Wang, Xiaoqiang; Zhu, Liyong Diffusive interface model for actomyosin driven cell oscillations. (English) Zbl 07331887 Bull. Math. Biol. 83, No. 4, Paper No. 37, 21 p. (2021). MSC: 92C37 92C10 PDF BibTeX XML Cite \textit{X. Wang} and \textit{L. Zhu}, Bull. Math. Biol. 83, No. 4, Paper No. 37, 21 p. (2021; Zbl 07331887) Full Text: DOI
Chen, Jingmin; Yu, Thomas; Brogan, Patrick; Kusner, Robert; Yang, Yilin; Zigerelli, Andrew Numerical methods for biomembranes: conforming subdivision methods versus non-conforming PL methods. (English) Zbl 1455.49023 Math. Comput. 90, No. 328, 471-516 (2021). MSC: 49M41 65D99 65K10 65Z05 30C30 90C30 41A15 PDF BibTeX XML Cite \textit{J. Chen} et al., Math. Comput. 90, No. 328, 471--516 (2021; Zbl 1455.49023) Full Text: DOI
Schimperna, Giulio; Wu, Hao On a class of sixth-order Cahn-Hilliard-type equations with logarithmic potential. (English) Zbl 1450.35136 SIAM J. Math. Anal. 52, No. 5, 5155-5195 (2020). MSC: 35K35 35K55 35A01 47H05 35B41 35B65 PDF BibTeX XML Cite \textit{G. Schimperna} and \textit{H. Wu}, SIAM J. Math. Anal. 52, No. 5, 5155--5195 (2020; Zbl 1450.35136) Full Text: DOI
Zhao, Xueping; Wang, Qi A second order fully-discrete linear energy stable scheme for a binary compressible viscous fluid model. (English) Zbl 1452.76165 J. Comput. Phys. 395, 382-409 (2019). MSC: 76M20 76T17 65M12 65M06 PDF BibTeX XML Cite \textit{X. Zhao} and \textit{Q. Wang}, J. Comput. Phys. 395, 382--409 (2019; Zbl 1452.76165) Full Text: DOI
Valizadeh, Navid; Rabczuk, Timon Isogeometric analysis for phase-field models of geometric PDEs and high-order PDEs on stationary and evolving surfaces. (English) Zbl 1441.65023 Comput. Methods Appl. Mech. Eng. 351, 599-642 (2019). MSC: 65D17 65M60 35K55 65D07 PDF BibTeX XML Cite \textit{N. Valizadeh} and \textit{T. Rabczuk}, Comput. Methods Appl. Mech. Eng. 351, 599--642 (2019; Zbl 1441.65023) Full Text: DOI
Lu, Min-Jhe; Liu, Chun; Li, Shuwang Nonlinear simulation of an elastic tumor-host interface. (English) Zbl 1425.92115 Comput. Math. Biophys. 7, No. 1, 25-47 (2019). MSC: 92C50 35Q92 PDF BibTeX XML Cite \textit{M.-J. Lu} et al., Comput. Math. Biophys. 7, No. 1, 25--47 (2019; Zbl 1425.92115) Full Text: DOI
Xu, Xiang; Zhao, Yanxiang Energy stable semi-implicit schemes for Allen-Cahn-Ohta-Kawasaki model in binary system. (English) Zbl 1428.65015 J. Sci. Comput. 80, No. 3, 1656-1680 (2019). MSC: 65M06 65N35 65T50 82D60 35Q82 35B35 35R09 65M15 65N15 PDF BibTeX XML Cite \textit{X. Xu} and \textit{Y. Zhao}, J. Sci. Comput. 80, No. 3, 1656--1680 (2019; Zbl 1428.65015) Full Text: DOI arXiv
Wu, Shuonan; Xu, Jinchao Nonconforming finite element spaces for \(2m\)th order partial differential equations on \(\mathbb {R}^n\) simplicial grids when \(m=n+1\). (English) Zbl 1407.65304 Math. Comput. 88, No. 316, 531-551 (2019). Reviewer: Abdallah Bradji (Annaba) MSC: 65N30 65N12 65N15 35B25 35J30 PDF BibTeX XML Cite \textit{S. Wu} and \textit{J. Xu}, Math. Comput. 88, No. 316, 531--551 (2019; Zbl 1407.65304) Full Text: DOI arXiv
