Mathematical Modelling Group

Publications of the Mathematical Modelling Group on curvature driven flow of curves and surfaces and applications

Peer reviewed articles in the impacted scientific periodicals

• M. Beneš, M. Kolář and D. Ševčovič, Qualitative and Numerical Aspects of a Motion of a Family of Interacting Curves in Space, SIAM Journal on Applied Mathematics, Vol. 82, Iss. 2 (2022), 10.1137/21M1417181, https://doi.org/10.1137/21M1417181


• J. Minarčík and M. Beneš, Minimal surface generating flow for space curves of non-vanishing torsion, Discrete Continuous Dynamical Systems B, 2022, 27(11): 6605--6617, doi: 10.3934/dcdsb.2022011


• J. Minarčík and M. Beneš, Nondegenerate homotopy and geometric flows, Homology, Homotopy and Applications, Volume 24, Number 2, 255--264 (2022)


• J. Minarčík, M. Beneš, Long-term behavior of curve shortening flow in $\mathbb{R}^3$, SIAM Journal on Mathematical Analysis 52(2):1221–1231, IF 1.334


• M. Beneš and M. Kolář and D. Ševčovič: Curvature driven flow of a family of interacting curves with applications, Math. Meth. Appl. Sci. 2020;43:4177–4190, IF 2.816


• J. Minarčík, M. Kimura, M. Beneš, Comparing Motion of Curves and Hypersurfaces in $\mathbb{R}^m$, Discrete and Continuous Dynamical Systems - Series B, 24 (2019): 4815–4826, doi: 10.3934/dcdsb.2019032, IF 1.008


• Strachota, P., Beneš, M. Error estimate of the finite volume scheme for the Allen–Cahn equation. BIT Numer. Math. 58 (2) (2018), pp. 489--507, https://doi.org/10.1007/s10543-017-0687-4. Impact factor (2016): 1.670.


• Kolář M., Beneš M. and Ševčovič D. Area Preserving Geodesic Curvature Driven Flow of Closed Curves on a Surface. Discrete Continuous Dynamical Systems B, Volume 22, Issue 10, December 2017, 3671--3689, doi:10.3934/dcdsb.2017148


• Kolář M., Beneš M. and Ševčovič D. Computational analysis of the conserved curvature driven flow for open curves in the plane, Mathematics and Computers in Simulations, vol. 126, pp. 1--13, 2016 (Impact factor 1.124)


• Oberhuber T., Numerical solution for the anisotropic Willmore flow of graphs, Applied Numerical Mathematics, Vol. 88, pp.1--17, 2015 (Impact factor 1.22).


• Hoang Dieu H., Beneš M. and Oberhuber T. Numerical Simulation of Anisotropic Mean Curvature of Graphs in Relative Geometry, Acta Polytechnica Hungarica Vol. 10, No. 7, 2013 pp. 99--115, Impact factor 0.588


• Pauš P. and Beneš M. Direct Approach to Mean-Curvature Flow with Topological Changes. Kybernetika Vol. 45 (2009), No. 4, 591--604, ISSN: 0023-5954, Impact factor 0.293


• Beneš M., Kimura M. and Yazaki S. Second order numerical scheme for motion of polygonal curves with constant area speed. Interfaces and Free Boundaries Vol. 11 (2009), No. 4, 515--536, ISSN 1463-9963, Impact factor 0.955


• Oberhuber T. Finite difference scheme for the Willmore flow of graphs. Kybernetika Vol. 43 (2007), No. 6, 855--867, ISSN: 0023-5954, Impact factor 0.293


• Yazaki S. An area-preserving motion by crystalline curvature. Kybernetika Vol. 43 (2007), No. 6, 903--912, ISSN: 0023-5954, Impact factor 0.293


• Yazaki S. On the tangential velocity arising in a crystalline algorithm. Kybernetika Vol. 43 (2007), No. 6, 913--918, ISSN: 0023-5954, Impact factor 0.293

Peer reviewed articles in the SCOPUS periodicals

• Hoang D. H. and Beneš M., Forced Anisotropic Mean Curvature Flow of Graphs in Relative Geometry, Mathematica Bohemica, Volume 139, Issue 2 (2014) pp. 429--436.


