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 -