Wigner crystallization


  • M. Cicalese and G.P. Leonardi.
    Maximal fluctuations on periodic lattices: an approach via quantitative Wulff inequalities.
    Commun. Math. Phys., September 2019. preprint.
    URL: http://cvgmt.sns.it/paper/4195/.
  • G. Orlando M. Cicalese and M. Ruf.
    From the N-clock model to the XY model: emergence of concentration effects in the variational analysis.
    preprint, August 2019.
    URL: http://cvgmt.sns.it/paper/4432/.
  • A. Bach M. Cicalese and A. Braides.
    Discrete-to-continuum limits of multi-body systems with bulk and surface long-range interactions.
    preprint, July 2019.
    URL: http://cvgmt.sns.it/paper/4406/.
  • A. Bach, M. Cicalese, and M. Ruf.
    Random finite-difference discretizations of the Ambrosio-Tortorelli functional with optimal mesh size.
    preprint, February 2019.
  • Gero Friesecke, Daniel Matthes, and Bernhard Schmitzer.
    Barycenters for the Hellinger–Kantorovich distance over $\mathbb R^d$.
    preprint at arXiv, 2019.
  • M. Forster M. Cicalese and G. Orlando.
    Variational analysis of a two-dimensional frustrated spin system: emergence and rigidity of chirality transitions.
    SIAM J. Math. Anal., 2019. preprint.
  • Marco Cicalese, Antoine Gloria, and Matthias Ruf.
    From statistical polymer physics to nonlinear elasticity.
    preprint, September 2018.
  • Rufat Badal, Marco Cicalese, Lucia De Luca, and Marcello Ponsiglione.
    Γ-Convergence Analysis of a Generalized $XY$ Model: Fractional Vortices and String Defects.
    Communications in Mathematical Physics, 358(2):705–739, March 2018.
  • A. Braides, M. Cicalese, and M. Ruf.
    Continuum limit and stochastic homogenization of discrete ferromagnetic thin films.
    Analysis & PDE, (2018), vol. 11, no.2, 499-553., March 2018.
    URL: https://msp.org/apde/2018/11-2/p06.xhtml.
  • C. Cotar, G. Friesecke, and C. Klüppelberg.
    Smoothing of transport plans with fixed marginals and rigorous semiclassical limit of the Hohenberg-Kohn functional.
    Archive for Rational Mechanics and Analysis, 228 (3):891–922, 2018.
  • Matthias Ruf.
    Motion of discrete interfaces in low-contrast random environments.
    ESAIM: COCV, Volume 24, Number 3, July–September 2018, October 2017.
  • G. Friesecke L. De Luca.
    Crystallization in two dimensions and a discrete Gauss-Bonnet theorem.
    J Nonlinear Sci 28, 69-90, 2017, June 2017.
    URL: https://link.springer.com/article/10.1007%2Fs00332-017-9401-6.
  • G. Friesecke L. De Luca.
    Classification of Particle Numbers with Unique Heitmann-Radin Minimizer.
    J. Stat. Phys. 167, Issue 6, 1586–1592, 2017, April 2017.
    URL: https://link.springer.com/article/10.1007/s10955-017-1781-3.
  • A. Braides and M. Cicalese.
    Interfaces, modulated phases and textures in lattice systems.
    Arch. Rat. Mech. Anal., 223, (2017), 977-1017, February 2017.
    URL: https://link.springer.com/article/10.1007/s00205-016-1050-7.
  • D. Jüstel.
    The Zak transform on strongly proper G-spaces and its applications.
    Journal of the London Math. Society, 97:47–76, 2017.
  • M. Cicalese A. Braides and N.K. Yip.
    Crystalline Motion of Interfaces Between Patterns.
    Journal of Statistical Physics October 2016, Volume 165, Issue 2, pp 274–319, October 2016.
    URL: https://link.springer.com/article/10.1007/s10955-016-1609-6.
  • Marco Cicalese, Matthias Ruf, and Francesco Solombrino.
    Chirality transitions in frustrated S2-valued spin systems.
    Math. Models Methods Appl. Sci., 26, (2016), no. 8, 1481-1529, July 2016.
  • Roberto Alicandro, Marco Cicalese, and Matthias Ruf.
    Domain formation in magnetic polymer composites: an approach via stochastic homogenization.
    Archive for Rational Mechanics and Analysis, 218(2):945–984, 2015.
  • M. Cicalese and F. Solombrino.
    Frustrated ferromagnetic spin chains: a variational approach to chirality transitions.
    Journal of Nonlinear Science, 25(291-313), 2015.
  • G. Friesecke, R. D. James and D. Jüstel.
    Twisted x-rays: incoming waveforms yielding discrete diffraction patterns for helical structures.
  • A. Garroni R. Alicandro, L. De Luca and M. Ponsiglione.
    Metastability and dynamics of discrete topological singularities in two dimensions: a Gamma-convergence approach.
    Archive for Rational Mechanics and Analysis, 214(1):269–330, 2014.

PhD thesis
  • Yuen Au Yeung.
    Crystalline Order, Surface Energy Densities and Wulff Shapes: Emergence from Atomistic Models.
    Dissertation, Technische Universität München, München, 2013.
    URL: http://mediatum.ub.tum.de/node?id=1142127.


Prof. Dr. Gero Friesecke   +

Projects: A13, B08
University: TU München, Department of Mathematics, 03.08.054
Address: Boltzmannstraße 3, 85748 Garching, GERMANY
Tel: +49 89 28917908
E-Mail: gf[at]ma.tum.de
Website: https://www-m7.ma.tum.de/bin/view/Analysis/GeroFriesecke

Dr. Camilla Brizzi   +

Projects: B08
University: TU München, Department of Mathematics
E-Mail: briz[at]ma.tum.de

Maximilian Penka   +

Projects: B08
University: TU München
E-Mail: maximilian.penka[at]tum.de