Dr. Nikolai Botkin
Technische Universität MünchenZentrum Mathematik - M6
Boltzmannstraße 3
85747 Garching Room: 03.04.059
Phone: +49-89-289-16828
eMail: botkin
ma.tum.deHomepage
Research Interests
- Development of mathematical models based on partial differential equations
- Mathematical analysis of models
- Numerical implementation with Finite Element, Finite Volume and Finite Difference techniques
- Optimal control of ordinary and distributed systems
- Hamilton-Jacobi equations
- Homogenization theory
- Hydrodynamics, elasticity theory, thermodynamics, phase field models
Projects
- Optimal control in cryopreservation of cells and tissues, DFG Priority Program SPP 1253: Optimization with partial differential equations, Intention of Prof. K-H. Hoffmann and Dr. N.Botkin
- Modelling of CO2 sequestration including parameter identification and numerical simulation, This subproject is a part of the Special Partnership between King Abdullah University of Science and Technology (KAUST) and Technische Universität München (TUM). The subproject deals with the simulation of different scenarios of CO2 sequestration in order to predict possible leakage sources of CO2, estimate expected storage capacities of CO2 repositories, and optimize the injection process. The development and numerical implementation of multiphase flow models including such phenomena as phase changes, hysteresis effects, chemical reactions, etc is the content oh the investigation. Intention of Prof. K-H. Hoffmann and Dr. N.Botkin
- KAUST
Publications
2011
- N.D. Botkin, K.-H. Hoffmann, V.L.Turova
Optimal control of ice formation in living cells during freezing
Applied Mathematical Modelling, Vol. 35 (4044-4057) - N.D. Botkin, K.-H. Hoffmann, V.L. Turova
Stable numerical schemes for solving Hamilton-Jacobi-Bellman-Isaacs equations
SIAM Journal on Scientific Computing, Vol. 33 (2) (992-1007) - A.E.Kovtanyuk, N.D.Botkin, K.-H.Hoffmann
Numerical simulations of a coupled radiative-conductive heat transfer model using a modified Monte Carlo method
International Journal of Heat and Mass Transfer 55 (649-564) - N.D.Botkin, K.-H.Hoffmann, N.Mayer, V.L.Turova
Approximation schemes for solving disturbed control problems with non-terminal time and state constraints
Analysis, Vol. 31 (355-379)
2010
- A.E. Kovtanyuk, N.D. Botkin, K.-H. Hoffmann
Numerical simulations of a coupled conductive-radiative heat transfer model using parallel computing
Priority programm 1253 "Optimization with Partial Differential Equations", 2010 (November), Preprint-Number: SPP1253-112 (1-13) - A. Frackowiak, N.D. Botkin, M. Cialkowski, and K.-H. Hoffmann
A fitting algorithm for solving inverse problems of heat conduction
International Journal of Heat and Mass Transfer, 53 (2123-2127) - N.D. Botkin, K.-H. Hoffmann, N. Mayer, V.L. Turova
Approximation schemes for solving disturbed control problems with nonterminal time and phase constraints
Priority programm 1253 "Optimization with Partial Differential Equations", 2010 (August), Preprint-Number: SPP1253-105 (1-21) - N.D. Botkin, K.-H. Hoffmann
Optimal control in cryopreservation of living cells
Proceedings of the International Conference "Actual Problems of Stability and Control Theory" (APSCT´2009), Volume 16(5), 2010, Russia, Ekaterinburg, September 22-26 (233-240) - K.-H. Hoffmann, N.D. Botkin, V.L. Turova
Freezing of living cells: mathematical models and design of optimal cooling protocols
accepted for publication in first thematical volume of SPP1253 - N.D. Botkin, E.A. Ryazantseva
Structure of viability kernels for some linear differential games
J. Optim. Theory Appl. 147 (42–57)
2009
- N.D.Botkin, K.-H.Hoffmann
Control design in cryopreservation of living cells
Abstracts of the International Conference "Actual Problems of Stability and Control Theory", September 21-26, 2009, Ekaterinburg, Russia (158-159) - T. G. Amler, N. D. Botkin, K.-H. Hoffmann, A. M. Meirmanov, V. N. Starovoitov
Transport equation with boundary conditions of hysteresis type
Mathematical Methods in the Applied Sciences, 32 (2177-2196) - N.D. Botkin, K.-H. Hoffmann, V.L.Turova
Stable solutions of Hamilton-Jacobi equations. Application to control of freezing processes.
