Publications of Bernd Schmidt

  • (with L. Kreutz, M. Friedrich) Emergence of rigid polycrystals from atomistic systems with Heitmann-Radin sticky disk energy. Preprint 2020. [Preprint]
     

  • (with M. Jesenko) Geometric linearization of theories for incompressible elastic materials and applications. Preprint 2020. [Preprint]
     

  • Effektive Theorien und Energie minimierende Konfigurationen für heterogene Schichten. In: GAMM-Rundbrief 2020/Heft 1, pp. 4-10 [Article]
     
  • (with E. Mainini) Maximal fluctuations around the Wulff shape for edge-isoperimetric sets in Zd: a sharp scaling law. Preprint 2020. [Preprint]
     
  • (with J. Braun) An atomistic derivation of von-Kármán plate theory. Preprint 2019. [Preprint]
     
  • (with M. de Benito Delgado) Energy minimising configurations of pre-strained multilayers. Preprint 2019.
    [Preprint]
     
  • (with M. de Benito Delgado) A hierarchy of multilayered plate models. Preprint 2019. [Preprint]
     
  • (with S. Jansen, W. König, F. Theil) Surface energy and boundary layers for a chain of atoms at low temperature. Preprint 2019. [Preprint]
     
  • (with P. Piovano, E. Mainini, U. Stefanelli) N3/4 law in the cubic lattice. J. Stat. Phys. 176 (2019) pp.

    1480-1499. [Article]
     

  • (with M. Ortiz, U. Stefanelli) A variational approach to Navier-Stokes. Nonlinearity 31 (2018) pp. 5664-5682. [Article]
     

  • (with M. Jesenko) Homogenization and the limit of vanishing hardening in Hencky plasticity with non-convex potentials. Calc. Var. Partial Diff. Eq. 57 (2018), Art. 2, 43 pp. [Preprint]
     
  • A Griffith-Euler-Bernoulli theory for thin brittle beams derived from nonlinear models in variational fracture mechanics. Math. Models Methods Appl. Sci. (M3AS) 27 (2017) pp. 1685-1726. [Article]
     
  • (with J. Braun) Existence and convergence of solutions of the boundary value problem in atomistic and continuum nonlinear elasticity theory. Calc. Var. Partial Diff. Eq. 55 (2016), Art. 125, 36 pp. [Article]
     
  • (with M. Friedrich) A quantitative geometric rigidity result in SBD. Preprint 2015. [Preprint]
     
  • (with M. Friedrich) On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime. Netw. Heterog. Media 10 (2015) pp. 321-342. [Article]
     
  • (with M. Friedrich) An analysis of crystal cleavage in the passage from atomistic models to continuum theory. Arch. Ration. Mech. Anal. 217 (2015) pp. 263-308. [Article]
     
  • (with M. Jesenko) Closure and commutability results for Gamma-limits and the geometric linearization and homogenization of multi-well energy functionals. SIAM J. Math. Anal. 46 (2014) pp. 2525-2553. [Article]
     
  • On the infinite particle limit in Lagrangian dynamics and convergence of optimal transportation meshfree methods. SIAM Mult. Model. Simul. 12 (2014) pp. 265-289. [Article]
     
  • (with M. Friedrich) An atomistic-to-continuum analysis of crystal cleavage in a two-dimensional model problem. J. Nonlin. Sci. 24 (2014) pp. 145-183. [Preprint]
     
  • (with J. Braun) On the passage from atomistic systems to nonlinear elasticity theory for general multi-body potentials with p-growth. Netw. Heterog. Media 8 (2013) pp. 879-912. [Article]
     
  • Ground states of the 2D sticky disc model: fine properties and N3/4 law for the deviation from the asymptotic Wulff shape. J. Stat. Phys. 153 (2013) pp. 727-738. [Article]
     
  • (with A. Bompadre, M. Ortiz) Convergence Analysis of Meshfree Approximation Schemes. SIAM J. Numer. Anal. 50 (2012) pp. 1344-1366. [Article]
     
  • (with Y. Au Yeung, G. Friesecke) Minimizing atomic configurations of short range pair potentials in two dimensions: crystallization in the Wulff shape. Calc. Var. Partial Diff. Eq. 44 (2012) pp. 81-100. [Article]
     
  • (with F. Fraternali) Universal formulae for the limiting elastic energy of static membrane networks. J. Mech. Phys. Solids 60 (2012) pp. 172-180. [Article]
     
  • Localized spectral asymptotics for boundary value problems and correlation effects in the free Fermi gas in general domains. J. Math. Phys. 52 (2011) p. 072106 (18 pp.). [Article]
     
  • On a semilinear variational problem. ESAIM Control Optim. Calc. Var. 17 (2011) pp. 86-101. [Article]
     
  • (with M. Gonzalez, M. Ortiz) Force-stepping integrators in Lagrangian mechanics. Internat. J. Numer. Methods Engrg. 84 (2010) pp. 1407-1450. [Article]
     
  • (with G. Friesecke) A sharp version of Ehrenfest's theorem for general self-adjoint operators. Proc. R. Soc. Lond. Ser. A. 466 (2010) pp. 2137-2143. [Article]
     
  • (with M. Gonzalez, M. Ortiz) Energy-stepping integrators in Lagrangian mechanics. Internat. J. Numer. Methods Engrg. 82 (2010) pp. 205-241. [Article]
     
  • On the derivation of linear elasticity from atomistic models. Netw. Heterog. Media 4 (2009) pp. 789-812. [Article]
     
  • (with F. Fraternali, M. Ortiz) Eigenfracture: an eigendeformation approach to variational fracture. SIAM Mult. Model. Simul. 7 (2009) pp. 1237-1266. [Article]
     
  • (with S. Leyendecker, M. Ortiz) Gamma-convergence of variational integrators for constrained systems. J. Nonlin. Sci. 19 (2009) pp. 153-177. [Article]
     
  • (with A. Schlömerkemper) Discrete-to-continuum limit of magnetic forces: dependence on the distance between bodies. Arch. Ration. Mech. Anal. 192 (2009) pp. 689-611. [Article]
     
  • Linear Gamma-limits of multiwell energies in nonlinear elasticity theory. Contin. Mech. Thermodyn. 20 (2008) pp. 375-396. [Article]
     
  • Effective theories for thin elastic films. PhD-Thesis, Universität Leipzig (2006). [Article]
     
  • Qualitative properties of a continuum theory for thin films. Annales de l'I.H.P. - Analyse non linéaire 25 (2008) pp. 43-75. [Article]
     
  • On the passage from atomic to continuum theory for thin films. Arch. Ration. Mech. Anal. 190 (2008) pp. 1-55. [Article]
     
  • Plate theory for stressed heterogeneous multilayers of finite bending energy. J. Math. Pures Appl. 88 (2007) pp. 107-122. [Article]
     
  • Minimal energy configurations of strained multi-layers. Calc. Var. Partial Diff. Eq. 30 (2007) pp. 477-497. [Article]
     
  • A derivation of continuum nonlinear plate theory from atomistic models. SIAM Mult. Model. Simul. 5 (2006) pp. 664-694. [Article]
     
  • (with W. Huisinga) Metastability and Dominant Eigenvalues of Transfer Operators. In 'Advances in Algorithms for Macromolecular Simulation', Lecture Notes in Computational Science and Engineering, Springer (2005). [Article]


 

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