TY - GEN A1 - Bestehorn, Michael A1 - Bestehorn, Michael A1 - Michelitsch, Thomas M. A1 - Collet, Bernard A. A1 - Riascos, Alejandro P. A1 - Nowakowski, Andrzej. F. T1 - Simple model of epidemic dynamics with memory effects T2 - Physical Review E N2 - We introduce a compartment model with memory for the dynamics of epidemic spreading in a constant population of individuals. Each individual is in one of the states S=susceptible, I=infected, or R=recovered (SIR model). In state R an individual is assumed to stay immune within a finite-time interval. In the first part, we introduce a random lifetime or duration of immunity which is drawn from a certain probability density function. Once the time of immunity is elapsed an individual makes an instantaneous transition to the susceptible state. By introducing a random duration of immunity a memory effect is introduced into the process which crucially determines the epidemic dynamics. In the second part, we investigate the influence of the memory effect on the space-time dynamics of the epidemic spreading by implementing this approach into computer simulations and employ a multiple random walker's model. If a susceptible walker meets an infectious one on the same site, then the susceptible one gets infected with a certain probability. The computer experiments allow us to identify relevant parameters for spread or extinction of an epidemic. In both parts, the finite duration of immunity causes persistent oscillations in the number of infected individuals with ongoing epidemic activity preventing the system from relaxation to a steady state solution. Such oscillatory behavior is supported by real-life observations and not captured by the classical standard SIR model. KW - Bifurcations KW - Diseases KW - Dynamics of networks KW - Patterns in complex systems KW - Nonlinear Dynamics KW - Interdisciplinary Physics KW - Biological Physics Y1 - 2022 UR - https://journals.aps.org/pre/abstract/10.1103/PhysRevE.105.024205 U6 - https://doi.org/10.1103/PhysRevE.105.024205 SN - 2470-0045 VL - 105 IS - 2 SP - 024205-1 EP - 024205-10 ER - TY - GEN A1 - Varlamova, Olga A1 - Reif, Jürgen A1 - Stolz, Michael A1 - Borcia, Rodica A1 - Borcia, Ion-Dan A1 - Bestehorn, Michael T1 - Wetting properties of LIPSS structured silicon surfaces T2 - The European Physical Journal B N2 - The controlled dynamics of liquid drops via generation of specific wetting states on a solid surface is of great interests both in the fundamental and applied sciences. Considering that the wettability is strongly dependent on the surface topography and surface roughness, we investigate – through experiments and theory – the effect of laser-induced periodic surface structures (LIPSS) generated on silicon (100) targets as a control parameter of wetting properties. To obtain structured silicon surfaces with different morphological features, we patterned the surface by irradiation with femtosecond pulses from an amplified Ti:Sapphire laser system (790 nm/100 fs/1 kHz) at a fluence in the range of 0.4–1.2 J/cm2 on a spot with a diameter about of 100 μm. Variation of the applied irradiation dose results in surface modifications with the roughness about of a few tens of nanometers