@article{MillanRodriguezPerezGarciaBestehornetal., author = {Mill{\´a}n-Rodriguez, J. and P{\´e}rez-Garc{\´i}a, C. and Bestehorn, Michael and Fantz, M. and Friedrich, R.}, title = {Pattern Formation in Convection of Rotating Fluids with Broken Vertical Symmetry}, language = {en} } @article{Bestehorn, author = {Bestehorn, Michael}, title = {Numerical Results of 3D Stationary Convection in a Binary Mixture}, language = {en} } @article{Bestehorn, author = {Bestehorn, Michael}, title = {Phase and Amplitude Instabilities for B{\´e}nard-Marangoni Convection in Fluid Layers with Large Aspect Ratio}, language = {en} } @article{Bestehorn, author = {Bestehorn, Michael}, title = {Pattern Selection in B{\´e}nard-Marangoni Convection}, language = {en} } @article{MillanRodriguezBestehornPerezGarciaetal., author = {Mill{\´a}n-Rodriguez, J. and Bestehorn, Michael and P{\´e}rez-Garc{\´i}a, C. and Friedrich, R. and Neufeld, M.}, title = {Defects Motion in Rotating Fluids}, language = {en} } @misc{Bestehorn, author = {Bestehorn, Michael}, title = {Square Patterns in B{\´e}nard-Marangoni Convection}, language = {en} } @article{Bestehorn, author = {Bestehorn, Michael}, title = {Two Layer Model Showing a Variety of Pattern Types near Nonequilibrium Phase Transitions}, language = {en} } @misc{BorciaBestehorn, author = {Borcia, Rodica and Bestehorn, Michael}, title = {Different behaviours of delayed fusion between drops with miscible liquids}, series = {Physical review E}, volume = {82}, journal = {Physical review E}, number = {3}, issn = {1063-651X}, pages = {036312}, language = {en} } @article{BestehornGrigorievaHakenetal., author = {Bestehorn, Michael and Grigorieva, E. V. and Haken, H. and Kaschenko, S. A.}, title = {Order Parameters for Class-B Lasers With a Long Time Delayed Feedback}, language = {en} } @article{BestehornGrigorievaKaschenko, author = {Bestehorn, Michael and Grigorieva, E. V. and Kaschenko, S. A.}, title = {Spatio-Temporal Structures in a Model With Delay And Diffusion}, language = {en} } @article{BestehornGrigorieva, author = {Bestehorn, Michael and Grigorieva, E. V.}, title = {Formation and Propagation of Localized States in Extended Systems}, language = {en} } @article{BestehornPerezGarcia, author = {Bestehorn, Michael and P{\´e}rez-Garc{\´i}a, C.}, title = {Modulated Rolls and Traveling Waves in a Secondary Convective Instability}, language = {en} } @article{Bestehorn, author = {Bestehorn, Michael}, title = {Numerical Results of 3D-Convection in a Binary Mixture for a Positive Separation Ratio}, language = {en} } @article{Bestehorn, author = {Bestehorn, Michael}, title = {Convection in thick and thin fluid layers with a free surface - The Influence of Evaporation}, language = {en} } @article{BorciaBestehorn, author = {Borcia, Rodica and Bestehorn, Michael}, title = {Phase field simulations for drops and bubbles}, language = {en} } @article{BorciaBorciaBestehorn, author = {Borcia, Rodica and Borcia, Ion-Dan and Bestehorn, Michael}, title = {Drops on an arbitrarily wetting substrate: A phase field description}, language = {en} } @article{BorciaBorciaBestehorn, author = {Borcia, Rodica and Borcia, Ion-Dan and Bestehorn, Michael}, title = {Liquid layers on a patterned surface}, series = {Soft Matter}, volume = {4}, journal = {Soft Matter}, number = {12}, pages = {2368 -- 2372}, language = {en} } @misc{BorciaBestehorn, author = {Borcia, Rodica and Bestehorn, Michael}, title = {Controlled Pattern Formation in Thin Liquid Layers}, language = {en} } @misc{BorciaBestehorn, author = {Borcia, Rodica and Bestehorn, Michael}, title = {A Phase Field Description of Spatio-Temporal Behavior in Thin Liquid Layers}, language = {en} } @article{BestehornHaken, author = {Bestehorn, Michael and Haken, H.}, title = {A Calculation of Transient Solutions Describing Roll and Hexagon Formation in the Convection Instability}, language = {en} } @article{BestehornHaken, author = {Bestehorn, Michael and Haken, H.}, title = {Transient Patterns of the Convection Instability: A Model Calculation}, language = {en} } @article{BestehornFriedrichHaken, author = {Bestehorn, Michael and Friedrich, R. and Haken, H.}, title = {The Oscillatory Instability of a Spatially Homogeneous State in Large Aspect Systems of Fluid Dynamics}, language = {en} } @article{BestehornFriedrichHaken, author = {Bestehorn, Michael and Friedrich, R. and Haken, H.