[1] A. Rätz. Diffuse-interface approximations of osmosis free boundary problems. SIAM J. Appl. Math., 76(3):910–929, 2016. [ http ]
[2] H. Garcke, J. Kampmann, A. Rätz, and M. Röger. A coupled surface-Cahn–Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes. Math. Models Methods Appl. Sci., 26(6):1149–1189, 2016. [ http ]
[3] A. Rätz. A benchmark for the surface Cahn–Hilliard equation. Appl. Math. Lett., 56:65–71, 2016. [ http ]
[4] A. Rätz. Turing-type instabilities in bulk–surface reaction–diffusion systems. J. Comput. Appl. Math., 289:142–152, 2015. [ http ]
[5] A. Rätz. A new diffuse-interface model for step flow in epitaxial growth. IMA J. Appl. Math., 80(3):697–711, 2015. [ http ]
[6] A. Rätz and M. Röger. Symmetry breaking in a bulk-surface reaction-diffusion model for signaling networks. Nonlinearity, 27:1805–1827, 2014. [ http ]
[7] S. Esedoglu, A. Rätz, and M. Röger. Colliding Interfaces in Old and New diffuse-interface Approximations of Willmore-flow. Commun. Math. Sci., 12(1):125–147, 2014. [ .html ]
[8] A. Rätz and B. Schweizer. Hysteresis models and gravity fingering in porous media. ZAMM Z. Angew. Math. Mech., 94(7–8):645–654, 2014. [ http ]
[9] J. Koch, A. Rätz, and B. Schweizer. Two-phase flow equations with a dynamic capillary pressure. Eur. J. Appl. Math., 24(1):49–75, 2013. [ http ]
[10] F. Haußer, W. Marth, S. Li, J. Lowengrub, A. Rätz, and A. Voigt. Thermodynamically consistent models for two-component vesicles. Int. J. Biomath. Biostat., 2(1):19–48, 2013.
[11] A. Rätz and M. Röger. Turing instabilities in a mathematical model for signaling networks. J. Math. Biol., 65(6):1215–1244, 2012. [ http ]
[12] S. Aland, A. Rätz, M. Röger, and A. Voigt. Buckling instability of viral capsids –- a continuum approach. SIAM Multiscale Model. Simul., 10(1):82–110, 2012. [ http ]
[13] A. Lamacz, A. Rätz, and B. Schweizer. A well-posed hysteresis model for flows in porous media and applications to fingering effects. Adv. Math. Sci. Appl., 21(1):33–63, 2011.
[14] J. Lowengrub, A. Rätz, and A. Voigt. Phase-field modeling of the dynamics of multicomponent vesicles: spinodal decomposition, coarsening, budding, and fission. Phys. Rev. E, 79(3):0311926, 2009. [ http ]
[15] B. Li, J. Lowengrub, A. Rätz, and A. Voigt. Geometric Evolution Laws for Thin Crystalline Films: Modeling and Numerics. Commun. Comput. Phys., 6(3):433–482, 2009. [ http ]
[16] X. Li, J. Lowengrub, A. Rätz, and A. Voigt. Solving PDEs in complex geometries: a diffuse domain approach. Commun. Math. Sci., 7(1):81–107, 2009. [ .html ]
[17] B. Berkels, A. Rätz, M. Rumpf, and A. Voigt. Extracting grain boundaries and macroscopic deformations from images on atomic scale. Journal of Scientific Computing, 35(1):1–23, 2008. [ http ]
[18] A. Redinger, O. Ricken, P. Kuhn, A. Rätz, A. Voigt, J. Krug, and T. Michely. Spiral Growth and Step Edge Barriers. Phys. Rev. Lett., 100(3):035506, 2008. [ http ]
[19] S. Torabi, S. Wise, J. Lowengrub, A. Rätz, and A. Voigt. A new method for simulating strongly anisotropic Cahn-Hilliard equations. In Materials Science and Technology Conference and Exhibition, MS and T'07, pages 1432–1444, 2007.
[20] B. Berkels, A. Rätz, M. Rumpf, and A. Voigt. Identification of grain boundary contours at atomic scale. In Proceedings of the First International Conference on Scale Space Methods and Variational Methods in Computer Vision, pages 765–776. Springer, 2007.
[21] R. Backofen, A. Rätz, and A. Voigt. Nucleation and growth by a phase field crystal (PFC) model. Phil. Mag. Lett., 87(11):813–820, 2007. [ http ]
[22] A. Rätz and A. Voigt. A diffuse-interface approximation for surface diffusion including adatoms. Nonlinearity, 20(1):177–192, 2007. [ http ]
[23] A. Rätz and A. Voigt. PDE's on surfaces –- a diffuse interface approach. Comm. Math. Sci., 4(3):575–590, 2006. [ .html ]
[24] A. Rätz and A. Voigt. Higher order regularization of anisotropic geometric evolution equations in three dimensions. J. Comput. Theor. Nanosci., 3(4):560–564, 2006. [ http ]
[25] A. Rätz, A. Ribalta, and A. Voigt. Surface evolution of elastically stressed films under deposition by a diffuse interface model. J. Comput. Phys., 214(1):187–208, 2006. [ http ]
[26] L. Balykov, V. Chalupecky, C. Eck, H. Emmerich, G. Krishnamoorthy, A. Rätz, and A. Voigt. Multiscale Modeling of Epitaxial Growth: From Discrete-Continuum to Continuum Equations. In A. Mielke, editor, Analysis, Modeling and Simulation of Multiscale Modeling, pages 65–85. Springer, 2006.
[27] A. Rätz and A. Voigt. A diffuse step-flow model with edge-diffusion. In A. Voigt, editor, Multiscale modeling of epitaxial growth, volume 149 of ISNM, pages 115–126. Birkhäuser, Basel, 2005.
[28] A. Rätz and A. Voigt. Continuum modeling of nanostructure evolution. In P. Vincenzini, editor, Proc. Computational Modeling and Simulation of Materials, volume 44 of Techna Group, Advances in Science and Technology, pages 217–226, 2004.
[29] A. Rätz and A. Voigt. Various phase-field approximations for epitaxial growth. J. Cryst. Growth, 266:278–282, 2004. [ http ]
[30] B. Li, A. Rätz, and A. Voigt. Stability of a circular epitaxial island. Physica D, 198:231–247, 2004. [ http ]
[31] F. Otto, P. Penzler, A. Rätz, T. Rump, and A. Voigt. A diffuse-interface approximation for step flow in epitaxial growth. Nonlinearity, 17:477–491, 2004. [ http ]
[32] A. Rätz and A. Voigt. Phase-field model for island dynamics in epitaxial growth. Appl. Anal., 83:1015–1025, 2004. [ http ]


[1] A. Rätz. A diffuse-interface approach for solving PDE's on and inside moving surfaces: applications in mathematical biology. Habilitation thesis, Fakultät für Mathematik der TU Dortmund, 2014.
[2] A. Rätz. Modelling and Numerical Treatment of Diffuse-Interface Models with Applications in Epitaxial Growth. PhD thesis, Mathematisch-Naturwissenschaftliche Fakultät der Rheinischen Friedrich-Wilhelms-Universität Bonn, 2007. [.pdf ]
[3] A. Rätz. Variationsprobleme und Liouville-Sätze für Euler-Gleichungen auf einem Torus. Diploma thesis, Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, 2001. [.pdf ]