are ranging from regular LIPSS patterns with the lateral period of about 500–700 nm to complex agglomerations of 3-D microstructures with several-μm feature size. The theoretical study on the correlation of wetting properties with the surface topography has been performed within a phase field model. We found an excellent agreement of numerical results with experiments. Y1 - 2019 U6 - https://doi.org/10.1140/epjb/e2019-90672-2 SN - 1434-6036 SN - 1434-6028 VL - 92 IS - 5 ER - TY - JOUR A1 - Bestehorn, Michael A1 - Neuffer, Kai T1 - Surface Patterns of Laterally Extended Thin Liquid Films in Three Dimensions JF - Physical review letters Y1 - 2001 SN - 1079-7114 VL - 87 IS - 4 SP - 046101 ER - TY - JOUR A1 - Bestehorn, Michael A1 - Merkt, Domnic A1 - Enculescu, Mihaela T1 - Entstehung und Dynamik makroskopischer Strukturen in Systemen fern vom Gleichgewicht JF - Forum der Forschung Y1 - 2005 SN - 0947-6989 VL - 9 IS - 18 SP - 31 EP - 40 ER - TY - GEN A1 - Varlamova, Olga A1 - Costache, Florenta Adriana A1 - Reif, Jürgen A1 - Bestehorn, Michael T1 - Self-organized pattern formation upon femtosecond laser ablation by circularly polarized light T2 - Applied Surface Science KW - femtosecond laser ablation KW - nanostructures KW - self-organization Y1 - 2006 SN - 0169-4332 VL - 252 IS - 13 SP - 4702 EP - 4706 ER - TY - CHAP A1 - Bestehorn, Michael A1 - Haken, H. T1 - Pattern Formation and Transients in the Convection Instability Y1 - 1985 ER - TY - CHAP A1 - Bestehorn, Michael A1 - Friedrich, R. A1 - Haken, H. T1 - Modulated Traveling Waves in Nonequilibrium Systems KW - 2D Order Parameter Models Y1 - 1990 ER - TY - JOUR A1 - Bestehorn, Michael T1 - Stationary and Traveling Pulses of the 2D Complex Ginzburg-Landau Equation KW - 2D Order Parameter Models Y1 - 1991 ER - TY - JOUR A1 - Bestehorn, Michael A1 - Fantz, M. A1 - Friedrich, R. A1 - Haken, H. A1 - Pérez-García, C. T1 - Spiral Patterns in Thermal Convection KW - 2D Order Parameter Models Y1 - 1992 ER - TY - JOUR A1 - Bestehorn, Michael A1 - Fantz, M. A1 - Friedrich, R. A1 - Haken, H. T1 - Pattern formation in rotating Bénard convection KW - 2D Order Parameter Models Y1 - 1992 ER - TY - JOUR A1 - Bestehorn, Michael A1 - Pérez-García, C. T1 - Coexistence of Patterns with Different Symmetries in Bénard-Marangoni Convection Y1 - 1987 ER - TY - JOUR A1 - Thess, A. A1 - Bestehorn, Michael T1 - Planform Selection in Bénard-Marangoni-Convection: l-hexagons versus g-hexagons Y1 - 1995 ER - TY - JOUR A1 - Pérez-García, C. A1 - Echebarria, B. A1 - Bestehorn, Michael T1 - Thermal Properties in Surface-Tension-Driven Convection Y1 - 1998 ER - TY - CHAP A1 - Vaerenbergh, S. van A1 - Legros, J. C. A1 - Colinet, P. A1 - Velarde, M. G. A1 - Bestehorn, Michael A1 - Lebon, G. A1 - Thess, A. A1 - Karcher, C. T1 - Processes With Double Diffusive Instabilities Studied in Microgravity T2 - The 2nd European Symposium on Utilisation of the International Space Station, 16 - 18 November 1998, ESTEC, Noordwijk, The Netherlands Y1 - 1999 SN - 92-9092-732-1 SP - 241 EP - 248 PB - ESA Publ. CY - Noordwijk ER - TY - JOUR A1 - Bestehorn, Michael A1 - Fantz, M. A1 - Friedrich, R. A1 - Haken, H. T1 - Hexagonal and Spiral Patterns of Thermal Convection KW - 