}, title = {Two-dimensional Traveling Wave Patterns in Nonequilibrium Systems}, language = {en} } @article{BestehornFriedrichHaken, author = {Bestehorn, Michael and Friedrich, R. and Haken, H.}, title = {Traveling Waves in Nonequilibrium Systems}, language = {en} } @article{BestehornFriedrichHaken, author = {Bestehorn, Michael and Friedrich, R. and Haken, H.}, title = {Modulated Traveling Waves in Nonequilibrium Systems: The Blinking State}, language = {en} } @misc{PototskyArcherBestehornetal., author = {Pototsky, Andrey and Archer, Andrew J. and Bestehorn, Michael and Merkt, Domnic and Savelev, S. and Marchesoni, F.}, title = {Collective shuttling of attracting particles in asymmetric narrow channels}, language = {en} } @misc{BestehornTyvand, author = {Bestehorn, Michael and Tyvand, Peder A.}, title = {Merging and colliding bores}, language = {en} } @misc{TyvandBestehorn, author = {Tyvand, Peder A. and Bestehorn, Michael}, title = {Diffraction of Poincare waves by a change in ocean depth}, language = {en} } @article{FriedrichBestehornHaken, author = {Friedrich, R. and Bestehorn, Michael and Haken, H.}, title = {Pattern Formation in Convective Instabilities}, language = {en} } @article{BestehornHaken, author = {Bestehorn, Michael and Haken, H.}, title = {Traveling Waves and Pulses in a Two-Dimensional Large-Aspect-Ratio System}, series = {Physical Review A}, volume = {42}, journal = {Physical Review A}, number = {12}, issn = {0556-2791}, pages = {7195 -- 7203}, language = {en} } @article{BestehornHaken, author = {Bestehorn, Michael and Haken, H.}, title = {Associative Memory of a Dynamical System: The Example of the Convection Instability}, series = {Zeitschrift f{\"u}r Physik B}, volume = {82}, journal = {Zeitschrift f{\"u}r Physik B}, number = {2}, issn = {1431-584}, pages = {305 -- 308}, language = {en} } @article{BestehornPerezGarcia, author = {Bestehorn, Michael and P{\´e}rez-Garc{\´i}a, C.}, title = {Study of a Model of Thermal Convection in Cylindrical Containers}, language = {en} } @article{MillanRodriguezBestehornPerezGarciaetal., author = {Mill{\´a}n-Rodriguez, J. and Bestehorn, Michael and P{\´e}rez-Garc{\´i}a, C. and Neufeld, M. and Friedrich, R.}, title = {Motion of Defects in Rotating Fluids}, language = {en} } @article{BestehornNeufeldFriedrichetal., author = {Bestehorn, Michael and Neufeld, M. and Friedrich, R. and Haken, H.}, title = {Comment on Spiral pattern formation in Rayleigh-B{\´e}nard Convection}, language = {en} } @article{BorciaBestehorn, author = {Borcia, Rodica and Bestehorn, Michael}, title = {Phase-field model for Marangoni convection in liquid-gas systems with deformable interface}, language = {en} } @article{PototskyBestehornMerktetal., author = {Pototsky, Andrey and Bestehorn, Michael and Merkt, Domnic and Thiele, Uwe}, title = {Alternative pathways of dewetting for a thin two-layer film of soft matter}, doi = {10.48550/arXiv.nlin/0401042}, language = {en} } @article{MerktPototskyBestehornetal., author = {Merkt, Domnic and Pototsky, Andrey and Bestehorn, Michael and Thiele, Uwe}, title = {Long-wave theory of bounded two-layer films with a free liquid-liquid interface: Short and long-time evolution}, doi = {10.1063/1.1935487}, language = {en} } @article{PototskyBestehornMerktetal., author = {Pototsky, Andrey and Bestehorn, Michael and Merkt, Domnic and Thiele, Uwe}, title = {Evolution of interface patterns of three-dimensional two-layer liquid films}, series = {Europhysics Letters}, volume = {74}, journal = {Europhysics Letters}, number = {4}, issn = {0302-072X}, doi = {10.1209/epl/i2006-10026-8}, pages = {665 -- 671}, language = {en} } @article{BestehornMerkt, author = {Bestehorn, Michael and Merkt, Domnic}, title = {Regular surface patterns on Rayleigh-Taylor unstable evaporating films heated from below}, language = {en} } @article{BorciaBorciaBestehorn, author = {Borcia, Ion-Dan and Borcia, Rodica and Bestehorn, Michael}, title = {Long wave instabilities in binary mixture thin liquid films}, language = {en} } @article{BorciaBorciaBestehorn, author = {Borcia, Ion-Dan and Borcia, Rodica and Bestehorn, Michael}, title = {Soret effect in thin liquid films:Localized running drops, holes and stripes}, language = {en} } @misc{BestehornBorcia, author = {Bestehorn, Michael and Borcia, Ion-Dan}, title = {Thin film lubrication dynamics of a binarymixture}, language = {en} } @article{EnculescuBestehorn, author = {Enculescu, Mihaela and Bestehorn, Michael}, title = {Activity dynamics in non - localinteracting neural fields}, language = {en} } @article{HuttBestehornWennekers, author = {Hutt, A. and Bestehorn, Michael and Wennekers, T.