Aland, Sebastian Phase field models for two-phase flow with surfactants and biomembranes. (English) Zbl 1391.76768 Bothe, Dieter (ed.) et al., Transport processes at fluidic interfaces. Basel: Birkhäuser/Springer (ISBN 978-3-319-56601-6/hbk; 978-3-319-56602-3/ebook). Advances in Mathematical Fluid Mechanics, 271-290 (2017). MSC: 76T10 76Z05 92C35 PDF BibTeX XML Cite \textit{S. Aland}, in: Transport processes at fluidic interfaces. Basel: Birkhäuser/Springer. 271--290 (2017; Zbl 1391.76768) Full Text: DOI
Dondl, Patrick W.; Lemenant, Antoine; Wojtowytsch, Stephan Phase field models for thin elastic structures with topological constraint. (English) Zbl 1366.35182 Arch. Ration. Mech. Anal. 223, No. 2, 693-736 (2017). Reviewer: Marin I. Marin (Braşov) MSC: 35Q74 74K15 35R05 74G65 49Q10 PDF BibTeX XML Cite \textit{P. W. Dondl} et al., Arch. Ration. Mech. Anal. 223, No. 2, 693--736 (2017; Zbl 1366.35182) Full Text: DOI arXiv
Winkler, Benjamin; Aranson, Igor S.; Ziebert, Falko Membrane tension feedback on shape and motility of eukaryotic cells. (English) Zbl 1373.92025 Physica D 318-319, 26-33 (2016). MSC: 92C17 92C10 PDF BibTeX XML Cite \textit{B. Winkler} et al., Physica D 318--319, 26--33 (2016; Zbl 1373.92025) Full Text: DOI
Lowengrub, John; Allard, Jun; Aland, Sebastian Numerical simulation of endocytosis: viscous flow driven by membranes with non-uniformly distributed curvature-inducing molecules. (English) Zbl 1351.76067 J. Comput. Phys. 309, 112-128 (2016). MSC: 76M10 65M60 92-08 76Z05 92C35 PDF BibTeX XML Cite \textit{J. Lowengrub} et al., J. Comput. Phys. 309, 112--128 (2016; Zbl 1351.76067) Full Text: DOI
Gu, Rui; Wang, Xiaoqiang; Gunzburger, Max A two phase field model for tracking vesicle-vesicle adhesion. (English) Zbl 1366.92019 J. Math. Biol. 73, No. 5, 1293-1319 (2016). MSC: 92C05 65M70 70G75 92C37 PDF BibTeX XML Cite \textit{R. Gu} et al., J. Math. Biol. 73, No. 5, 1293--1319 (2016; Zbl 1366.92019) Full Text: DOI
Wang, Xiaoqiang; Ju, Lili; Du, Qiang Efficient and stable exponential time differencing Runge-Kutta methods for phase field elastic bending energy models. (English) Zbl 1349.92015 J. Comput. Phys. 316, 21-38 (2016). MSC: 92-08 65M70 74K15 92C37 PDF BibTeX XML Cite \textit{X. Wang} et al., J. Comput. Phys. 316, 21--38 (2016; Zbl 1349.92015) Full Text: DOI
Walker, Shawn W. Shape optimization of self-avoiding curves. (English) Zbl 1349.74294 J. Comput. Phys. 311, 275-298 (2016). MSC: 74P10 74P15 74S05 74M15 65N30 82D60 65K05 90C59 PDF BibTeX XML Cite \textit{S. W. Walker}, J. Comput. Phys. 311, 275--298 (2016; Zbl 1349.74294) Full Text: DOI
Ling, Siqi; Marth, Wieland; Praetorius, Simon; Voigt, Axel An adaptive finite element multi-mesh approach for interacting deformable objects in flow. (English) Zbl 1342.35382 Comput. Methods Appl. Math. 16, No. 3, 475-484 (2016). MSC: 35Q74 74F10 76Txx 76Zxx PDF BibTeX XML Cite \textit{S. Ling} et al., Comput. Methods Appl. Math. 16, No. 3, 475--484 (2016; Zbl 1342.35382) Full Text: DOI
