TY - GEN A1 - Bestehorn, Michael A1 - Pototsky, Andrey T1 - Faraday instability and nonlinear pattern formation of a two-layer system: A reduced model T2 - Physical Review Fluids N2 - Stability and pattern formation of a two-layer liquid system with large aspect ratio subjected to vertical harmonic oscillations is studied by means of an integrated boundary layer model. The lower layer rests on an oscillating solid substrate, the upper layer is separated by a deformable interface from the lower layer and bounded at the top with a second, free interface to the ambient passive air. The model is derived from the Navier-Stokes equations in long-wave approximation, including inertial terms. Applying a Floquet analysis, linear stability charts and dispersion relations are computed and compared with results from the full linearized Navier-Stokes equations and the long-wave approximation. Nonlinear Faraday patterns simultaneously occurring at the interface and at the film surface are studied by numerically solving the integrated boundary layer model in two and three spatial dimensions. For gravitationally stable two-layer films with a lighter fluid on top of the heavier fluid, we find squares, hexagons, quasiperiodic patterns with eightfold symmetry as well as localized states in the form of large scale depletion regions or finite depth holes, occurring at the interface and surface. For a Rayleigh-Taylor unstable combination (heavier fluid above the light one) we show that external vibration increases the lifetime of the film by delaying or completely suppressing the film rupture. Y1 - 2016 UR - http://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.1.063905 U6 - https://doi.org/10.1103/PhysRevFluids.1.063905 SN - 2469-990X VL - 1 IS - 6 SP - 063905-1 EP - 063905-24 ER - TY - GEN A1 - Borcia, Rodica A1 - Borcia, Ion-Dan A1 - Helbig, Markus A1 - Meier, Martin A1 - Egbers, Christoph A1 - Bestehorn, Michael T1 - Dancing drops over vibrating substrates T2 - The European Physical Journal Special Topics KW - Thin Film Instabilities Y1 - 2017 UR - https://link.springer.com/article/10.1140/epjst/e2016-60202-6 U6 - https://doi.org/10.1140/epjst/e2016-60202-6 SN - 1951-6355 SN - 1951-6401 VL - 226 IS - 6 SP - 1297 EP - 1306 ER - TY - GEN A1 - Richter, Sebastian A1 - Bestehorn, Michael T1 - Thin-film Faraday patterns in three dimensions T2 - The European Physical Journal Special Topics N2 - We investigate the long time evolution of a thin fluid layer in three spatial dimensions located on a horizontal planar substrate. The substrate is subjected to time-periodic external vibrations in normal and in tangential direction with respect to the plane surface. The governing partial differential equation system of our model is obtained from the incompressible Navier-Stokes equations considering the limit of a thin fluid geometry and using the long wave lubrication approximation. It includes inertia and viscous friction. Numerical simulations evince the existence of persistent spatially complex surface patterns (periodic and quasiperiodic) for certain superpositions of two vertical excitations and initial conditions. Additional harmonic lateral excitations cause deformations but retain the basic structure of the patterns. Horizontal ratchet-shaped forces lead to a controllable lateral movement of the fluid. A Floquet analysis is used to determine the stability of the linearized system. KW - Thin Film Instabilities Y1 - 2017 UR - https://link.springer.com/article/10.1140/epjst/e2016-60234-4 U6 - https://doi.org/10.1140/epjst/e2016-60234-4 SN - 1951-6401 SN - 1951-6355 VL - 226 IS - 6 SP - 1253 EP - 1261 ER - TY - GEN A1 - Sterman-Cohen, Elad A1 - Bestehorn, Michael A1 - Oron, Alexander T1 - Rayleigh-Taylor instability in thin liquid films subjected to harmonic vibration T2 - Physics of Fluids N2 - The dynamics of the Rayleigh-Taylor instability of a two-dimensional thin liquid film placed on the underside of a planar substrate subjected to either normal or tangential harmonic forcing is investigated here in the framework of a set of long-wave evolution equations accounting for inertial effects derived earlier by Bestehorn, Han, and Oron [“Nonlinear pattern formation in thin liquid films under external vibrations,” Phys. Rev. E 88, 023025 (2013)]. In the case of tangential vibration, the linear stability analysis of the time-periodic base state with a flat interface shows the existence of the domain of wavenumbers where the film is unstable. In the case of normal vibration, the linear stability analysis of the quiescent base state reveals that the instability threshold of the system is depicted by a combination of distinct thresholds separate for the Rayleigh-Taylor and Faraday instabilities. The nonlinear dynamics of the film interface in the case of the static substrate results in film rupture. However, in the presence of the substrate vibration in the lateral direction, the film interface saturates in certain domains in the parameter space via the mechanism of advection induced by forcing, so that the continuity of the film interface is preserved even in the domains of linear instability while undergoing the time-periodic harmonic evolution. On the other hand, sufficiently strong forcing introduces a new inertial mode of rupture. In the case of the normal vibration, the film evolution may exhibit time-periodic, harmonic or subharmonic saturated waves apart of rupture. The enhancement of the frequency or amplitude of the substrate forcing promotes the destabilization of the system and a tendency to film rupture at the nonlinear stage of its evolution. A possibility of saturation of the Rayleigh-Taylor instability by either normal or unidirectional tangential forcing in three dimensions is also demonstrated. KW - Materials KW - Condensed matter properties KW - Interfaces KW - Liquid surfaces KW - Lasers KW - Surface and interface chemistry KW - Surfaces KW - Optical metrology KW - Thermal effects KW - Thin films Y1 - 2017 UR - https://aip.scitation.org/doi/abs/10.1063/1.4984082 U6 - https://doi.org/10.1063/1.4984082 SN - 1089-7666 VL - 29 IS - 5 SP - 052105-1 EP - 052105-17 ER - TY - GEN A1 - Sterman-Cohen, Elad A1 - Bestehorn, Michael A1 - Oron, Alexander