}, title = {Pattern Formation in Intracortical Neuronal Fields}, language = {en} } @article{PenaPerezGarciaBestehorn, author = {Pena, B. and P{\´e}rez-Garc{\´i}a, C. and Bestehorn, Michael}, title = {Modulated standing waves resulting from a Hopf-wave interaction in a chemical model}, language = {en} } @article{EnculescuBestehorn, author = {Enculescu, Mihaela and Bestehorn, Michael}, title = {Liapunov functional for a delayedintegro-differential equation model of a neural field}, language = {en} } @article{PenaBestehorn, author = {Pena, B. and Bestehorn, Michael}, title = {Two-dimensional wave patterns near a Hopf-wave interaction in a chemical model}, language = {en} } @article{EnculescuBestehorn, author = {Enculescu, Mihaela and Bestehorn, Michael}, title = {Mechanisms for activity spread in a neural field model}, language = {en} } @misc{BorciaBestehorn, author = {Borcia, Rodica and Bestehorn, Michael}, title = {On the coalescence of sessile drops with miscible liquids}, series = {European Physical Journal E}, volume = {34}, journal = {European Physical Journal E}, number = {8}, issn = {1292-8941}, pages = {81}, language = {en} } @misc{BorciaMenzelBestehornetal., author = {Borcia, Rodica and Menzel, Stefan and Bestehorn, Michael and Karpitschka, Stefan and Riegler, Horst}, title = {Delayed coalescence of droplets with miscible liquids: Lubrication and phasefield theories}, series = {European Physical Journal E}, volume = {34}, journal = {European Physical Journal E}, number = {3}, issn = {1292-8941}, pages = {11024-9}, language = {en} } @misc{ReifVarlamovaVarlamovetal., author = {Reif, J{\"u}rgen and Varlamova, Olga and Varlamov, Sergej and Bestehorn, Michael}, title = {The role of asymmetric excitation in self-organized nanostructure formation upon femtosecond laser ablation}, series = {Applied Physics / A}, volume = {104}, journal = {Applied Physics / A}, number = {3}, issn = {1432-0630}, pages = {969 -- 973}, language = {en} } @misc{VarlamovaReifVarlamovetal., author = {Varlamova, Olga and Reif, J{\"u}rgen and Varlamov, Sergej and Bestehorn, Michael}, title = {The laser polarization as control parameter in the formation of laser-induced periodic surface structures: Comparison of numerical and experimental results}, series = {Applied Surface Science}, volume = {257}, journal = {Applied Surface Science}, number = {12}, issn = {0169-4332}, pages = {5465 -- 5469}, language = {en} } @misc{BorciaBestehorn, author = {Borcia, Rodica and Bestehorn, Michael}, title = {Numerical simulations on delayed coalescence of droplets in confinedgeometries}, language = {en} } @misc{BorciaBestehorn, author = {Borcia, Ion-Dan and Bestehorn, Michael}, title = {Simulation of pattern morphology in binary liquid mixtures}, language = {en} } @inproceedings{BorciaBestehornEgbers, author = {Borcia, Rodica and Bestehorn, Michael and Egbers, Christoph}, title = {Surface effects at the mixing of two perfectly miscible components in a thin liquid film}, series = {International Topical Team Workshop on Two-Phase Systems for Ground and Space Applications, ITTW 2013}, booktitle = {International Topical Team Workshop on Two-Phase Systems for Ground and Space Applications, ITTW 2013}, language = {en} } @inproceedings{BorciaBorciaBestehornetal., author = {Borcia, Ion-Dan and Borcia, Rodica and Bestehorn, Michael and Egbers, Christoph}, title = {Drops on cylindrical wires}, series = {International Topical Team Workshop on Two-Phase Systems for Ground and Space Applications, ITTW 2013}, booktitle = {International Topical Team Workshop on Two-Phase Systems for Ground and Space Applications, ITTW 2013}, language = {en} } @inproceedings{BorciaBorciaBestehornetal., author = {Borcia, Ion-Dan and Borcia, Rodica and Bestehorn, Michael and Borcia, C. and Dumitrascu, N. and Egbers, Christoph}, title = {Drops on cylindrical surfaces}, series = {7th Conference of the International Marangoni Association, Vienna (Austria), June 23-26, 2014}, booktitle = {7th Conference of the International Marangoni Association, Vienna (Austria), June 23-26, 2014}, publisher = {Techn. Univ.