Marth, Wieland; Aland, Sebastian; Voigt, Axel Margination of white blood cells: a computational approach by a hydrodynamic phase field model. (English) Zbl 1382.76304 J. Fluid Mech. 790, 389-406 (2016). MSC: 76Z05 92C35 PDF BibTeX XML Cite \textit{W. Marth} et al., J. Fluid Mech. 790, 389--406 (2016; Zbl 1382.76304) Full Text: DOI
Chen, Rui; Ji, Guanghua; Yang, Xiaofeng; Zhang, Hui Decoupled energy stable schemes for phase-field vesicle membrane model. (English) Zbl 1349.76842 J. Comput. Phys. 302, 509-523 (2015). MSC: 76T10 65M60 76D05 76Z05 92C37 PDF BibTeX XML Cite \textit{R. Chen} et al., J. Comput. Phys. 302, 509--523 (2015; Zbl 1349.76842) Full Text: DOI
Zhao, Jihong A Beale-Kato-Majda blow-up criterion for a hydrodynamic system modeling vesicle and fluid interactions. (English) Zbl 1330.35302 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 128, 20-35 (2015). MSC: 35Q30 35B65 76D09 76T10 35B44 PDF BibTeX XML Cite \textit{J. Zhao}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 128, 20--35 (2015; Zbl 1330.35302) Full Text: DOI arXiv
Medjo, T. Tachim; Tone, C.; Tone, F. Long-time dynamics of a regularized family of models for homogeneous incompressible two-phase flows. (English) Zbl 1327.35323 Asymptotic Anal. 94, No. 1-2, 125-160 (2015). MSC: 35Q35 35Q30 35B40 35B35 76Txx 76D05 35B41 65N06 PDF BibTeX XML Cite \textit{T. T. Medjo} et al., Asymptotic Anal. 94, No. 1--2, 125--160 (2015; Zbl 1327.35323) Full Text: DOI
Heintz, A. A numerical method for simulation dynamics of incompressible lipid membranes in viscous fluid. (English) Zbl 1320.76098 J. Comput. Appl. Math. 289, 87-100 (2015). MSC: 76M28 76Z05 92C35 PDF BibTeX XML Cite \textit{A. Heintz}, J. Comput. Appl. Math. 289, 87--100 (2015; Zbl 1320.76098) Full Text: DOI
Hilhorst, Danielle; Kampmann, Johannes; Nguyen, Thanh Nam; van der Zee, Kristoffer George Formal asymptotic limit of a diffuse-interface tumor-growth model. (English) Zbl 1317.35123 Math. Models Methods Appl. Sci. 25, No. 6, 1011-1043 (2015). Reviewer: Eugene Postnikov (Kursk) MSC: 35K57 35B40 35R35 92C50 35Q92 PDF BibTeX XML Cite \textit{D. Hilhorst} et al., Math. Models Methods Appl. Sci. 25, No. 6, 1011--1043 (2015; Zbl 1317.35123) Full Text: DOI
Boldrini, José Luiz; Piovezan Entringer, Ariane A phase field \(\alpha\)-Navier-Stokes vesicle-fluid interaction model: existence and uniqueness of solutions. (English) Zbl 1304.35209 Discrete Contin. Dyn. Syst., Ser. B 20, No. 2, 397-422 (2015). MSC: 35D30 35Q35 35Q92 76D03 92C10 PDF BibTeX XML Cite \textit{J. L. Boldrini} and \textit{A. Piovezan Entringer}, Discrete Contin. Dyn. Syst., Ser. B 20, No. 2, 397--422 (2015; Zbl 1304.35209) Full Text: DOI