T1 - Ratchet flow of thin liquid films induced by a two-frequency tangential forcing T2 - Physics of Fluids N2 - A possibility of saturating Rayleigh-Taylor instability in a thin liquid film on the underside of a substrate in the gravity field by harmonic vibration of the substrate was recently investigated [E. Sterman-Cohen, M. Bestehorn, and A. Oron, Phys. Fluids 29, 052105 (2017); Erratum, Phys. Fluids 29, 109901 (2017)]. In the present work, we investigate the feasibility of creating a directional flow of the fluid in a film in the Rayleigh-Taylor configuration and controlling its flow rate by applying a two-frequency tangential forcing to the substrate. It is shown that in this situation, a ratchet flow develops, and the dependence of its flow rate on the vibration frequency, amplitude, its periodicity, and asymmetry level is investigated for water and silicone-oil films. A cause for the emergence of symmetry-breaking and an ensuing flow in a preferred direction is discussed. Some aspects of a ratchet flow in a liquid film placed on top of the substrate are discussed as well. A comparison with the case of a neglected fluid inertia is made, and the differences are explained. KW - Materials KW - Microfluidics KW - Materials science KW - Polymers KW - Fluidics KW - Applied fluid dynamics KW - Navier Stokes equations KW - Rheology and fluid dynamics KW - Thin films KW - Statistical physics Y1 - 2018 UR - https://aip.scitation.org/doi/full/10.1063/1.5010262 U6 - https://doi.org/10.1063/1.5010262 SN - 1089-7666 VL - 30 IS - 2 SP - 022101-1 EP - 022101-13 ER - TY - GEN A1 - Razi, Sepehr A1 - Varlamova, Olga A1 - Reif, Jürgen A1 - Bestehorn, Michael A1 - Varlamov, Sergej A1 - Mollabashi, Mahmoud A1 - Madanipour, Khosro A1 - Ratzke, Markus T1 - Birth of periodic Micro/Nano structures on 316L stainless steel surface following femtosecond laser irradiation; single and multi scanning study T2 - Optics & Laser Technology N2 - Formation of coherent laser induced periodic surface structures (LIPSS) on stainless steel type 316L by 100 fs laser pulses at 800 nm wavelength is investigated. Specifically focusing on the large area treatment, effect of the irradiation dose (fluence × pulse number) on the uniformity of the morphology, orientation of the ripples respect to the laser polarization and their periodicity is studied systematically. Controlling the pulse number via varying the scanning speed, the difference between irradiating one particular dose in single scan with its irradiation in separate steps is inspected. Results clearly point out that not only the irradiation dose but also the irradiation way and the time delay between the pulse trains might have a significant effect on the final outcomes. It is discussed in detail that the experimental observations are supporting the model of self-organized structure formation due to irradiation induced instability. KW - Laser surface processing KW - Laser induced periodic surface structures KW - Steel Y1 - 2018 UR - https://www.sciencedirect.com/science/article/pii/S0030399217310320#! U6 - https://doi.org/10.1016/j.optlastec.2018.02.001 SN - 0030-3992 SN - 0308-4280 VL - 104 SP - 8 EP - 16 ER - TY - BOOK A1 - Bestehorn, Michael T1 - Hydrodynamik und Strukturbildung N2 - Das vorliegende Buch wendet sich an Studierende der Physik und der Ingenieurwissenschaften. Aufbauend auf den klassischen Problemstellungen der Hydrodynamik stellt es, über eine detaillierte Analyse hydrodynamischer Instabilitäten, die Verbindung zu dem weiten Themenkreis der makroskopischen Strukturen her. Es kann somit sowohl als ein Lehrbuch der Hydrodynamik als auch als Einstieg in die faszinierende Welt der Musterbildung Verwendung finden. Viele aus Computerrechnungen erhaltene Grafiken sollen das Thema veranschaulichen und das Verständnis erleichtern. KW - Hydrodynamik KW - Strukturbildung Y1 - 2006 UR - http://www.springer.com/de/book/9783540337966#aboutBook SN - 978-3-540-33796-6 U6 - https://doi.org/10.1007/3-540-33797-0 PB - Springer CY - Berlin [u.a.] ER - TY - CHAP A1 - Bestehorn, Michael T1 - IMA8 - Interfacial Fluid Dynamics and Process T2 - The European Physical Journal Special Topics KW - Fluid Dynamics Y1 - 2017 UR - https://link.springer.com/article/10.1140/epjst/e2017-70057-9 U6 - https://doi.org/10.1140/epjst/e2017-70057-9 SN - 1951-6355 VL - 26 IS - 6 SP - 1151 EP - 1153 ER - TY - CHAP A1 - Bestehorn, Michael T1 - Fluid Dynamics and Pattern Formation T2 - Encyclopedia of Complexity and Systems Science N2 - The state of a fluid is described by its velocity, density, pressure, and temperature. All these variables depend in general on space andtime. Pattern formation refers to the situation where one or more of these variables are organized within a certain spatial and/or temporalorder. This order has macroscopic length and time scales, that is, characteristic lengths and times are much larger than those of the atoms or moleculeswhich constitute the fluid. Therefore a continuous description is appropriate. Macroscopic fluid patterns may be encountered in nature as well as in technological applications for a large variety of different systems. Farfrom being complete, we mention some examples: Water waves caused by wind or by sea quakes and land slides (Tsunamis). Localized excitations of the surface of a fluid (solitons), such as that seen on shallow water channels. Shear instabilities in clouds or in multi-layer systems such as the Kelvin–Helmholtz instability or... KW - Fluid Dynamics Y1 - 2009 UR - https://link.springer.com/referenceworkentry/10.1007%2F978-0-387-30440-3_214 SN - 978-0-387-75888-6 U6 - https://doi.org/10.1007/978-0-387-30440-3 PB - Springer CY - New York, NY ER - TY - GEN A1 - Pototsky, Andrey A1 - Bestehorn, Michael T1 - Shaping liquid drops by vibration T2 - epl : a letters journal exploring the frontiers of physics N2 - We present and analyze a minimal hydrodynamic model of a vertically vibrated liquid drop that undergoes dynamic shape transformations. In agreement with experiments, a circular lens-shaped drop is unstable above a critical vibration amplitude, spontaneously elongating in the horizontal direction. Smaller drops elongate into localized states that oscillate with