Preprint SPP 1253-080 (1-25) - K.-H. Hoffmann, N. D. Botkin
Modeling and optimization in cryopreservation using phase field models
Abstracts of the 4th International Conference on High Performance Scientific Computing, Hanoi, Vietnam, March 2-6, 2009 (88) - N.D. Botkin, K.-H. Hoffmann, A. Frackowiak, A.M. Cialkowski
Heat exchange between air and solid surface covered with a nanostructure
submitted to International Journal of Heat and Mass Transfer - N.D. Botkin, V.L. Turova
Simulation of cell shrinkage caused by osmotic cellular dehydration during freezing
Abstracts of the 4th International Conference on High Performance Scientific Computing, Hanoi, Vietnam, March 2-6, 2009 (40)
2008
- K.-H. Hoffmann, N.D. Botkin, V.L. Turova
Optimal control in cryopreservation of living tissues
Preprints of the International Conference "Differential Equations and Topology", Moscow, June 16-22, 2008 (254-255) - K-H. Hoffmann, N. D. Botkin
Optimal Control in Cryopreservation of Cells and Tissues.
Advances in Mathematical Sciences and Applications, 29, Japan, Tokyo (177-200) - K-H. Hoffmann, T. G. Amler, N. D. Botkin, V. L. Turova
Propagation and Deposition of Air Driven Nanoparticles in Complex Channeled Structures.
Poster presentation. Abstracts of the conference "Mathematics in Biosciences", Helmholtz Zentrum München (p. 32) - K-H. Hoffmann, N. D. Botkin, O. A. Pykhteev
Optimal Control in Cryopreservation of Cells and Tissues.
Poster presentation. Abstracts of the conference "Mathematics in Biosciences", Helmholtz Zentrum München (p. 26) - N.D. Botkin, K.-H. Hoffmann, A. Frackowiak, A.M. Cialkowski
Study of the heat transfer between gases and solid surfaces covered with micro rods
Preprint SPP1253-10-05, Priority programm 1253 (1-13) - N.D. Botkin, K.-H. Hoffmann, A. Frackowiak, A.M. Cialkowski
L^2 and H^(1/2) fitting algorithmus for solving inverse problems of heat transfer
Preprint SPP1253-10-06, Priority programm 1253 (1-10) - N.D. Botkin, K.-H. Hoffmann
Optimal control in cryopreservation of cells and tissues
Preprint SPP1253-10-07, Priority programm 1253 (1-34)
2007
- N.D. Botkin, K.-H. Hoffmann, O.A. Pykhteev, V.L. Turova
Dispersion relations for acoustic waves in heterogeneous multi-layered structures contacting with fluids
Journal of the Franklin Institute , Vol. 34, no. 5 (520-534) - N.D. Botkin, K.-H. Hoffmann, D. Marx
Drag on spheres in micropolar fluids with nonzero boundary conditions for microrotations
J. Fluid Mech., Vol. 590 (319-330) - N. Botkin, Ö. Degistrici, B. Fassbender, J. Simonsmeier, M. Thie
Zahn-Einfrierer-Behälter
Deutchen Patent- und Markenamt. DE 10 2005 047 438 A1, 2007.04.05 (8) - J. Stoer, N.D. Botkin, O.A. Pykhteev
An interior-point method for minimizing convex functions on the convex hull of a point set
Optimization, Vol. 56, No. 4 (515-524) - D.Hoffmann, N.Botkin, C.Egler, B.Fassbender, M.Hidendorff, M.Giersig, J.Knekties, R.Pascal, P.Patoka, U.Schuldenzucker, S.Troszczynska, V.Turova, A.Weckmann, M.Zabe-Kühn
Nanosafe2
caesar Annual Report 2007 (Molecular Biomedicine and Medical Technology) (64-65)
2006
- N.D. Botkin, K.-H. Hoffmann, O.A. Pykhteev, B.N. Starovoitova, V.L. Turova
Two complementary approaches to modelling a biosensor