• Kolář M., Beneš M. and Ševčovič D. Computational studies of conserved mean-curvature flow, Mathematica Bohemica, Vol. 139, No. 4, pp. 677--684, 2014


• Beneš M., Mikula K., Oberhuber T. and Ševčovič D. Comparison study for level set and direct Lagrangian methods for computing Willmore flow of closed planar curves, Computing and Visualization in Science 12(6), 2009, 307--317, ISSN 1432-9360


• Beneš M., Mikula K., Oberhuber T. and Ševčovič D. Comparison study for Level set and Direct Lagrangian methods for computing Willmore flow of closed planar curves, Comput. Visual Sci. 12, 307 (2009)


• Beneš, M., Diffuse-Interface Treatment of the Anisotropic Mean-Curvature Flow, Applications of Mathematics, Vol. 48, No. 6, pp. 437-453, 2003, ISSN: 0862-7940

Articles in the ISI listed conference proceedings

• M. Kolář and S. Kobayashi and Y. Uegata and S. Yazaki and M. Beneš: Analysis of Kuramoto-Sivashinsky model of flame/smoldering front by means of curvature driven flow, In Numerical Mathematics and Advanced Applications ENUMATH 2019, Vermolen, Fred J., Vuik, Cornelis (Eds.), Lecture Notes in Computational Science and Engineering vol. 139, Sequence #60, Springer International Publishing, 2021.


• Kolář, M., Beneš, M. and Ševčovič, D., 2019, On Surface Area and Length Preserving Flows of Closed Curves on a Given Surface, In F. A. Radu, K. Kumar, I. Berre, J. M. Nordbotten, and I. S. Pop, editors, Numerical Mathematics and Advanced Applications ENUMATH 2017, pages 279-287. Springer International Publishing


• Kolář M., Beneš M., Kratochvíl J. Modelling and Numerical Studies of Discrete Dislocation Dynamics. In ALGORITMY 2016, 20th Conference on Scientific Computing, Vysoké Tatry - Podbanské, Slovakia, March 14 - 18, 2016, Proceedings of contributed papers and posters, Comenius University, Bratislava, 2016, pages 302--311


• Kolář M., Beneš M., Ševčovič D., Numerical Solution of Constrained Curvature Flow for Closed Planar Curves, In: Karasözen B., Manguoglu M., Tezer-Sezgin M., Göktepe S., Ugur Ö. (Eds.) Numerical Mathematics and Advanced Applications ENUMATH 2015, Volume 112 of the series Lecture Notes in Computational Science and Engineering, pp. 539--546.


• Oberhuber T. Complementary finite volume scheme for the anisotropic surface diffusion flow, in Algoritmy 2009, Proceedings of contributed papers and posters, ed. Handlovičová A., Frolkovič P., Mikula K. and Ševčovič D. Slovak University of Technology in Bratislava, Publishing House of STU, 2009, pp. 153--164, ISBN 978-80-227-3032-7


• Pauš P. and Beneš M. Algorithm for topological changes of parametrically described curves, in Algoritmy 2009, Proceedings of contributed papers and posters, ed. Handlovičová A., Frolkovič P., Mikula K. and Ševčovič D. Slovak University of Technology in Bratislava, Publishing House of STU, 2009, pp. 176--184, ISBN 978-80-227-3032-7


• Minárik, V. and Beneš, M., Numerical solution of degenerate parabolic equations of Hamilton-Jacobi type within the context of computer image processing, in ALGORITMY 2002, peer reviewed Proceedings of contributed papers and posters, pp. 162--170, Publ. house of STU, 2002, ISBN 80-227-1750-9

Peer reviewed articles in the non-impacted scientific periodicals

• Beneš M., Kimura M., Pauš P., Ševčovič D., Tsujikawa T. and Yazaki S. Application of a Curvature Adjusted Method in Image Segmentation, Bulletin of the Institute of Mathematics, Academia Sinica (New Series), Vol. 3 (2008), No. 4, pp. 509-523, ISSN 0304-9825


• Beneš M. Numerical Solution for Surface Diffusion on Graphs, In: Beneš M., Kimura M. and Nakaki T., Eds. Proceedings of Czech Japanese Seminar in Applied Mathematics 2005, COE Lecture Note Vol.3,  Faculty of Mathematics, Kyushu University Fukuoka, October 2006, ISSN 1881-4042, pp. 9--25


• Oberhuber T. Numerical Solution for the Willmore Flow of Graphs, In: Beneš M., Kimura M. and Nakaki T., Eds. Proceedings of Czech Japanese Seminar in Applied Mathematics 2005, COE Lecture Note Vol.3,  Faculty of Mathematics, Kyushu University Fukuoka, October 2006, ISSN 1881-4042, pp. 126--138


• Beneš M., Hilhorst D. and Weidenfeld R., Interface dynamics of an anisotropic Allen/Cahn equation , in Nonlocal elliptic and parabolic problems, pp. 39-45, eds. Biler P., Karch G. and Nadzieja T., Banach Center Publications, Volume 66, 2004, Institute of Mathematics, Polish Academy of Sciences, Warszawa 2004, ISSN 0137-6934

Articles in the conference proceedings

• J. Minarčík: Nondegenerate Homotopy and Geometric Flows, 109-110, P. Ambrož, Z. Masáková (eds), Doktorandské dny 2022, sborník workshopu doktorandů FJFI oboru Matematické inženýrství, České vysoké učení technické v Praze, 2022 pp. 109--110


• J. Minarčík, Nondegenerate Homotopy and Geometric Flows, In: AMBROŽ, P. and MASÁKOVÁ, Z., eds. Doktoranské dny 2020. Doktorandské dny 2020, Praha, 2020-11-20/2020-11-27. Praha: FJFI ČVUT katedra matematiky, 2020.