2D Order Parameter Models Y1 - 1993 ER - TY - JOUR A1 - Bestehorn, Michael A1 - Neufeld, M. A1 - Friedrich, R. A1 - Haken, H. T1 - Pattern formation in rotating Bénard convection KW - 2D Order Parameter Models Y1 - 1994 ER - TY - JOUR A1 - Herrero, H. A1 - Pérez-García, C. A1 - Bestehorn, Michael T1 - Stability of fronts separating domains with different symmetries in hydrodynamical instabilities KW - 2D Order Parameter Models Y1 - 1994 ER - TY - CHAP A1 - Bestehorn, Michael A1 - Friedrich, R. T1 - Natural Patterns in Nonequilibrium Systems, in A Perspective Look at Nonlinear Media - From Physics to Biology and Social Sciences KW - 2D Order Parameter Models Y1 - 1998 ER - TY - JOUR A1 - Bestehorn, Michael A1 - Friedrich, R. T1 - Rotationally invariant order parameter equations for natural patterns in nonequilibrium systems KW - 2D Order Parameter Models Y1 - 1999 ER - TY - JOUR A1 - Thiele, Uwe A1 - Velarde, M. G. A1 - Neuffer, Kai A1 - Bestehorn, Michael A1 - Pomeau, Y. T1 - Sliding drops in the diffusive interface model coupled to hydrodynamics JF - Physical Review E Y1 - 2001 SN - 1550-2376 VL - 64 IS - 4 SP - 061601 ER - TY - JOUR A1 - Thiele, Uwe A1 - Neuffer, Kai A1 - Bestehorn, Michael A1 - Pomeau, Y. A1 - Velarde, M. G. T1 - Sliding drops on an inclined plane JF - Colloids and Surfaces A Y1 - 2002 UR - 0927-7757 VL - 206 IS - 1-3 SP - 87 EP - 104 ER - TY - JOUR A1 - Bestehorn, Michael A1 - Pototsky, Andrey A1 - Thiele, Uwe T1 - 3D Large scale Marangoni convection in liquid films Y1 - 2003 ER - TY - JOUR A1 - Thiele, Uwe A1 - Brusch, L. A1 - Bestehorn, Michael A1 - Bär, Marcus T1 - Modelling thin-film dewetting on structured substrates and templates Y1 - 2003 ER - TY - JOUR A1 - Pototsky, Andrey A1 - Bestehorn, Michael A1 - Thiele, Uwe T1 - Control of the structuring of thin softmatter films by means of different types of external disturbance Y1 - 2004 ER - TY - JOUR A1 - Nitschke, K. A1 - Bestehorn, Michael A1 - Thess, A. T1 - Square Cells in Surface-Tension-Driven Bénard Convection Y1 - 1998 ER - TY - JOUR A1 - Bestehorn, Michael A1 - Colinet, P. T1 - Bénard–Marangoni convection of a binary mixture as an example of an oscillatory bifurcation under strong symmetry-breaking effects JF - Physica D: Nonlinear Phenomena Y1 - 2000 SN - 1872-8022 VL - 145 IS - 1-2 SP - 84 EP - 109 ER - TY - JOUR A1 - Merkt, Domnic A1 - Bestehorn, Michael T1 - Bénard-Marangoni convection in a stronglyevaporating fluid Y1 - 2003 ER - TY - JOUR A1 - Colinet, P. A1 - Joannes, L. A1 - Iorio, C. S. A1 - Haut, B. A1 - Bestehorn, Michael A1 - Lebon, G. A1 - Legros, J. C. T1 - Interfacial turbulence in evaporating liquids: Theory and preliminary results of the ITEL-Master 9 sounding rocket experiment Y1 - 2003 ER - TY - JOUR A1 - Borcia, Rodica A1 - Merkt, Domnic A1 - Bestehorn, Michael T1 - A phase-field description of surface-tension-driven instability Y1 - 2004 ER - TY - JOUR A1 - Borcia, Rodica A1 - Bestehorn, Michael T1 - Phase-field simulations for evaporation with convection in liquid-vapor systems JF - The European physical journal B Y1 - 2005 SN - 1434-6028 VL - 44 IS - 1 SP - 101 EP - 108 ER - TY - JOUR A1 - Borcia, Rodica A1 - Bestehorn, Michael T1 - Phase field models for Marangoni