}, address = {Vienna}, pages = {S. 33}, language = {en} } @inproceedings{ReifVarlamovaVarlamovetal., author = {Reif, J{\"u}rgen and Varlamova, Olga and Varlamov, Sergej and Bestehorn, Michael}, title = {The role of asymmetric excitation in self-organized nanostructure formation upon femtosecondlaser ablation}, series = {International Symposium on High Power Laser Ablation 2012, Santa Fe, New Mexico, USA, 30 April - 3 May 2012}, booktitle = {International Symposium on High Power Laser Ablation 2012, Santa Fe, New Mexico, USA, 30 April - 3 May 2012}, editor = {Phipps, Claude R.}, publisher = {American Institute of Physics}, address = {Melville, NY}, isbn = {978-0-7354-1068-8}, pages = {428 -- 441}, language = {en} } @misc{VarlamovaReifVarlamovetal., author = {Varlamova, Olga and Reif, J{\"u}rgen and Varlamov, Sergej and Bestehorn, Michael}, title = {Modeling of the Laser Polarization as Control Parameter in Self-Organized Surface Pattern}, series = {Journal of Nanoscience and Nanotechnology}, volume = {11}, journal = {Journal of Nanoscience and Nanotechnology}, number = {10}, issn = {1533-4880}, pages = {9274 -- 9281}, language = {en} } @misc{VarlamovaCostacheReifetal., author = {Varlamova, Olga and Costache, Florenta Adriana and Reif, J{\"u}rgen and Bestehorn, Michael}, title = {Self-organized pattern formation upon femtosecond laser ablation by circular polarized light}, series = {Applied Surface Science}, volume = {252}, journal = {Applied Surface Science}, number = {13}, issn = {0169-4332}, pages = {4702 -- 4706}, language = {en} } @inproceedings{ReifCostacheEckertetal., author = {Reif, J{\"u}rgen and Costache, Florenta Adriana and Eckert, Sebastian and Kouteva-Arguirova, Simona and Bestehorn, Michael and Georgescu, Ionut and Semorek, A. F. and Martin, P. and Gobert, O. and Seifert, Winfried}, title = {Formation of self-organized regular nanostructures upon femtosecond laser ablation}, series = {Fifth International Symposium on Laser Precision Microfabrication, 11 - 14 May, 2004, Nara, Japan}, booktitle = {Fifth International Symposium on Laser Precision Microfabrication, 11 - 14 May, 2004, Nara, Japan}, publisher = {SPIE}, address = {Bellingham, Wash.}, isbn = {0-8194-5623-3}, pages = {S. 737}, language = {en} } @incollection{VarlamovaReifVarlamovetal., author = {Varlamova, Olga and Reif, J{\"u}rgen and Varlamov, Sergej and Bestehorn, Michael}, title = {Self-organized Surface Patterns Originatin from Laser-Induced Instability}, series = {Progress in nonlinear nano-optics}, booktitle = {Progress in nonlinear nano-optics}, editor = {Sakabe, Shuji and Lienau, Christoph and Grunwald, R{\"u}diger}, publisher = {Springer}, address = {Cham [u.a.]}, isbn = {978-3-319-12216-8}, pages = {3 -- 29}, language = {en} } @misc{ChengBestehornFiroozabadi, author = {Cheng, Philip and Bestehorn, Michael and Firoozabadi, Abbas}, title = {Effect of permeability anisotropy on density-driven flow for CO2 sequestration in saline aquifers}, series = {Water Resources Research}, volume = {48}, journal = {Water Resources Research}, number = {9}, issn = {1944-7973}, doi = {10.1029/2012WR011939}, pages = {W09539}, abstract = {Solubility trapping of carbon dioxide (CO2) in deep saline aquifers is considered one of the most effective methods for carbon sequestration. Dissolution of CO2 into the brine may create gravitational instabilities that lead to the onset of convection, which greatly enhances the storage efficiency and reduces the possibilities of leakage. Convection appears in the form of downward traveling fingers of relatively dense, CO2-dissolved fluid. Many natural aquifer formations display considerable permeability anisotropy, where the horizontal permeability kh may be several times greater than the vertical permeability kz. It has been previously found that increasing kh for a fixed kz reduces the critical time tc at which onset occurs and the critical wavelength λc with which the fingers initially form. We extend earlier work by showing how and why this occurs. Our results reveal new insights about λc. We have studied the behavior for times greater than tc using high-resolution numerical simulations. We show that the enhanced dissolution from convection can become significant much earlier in anisotropic media. Furthermore, the effects of anisotropy may be sustained for a long period of time. Our results suggest that permeability anisotropy can allow a wider range of aquifer formations to be considered for effective sequestration.