Profile
Profile

Prof. Dr. Barbara Niethammer

Director of Graduate Studies

E-Mail: niethammer(at)iam.uni-bonn.de
Telefon: +49 228 73 2216
Homepage: http://www.iam.uni-bonn.de/abteilung-mathphys/people/niethammer/
Raum: 2.039
Standort: Mathematics Center
Institute: Institute for Applied Mathematics
Forschungsbereich: Research Area B

Academic Career

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

Research Profile

My research interests are in applied mathematics and include the analysis of problems with multiple scales, dynamics in high-dimensional 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 mean-field equation for the size distribution of particles and predicts universal long-time 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 long-time 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 long-range are screened by neighbouring particles [13]. Subsequently I investigated further mean-field 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 mean-field 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 one-dimensional toy model can be found in [6].
I am also interested in the reduction of high-dimensional dynamical systems with small parameters to low-dimensional evolution equations. On example arises in the description of many-particle storage systems. The corresponding mathematical problem involves nonlocal Fokker-Planck equations with multiple scales that can be reduced in certain regimes to rate independent systems that exhibit hysteresis [9].

Research Projects and Activities

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 “Self-similarity 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

Contribution to Research Areas


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 long-time behaviour of solutions to this model is described by self-similar solutions. This issue is however only understood for the solvable kernels such as the constant one, while for the other non-solvable kernels much less is understood. We have contributed to the understanding of self-similar 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 self-similar long-time 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 mean-field 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 Fokker-Planck equations with nonlocal forcing term that arises in the description of many-particle 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 rate-independent model exhibiting hysteresis [9].

Selected Publications

[1] B. Niethammer, J. J. L. Velázquez
Self-similar solutions with fat tails for Smoluchowski's coagulation equation with locally bounded kernels
Comm. Math. Phys. , 318: (2): 505--532
2013
[2] B. Niethammer, S. Throm, J. J. L. Velázquez
Self-similar solutions with fat tails for Smoluchowski's coagulation equation with singular kernels
Ann. Inst. H. Poincaré Anal. Non Linéaire , 33: (5): 1223--1257
2016
[3]
Self-similar solutions to coagulation equations with time-dependent tails: the case of homogeneity one
eprint arXiv , 1612.06610:
12
[4] Marco; Niethammer, Barbara; Velazquez, Juan J. L. Bonacini
Self-similar solutions to coagulation equations with time-dependent tails: the case of homogeneity smaller than one
eprint arXiv , 1704.08905:
4
[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): 105--130
2017
[6] Michael Helmers, Barbara Niethammer, Juan J. L. Velázquez
Mathematical analysis of a coarsening model with local interactions
J. Nonlinear Sci. , 26: (5): 1227--1291
2016
[7] Simon Eberle, Barbara Niethammer, André Schlichting
Gradient flow formulation and longtime behaviour of a constrained Fokker-Planck equation
Nonlinear Anal. , 158: : 142--167
2017
[8] Michael Herrmann, Barbara Niethammer, Juan J. L. Velázquez
Kramers and non-Kramers phase transitions in many-particle systems with dynamical constraint
Multiscale Model. Simul. , 10: (3): 818--852
2012
[9] Michael Herrmann, Barbara Niethammer, Juan J. L. Velázquez
Rate-independent dynamics and Kramers-type phase transitions in nonlocal Fokker-Planck equations with dynamical control
Arch. Ration. Mech. Anal. , 214: (3): 803--866
2014
[10] Barbara Niethammer
Derivation of the LSW-theory for Ostwald ripening by homogenization methods
Arch. Ration. Mech. Anal. , 147: (2): 119--178
1999
[11] Barbara Niethammer, Felix Otto
Domain coarsening in thin films
Comm. Pure Appl. Math. , 54: (3): 361--384
2001
[12] Barbara Niethammer, Robert L. Pego
Non-self-similar behavior in the LSW theory of Ostwald ripening
J. Statist. Phys. , 95: (5-6): 867--902
1999
[13] B. Niethammer, J. J. L. Velázquez
Screening in interacting particle systems
Arch. Ration. Mech. Anal. , 180: (3): 493--506
2006
[14] B. Niethammer
On the evolution of large clusters in the Becker-Döring model
J. Nonlinear Sci. , 13: (1): 115--155
2003
[15] Govind Menon, Barbara Niethammer, Robert L. Pego
Dynamics and self-similarity in min-driven clustering
Trans. Amer. Math. Soc. , 362: (12): 6591--6618
2010
[16] Michael Herrmann, Philippe Laurençot, Barbara Niethammer
Self-similar solutions to a kinetic model for grain growth
J. Nonlinear Sci. , 22: (3): 399--427
2012

Publication List

MathSciNet Publication List (external link)

Editorships

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

Awards

2003

Richard von Mises Prize, GAMM

2011

Whitehead Prize, London Mathematical Society

Selected Invited Lectures

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

Selected PhD students

Reiner Henseler (2007): “A Kinetic Model for Grain Growth”

Dirk Peschka (2008): “Self-Similar Rupture of Thin Liquid Films with Slippage” (joint with Andreas Münch),
now Assistant, Weierstrass Institute, Berlin

Sven-Joachim 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 two-phase lipid bilayer membranes”

Sebastian Throm (2016): “Self-similar solutions with fat tails for Smoluchowski's coagulation equation”
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