half of the vibration frequency. Larger drops evolve by transforming into a snake-like structure with gradually increasing length. The worm state is long-lasting with a potential to fragment into smaller drops. KW - Thin Films KW - Drop formation Y1 - 2018 UR - http://iopscience.iop.org/article/10.1209/0295-5075/121/46001#epl19033s1 U6 - https://doi.org/10.1209/0295-5075/121/46001 SN - 1286-4854 SN - 0302-072X VL - 121 IS - 4 SP - 46001-p1 EP - 46001-p6 ER - TY - GEN A1 - Borcia, Rodica A1 - Bestehorn, Michael A1 - Uhlig, Sebastian A1 - Gaudet, Matthieu A1 - Schenk, Harald T1 - Liquid pumping induced by transverse forced vibrations of an elastic beam: A lubrication approach T2 - Physical Review Fluids N2 - Two liquid pumps are investigated theoretically and numerically: a single thin liquid layer actuated by a periodic force at an elastic beam and a two-layer geometry actuated by an elastic beam. For the second geometry, the beam actuates the liquid from both sides. For both pumps, the liquid film thickness is small compared to the lateral characteristic length of the system. A lubrication theory is developed. The Euler-Bernoulli equation for transverse deformations of an elastic beam is coupled to the fundamental hydrodynamic equations: the Navier-Stokes equation and a continuity equation in the long-wave approximation. In this way, one connects the transverse displacement of the beam with the hydrodynamic quantities (pressure, velocity fields, and flow rates). Appropriate boundary conditions incorporate the function of the valves. The derivation of the theoretical model is followed by numerical simulations. We estimate flow rates (in two and three spatial dimensions) for different system parameters and we compute the efficiency of a well-designed liquid pump. KW - Microfluidic devices KW - Thin fluid films Y1 - 2018 UR - https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.3.084202 U6 - https://doi.org/10.1103/PhysRevFluids.3.084202 SN - 2469-990X VL - 3 IS - 8 ER - TY - CHAP A1 - Borcia, Ion-Dan A1 - Borcia, Rodica A1 - Bestehorn, Michael A1 - Xu, Wenchao A1 - Harlander, Uwe T1 - Surface waves generated by libration in a circular channel T2 - The 12th European Fluid Mechanics Conference, 9 September 2018 – 13 September 2018, Vienna, Austria Y1 - 2018 UR - http://info.tuwien.ac.at/efmc12/EFMC12_program_v3.2.pdf ER - TY - GEN A1 - Borcia, Rodica A1 - Borcia, Ion-Dan A1 - Bestehorn, Michael A1 - Varlamova, Olga A1 - Hoefner, Kevin A1 - Reif, Jürgen T1 - Drop Behavior Influenced by the Correlation Length on Noisy Surfaces T2 - Langmuir Y1 - 2019 U6 - https://doi.org/10.1021/acs.langmuir.8b03878 VL - 35 SP - 928 EP - 934 ER - TY - BOOK A1 - Bestehorn, Michael T1 - Computational Physics : With Worked Out Examples in FORTRAN and MATLAB N2 - Drawing on examples from various areas of physics, this textbook introduces the reader to computer-based physics using Fortran® and Matlab®. It elucidates a broad palette of topics, including fundamental phenomena in classical and quantum mechanics, hydrodynamics and dynamical systems, as well as effects in field theories and macroscopic pattern formation described by (nonlinear) partial differential equations. A chapter on Monte Carlo methods is devoted to problems typically occurring in statistical physics. KW - Numerical methods KW - Computer physics KW - Fluid dynamics KW - Differential equations Y1 - 2018 SN - 978-3-11-051513-8 PB - De Gruyter CY - Berlin ET - 1. Auflage ER - TY - GEN A1 - Richter, Sebastian A1 - Bestehorn, Michael T1 - Direct numerical simulations of liquid films in two dimensions under horizontal and vertical external vibrations T2 - Physical Review Fluids N2 - We consider Newtonian liquid films on a horizontal substrate with a free and deformable surface. The substrate is subjected to oscillatory accelerations in the normal or in the horizontal direction. An algorithm based on a nonlinear coordinate transformation is presented that allows for direct numerical solutions of the fully nonlinear Navier-Stokes equations and appropriate boundary conditions. No surface tracking is necessary. Normal oscillations generate the traditional subharmonic and harmonic Faraday patterns. Lateral oscillations cause a pattern formation scenario qualitatively similar to spinodal dewetting, namely the disintegration of the film into isolated drops followed by coarsening or fusion, the stabilization of a “precursor” film, and no rupture. Ratchet-like lateral excitations break the horizontal mirror symmetry x→−x and give the patterns a preferred direction. We show that drops formed due to instability of the flat film start to travel in a distinguished direction. For thin films, the results are in good agreement to those of a recently studied lubrication-based dimension-reduced model [Bestehorn et al., Phys. Rev. E 88, 023025 (2013); Bestehorn, Phys. Fluids 25, 114106 (2013)]. KW - Flow instability KW - Interfacial Flows KW - Naviar-Stokes equation KW - Nonlinear Dynamics KW - Fluid Dynamics Y1 - 2019 UR - https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.4.044004 U6 - https://doi.org/10.1103/PhysRevFluids.4.044004 SN - 2469-990X VL - 4 IS - 4 SP - 044004-1 EP - 044004-21 ER - TY - GEN A1 - Sterman-Cohen, Elad A1 - Bestehorn, Michael A1 - Oron, Alexander T1 - Driving mechanisms of ratchet flow in thin liquid films under tangential two-frequency forcing T2 - Physics of Fluids N2 - In a recent paper, we demonstrated the emergence of ratchet flows in thin liquid films subjected to tangential two-frequency vibrations [E. Sterman-Cohen, M. Bestehorn, and A. Oron, “Ratchet flow of thin liquid films induced by a two-frequency tangential forcing,” Phys. Fluids 30, 022101 (2018)], and asymmetric forcing was found to be a sole driving mechanism for these ratchet flows. In this paper, we consider other two-frequency excitations and reveal an additional driving mechanism of an emerging ratchet flow when the acceleration imparted by forcing is symmetric with respect to a certain moment of time within the forcing period (this type of forcing referred to as “symmetric forcing”). This driving mechanism exhibits an intricate interaction between forcing, capillarity, and gravity. We find that in