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 -