Proceedings of ASM 2006 (Applied Simulation and Modelling), June 26-28, 2006, Rhodos, Greece (525-530) - N.D. Botkin, A. M. Khludnev, K.-H. Hoffmann
The variational contact problem for elastic objects of different dimensions
Siberian Mathematical Journal, Vol. 47, no. 3 (584-593) - N.D. Botkin, H. Hölscher, M. Tewes, M. Löhndorf, K.-H. Hoffmann, E. Quandt
Modeling of pneumatic tires by a finite element model for the development a tire friction remote sensor
Computers and Structures (submitted) - N. Botkin, R. Hassdorf, J. Feydt, S. Thienhaus, L. Buforn, N. Conte, O. Pykhteev, M. Kruzik, M. Moske
Probing Superelasticity in NiTi-Based Shape Memory Thin Films and Foils
Proceedings of the International Conference on Shape Memory and Superelastic Technologies held in Baden-Baden, Germany, October 3-7, 2004 (eds. T.W. Duerig and A.R. Pelton), ASM International, Materials Park, OH, 2006 (399-407) - A. Voigt, R. Backofen, N. Botkin, A. Goepfert, O. Pykhteev, B. Starovoitova, V. Turova, S. Vey, A. Zollorsch
VIOLA-TechSim
caesar Annual Report 2005 (Nanotechnogy/Materials Science 2_1_35) - K.-H. Hoffmann, N.D. Botkin, O.A. Pykhteev
Optimization of cooling protocols in cryopreservation of living tissues
caesar Annual Report 2005 (Biotechnology 2_2_5) - K.-H.Hoffmann, N.D.Botkin, O.A.Pykhteev
Finite element modelling of a microfluidic reaktor
caesar Annual Report 2005 (Nanotechnology/Materials Science 2_1_28) - K.-H. Hoffmann, N.D. Botkin, O.A. Pykhteev
Orthodontic film composites-superelastic composite material
caesar Annual Report 2005 (Nanotechnology/Materials Science 2_1_12) - D. Hoffmann, M. Moske, K.-H. Hoffmann, M. Giersig, R. Pascal, N. Botkin, V. Starovoitov, M. Hilgendorff, G. Treitz, M. Zabe-Kühn, B. Fassbender
ELOBIS- Elasto-optical biosensor based on nanostructures
caesar Annual Report 2005 (Biotechnology 2_2_1)
2005
- N.D. Botkin, K.-H. Hoffmann, O.A. Pykhteev, V.L. Turova
Dispersion relations for acoustic waves in heterogeneous multi-layered structures contacting with fluids
Proceedings of the First International Conference on Modeling, Simulation and Applied Optimization, February 1-3, 2005, Sharjah, U.A.E. - N.D. Botkin, K.-H. Hoffmann, V.N. Starovoitov
Homogenization of interfaces between rapidly oscillating fine elastic structures and fluids
SIAM J. Appl. Math. Vol. 65, No. 3 (983-1005) - N.D. Botkin, K.-H. Hoffmann, A.M. Meirmanov, V.N. Starovoitov
Description of adhering with saturation using boundary conditions of hysteresis type
Nonlinear Analysis 63 (1467-1473) - N. Botkin, J. Stoer
Minimumization of a convex function on the convex hull of a point set
Mathematical Methods of Operations Research 62, no. 2 (167-185) - N. Botkin, R.Hassdorf, J. Feydt, S. Thienhaus, L. Buforn, N. Conte, O. Pykhteev, M.Kruzik, M. Moske
Spherical load indetation in submicron NiTiCu shape memory thin films
Proc. of the 2004 Mater. Res Soc. Fall Meeting: Symp. on Fundamentals of Nanoindentation and Nanotribology III Boston, MA, (Eds. D.F. Bahr, at al.) Vol. 841 (R 9.7.1-R 9.7.6) - N.D. Botkin, A.A. Melikyan, V.L. Turova
Modelling of disturbance propagation in anisotropic media using differential game methods
Proceedings of the 16th IFAC World Congress, July 3-8, 2005, Prague - N.D. Botkin, A.A. Melikyan, V.L. Turova