contradistinction with the case of asymmetric forcing where the flow intensity reaches a constant value in the large-time limit, in the case of symmetric forcing the flow intensity exhibits oscillatory variation in time. We also discuss the flow intensity variation of the emerging ratchet flows with the fundamental wavenumber of the disturbance. KW - Thin films KW - Flow instabilities KW - Linear stability analysis KW - Capillarity KW - Non linear dynamics KW - Navier Stokes equations Y1 - 2019 UR - https://aip.scitation.org/doi/10.1063/1.5098941 U6 - https://doi.org/10.1063/1.5098941 VL - 31 IS - 7 ER - TY - GEN A1 - Borcia, Ion-Dan A1 - Borcia, Rodica A1 - Bestehorn, Michael A1 - Richter, Stefan A1 - Xu, Wenchao A1 - Harlander, Uwe T1 - Horizontal Faraday instability and parametric excitation in a circular channel T2 - GAMM 2019, 90th Annual Meeting of the International Assoociation of Applied Mathematics and Mechanics, February 18-22, 2019, Vienna, Austria Y1 - 2018 UR - https://jahrestagung.gamm-ev.de/images/2019/Photos/GAMM2019_BookofAbstracts.pdf SN - 978-3-903024-84-7 SP - 338 PB - TU Verlag CY - Wien ER - TY - GEN A1 - Bestehorn, Michael A1 - Tyvand, Peder A. A1 - Michelitsch, Thomas M. T1 - Dimension-Reduced Model for Deep-Water Waves T2 - Journal of Applied Mathematics and Physics N2 - Starting from the 2D Euler equations for an incompressible potential flow, a dimension-reduced model describing deep-water surface waves is derived. Similar to the Shallow-Water case, the z-dependence of the dependent variables is found explicitly from the Laplace equation and a set of two one- dimensional equations in x for the surface velocity and the surface elevation remains. The model is nonlocal and can be formulated in conservative form, describing waves over an infinitely deep layer. Finally, numerical solutions are presented for several initial conditions. The side-band instability of Stokes waves and stable envelope solitons are obtained in agreement with other work. The conservation of the total energy is checked. KW - Hydrodynamics KW - Ocean Waves KW - DeepWater Waves KW - Numerical Solutions KW - Fractal Derivatives Y1 - 2019 UR - https://www.scirp.org/journal/paperabs.aspx?paperid=89888 U6 - https://doi.org/10.4236/jamp.2019.71007 SN - 2327-4379 SN - 2327-4352 VL - 7 IS - 1 SP - 72 EP - 92 ER - TY - GEN A1 - Borcia, Ion-Dan A1 - Borcia, Rodica A1 - Richter, Sebastian A1 - Xu, Wenchao A1 - Bestehorn, Michael A1 - Harlander, Uwe T1 - Horizontal Faraday instability in a circular channel T2 - Proceedings in Applied Mathematics and Mechanics (PAMM) N2 - We study surface waves in a circular channel placed on a rotating table. The tank can rotate with constant velocity and/or can oscillate. For a glycerin‐water‐solution with high viscosity, oscillation amplitudes about 20 cm and frequencies of 0.5 Hz, we observe surface patterns generated by a parametric instability. The circular geometry of the channel assures in a natural way the periodic lateral boundary conditions often used in the numerical simulations. Up to our knowledge this is the first experiment which evidences the horizontal Faraday instability in a container without walls blocking the flow in the oscillation direction. Experimental and numerical results are compared and discussed. KW - Faraday instability KW - Numerical solutions Y1 - 2019 UR - https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.201900242 U6 - https://doi.org/10.1002/pamm.201900242 SN - 1617-7061 VL - 19 IS - 1 ER - TY - GEN A1 - Borcia, Ion-Dan A1 - Borcia, Rodica A1 - Xu, Wenchao A1 - Bestehorn, Michael A1 - Richter, Sebastian A1 - Harlander, Uwe T1 - Undular bores in a large circular channel T2 - European Journal of Mechanics - B/Fluids N2 - An experimental device previously developed for studying rotating baroclinic flows has been used to investigate undular bores formation, propagation and collision. Up to our knowledge this is the first experimental study of undular bores in a circular channel. For a setup without barriers, this geometry accomplishes in a natural way the periodic lateral boundary conditions, very often used in numerical simulations. An excellent agreement between the experiment and simulation has been achieved. The spatio-temporal structure of bores is well reproduced for the first few reflections or collisions. KW - Undular bores KW - Bore collision KW - Periodical boundary conditions Y1 - 2020 UR - https://www.sciencedirect.com/science/article/pii/S0997754619300706?via%3Dihub U6 - https://doi.org/10.1016/j.euromechflu.2019.09.003 SN - 0997-7546 VL - 79 SP - 67 EP - 73 ER - TY - GEN A1 - Granger, Téo A1 - Michelitsch, Thomas M. A1 - Bestehorn, Michael A1 - Riascos, Alejandro P. A1 - Collet, Bernard A. T1 - Stochastic Compartment Model with Mortality and Its Application to Epidemic Spreading in Complex Networks T2 - Entropy N2 - We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on the Barabási–Albert (BA), Erdös–Rényi (ER), and Watts–Strogatz (WS) types. Both walkers and nodes can be either susceptible (S) or infected and infectious (I), representing their state of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with the transmission of the disease via vectors (mosquitoes). Infected walkers may die during the time span of their infection, introducing an additional compartment D of dead walkers. Contrary to the walkers, there is no mortality of infected nodes. Infected nodes always recover from their infection after a random finite time span. This assumption is based on the observation that infectious vectors (mosquitoes) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with the mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers RM,R0with and without mortality, respectively, and prove that RM1, the healthy state is unstable, whereas for zero mortality, a stable endemic equilibrium exists (independent of the initial conditions), which we obtained explicitly. We observed that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, and others. KW - epidemic spreading KW - compartment model with mortality KW - memory effects KW - random walks KW - random graphs Y1 - 2024 U6 - https://doi.org/10.3390/e26050362 SN - 1099-4300 VL - 26 IS - 5 ER - TY - GEN