}, language = {en} } @misc{BestehornFiroozabadi, author = {Bestehorn, Michael and Firoozabadi, Abbas}, title = {Effect of fluctuations on the onset of density-driven convection in porous media}, series = {Physics of Fluids}, volume = {24}, journal = {Physics of Fluids}, number = {11}, issn = {1089-7666}, doi = {10.1063/1.4767467}, pages = {114102}, abstract = {We study the dissolution of CO2 in saline aquifers. The long diffusion times can be accelerated by orders of magnitude from mass transfer that origins from convection.Convection occurs at a critical time via a phase transition from the horizontally homogeneous diffusion state. To start the instability, perturbations that break the horizontal translation symmetry are necessary. We start with the basic equations and the boundary conditions, examine the linearized equations around the diffusive time and z-dependent base state and compare different definitions of the critical time found in the literature. Taking a simple model we show the role of fluctuations for delayed instabilities if the control parameter is slowly swept through the bifurcation point. Apart from the critical time we use a "visible" time where convection is manifested in the vertical CO2 transport. We specify the perturbations with respect to their strength and length scale, and compute the critical times for various cases by numerical integration of the basic equations in two spatial dimensions. Fluctuating concentration at the upper boundary, fluctuating porosity as well fluctuating permeability are studied in detail. For the permeability fluctuation, the compressibility of the fluid becomes important and the velocity field cannot be derived from a stream function. Our work also includes non-isothermal conditions with a prescribed vertical geothermal gradient and space dependent thermal conductivity. Temperature fields for different standard configurations are computed numerically and serve as starting condition for density-driven convection. Based on our work, we conclude that the visible time is much larger than the critical time. The visible time is a strong function of strength and length scale of the perturbations.}, language = {en} } @misc{ReifVarlamovaUhligetal., author = {Reif, J{\"u}rgen and Varlamova, Olga and Uhlig, Sebastian and Varlamov, Sergej and Bestehorn, Michael}, title = {On the physics of self-organized nanostructure formation upon femtosecond laser ablation}, series = {Applied Physics A}, volume = {117}, journal = {Applied Physics A}, number = {1}, issn = {0947-8396}, doi = {10.1007/s00339-014-8339-x}, pages = {179 -- 184}, abstract = {We present new results on femtosecond LIPSS on silicon, fostering the dynamic model of self-organized structure formation. The first set of experiments demonstrates LIPSS formation by irradiation with a femtosecond white light continuum. The ripples are, as usual, perpendicular to the light polarization with a fluence-dependent wavelength between 500 and 700 nm. At higher dose (fluence × number of shots), the LIPSS turn to much coarser structures. The second set of experiments displays the dose dependence of pattern evolution at about threshold fluence. In contrast to the general case of multi-pulse LIPSS, where a strong dependence of the structures on the laser polarization is observed, single-shot exposition of silicon at about the ablation threshold results in a concentric pattern of very regular sub-wavelength ripples following the oval shape of the irradiated spot, without any reference to the laser polarization. When increasing the number of pulses, the usual, typical ripples develop and then coalesce into broader perpendicular structures, interlaced with remnants of the first, finer ripples.