Singularity phenomena in ray propagation in anisotropic media
Proceedings of the International Conference ``Physics and Control'', August 24-26, 2005, St.-Petersburg (373-378) - A. Voigt, K.-H. Hoffmann, R. Backofen, N. Botkin, A.Goepfert, O.Pykhteev, V.Turova, S.Vey, A.Zollorsch
Viola
caesar Annual Report 2004 (Nanotechnology/Materials Science 2_1_30) - K.-H.Hoffmann, N.D.Botkin, O.A.Pykhteev, V.L.Turova
MAMS: Mathematical Modeling of a Biosensor
caesar Annual Report 2004 (Coupling of Biological and Electronic Systems 2_2_1)
2004
- N.D. Botkin, V.L. Turova
Mathematical models of a biosensor
Applied Mathematical Modelling, Vol. 28, No. 6 (573-589) - N.D. Botkin, K.-H. Hoffmann, O.A. Pykhteev, V.L. Turova
Numerical computation of dispersion relations for multi-layered anisotropic structures
Proceedings of the Nanotechnology conference and trade show, Boston, March 7-11, 2004 (401-414) - N.D. Botkin, A.A. Melikyan, V.L. Turova
Propagation of disturbances in inhomogeneous anisotropic media
Preprint N181, SFB611 ``Singuläre Phänomene und Skalierung in mathematischen Modellen'', Bonn (1-25) - Nikolai Botkin, Hendrik Hölscher, Michael Tewes, Markus Löhndorf, Karl-Heinz Hoffmann, Eckhardt Quandt
Modelling of pneumatic tires by a finite element model for the developement of a tire friction remote sensor
Preprint 2004-10-28 40. caesar, Bonn - N.D. Botkin, K.-H. Hoffmann, F. Otto, V.N. Starovoitov, V.L. Turova
Nonlinear interaction of piezoelectrically excited surface waves
Singular Phenomena und Skaling in mathematical Models. Reinsche Fridrich-Wilhelms-Universität Bonn. Sonderforschungsbereich 611, Arbeits- und Ergebnisbericht 2002-2004 (279-303) - N. Botkin, M. Arndt, C. Bourauel, D. Drescher, R. Hassdorf, M. Kruzik, M. Moske, O. Pykhteev, E. Quandt, H. Rumpf, F. Sernetz, T. Sterzl
Analysis of force systems of superelastic nickel titanium alloy leveling arches and development of superelastic compound wires for use in orthodontics
Proceedings of the 6th International Symposium on Computer Methods in Biomechanics & Biomechanical Engineering. February 25-28, 2004, Tryp Atocha Hotel, Madrid, Spain - K.-H. Hoffmann, N.D. Botkin, O.A. Pykhteev, V.L. Turova
MAMS: Mathematical Modeling of a Biosensor
caesar Annual Report 2003 (Coupling of Biological and Electronic Systems 2_2_2)
2003
- K.-H. Hoffmann, N.D. Botkin, V.N. Starovoitov, V.L. Turova
Treatment of the interface between fine elastic structures and fluids with homogenization method
Preprint N100, SFB611 ``Singuläre Phänomene und Skalierung in mathematischen Modellen'', Bonn (1-24) - N.D. Botkin, K.-H. Hoffmann, V.N. Starovoitov, V.L. Turova
Treatment of the interface between fine elastic structures and fluids
Proceedings of the International Conference ``Physics and Control'', August 20-22, 2003, St.-Petersburg (1367-1372) - N.D. Botkin, K.-H. Hoffmann, V.N. Starovoitov, V.L. Turova
Modeling the interaction between bristle elastic structures and fluids
Proceedings of the 6th International Conference on Modeling and Simulation of Microsystems, Vol. 1, San Francisco, February 23-27, 2003 (126-129) - N.D. Botkin, V.L. Turova
Finite element modelling of a biosensor
Preprint N110, SFB611 ``Singuläre Phänomene und Skalierung in mathematischen Modellen'', Bonn (1-19) - N.D. Botkin, K.-H. Hoffmann, A.M. Meirmanov, V.N. Starovoitov