A1 - Borcia, Ion-Dan A1 - Richter, Sebastian A1 - Borcia, Rodica A1 - Schön, Franz-Theo A1 - Harlander, Uwe A1 - Bestehorn, Michael T1 - Wave propagation in a circular channel: sloshing and resonance T2 - The European Physical Journal Special Topics N2 - Surface wave resonance of a liquid (water) layer confined in a circular channel is studied both experimentally and numerically. For the experiment, eight unevenly distributed ultrasonic distance sensors measure the local height of the wave surface. The resonance curves show maxima only for odd multiples of the fundamental resonance frequency . We explained this behavior using a simple intuitive “ping-pong” like model. Collision of wave fronts can be observed for higher frequencies. Also, the wave reflection on the walls can be treated as wave collision with itself. The non-linearity seems to be weak in our study so the delay in the wave propagation before and after the collision is small. Time-space plots show localized propagating waves with high amplitudes for frequencies near resonance. Between the peaks low amplitude and harmonic patterns are observed. However, for higher frequencies, the frequency band for localized waves becomes wider. In the Fourier space-time plane, this can be observed as a point for the harmonic patterns or a superposition of two lines: one line parallel to wave-vector k axis corresponding to the excitation frequency and a second line with inclination given by wave propagation velocity . For planned future work, this result will help us to reconstruct the whole water surface elevation using time-series from only a few measurement points Y1 - 2023 UR - https://link.springer.com/article/10.1140/epjs/s11734-023-00790-z U6 - https://doi.org/10.1140/epjs/s11734-023-00790-z SN - 1951-6401 SN - 1951-6355 VL - Vol. 232 IS - 4 SP - 461 EP - 468 ER - TY - GEN A1 - Schön, Franz-Theo A1 - Bestehorn, Michael T1 - Instabilities and pattern formation in viscoelastic fluids T2 - The European Physical Journal Special Topics Y1 - 2023 UR - https://link.springer.com/article/10.1140/epjs/s11734-023-00792-x U6 - https://doi.org/10.1140/epjs/s11734-023-00792-x SN - 1951-6401 VL - Vol. 232 IS - 4 SP - 375 EP - 383 ER - TY - GEN A1 - Granger, Téo A1 - Michelitsch, Thomas M. A1 - Bestehorn, Michael A1 - Riascos, Alejandro P. A1 - Collet, Bernard A. T1 - Four-compartment epidemic model with retarded transition rates T2 - Physical Review E N2 - We study an epidemic model for a constant population by taking into account four compartments of the individuals characterizing their states of health. Each individual is in one of the following compartments: susceptible S; incubated, i.e., infected yet not infectious, C; infected and infectious I; and recovered, i.e., immune, R. An infection is visible only when an individual is in state I. Upon infection, an individual performs the transition pathway S→C→I→R→S, remaining in compartments C, I, and R for a certain random waiting time tC, tI, and tR, respectively. The waiting times for each compartment are independent and drawn from specific probability density functions (PDFs) introducing memory into the model. The first part of the paper is devoted to the macroscopic S−C−I−R−S model. We derive memory evolution equations involving convolutions (time derivatives of general fractional type). We consider several cases. The memoryless case is represented by exponentially distributed waiting times. Cases of long waiting times with fat-tailed waiting-time distributions are considered as well where the S−C−I−R−S evolution equations take the form of time-fractional ordinary differential equations. We obtain formulas for the endemic equilibrium and a condition of its existence for cases when the waiting-time PDFs have existing means. We analyze the stability of healthy and endemic equilibria and derive conditions for which the endemic state becomes oscillatory (Hopf) unstable. In the second part, we implement a simple multiple-random-walker approach (microscopic model of Brownian motion of Z independent walkers) with random S−C−I−R−S waiting times in computer simulations. Infections occur with a certain probability by collisions of walkers in compartments I and S. We compare the endemic states predicted in the macroscopic model with the numerical results of the simulations and find accordance of high accuracy. We conclude that a simple random-walker approach offers an appropriate microscopic description for the macroscopic model. The S−C−I−R−S–type models open a wide field of applications allowing the identification of pertinent parameters governing the phenomenology of epidemic dynamics such as extinction, convergence to a stable endemic equilibrium, or persistent oscillatory behavior. KW - Nonlinear time-delay systems KW - Techniques Brownian dynamics KW - Diffusion & random walks KW - Epidemic spreading KW - Non-Markovian processes KW - Interdisciplinary Physics KW - Biological Physics KW - Statistical Physics Y1 - 2023 UR - https://journals.aps.org/pre/abstract/10.1103/PhysRevE.107.044207 U6 - https://doi.org/10.1103/PhysRevE.107.044207 SN - 2470-0045 VL - 107 IS - 4 SP - 044207-1 EP - 044207-15 ER - TY - GEN A1 - Bestehorn, Michael A1 - Riascos, Alejandro P. A1 - Michelitsch, Thomas M. A1 - Collet, Bernard A. T1 - A Markovian random walk model of epidemic spreading T2 - Continuum Mechanics and Thermodynamics N2 - We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time Markovian walk governed by his specific transition matrix. With this assumption, we first derive an upper bound for the reproduction numbers. Then, we assume that a walker is in one of the states: susceptible, infectious, or recovered. An infectious walker remains infectious during a certain characteristic time. If an infectious walker meets a susceptible one on the same node, there is a certain probability for the susceptible walker to get infected. By implementing this hypothesis in computer simulations, we study the space-time evolution of the emerging infection patterns. Generally, random walk approaches seem to have a large potential to study epidemic spreading and to identify the pertinent parameters in epidemic dynamics. KW - Markovian random walks KW - Ergodic