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Publications

Preprints

Peer-Reviewed

2012

R. Basile, R. Grima, N. Popovic, A graph-based approach for the approximate solution of the Chemical Master Equation. Submitted (2012).
N. Popovic, A geometric analysis of front propagation in an integrable Nagumo equation with a linear cut-off, Phys. D 241(22), 1976-1984 (2012). Download revised preprint.
P. de Maesschalck, N. Popovic, Gevrey properties of the asymptotic critical wave speed in a family of scalar reaction-diffusion equations, J. Math. Anal. Appl. 386(2), 542-558 (2012). Download revised preprint.

2011

N. Popovic, A Geometric Analysis of Front Propagation in a Family of Degenerate Reaction-Diffusion Equations with Cut-Off, Z. Angew. Math. Phys. 62(3), 405-437 (2011). Download revised preprint.
N. Popovic, A Geometric Classification of Traveling Front Propagation in the Nagumo Equation with Cut-Off, in "MURPHYS 2010: Proceedings of the International Workshop on Multi-Rate Processes and Hysteresis, Pecs, 2010", J. Phys. Conference Series 268, 012023 (2011). Download revised preprint.

2010

F. Dumortier, N. Popovic, T.J. Kaper, A Geometric Approach to Bistable Front Propagation in Scalar Reaction-Diffusion Equations with Cut-Off, Phys. D 239(20-22), 1984-1999 (2010). Download revised preprint.

2009

P. de Maesschalck, N. Popovic, T.J. Kaper, Canards and Bifurcation Delays of Spatially Homogeneous and Inhomogeneous Types in Reaction-Diffusion Equations, Adv. Differential Equations 14(9-10), 943-962 (2009). Download revised preprint.
C. Burton, H. Knoop, N. Popovic, M. Sharpe, G. Bleijenberg, Reduced complexity of activity patterns in patients with Chronic Fatigue Syndrome: a case control study, BioPsychoSocial Medicine 3(7) (2009). Download revised preprint.

2008

N. Popovic, Mixed-Mode Dynamics and the Canard Phenomenon: Towards a Classification, in "MURPHYS 2008: Proceedings of the International Workshop on Multi-Rate Processes and Hysteresis, Cork 2008", J. Phys. Conference Series 138, 012020 (2008). Download revised preprint.
M. Krupa, N. Popovic, N. Kopell, Mixed-Mode Oscillations in Three Time-Scale Systems: A Prototypical Example. SIAM J. Appl. Dyn. Syst. 7(2), 361-420 (2008). Download revised preprint.
G. van Baalen, N. Popovic, C.E. Wayne, Long tails in the long time asymptotics of quasi-linear hyperbolic-parabolic systems of conservation laws. SIAM J. Math. Anal. 39(6), 1951-1977 (2008). Download revised preprint
M. Krupa, N. Popovic, N. Kopell, H.G. Rotstein, Mixed-Mode Oscillations in a Three Time-Scale Model for the Dopaminergic Neuron, Chaos 18(1), 015106 (2008). Download revised preprint.

2007

L.V. Kalachev, H.G. Kaper, T.J. Kaper, N. Popovic, A. Zagaris, Reduction for Michaelis-Menten-Henri Kinetics in the Presence of Diffusion, in "Proceedings of the International Conference in Honor of Jacqueline Fleckinger, Toulouse, France 2006", Electron. J. Differential Equations Conf. 16, 155-184 (2007). Download revised preprint.
N. Popovic, Front Speeds, Cut-Offs, and Desingularization: A Brief Case Study, in "Proceedings of the Conference on Fluids and Waves-Recent Trends in Applied Analysis, Memphis 2006", Contemp. Math. 440, 187-195 (2007). Download revised preprint.
N. Popovic, D. Praetorius, A. Schlömerkemper, Analysis and Numerical Simulation of Magnetic Forces between Rigid Polygonal Bodies. Part I: Analysis, Contin. Mech. Thermodyn. 19(1-2), 67-80 (2007). Download revised preprint.
N. Popovic, D. Praetorius, A. Schlömerkemper, Analysis and Numerical Simulation of Magnetic Forces between Rigid Polygonal Bodies. Part II: Numerical Simulation, Contin. Mech. Thermodyn. 19(1-2), 81-109 (2007). Download revised preprint.
F. Dumortier, N. Popovic, T.J. Kaper, The Critical Wave Speed for the Fisher-Kolmogorov-Petrowskii-Piscounov Equation with Cut-Off, Nonlinearity 20(4), 855-877 (2007). Download revised preprint.
F. Dumortier, N. Popovic, T.J. Kaper, The asymptotic critical wave speed in a family of scalar reaction-diffusion equations, J. Math. Anal. Appl. 326(2), 1007-1023 (2007). Download revised preprint.

2006

N. Popovic, T.J. Kaper, Rigorous asymptotic expansions for critical wave speeds in a family of scalar reaction-diffusion equations, J. Dynam. Differential Equations 18(1), 103-139 (2006). Download revised preprint.
N. Popovic, D. Praetorius, H-Matrix Techniques for Stray-Field Computations in Computational Micromagnetics, in "Large-Scale Scientific Computing: Proceedings of the 5th International Conference LSSC 2005, Sozopol, Bulgaria", Lecture Notes in Comput. Sci. 3743, 102-110 (2006). Download revised preprint.

2005

N. Popovic, D. Praetorius, A. Schlömerkemper, Magnetic Force Formulae for Magnets at Small Distances, in "Proceedings of the GAMM Annual Meeting 2005, Luxembourg", Proc. Appl. Math. Mech. 5(1), 631-632 (2005). Download revised preprint.
N. Popovic, A Geometric Analysis of Logarithmic Switchback Phenomena, in "HAMSA 2004: Proceedings of the International Workshop on Hysteresis and Multi-Scale Asymptotics, Cork 2004", J. Phys. Conference Series 22, 164-173 (2005). Download revised preprint.
N. Popovic, D. Praetorius, Applications of H-Matrix Techniques in Micromagnetics, Computing 74(3), 177-204 (2005). Download revised preprint.
N. Popovic, A Geometric Analysis of the Lagerstrom Model: Existence of Solutions and Rigorous Asymptotic Expansions, in "Equadiff 2003: Proceedings of the International Conference on Differential Equations, Hasselt 2003", 916-918 (2005). Download revised preprint.

2004

N. Popovic, P. Szmolyan, Rigorous asymptotic expansions for Lagerstrom's model equation - a geometric approach, Nonlinear Anal. 59(4), 531-565 (2004). Download revised preprint.
N. Popovic, P. Szmolyan, A geometric analysis of the Lagerstrom model problem, J. Differential Equations 199(2), 290-325 (2004). Download revised preprint.

Theses

2002

N. Popovic, A Geometric Analysis of the Lagerstrom Model: Existence of Solutions and Rigorous Asymptotic Expansions, PhD Thesis, Vienna University of Technology, Vienna, Austria, 2002.

2000

N. Popovic, Geometric Aspects of WKB Approximation: A Dynamical Systems Approach for the One-Dimensional Stationary Schrödinger Equation, Master's Thesis, Vienna University of Technology, Vienna, Austria, 2000.

Preprints have been revised in accordance with peer reviewers' reports; moreover, typographical errors and other minor mistakes have been corrected where appropriate.