Research

Interests

I work on the qualitative description of the dynamic behavior of complex systems. This combines methods of partial differential equations and stochastic analysis, but also numerical analysis.

The questions arising in this context are related to statistical mechanics, Markov processes, machine learning, and variation methods. The equations under consideration usually have a physical or engineering background, such as a mathematical battery model, droplet formation in chemical-physical reaction kinetics or consensus formation among interacting agents. At the interface to stochastic analysis I am interested in particle systems and their many-particle limits mostly motivated from statistical physics with particular attention to models that can show phase transitions. Under the stochastic influence of the particle model, metastable behavior usually occurs in such models.

Keywords

  • Metastability in molecular dynamics and statistical mechanics
  • phase-transitions, nucleation and coarsening
  • variational methods for evolution equations:
    • entropy method for the longtime behaviour
    • gradient flows and their limits
    • quantifications of approximation errors
    • dimension reduction of multi-scale dynamics
    • discrete and nonlocal dynamics
    • convergence rate analysis of numerical schemes

Publications

Preprints submitted

  1. Víctor Navarro-Fernández, André Schlichting, Christian Seis, Optimal stability estimates and a new uniqueness result for advection-diffusion equations. [ arXiv | pdf ]
  2. Barbara Niethammer, Robert L. Pego, André Schlichting, Juan J. L. Velázquez, Oscillations in a Becker-Döring model with injection and depletion. [ arXiv | pdf ]
  3. André Schlichting, Christian Seis. The Scharfetter-Gummel scheme for aggregation-diffusion equations. [ arXiv | pdf ]
  4. Georg Menz, André Schlichting, Wenpin Tang, Tianqi Wu. Ergodicity of the infinite swapping algorithm at low temperature. [ arXiv | pdf ]

Peer reviewed

  1. Constantin Eichenberg, André Schlichting. Self-similar behavior of the exchange-driven growth model with product kernel. Commun. Partial. Differ. Equ. 46(3), 2021. [ doi | free access | arXiv | pdf ]
  2. Antonio Esposito, Francesco S. Patacchini, André Schlichting, Dejan Slepčev. Nonlocal-interaction equation on graphs: gradient flow structure and continuum limit. Archive for Rational Mechanics and Analysis [ doi | arXiv | pdf ]
  3. Rishabh S. Gvalani, André Schlichting. Barriers of the McKean-Vlasov energy via a mountain pass theorem in the space of probability measures. Journal for Functional Analysis, 279(11), 108720 (2020). [ doi | arXiv | pdf ]
  4. Matthias Erbar, Max Fathi, André Schlichting, Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces. ALEA – Latin American Journal of Probability and Mathematical Statistics, 17, 445-471 (2020). [ doi | arXiv | pdf ]
  5. André Schlichting. The exchange-driven growth model: basic properties and longtime behavior. Journal Nonlinear Science, 30, 793–830 (2020) [ link | doiarXiv | pdf ]
  6. José A. Carrillo, Rishabh S. Gvalani, Grigorios A. Pavliotis, André Schlichting. Long-time behaviour and phase transitions for the McKean–Vlasov equation on the torus. Archive for Rational Mechanics and Analysis, 235, 635–690 (2020) [ link | doi | arXiv | pdf ]
  7. André Schlichting, Martin Slowik.  Poincaré and logarithmic Sobolev constants for metastable Markov chains via capacitary inequalities. Annals of Applied Probability, 29(6), 3438-3488 (2019) [ arXiv | doipdf ]
  8. André Schlichting. Poincaré and Log–Sobolev Inequalities for Mixtures. Entropy 2019, 21(1). [ doi | arXiv | pdf ]
  9. Joseph G. Conlon, André Schlichting. A non-local problem for the Fokker-Planck equation related to the Becker-Döring model. Discret. Contin. Dyn. Syst. 39-4, 2019. [ doi | arXiv | pdf ]
  10. Manh Hong Duong, Agnes Lamacz, Mark A. Peletier, André Schlichting, Upanshu Sharma. Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics. Nonlinearity 31(10), 2018. [ doiarXivpdf ]
  11. André Schlichting. Macroscopic limit of the Becker-Döring equation via gradient flows. ESAIM:COCV 25(22), 2019. [ doi | arXiv | pdf ]
  12. André Schlichting, Christian Seis.  Analysis of the implicit upwind finite volume scheme with rough coefficients. Numer. Math., 2017. [ doi | view only | arXiv | pdf ]
  13. Simon Eberle, Barbara Niethammer, André Schlichting. Gradient flow formulation and longtime behaviour of a constrained Fokker-Planck equation. Nonlinear Anal. 158C, 2017). [ doi | journal | arXiv| pdf ]
  14. André Schlichting, Christian Seis. Convergence rates for upwind schemes with rough
    coefficients. SIAM J. Numer. Anal. 55 (2), 812–840, 2017. [ doi | arXiv |pdf ]
  15. Matthias Erbar, Max Fathi, Vaios Laschos, André Schlichting. Gradient flow structure for McKean-Vlasov equations on discrete spaces. Discret. Contin. Dyn. Syst. 36, 2016. [ doi | arXiv | pdf ]
  16. Georg Menz, André Schlichting. Poincaré and logarithmic Sobolev inequalities by decomposition of the energy landscape. Ann. Probab. 42(5), 2014. [ link | arXiv | pdf ]
  17. André. Schlichting. Time discretisation for a class of singular phase field models. Adv. Math. Sci. Appl. 55 (2009) 665–700. [ link | pdf ]

Proceedings

  1. A. Schlichting, M. Slowik. Capacitary inequalities in discrete setting and application to metastable Markov chains, Oberwolfach Report 35/2015. [ link | pdf ]
  2. E. Boissard, N. Gozlan, J. Lehec, C. Léonard, G. Menz, A. Schlichting.
    Some recent developments in functional inequalities. [ link | pdf ] Journées MAS 2012. ESAIM: Proc. 44 338-354 (2014)
  3. A. Schlichting and W. Sproessig. Norm estimations of the modified teodorescu transform with application to a multidimensional equation of airy type.
    AIP Conference Proceedings, 1048(1):701-705, September 2008. [ DOI | pdf ]

Thesis

  1. André Schlichting. Phase Transitions in Interacting Systems, Universität Bonn, Habilitation thesis, 2020. [ pdf ]
  2. André Schlichting. The Eyring-Kramers formula for Poincaré and logarithmic Sobolev inequalities, Universität Leipzig, PhD thesis, 2012. [ Qucosa | pdf ]
  3. A. Schlichting. Solvability, approximation and estimates for a class of singular
    phase field models. Master’s thesis, University of Mining and Technology Freiberg and University of Pavia, Diploma thesis, 2008. [ pdf ]