• Minarčík, J.: On long-term properties of geometric flows of space curves. In: AMBROŽ, P. and MASÁKOVÁ, Z., eds. Doktoranské dny 2019. Doktorandské dny 2019, Praha, 2019-11-15/2019-11-22. Praha: FJFI ČVUT katedra matematiky, 2019.


• Minarčík, J.: On long-term properties of geometric flows of space curves. In: AMBROŽ, P. and MASÁKOVÁ, Z., eds. Doktoranské dny 2019. Doktorandské dny 2019, Praha, 2019-11-15/2019-11-22. Praha: FJFI ČVUT katedra matematiky, 2019.


• J. Minarčík: Properties of Curvature Flow in Codimension Two. In: Ambrož P., Masáková Z., eds. Doktoranské dny 2018. Doktorandské dny 2018, Praha, 2018-11-16/2018-12-23. Praha: FJFI ČVUT katedra matematiky, 2018, pp. 101--102.


• Hoang D. H. And Beneš M. Numerical Simulation of Anisotropic SurfaceDiffusion of Graphs, RIMS Kokyuroku Bessatsu B35 (2012), 115--124, Kyoto, Japan


• Oberhuber T. Numerical Scheme foro the Willmore Flow, in HPC-Europa: Science and Supercomputing in Europe, Report 2006, Eds. P. Alberigo, G. Erbacci, F. Garofalo, CINECA Consortio Interuniversitario, pp. 554--558, ISBN 978-88-86037-19-8


• Oberhuber T., Computational Study of the Willmore Flow on Graphs, in Proceedings of EQUADIFF 11, 2005, Bratislava 2006, ISBN 978-80-227-2624-5, pp. 321--331


• Oberhuber T., Numerical Recovery of the Signed Distance Function., in Beneš M., Mikyška J. and Oberhuber T., editors, Proceedings of the Czech Japanese Seminar in Applied Mathematics. Prague: Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, 2005. ISBN 80-01-03181-0, pp. 148--164


• Beneš M., Diffuse-Interace Model of the Mean-Curvature Flow, in: Diblík, J. and Vala, J., eds., Proceedings on 4th Mathematical Workshop, Faculty of Civil Engineering, Brno University of Technology, October 2005, ISBN 80-214-2998-4, pp. 21--22

Industrial Technical Reports

Ph.D. theses

• M. Kolář: Motion of Curves with the Application to Dislocation Dynamics, Ph.D. dissertation thesis, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, supervisor M. Beneš, defended September 21 2018


• Máca R. Application of degenerate diffusion methods in medical image processing, Ph.D. dissertation thesis, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, supervisor M. Beneš, defended December 8 2017


• Pauš P. Mathematical model of interactions in discrete dislocation dynamics, Ph.D. thesis, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, supervisor Beneš M., December 2013


• Strachota P. Analysis and Application of Numerical Methods for Solving Nonlinear Reaction-Diffusion Equations, Ph.D. thesis, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, supervisor Beneš M., December 2012


• Chalupecký V. Nonlinear Diffusion PDEs and Their Application, PhD thesis, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, supervisor Beneš M., February 2009


• Minárik V. Mathematical Model of Discrete Dislocation Dynamics, PhD thesis, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, supervisor Beneš M., June 2009


• Oberhuber T. Numerical Solution of Willmore Flow, PhD thesis, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, supervisor Beneš M., December 2009

Chapters in books

• Kimura M. Shape derivative of minimum potential energy: abstract theory and applications, in Beneš M. and Feireisl E., Eds. Topics in mathematical modeling, Jindřich Nečas Center for Mathematical Modelling, Lecture Notes, Vol. 4, MATFYZPRESS Publishing House of the Faculty of Mathematics and Physics, Charles University in Prague, 2008, pp. 1--92, ISBN 978-80-7378-060-9


• Yazaki S. An area-preserving crystalline curvature flow equation, in Beneš M. and Feireisl E., Eds. Topics in mathematical modeling, Jindřich Nečas Center for Mathematical Modelling, Lecture Notes, Vol. 4, MATFYZPRESS Publishing House of the Faculty of Mathematics and Physics, Charles University in Prague, 2008, pp. 169--213, ISBN 978-80-7378-060-9

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