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Preprints
[P1] Stochastic homogenization on perforated domains I: Extension operators. WIAS Preprint 2849, 2021.
[P2] Precompact probability spaces in applied stochastic homogenization. WIAS Preprint 2852, 2021.
[P5] MH, Benedikt Jahnel and Anh Duc Vu. Stochastic homogenization on irregularly perforated domains. WIAS Preprint 2880, 2021.
[P7] MH, Manuel Landstorfer, Matthias Liero. Homogenization of a porous intercalation electrode with phase separation. WIAS Preprint 2905, 2021.
[P8] MH, Alexander Sikorski, Marcus Weber. Consistency and order 1 convergence of cell-centered finite volume discretizations of degenerate elliptic problems in any space dimension. WIAS Preprint 2913, 2022.
[P9] Stochastic homogenization on perforated domains III -- General estimates for stationary ergodic random connected Lipschitz domains. WIAS Preprint 2932, 2022.
[P10] On quenched homogenization of long-range random conductance models on stationary ergodic point processes. WIAS Preprint 2942, 2022.
Publications in refereed journals
[H29] Stochastic homogenization on perforated domains II -- Application to nonlinear elasticity models.. ZAMM, 102(12), 2022. (WIAS preprint 2865)
[H28] MH, Marita Thomas. GENERIC for dissipative solids with bulk-interface interaction.. in Research in Mathematics of Materials Science , 333–364, 2022. (WIAS preprint 2872)
[H27] MH, Stefan Neukamm and Mario Varga. Stochastic two-scale convergence and Young measures.. Networks and Heterogeneous Media, 17(2):227–254, 2022. (WIAS preprint 2885)
[H26] MH, M. Kantner, and A. Stephan. Consistency and convergence
for a family of finite volume discretizations of the Fokker–Planck
operator. ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 55:3017–3042, 2021. (WIAS preprint 2684)
[H25] O. Souček , MH, and J. Málek. On a thermodynamic framework
for developing boundary conditions for Korteweg fluids. International
Journal of Engineering Science, 154, 2020. (Preprint)
[H24] B. Franchi, MH, and S. Lorenzani. A mathematical model for
Alzheimer’s disease: An approach via stochastic homogenization of the
Smoluchowski equation. Communications in Mathematical Sciences,
18(4):1105–1134, 2020. (Preprint)
[H23] MH, R. Kornhuber, and J. Podlesny. Fractal homogenization
of multiscale interface problems. SIAM Multiscale Modeling and
Simulation, 18(1):294–314, 2020.(Preprint)
[H22] MH, S. Neukamm, and M. Varga. Stochastic
homogenization of Λ-convex gradient flows. Accepted
by Discrete and Continuous Dynamical Systems – S,
2020. (Preprint)
[H21] F. Flegel and MH. The fractional p-Laplacian emerging from
homogenization of the random conductance model with degenerate
ergodic weights and unbounded-range jumps. Calculus of Variations
and Partial Differential Equations, 59(1):8, 2020. (Preprint)
[H20] F. Flegel, MH, and M. Slowik. Homogenization theory for
the random conductance model with degenerate ergodic weights
and unbounded-range jumps. Annales de l’Institut Henry Poincaré
probabilités et statistiques, 55(3):1226–1257, 2019. (Preprint)
[H19] MH and S. Nesenenko.
Stochastic homogenization of rate-dependent models of monotone type
in plasticity. Asymptotic Analysis, 112(3-4):185–212, 2019. (Preprint)
[H18] MH, R. I. Patterson, and D. M. Renger. Topologies and measures
on the space of functions of bounded variation taking values in a Banach
or metric space. Journal of Evolution Equations, 19(1):111–152, 2019.
(Preprint)
[H17] MH and M. Röger. Large deviation principle for a stochastic
Allen–Cahn equation. Journal of Theoretical Probability, 31(1):364–401,
2018. (Preprint)
[H16] Convergences of the squareroot approximation scheme to the
Fokker–Planck operator. Mathematical Models and Methods in Applied
Sciences, 28(13):2599–2635, 2018. (Preprint)
[H15] L. Donati, MH, B. G. Keller, and M. Weber. Estimation of
the infinitesimal generator by square-root approximation. Journal of
Physics: Condensed Matter, 30(42):425201, 2018. (Preprint)
[H14] MH and B. Schweizer. Stochastic homogenization of plasticity
equations. ESAIM: Control, Optimisation and Calculus of Variations,
24(1):153–176, 2018. (Preprint)
[H13] C. Dörlemann, MH, and B. Schweizer. Transmission conditions
for the Helmholtz-equation in perforated domains. Vietnam Journal
of Mathematics, On the occasion of the 75th Birthday of W. Jäger,
45(1-2):241–253, 2017. (Preprint)
[H12] Stochastic homogenization of
rate-independent systems and applications. Continuum Mechanics and
Thermodynamics, 29(3):853–894, 2017. (Preprint)
[H11] MH and A. Mielke. Averaging of time-periodic dissipation
potentials in rate-independent processes. Discrete & Continuous
Dynamical Systems-Series S, 10(6), 2017. (Preprint)
[H10] MH and B. Schweizer. Non-periodic homogenization of
infinitesimal strain plasticity equations. ZAMM-Journal of Applied
Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik
und Mechanik, 96(1):5–23, 2016. (Preprint)
[H09] Existence of solutions for two types of generalized versions of
the Cahn–Hilliard equation. Applications of Mathematics, 60(1):51–90,
2015. (Preprint)
[H08] On systems of Cahn–Hilliard and Allen–Cahn equations considered
as gradient flows in Hilbert spaces. Journal of Mathematical Analysis
and Applications, 423(1):410–455, 2015. (Preprint)
[H07] On thermodynamics of fluid interfaces. International Journal of
Engineering Science, 82:178–195, 2014. (Preprint)
[H06] On the derivation of thermodynamically consistent boundary
conditions for the Cahn–Hilliard–Navier–Stokes system. International
Journal of Engineering Science, 62:126–156, 2013. (Preprint)
[H05] MH, J. Málek, and K. Rajagopal. On the development
and generalizations of Allen–Cahn and Stefan equations within a
thermodynamic framework. Zeitschrift für angewandte Mathematik und
Physik, 63(4):759–776, 2012. (Preprint)
[H04] MH, J. Málek, and K. R. Rajagopal. On the development and
generalizations of Cahn–Hilliard equations within a thermodynamic
framework. Zeitschrift für angewandte Mathematik und Physik,
63(1):145–169, 2012. (Preprint)
[H03] Stochastic homogenization of heat transfer in polycrystals with
nonlinear contact conductivities. Applicable Analysis, 91(7):1243–1264,
2012.
[H02] An extension of the stochastic two-scale convergence method and
application. Asymptotic Analysis, 72(1-2):1–30, 2011.
[H01] MH and J. Málek. On compressible Korteweg fluid-like materials.
International Journal of Engineering Science, 48(11):1313–1324, 2010.
(Preprint)
PhD Thesis
Modeling Multiphase Flow in Porous Media with an Application to Permafrost Soil. (Access to full text.)
Diploma Thesis
Stochastic Homogenization of Heat Transfer through a Polycrystal,
University of Heidelberg, 2008.
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Last modified: 2018-04-08 by Martin Heida