael Helmers (2011): “Kinks in a model for twophase lipid bilayer membranes”
Sebastian Throm (2016): “Selfsimilar solutions with fat tails for Smoluchowski's coagulation equation”


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