Diffusion problem with boundary conditions of hysteresis type
Preprint N111, SFB611 ``Singuläre Phänomene und Skalierung in mathematischen Modellen'', Bonn (1-15) - N. Botkin, A. Khludnev
Shape optimization for elastic structures with nonlinear cracks
Preprint N121, SFB611 ``Singuläre Phänomene und Skalierung in mathematischen Modellen'', Bonn (1-15) - K.-H. Hoffmann, N.D. Botkin, V.N. Starovoitov, V.L. Turova
Mathematical modeling and simulation of the biosensor
caesar Annual Report 2002 (Coupling of Biological and Electronic Systems 2_2_2) - K.-H.Hoffmann, N.D.Botkin, V.L.Turova
Biosensor: Development of Numerical Methods and Software
caesar Annual Report 2002 (Coupling of Biological and Electronic Systems 2_2_3)
2002
- N.D. Botkin, K.-H. Hoffmann
Fully coupled model of a nonlinear thin plate excited by piezoelectric actuators
Optimal control of complex structures (Oberwolfach, 2000), Internat. Ser. Numer. Math., Vol.139, Birkhäuser, Basel (107-118) - N.D. Botkin, V.L. Turova
Mathematical models of a biosensor
Preprint 2002-12-30 31. caesar, Bonn - N.D. Botkin, K.-H. Hoffmann, V.N. Starovoitov
Homogenization of interfaces between rapidly oscillating fine elastic structures and fluids
Preprint 2002-12-30 30. caesar, Bonn - N. Botkin, B. Winzek, T. Sterzl, H. Rumpf, E. Quandt
Thin film shape memory composites
Proceedings NATO Advanced Research Workshop, France - K.-H. Hoffmann, N.D. Botkin, V.L. Turova
Biosensor: Modeling and Simulation
caesar Annual Report 2001 (Coupling of Biological and Electronic Systems 2_2_2)
2001
- N.D. Botkin, K.-H. Hoffmann
Real-time optimization and stabilization of distributed parameter systems with piezoelectric elements
Online optimization of large scale systems, Springer, Berlin (205-228) - N.D. Botkin, M. Schlensog, M. Tewes, V.L. Turova
A mathematical model of a biosensor
Technical Proceedings of the Fourth International Conference on Modeling and Simulation of Microsystems, Hilton Head Island, South Caroline, March 19-21, 2001 (231-234) - N.D. Botkin, K.-H. Hoffmann
A fully coupled model of a nonlinear thin plate excited by piezoelectric actuators
Smart materials. Proceedings of the first caesarium (Bonn, Nov. 17-19, 1999), Springer, 2001 ( 9-22 ) - K.-H. Hoffmann, N.D. Botkin, M. Tewes, M. Schlensog, V.L. Turova
Wave propagation in biosensors
caesar Annual Report 2000 (Nanotechnology/Materials Science 2_1_3)
Other years
- N.D. Botkin, K.-H. Hoffmann
Homogenization of von Kármán plates excited by piezoelectric patches
ZAMM, Vol.80, no.9 , 2000 (579-590) - N.D. Botkin, A.O. Govorov, A.V. Kalameitsev, M. Rotter, A. Wixforth, J. Kotthaus, K.-H. Hoffmann
Nonlinear acoustoelectrictransport in a two-dimensional electron system
Physical Review B, 62 (4) , 2000 (2659-2668) - N.D. Botkin, K.-H. Hoffmann
Homogenization of a fully coupled model for a nonlinear thin plate excited by piezoelectric transducers
Preprint 00-23, DFG-Project ``Echtzeit-Optimierung großer Systeme'' , 2000 (1-11) - N.D. Botkin, K.-H. Hoffmann
A fully coupled model of a nonlinear thin plate excited by piezoelectric actuators
Preprint 00-25, DFG-Project ``Echtzeit-Optimierung großer Systeme'' , 2000 (1-13)
Supervision
- Diplomarbeiten
- Dissertationen