}, language = {en} } @misc{Bestehorn, author = {Bestehorn, Michael}, title = {Laterally Extended Thin Liquid Films with inertia Under External Vibrations}, series = {Physics of Fluids}, volume = {25}, journal = {Physics of Fluids}, number = {11}, issn = {1089-7666}, doi = {10.1063/1.4830255}, pages = {114106}, abstract = {We consider thin liquid films on a horizontal, solid, and completely wetting substrate. The substrate is subjected to oscillatory accelerations in the normal direction and/or in the horizontal direction. A linear Floquet analysis shows that the planar film surface loses stability if amplitudes and frequencies of the harmonic oscillations meet certain criteria. Based on the long wave lubrication approximation, we present an integral boundary layer model where the z component is integrated out and the spatial dimension is reduced by one. The linear stability analysis of this model shows good agreement with the exact problem and with the linearized long wave equations. Pattern formation in the nonlinear regime is computed numerically from the long wave model in two and three spatial dimensions. Normal oscillations show the traditional Faraday patterns such as squares and hexagons. Lateral oscillations cause a pattern formation scenario similar to spinodal dewetting, namely coarsening and no rupture. For certain amplitude and frequency ranges, combined lateral and normal oscillations can give rise to one or more traveling drops. Finally, we discuss the control of a drop's motion in the horizontal plane.}, language = {en} } @misc{BestehornHanOron, author = {Bestehorn, Michael and Han, Qi and Oron, Alexander}, title = {Nonlinear Pattern Formation in Thin Liqiud Films Under External Vibrations}, series = {Physical Review E}, volume = {88}, journal = {Physical Review E}, number = {2}, issn = {2470-0053}, doi = {10.1103/PhysRevE.88.023025}, pages = {023025}, abstract = {We study a thin liquid film with a free surface on a planar horizontal substrate. The substrate is subjected to oscillatory accelerations in the normal and/or in the horizontal direction(s). The description is based on the longwave approximation including inertia effects, which are important due to the large velocities imparted by external vibrations. The linearized system is examined using the Floquet analysis. Pattern formation in the nonlinear regime is computed numerically from the longwave equations for the thickness and the flow rate of the fluid in two and in three spatial dimensions. For certain amplitude and frequency ranges, combined lateral and normal oscillations can give rise to one or more traveling drops, similar to recent experimental findings by Brunet et al. [Phys. Rev. Lett. 99, 144501 (2007)].}, language = {en} } @misc{Bestehorn, author = {Bestehorn, Michael}, title = {Regular Hexagons and Stripes on Marangoni and Rayleigh-Taylor unstable volatile thin films}, series = {European Journal of Mechanics - B/Fluids}, volume = {47}, journal = {European Journal of Mechanics - B/Fluids}, doi = {10.1016/j.euromechflu.2013.12.005}, pages = {48 -- 56}, abstract = {Thin volatile Newtonian liquid films with a free surface on a cooled horizontal substrate are studied theoretically and numerically. We show that if the fluid is initially in equilibrium with its own vapor in the gas phase, regular surface deformation patterns in the form of long-wave hexagons or stripes having a well defined lateral length scale are observed, depending on the instability mechanism. This is different to the case without evaporation where rupture or coarsening to larger and larger spatially disordered patterns is seen in the long time limit. We propose to use such a system to create a regular structuring of the film's surface. Heat production by latent heat and the influence of a temperature dependent surface tension (Marangoni effect) are included as well. Special emphasis is laid on the so-called anomalous Marangoni effect. In this case a parameter region where stripes should occur already at threshold is found by means of a systematic weakly non-linear analysis.}, language = {en} } @misc{BorciaBorciaBestehorn, author = {Borcia, Rodica and Borcia, Ion-Dan and Bestehorn, Michael}, title = {Nonlinear dynamics of thin liqiud films consisting of two miscible components}, series = {Physical Review E}, volume = {86}, journal = {Physical Review E}, number = {5}, issn = {2470-0053}, doi = {10.1103/PhysRevE.86.056319}, pages = {056319}, abstract = {Recently, we systematically derived a system of two coupled conservation equations governing a thin liquid layer with a deformable surface composed of two completely miscible components [Phys. Fluids 22, 104102 (2010)]. One equation describes the location of the free surface and the second one the evolution of the mean concentration. This lubrication model was investigated previously in linearized form. The study is now extended