networks KW - Epidemic spreading Y1 - 2021 UR - https://link.springer.com/article/10.1007/s00161-021-00970-z U6 - https://doi.org/10.1007/s00161-021-00970-z SN - 1432-0959 SN - 0935-1175 VL - 33 IS - 4 SP - 1207 EP - 1221 ER - TY - GEN A1 - Pototsky, Andrey A1 - Oron, Alexander A1 - Bestehorn, Michael T1 - Equilibrium shapes and floatability of static and vertically vibrated heavy liquid drops on the surface of a lighter fluid T2 - Journal of Fluid Mechanics N2 - A small drop of a heavier fluid may float on the surface of a lighter fluid supported by surface tension forces. In equilibrium, the drop assumes a radially symmetric shape with a circular triple-phase contact line. We show that such a floating liquid drop with a sufficiently small volume has two distinct equilibrium shapes at terrestrial gravity: one with a larger and one with a smaller radius of the triple-phase contact line. Static stability analysis reveals that both shapes could be stable if the drop volume is below a certain critical value. Experiments conducted with μL-sized water drops floating on commercial oil support the existence of multiple contact line radii for a drop with fixed volume. Next, we experimentally study the floatability of a less viscous water drop on the surface of a more viscous and less dense oil, subjected to a low-frequency (Hz-order) vertical vibration. We find that in a certain range of amplitudes, vibration helps heavy liquid drops to stay afloat. The physical mechanism of the increased floatability is explained by the horizontal elongation of the drop driven by subharmonic Faraday waves. The average length of the triple-phase contact line increases as the drop elongates that leads to a larger average lifting force produced by the surface tension. KW - Drops KW - Faraday waves Y1 - 2021 U6 - https://doi.org/10.1017/jfm.2021.546 SN - 1469-7645 SN - 0022-1120 VL - 922 SP - A31-1 EP - A31-21 ER - TY - GEN A1 - Piriz, S. A. A1 - Piriz, Antonio R. A1 - Tahir, Naeem A. A1 - Richter, Sebastian A1 - Bestehorn, Michael T1 - Rayleigh-Taylor instability in elastic-plastic solid slabs bounded by a rigid wall T2 - Physical Review E N2 - The linear evolution of the incompressible Rayleigh-Taylor instability for the interface between an elastic-plastic slab medium and a lighter semi-infinite ideal fluid beneath the slab is developed for the case in which slab is attached to a rigid wall at the top surface. The theory yields the maps for the stability in the space determined by the initial perturbation amplitude and wavelength, as well as for the transition boundary from the elastic to the plastic regimes for arbitrary thicknesses of the slab and density contrasts between the media. In particular, an approximate but very accurate scaling law is found for the minimum initial perturbation amplitude required for instability and for the corresponding perturbation wavelength at which it occurs. These results allows for an interpretation of the recent experiments by Maimouni et al. [Phys. Rev. Lett. 116, 154502 (2016)]. KW - Rayleigh-Taylor instability KW - Research Areas Flow instability KW - Research Areas Nonlinear phenomena in plasmas KW - Plasma instabilities Plasma macroinstabilities Y1 - 2021 UR - https://journals.aps.org/pre/abstract/10.1103/PhysRevE.103.023105 U6 - https://doi.org/10.1103/PhysRevE.103.023105 SN - 2470-0045 VL - 103 IS - 2 SP - 023105-1 EP - 023105-12 ER - TY - GEN A1 - Tyvand, Peder A. A1 - Mulstad, Camilla A1 - Bestehorn, Michael T1 - A nonlinear impulsive Cauchy–Poisson problem. Part 1. Eulerian description T2 - Journal of Fluid Mechanics N2 - A nonlinear Cauchy–Poisson problem with impulsive surface forcing is investigated analytically and numerically. An incompressible liquid with an initially horizontal surface is instantaneously put into motion by an impulsive surface pressure distribution turned on and off during an infinitesimal time interval. We consider symmetric, antisymmetric and asymmetric pressure impulses based on dipoles and quadrupoles. The subsequent inviscid free-surface flow is governed by fully nonlinear surface conditions, which are solved exactly to third order in a small-time expansion. The small-time expansion applies to flows dominated by inertia. Such flows are generated by relatively strong pressure impulses, measured in gravitational units. We solve the problem numerically and find that only relatively weak pressure impulses will lead to oscillatory waves. The free surface will break before a full gravitational oscillation is completed when the amplitude of the pressure impulse exceeds one gravitational unit. KW - Surface gravity waves KW - Air/sea interactions Y1 - 2021 UR - https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/nonlinear-impulsive-cauchypoisson-problem-part-1-eulerian-description/F353BA9CA7AD0059F023BE50B4942D64# U6 - https://doi.org/10.1017/jfm.2020.787 SN - 1469-7645 SN - 0022-1120 VL - 906 SP - A24-1 EP - A24-32 ER - TY - GEN A1 - Tyvand, Peder A. A1 - Mulstad, Camilla A1 - Bestehorn, Michael T1 - A nonlinear impulsive Cauchy–Poisson problem. Part 2. Lagrangian description T2 - Journal of Fluid Mechanics N2 - A fully nonlinear Cauchy–Poisson problem is investigated analytically by a small-time expansion. The inviscid incompressible fluid layer has an initially horizontal surface. The fluid is forced into motion by an impulsive surface pressure. The early nonlinear free-surface problem is solved to second order in a small-time expansion by the Lagrangian description of motion. Comparisons are made with two other solution procedures for the same nonlinear problem in the absence of gravity: a third-order small-time expansion and a numerical solution, based on full nonlinearity according to the standard Eulerian description. Good agreement is found between the present second-order Lagrangian solution and the previous third-order Eulerian solution, until both these asymptotic expansions diverge rather abruptly at the same time. KW - Air/sea interactions KW - Surface gravity waves Y1 - 2021 UR - https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/nonlinear-impulsive-cauchypoisson-problem-part-2-lagrangian-description/1934256B0F16ABDDAE313EF9FD9D3ADA U6 - https://doi.org/10.1017/jfm.2020.788 