Oberhuber, Tomáš Numerical solution for the anisotropic Willmore flow of graphs. (English) Zbl 1309.65122 Appl. Numer. Math. 88, 1-17 (2015). MSC: 65N08 05C21 53C44 PDF BibTeX XML Cite \textit{T. Oberhuber}, Appl. Numer. Math. 88, 1--17 (2015; Zbl 1309.65122) Full Text: DOI
Aland, Sebastian; Egerer, Sabine; Lowengrub, John; Voigt, Axel Diffuse interface models of locally inextensible vesicles in a viscous fluid. (English) Zbl 1349.76933 J. Comput. Phys. 277, 32-47 (2014). MSC: 76Z05 76M10 65M60 76D05 92C35 PDF BibTeX XML Cite \textit{S. Aland} et al., J. Comput. Phys. 277, 32--47 (2014; Zbl 1349.76933) Full Text: DOI arXiv
Gu, R.; Wang, X.; Gunzburger, M. Simulating vesicle-substrate adhesion using two phase field functions. (English) Zbl 1349.92050 J. Comput. Phys. 275, 626-641 (2014). MSC: 92C37 74K35 76Z05 74L15 PDF BibTeX XML Cite \textit{R. Gu} et al., J. Comput. Phys. 275, 626--641 (2014; Zbl 1349.92050) Full Text: DOI
Gal, Ciprian G.; Medjo, T. Tachim On a regularized family of models for homogeneous incompressible two-phase flows. (English) Zbl 1317.35172 J. Nonlinear Sci. 24, No. 6, 1033-1103 (2014). Reviewer: Ruxandra Stavre (Bucureşti) MSC: 35Q30 35Q31 35K58 35K59 37L30 35B41 76D05 76T10 35B65 PDF BibTeX XML Cite \textit{C. G. Gal} and \textit{T. T. Medjo}, J. Nonlinear Sci. 24, No. 6, 1033--1103 (2014; Zbl 1317.35172) Full Text: DOI arXiv
Marth, Wieland; Voigt, Axel Signaling networks and cell motility: a computational approach using a phase field description. (English) Zbl 1345.92033 J. Math. Biol. 69, No. 1, 91-112 (2014). MSC: 92C17 35K57 76Z10 PDF BibTeX XML Cite \textit{W. Marth} and \textit{A. Voigt}, J. Math. Biol. 69, No. 1, 91--112 (2014; Zbl 1345.92033) Full Text: DOI
Zhu, Liyong; Du, Qiang Error estimates for approximations of a gradient dynamics for phase field elastic bending energy of vesicle membrane deformation. (English) Zbl 1432.74211 Math. Methods Appl. Sci. 37, No. 6, 913-930 (2014). MSC: 74S05 74K15 65M15 65M60 74S20 PDF BibTeX XML Cite \textit{L. Zhu} and \textit{Q. Du}, Math. Methods Appl. Sci. 37, No. 6, 913--930 (2014; Zbl 1432.74211) Full Text: DOI
Zhao, Jihong; Liu, Qiao Logarithmically improved blow-up criteria for a phase field Navier-Stokes vesicle-fluid interaction model. (English) Zbl 1306.35105 J. Math. Anal. Appl. 405, No. 2, 422-437 (2013). MSC: 35Q35 76Z05 PDF BibTeX XML Cite \textit{J. Zhao} and \textit{Q. Liu}, J. Math. Anal. Appl. 405, No. 2, 422--437 (2013; Zbl 1306.35105) Full Text: DOI arXiv
Bartels, Sören Finite element approximation of large bending isometries. (English) Zbl 1267.74109 Numer. Math. 124, No. 3, 415-440 (2013). MSC: 74S05 74K20 65N30 65N12 PDF BibTeX XML Cite \textit{S. Bartels}, Numer. Math. 124, No. 3, 415--440 (2013; Zbl 1267.74109) Full Text: DOI
Bretin, E.; Lachaud, J.-O.; Oudet, É. Regularization of discrete contour by Willmore energy. (English) Zbl 1255.68212 J. Math. Imaging Vis. 40, No. 2, 214-229 (2011). MSC: 68U10 49Q10 68U05 PDF BibTeX XML Cite \textit{E. Bretin} et al., J. Math. Imaging Vis. 40, No. 2, 214--229 (2011; Zbl 1255.68212) Full Text: DOI
