|
[1]
|
A. Rätz and M. Röger.
A new Diffuse-interface approximation of the Willmore flow.
ESAIM: Control, Optimisation and Calculus of Variations, 2021.
[ http ]
|
|
[2]
|
S. Voss, F. Li, A. Rätz, M. Röger, and Y.-W. Wu.
Spatial Cycling of Rab GTPase, Driven by the GTPase
Cycle, Controls Rab's Subcellular Distribution.
Biochemistry, 58(4):276--285, 2019.
[ http ]
|
|
[3]
|
A. Rätz.
Diffuse-interface approximations of osmosis free boundary problems.
SIAM J. Appl. Math., 76(3):910--929, 2016.
[ http ]
|
|
[4]
|
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 ]
|
|
[5]
|
A. Rätz.
A benchmark for the surface Cahn--Hilliard equation.
Appl. Math. Lett., 56:65--71, 2016.
[ http ]
|
|
[6]
|
A. Rätz.
Turing-type instabilities in bulk--surface reaction--diffusion
systems.
J. Comput. Appl. Math., 289:142--152, 2015.
[ http ]
|
|
[7]
|
A. Rätz.
A new diffuse-interface model for step flow in epitaxial growth.
IMA J. Appl. Math., 80(3):697--711, 2015.
[ http ]
|
|
[8]
|
A. Rätz and M. Röger.
Symmetry breaking in a bulk-surface reaction-diffusion model for
signaling networks.
Nonlinearity, 27:1805--1827, 2014.
[ http ]
|
|
[9]
|
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 ]
|
|
[10]
|
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 ]
|
|
[11]
|
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 ]
|
|
[12]
|
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.
|
|
[13]
|
A. Rätz and M. Röger.
Turing instabilities in a mathematical model for signaling networks.
J. Math. Biol., 65(6):1215--1244, 2012.
[ http ]
|
|
[14]
|
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 ]
|
|
[15]
|
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.
|
|
[16]
|
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 ]
|
|
[17]
|
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 ]
|
|
[18]
|
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 ]
|
|
[19]
|
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 ]
|
|
[20]
|
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 ]
|
|
[21]
|
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.
|
|
[22]
|
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.
|
|
[23]
|
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 ]
|
|
[24]
|
A. Rätz and A. Voigt.
A diffuse-interface approximation for surface diffusion including
adatoms.
Nonlinearity, 20(1):177--192, 2007.
[ http ]
|
|
[25]
|
A. Rätz and A. Voigt.
PDE's on surfaces --- a diffuse interface approach.
Comm. Math. Sci., 4(3):575--590, 2006.
[ .html ]
|
|
[26]
|
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 ]
|
|
[27]
|
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 ]
|
|
[28]
|
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.
|
|
[29]
|
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.
|
|
[30]
|
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.
|
|
[31]
|
A. Rätz and A. Voigt.
Various phase-field approximations for epitaxial growth.
J. Cryst. Growth, 266:278--282, 2004.
[ http ]
|
|
[32]
|
B. Li, A. Rätz, and A. Voigt.
Stability of a circular epitaxial island.
Physica D, 198:231--247, 2004.
[ http ]
|
|
[33]
|
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 ]
|
|
[34]
|
A. Rätz and A. Voigt.
Phase-field model for island dynamics in epitaxial growth.
Appl. Anal., 83:1015--1025, 2004.
[ http ]
|