SN - 1469-7645 SN - 0022-1120 VL - 906 SP - A25-1 EP - A25-19 ER - TY - GEN A1 - Bestehorn, Michael T1 - Rayleigh–Taylor and Kelvin–Helmholtz instability studied in the frame of a dimension-reduced model T2 - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences N2 - Introducing an extension of a recently derived dimension-reduced model for an infinitely deep inviscid and irrotational layer, a two-layer system is examined in the present paper. A second thin viscous layer is added on top of the original one-layer system. The set-up is a combination of a long-wave approximation (upper layer) and a deep-water approximation (lower layer). Linear stability analysis shows the emergency of Rayleigh–Taylor and Kelvin–Helmholtz instabilities. Finally, numerical solutions of the model reveal spatial and temporal pattern formation in the weakly nonlinear regime of both instabilities. This article is part of the theme issue ‘Stokes at 200 (Part 1)’. KW - hydrodynamic waves KW - two-layer system KW - reduced models KW - numerical solutions Y1 - 2020 UR - https://royalsocietypublishing.org/doi/epdf/10.1098/rsta.2019.0508 U6 - https://doi.org/10.1098/rsta.2019.0508 SN - 1471-2962 SN - 1364-503X VL - 378 SP - 1 EP - 10 ER - TY - GEN A1 - Tyvand, Peder A. A1 - Bestehorn, Michael T1 - Nonlinear wave resonance from bottom vibrations in uniform open-channel flow T2 - European Journal of Mechanics. B, Fluids N2 - It is known from linear theory that bottom oscillations in uniform open-channel flow can produce resonant surface waves with zero group velocity and diverging amplitude (Tyvand and Torheim 2012). This resonance exists for Froude numbers smaller than one, at a critical frequency dependent on the Froude number. This resonance phenomenon is studied numerically in the time domain, with fully nonlinear free-surface conditions. An oscillatory 2D bottom source is started, and the local elevation at resonance grows until it may reach a saturation amplitude. Four waves exist at subcritical Froude numbers, where resonance represents the third and the fourth wave merging. In the zero-frequency limit, the dispersive second and fourth wave merge into a steady wave with finite group velocity and amplitude, and no other periodic waves exist. In the time-dependent nonlinear analysis at zero frequency, a transient undular bore may emerge as the dominating phenomenon. KW - Froude number KW - Open-channel flow KW - Oscillating source KW - Resonance KW - Undular bore KW - Water waves Y1 - 2020 UR - https://www.sciencedirect.com/science/article/pii/S0997754618307544 U6 - https://doi.org/10.1016/j.euromechflu.2019.07.004 SN - 1873-7390 SN - 0997-7546 VL - 79 SP - 74 EP - 86 ER - TY - GEN A1 - Pototsky, Andrey A1 - Oron, Alexander A1 - Bestehorn, Michael T1 - Vibration-induced floatation of a heavy liquid drop on a lighter liquid film T2 - Physic of Fluids N2 - We carry out a theoretical study of vibration-induced saturation of the Rayleigh-Taylor instability for an isolated liquid drop on the surface of a less dense finite-thickness carrier film. Without vibration, a heavy drop falls through the carrier film by forming a stretching liquid column until the bottom tip of the column reaches the solid substrate and the carrier film ruptures. We show that an externally applied vertical vibration prevents the rupture of the film and enables stable flotation of the drop. A hydrodynamic model is used to study the effect of inertia on the long-time dynamics of the drop. It is shown that rupture can only be prevented when the Reynolds number is nonzero. KW - Wave mechanics KW - Thin films KW - Liquid liquid interfaces KW - Liquid solid interfaces KW - Flow instabilities KW - Navier Stokes equations KW - Oscillating flow KW - Surface waves KW - Hydrodynamics simulations Y1 - 2019 UR - https://pubs.aip.org/aip/pof/article/31/8/087101/1059058/Vibration-induced-floatation-of-a-heavy-liquid U6 - https://doi.org/10.1063/1.5099661 SN - 1089-7666 SN - 1070-6631 VL - 31 IS - 8 SP - 087101-1 EP - 087101-13 ER - TY - GEN A1 - Bestehorn, Michael A1 - Michelitsch, Thomas M. T1 - Oscillating Behavior of a Compartmental Model with Retarded Noisy Dynamic Infection Rate T2 - International Journal of Bifurcation and Chaos N2 - Our study is based on an epidemiological compartmental model, the SIRS model. In the SIRS model, each individual is in one of the states susceptible (S), infected (I) or recovered (R), depending on its state of health. In compartment R, an individual is assumed to stay immune within a finite time interval only and then transfers back to the S compartment. We extend the model and allow for a feedback control of the infection rate by mitigation measures which are related to the number of infections. A finite response time of the feedback mechanism is supposed that changes the low-dimensional SIRS model into an infinite-dimensional set of integro-differential (delay-differential) equations. It turns out that the retarded feedback renders the originally stable endemic equilibrium of SIRS (stable focus) to an unstable focus if the delay exceeds a certain critical value. Nonlinear solutions show persistent regular oscillations of the number of infected and susceptible individuals. In the last part we include noise effects from the environment and allow for a fluctuating infection rate. This results in multiplicative noise terms and our model turns into a set of stochastic nonlinear integro-differential equations. Numerical solutions reveal an irregular behavior of repeated disease outbreaks in the form of infection waves with a variety of frequencies and amplitudes. KW - Epidemic models KW - delay-differential equation KW - bifurcation theory KW - numerical simulation KW - sstability analysis Y1 - 2023 UR - https://www.worldscientific.com/doi/epdf/10.1142/S0218127423500566 U6 - https://doi.org/10.1142/S0218127423500566 SN - 1793-6551 VL - 33 IS - 5 ER - TY - GEN A1 - Bestehorn, Michael A1 - Sharma, Deewakar A1 - Borcia, Rodica A1 - Amiroudine, Sakir T1 - Faraday instability of binary miscible/immiscible fluids with phase field approach T2 - Physical Review Fluids N2 - The objective in the present paper is to study binary fluids with phase field modeling