Mori, Yoichiro; Liu, Chun; Eisenberg, Robert S. A model of electrodiffusion and osmotic water flow and its energetic structure. (English) Zbl 1227.92007 Physica D 240, No. 22, 1835-1852 (2011). MSC: 92C05 92C37 35Q92 65C20 PDF BibTeX XML Cite \textit{Y. Mori} et al., Physica D 240, No. 22, 1835--1852 (2011; Zbl 1227.92007) Full Text: DOI arXiv
Du, Qiang; Li, Manlin Analysis of a stochastic implicit interface model for an immersed elastic surface in a fluctuating fluid. (English) Zbl 1294.35200 Arch. Ration. Mech. Anal. 199, No. 1, 329-352 (2011). MSC: 35R60 60H30 74F10 76D06 76M35 35Q35 35B35 PDF BibTeX XML Cite \textit{Q. Du} and \textit{M. Li}, Arch. Ration. Mech. Anal. 199, No. 1, 329--352 (2011; Zbl 1294.35200) Full Text: DOI
Bänsch, Eberhard; Morin, Pedro; Nochetto, Ricardo H. Preconditioning a class of fourth order problems by operator splitting. (English) Zbl 1241.65031 Numer. Math. 118, No. 2, 197-228 (2011). Reviewer: Martin Plešinger (Liberec) MSC: 65F08 65M60 35K46 65F10 PDF BibTeX XML Cite \textit{E. Bänsch} et al., Numer. Math. 118, No. 2, 197--228 (2011; Zbl 1241.65031) Full Text: DOI
Gal, Ciprian G.; Grasselli, Maurizio Trajectory attractors for binary fluid mixtures in 3D. (English) Zbl 1223.35079 Chin. Ann. Math., Ser. B 31, No. 5, 655-678 (2010). Reviewer: Athanasios Yannacopoulos (Athens) MSC: 35B41 35B40 35K55 35Q35 76D05 35Q30 PDF BibTeX XML Cite \textit{C. G. Gal} and \textit{M. Grasselli}, Chin. Ann. Math., Ser. B 31, No. 5, 655--678 (2010; Zbl 1223.35079) Full Text: DOI
Xu, Yan; Shu, Chi-Wang Local discontinuous Galerkin method for surface diffusion and Willmore flow of graphs. (English) Zbl 1203.65190 J. Sci. Comput. 40, No. 1-3, 375-390 (2009). MSC: 65M60 05C90 PDF BibTeX XML Cite \textit{Y. Xu} and \textit{C.-W. Shu}, J. Sci. Comput. 40, No. 1--3, 375--390 (2009; Zbl 1203.65190) Full Text: DOI
Zhang, Jian; Das, Sovan; Du, Qiang A phase field model for vesicle-substrate adhesion. (English) Zbl 1173.74028 J. Comput. Phys. 228, No. 20, 7837-7849 (2009). MSC: 74L15 74G65 74S05 92C10 PDF BibTeX XML Cite \textit{J. Zhang} et al., J. Comput. Phys. 228, No. 20, 7837--7849 (2009; Zbl 1173.74028) Full Text: DOI
Maitre, Emmanuel; Milcent, Thomas; Cottet, Georges-Henri; Raoult, Annie; Usson, Yves Applications of level set methods in computational biophysics. (English) Zbl 1171.76435 Math. Comput. Modelling 49, No. 11-12, 2161-2169 (2009). MSC: 76M25 65M99 92C05 PDF BibTeX XML Cite \textit{E. Maitre} et al., Math. Comput. Modelling 49, No. 11--12, 2161--2169 (2009; Zbl 1171.76435) Full Text: DOI
Du, Qiang; Liu, Chun; Ryham, Rolf; Wang, Xiaoqiang Energetic variational approaches in modeling vesicle and fluid interactions. (English) Zbl 1183.74056 Physica D 238, No. 9-10, 923-930 (2009). Reviewer: Felix Kaplanski (Tallinn) MSC: 74F10 74K15 76M30 76T99 76D05 PDF BibTeX XML Cite \textit{Q. Du} et al., Physica D 238, No. 9--10, 923--930 (2009; Zbl 1183.74056) Full Text: DOI
