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 -