coupled with Navier-Stokes equations. An extended free energy is proposed to account for the continuous path from immiscible to miscible states. We consider fluid pairs that are immiscible for temperatures below the critical one (consolute temperature) and miscible above it. Our extended phase field equation permits us to move from the immiscible state (governed by the Cahn-Hilliard equation) to the miscible state (defined by the species diffusion equation). The scaling of interface tension and interface width with the distance to the critical point is highlighted. The whole system is mechanically excited showing Faraday instability of a flat interface. A linear stability analysis is performed for the stable case (interface waves) as well as for the unstable Faraday one. For the latter, a Floquet analysis shows the well-known Arnold's tongues as a function of the consolute temperature and depth layer. Moreover, two-dimensional finite difference simulations have been performed allowing us to model nonlinear flow patterns both in miscible and immiscible phases. Linear theory and nonlinear simulations show interesting results such as the diminishing of the wavelength of Faraday waves or a shift of the critical vibration amplitude when the consolute temperature is approached. KW - Binary fluids KW - Hydrodynamic waves KW - Instability of free-surface flows KW - Surface tension effects Y1 - 2021 UR - https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.6.064002 U6 - https://doi.org/10.1103/PhysRevFluids.6.064002 SN - 2469-990X VL - 6 IS - 6 SP - 1 EP - 26 ER - TY - GEN A1 - Borcia, Rodica A1 - Borcia, Ion-Dan A1 - Bestehorn, Michael A1 - Sharma, Deewakar A1 - Amiroudine, Sakir T1 - Phase field modeling in liquid binary mixtures: isothermal and non-isothermal problems T2 - Physical Review Fluids N2 - The objective in the present paper is to study binary fluids with phase field modeling coupled with Navier-Stokes equations. An extended free energy is proposed to account for the continuous path from immiscible to miscible states. We consider fluid pairs that are immiscible for temperatures below the critical one (consolute temperature) and miscible above it. Our extended phase field equation permits us to move from the immiscible state (governed by the Cahn-Hilliard equation) to the miscible state (defined by the species diffusion equation). The scaling of interface tension and interface width with the distance to the critical point is highlighted. The whole system is mechanically excited showing Faraday instability of a flat interface. A linear stability analysis is performed for the stable case (interface waves) as well as for the unstable Faraday one. For the latter, a Floquet analysis shows the well-known Arnold's tongues as a function of the consolute temperature and depth layer. Moreover, two-dimensional finite difference simulations have been performed allowing us to model nonlinear flow patterns both in miscible and immiscible phases. Linear theory and nonlinear simulations show interesting results such as the diminishing of the wavelength of Faraday waves or a shift of the critical vibration amplitude when the consolute temperature is approached. KW - Binary fluids KW - Drop coalescence KW - Drop interactions KW - Drops & bubbles KW - Microfluidics Y1 - 2022 UR - https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.7.064005 U6 - https://doi.org/10.1103/PhysRevFluids.7.064005 SN - 2469-990X VL - 7 IS - 6 SP - 1 EP - 19 ER - TY - GEN A1 - Bestehorn, Michael A1 - Oron, Alexander T1 - Hopf instability of a Rayleigh–Taylor unstable thin film heated from the gas side T2 - European Physical Journal Special Topics N2 - A thin liquid film located on the underside of a horizontal solid substrate can be stabilized by the Marangoni effect if the liquid is heated at its free surface. Applying long-wave approximation and projecting the velocity and temperature fields onto a basis of low-order polynomials, we derive a dimension-reduced set of three coupled evolution equations where nonlinearities of both the Navier–Stokes and the heat equation are included. We find that in a certain range of fluid parameters and layer depth, the first bifurcation from the motionless state is oscillatory which sets in with a finite but small wave number. The oscillatory branch is determined using a linear stability analysis of the long-wave model, but also by solving the linearized original hydrodynamic equations. Finally, numerical solutions of the reduced nonlinear model equations in three spatial dimensions are presented. Y1 - 2023 UR - https://epjst.epj.org/articles/epjst/abs/2023/04/11734_2023_Article_782/11734_2023_Article_782.html U6 - https://doi.org/10.1140/epjs/s11734-023-00782-z SN - 1951-6401 SN - 1951-6355 VL - 232 IS - 4 SP - 367 EP - 374 ER - TY - GEN A1 - Schön, Franz-Theo A1 - Harlander, Uwe A1 - Borcia, Ion Dan A1 - Borcia, Rodica A1 - Bestehorn, Michael T1 - Mean fluid transport in an oscillating circular channel with asymmetric forcing T2 - Water waves : an interdisciplinary journal N2 - We investigate surface waves in an oscillating circular channel with local topography. The focus is on spatially or temporally breaking this dynamic system’s symmetry. Asymmetrical wave dynamics and a mean flux excitation are detected to varying degrees, depending on the two input parameters, fluid depth and the tank’s oscillation frequency. The fluid resonates around multiples of the fundamental eigenfrequency of the channel. The development of solitary wave-trains (undular bores) is observed in these resonance bands. A particle image velocimetry system measures the velocity field in the vertical plane of the free surface flow. Moreover, we are using 17 evenly distributed ultrasonic sensors to measure the surface displacement. This makes it possible to find out how strongly the mean flux depends on the resonance frequencies and to study the influence of the surface waves on the symmetry breaking. A numerical long-wave model helps to isolate the various factors influencing the mean flux. Y1 - 2025 U6 - https://doi.org/10.1007/s42286-025-00121-w SN - 2523-3688 VL - 2025 SP - 1 EP - 21 PB - Birkhäuser, part of Springer Nature CY - Basel ER -