Wang, Xiaoqiang; Du, Qiang Modelling and simulations of multi-component lipid membranes and open membranes via diffuse interface approaches. (English) Zbl 1143.92001 J. Math. Biol. 56, No. 3, 347-371 (2008). MSC: 92C05 65C20 92C10 92-08 PDF BibTeX XML Cite \textit{X. Wang} and \textit{Q. Du}, J. Math. Biol. 56, No. 3, 347--371 (2008; Zbl 1143.92001) Full Text: DOI
Oberhuber, Tomás Finite difference scheme for the Willmore flow of graphs. (English) Zbl 1140.53032 Kybernetika 43, No. 6, 855-867 (2007). MSC: 53C44 65M12 65M20 74S20 35K35 35K55 PDF BibTeX XML Cite \textit{T. Oberhuber}, Kybernetika 43, No. 6, 855--867 (2007; Zbl 1140.53032) Full Text: Link EuDML
Wise, Steven; Kim, Junseok; Lowengrub, John Solving the regularized, strongly anisotropic Cahn-Hilliard equation by an adaptive nonlinear multigrid method. (English) Zbl 1310.82044 J. Comput. Phys. 226, No. 1, 414-446 (2007). MSC: 82C80 65M55 PDF BibTeX XML Cite \textit{S. Wise} et al., J. Comput. Phys. 226, No. 1, 414--446 (2007; Zbl 1310.82044) Full Text: DOI
Burger, Martin; Haußer, Frank; Stöcker, Christina; Voigt, Axel A level set approach to anisotropic flows with curvature regularization. (English) Zbl 1201.82049 J. Comput. Phys. 225, No. 1, 183-205 (2007). MSC: 82D25 82D80 35R25 58E50 65N50 74N05 PDF BibTeX XML Cite \textit{M. Burger} et al., J. Comput. Phys. 225, No. 1, 183--205 (2007; Zbl 1201.82049) Full Text: DOI
Wheeler, A. A. Phase-field theory of edges in an anisotropic crystal. (English) Zbl 1149.74322 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 462, No. 2075, 3363-3384 (2006). MSC: 74E15 82D25 PDF BibTeX XML Cite \textit{A. A. Wheeler}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 462, No. 2075, 3363--3384 (2006; Zbl 1149.74322) Full Text: DOI
Rätz, Andreas; Ribalta, Angel; Voigt, Axel Surface evolution of elastically stressed films under deposition by a diffuse interface model. (English) Zbl 1088.74035 J. Comput. Phys. 214, No. 1, 187-208 (2006). MSC: 74K35 74S05 74M25 PDF BibTeX XML Cite \textit{A. Rätz} et al., J. Comput. Phys. 214, No. 1, 187--208 (2006; Zbl 1088.74035) Full Text: DOI
Du, Qiang; Liu, Chun; Wang, Xiaoqiang Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions. (English) Zbl 1086.74024 J. Comput. Phys. 212, No. 2, 757-777 (2006). MSC: 74K15 74G65 PDF BibTeX XML Cite \textit{Q. Du} et al., J. Comput. Phys. 212, No. 2, 757--777 (2006; Zbl 1086.74024) Full Text: DOI
Tonegawa, Yoshihiro A diffused interface whose chemical potential lies in a Sobolev space. (English) Zbl 1170.35416 Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 4, No. 3, 487-510 (2005). MSC: 35J60 35B25 35J20 80A22 PDF BibTeX XML Cite \textit{Y. Tonegawa}, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 4, No. 3, 487--510 (2005; Zbl 1170.35416) Full Text: EuDML