convection in planar layers Y1 - 2006 ER - TY - JOUR A1 - Borcia, Rodica A1 - Merkt, Domnic A1 - Bestehorn, Michael T1 - Convective patterns in liquid-vaporsystems with diffuse interface Y1 - 2006 ER - TY - JOUR A1 - Borcia, Rodica A1 - Bestehorn, Michael T1 - Phase field models and Marangoni flows Y1 - 2007 ER - TY - JOUR A1 - Millán-Rodriguez, J. A1 - Pérez-García, C. A1 - Bestehorn, Michael A1 - Fantz, M. A1 - Friedrich, R. T1 - Pattern Formation in Convection of Rotating Fluids with Broken Vertical Symmetry Y1 - 1992 ER - TY - JOUR A1 - Bestehorn, Michael T1 - Numerical Results of 3D Stationary Convection in a Binary Mixture Y1 - 1993 ER - TY - JOUR A1 - Bestehorn, Michael T1 - Phase and Amplitude Instabilities for Bénard-Marangoni Convection in Fluid Layers with Large Aspect Ratio Y1 - 1993 ER - TY - JOUR A1 - Bestehorn, Michael T1 - Pattern Selection in Bénard-Marangoni Convection Y1 - 1994 ER - TY - JOUR A1 - Millán-Rodriguez, J. A1 - Bestehorn, Michael A1 - Pérez-García, C. A1 - Friedrich, R. A1 - Neufeld, M. T1 - Defects Motion in Rotating Fluids Y1 - 1995 ER - TY - GEN A1 - Bestehorn, Michael T1 - Square Patterns in Bénard-Marangoni Convection Y1 - 1996 ER - TY - JOUR A1 - Bestehorn, Michael T1 - Two Layer Model Showing a Variety of Pattern Types near Nonequilibrium Phase Transitions Y1 - 1996 ER - TY - GEN A1 - Borcia, Rodica A1 - Bestehorn, Michael T1 - Different behaviours of delayed fusion between drops with miscible liquids T2 - Physical review E Y1 - 2010 SN - 1063-651X VL - 82 IS - 3 SP - 036312 ER - TY - JOUR A1 - Bestehorn, Michael A1 - Grigorieva, E. V. A1 - Haken, H. A1 - Kaschenko, S. A. T1 - Order Parameters for Class-B Lasers With a Long Time Delayed Feedback Y1 - 2000 ER - TY - JOUR A1 - Bestehorn, Michael A1 - Grigorieva, E. V. A1 - Kaschenko, S. A. T1 - Spatio-Temporal Structures in a Model With Delay And Diffusion Y1 - 2004 ER - TY - JOUR A1 - Bestehorn, Michael A1 - Grigorieva, E. V. T1 - Formation and Propagation of Localized States in Extended Systems Y1 - 2004 ER - TY - JOUR A1 - Bestehorn, Michael A1 - Pérez-García, C. T1 - Modulated Rolls and Traveling Waves in a Secondary Convective Instability Y1 - 1991 ER - TY - JOUR A1 - Bestehorn, Michael T1 - Numerical Results of 3D-Convection in a Binary Mixture for a Positive Separation Ratio Y1 - 1992 ER - TY - JOUR A1 - Bestehorn, Michael T1 - Convection in thick and thin fluid layers with a free surface - The Influence of Evaporation Y1 - 2007 ER - TY - JOUR A1 - Borcia, Rodica A1 - Bestehorn, Michael T1 - Phase field simulations for drops and bubbles Y1 - 2007 ER - TY - JOUR A1 - Borcia, Rodica A1 - Borcia, Ion-Dan A1 - Bestehorn, Michael T1 - Drops on an arbitrarily wetting substrate: A phase field description Y1 - 2008 ER - TY - JOUR A1 - Borcia, Rodica A1 - Borcia, Ion-Dan A1 - Bestehorn, Michael T1 - Liquid layers on a patterned surface JF - Soft Matter Y1 - 2008 UR - 1744-6848 VL - 4 IS - 12 SP - 2368 EP - 2372 ER - TY - GEN A1 - Borcia, Rodica A1 - Bestehorn, Michael T1 - Controlled Pattern Formation in Thin Liquid Layers Y1 - 2009 ER - TY - GEN A1 - Borcia, Rodica A1 - Bestehorn, Michael T1 - A Phase Field Description of Spatio-Temporal Behavior in Thin Liquid Layers Y1 - 2010 ER -