to the fully nonlinear case of thin liquid films of a binary mixture (in one and two horizontal spatial dimensions) with and without heat transport. For an initially flat and motionless film heated from below, we analyze the component separation induced by the Soret effect. Nonlinear simulations show that the Soret effect can cause a multitude of interesting behaviors, such as oscillatory patterns and solitonlike structures (localized traveling drops or holes). A stronger component separation induced by stronger Soret effects favors faster-moving localized structures. For isothermal systems, we study the fusion and the mixing of two thin liquid films of different but perfectly miscible liquids. Marangoni-driven forces can cause delayed coalescence, ripple formation, and fingering patterns at the borderline between the two liquid layers. A systematic analysis for ripple pattern formation and finger instabilities at different diffusion constants shows that these phenomena appear more pronounced for lower diffusion in the system.}, language = {en} } @misc{BorciaBestehorn, author = {Borcia, Rodica and Bestehorn, Michael}, title = {Partial coalescence of sessile drops with different miscible liquids}, series = {Langmuir}, volume = {29}, journal = {Langmuir}, number = {14}, issn = {1520-5827}, doi = {10.1021/la3050835}, pages = {4426 -- 4429}, abstract = {Using computer simulations in three spatial dimensions, we examine the interaction between two deformable drops consisting of two perfectly miscible liquids sitting on a solid substrate under a given contact angle. Driven by capillarity and assisted by Marangoni effects at the droplet interfaces, several distinct coalescence regimes are achieved after the droplets' collision.}, language = {en} } @misc{BorciaBestehorn, author = {Borcia, Rodica and Bestehorn, Michael}, title = {A phase field description of self-propulsion of twin sessile drops induced by surface tension gradients}, series = {Fluid Dynamics Research}, volume = {46}, journal = {Fluid Dynamics Research}, number = {4}, issn = {0169-5983}, doi = {10.1088/0169-5983/46/4/041405}, pages = {041405}, abstract = {We describe the self-propulsion of two sessile drops induced by surface tension gradients at the droplet interfaces using a three-dimensional phase field model. We study the problem for the low viscosity regime when the width of the connecting neck between the interacting drops increases linearly with increasing t1/2 and the merger is dominated by capillary forces. We investigate the dependence of the displacement achieved by self-propulsion on viscous shearing as well as the internal flow structure during the coalescence process.}, language = {en} } @misc{BorciaBestehorn, author = {Borcia, Rodica and Bestehorn, Michael}, title = {Phase field modelling of non-equilibrium patterns on the surface of a liquid film under lateral oscillations at the substrate}, series = {International Journal of Bifurcation and Chaos}, volume = {24}, journal = {International Journal of Bifurcation and Chaos}, number = {9}, issn = {0218-1274}, doi = {10.1142/S0218127414501107}, pages = {1450110}, abstract = {We use a phase field model which couples the generalized Navier-Stokes equation (including the Korteweg stress tensor) with the continuity equation for studying nonlinear pattern formation on the surface of a liquid film under (linear and circular) lateral harmonic vibrations at the solid substrate. First, we prove the thermodynamic consistency of our phase field model. Next, we present computer simulations in three spatial dimensions. We illustrate nonequilibrium patterns at the instability onset, confirming in this way the results recently reported in Phys. Rev. E 88, 023025 (2013). The lateral profiles of the deflected surface are compared with those reported in J. Fluid Mech. 686, 409 (2011) for Faraday instability excited by vertical harmonic vibrations at the bottom plate.}, language = {en} } @misc{BorciaBorciaBestehorn, author = {Borcia, Rodica and Borcia, Ion-Dan and Bestehorn, Michael}, title = {Can vibrations control drop motion?}, series = {Langmuir}, volume = {30}, journal = {Langmuir}, number = {47}, issn = {1520-5827}, doi = {10.1021/la503415r}, pages = {14113 -- 14117}, abstract = {We discuss a mechanism for controlled motion of drops with applications for microfluidics and microgravity. The mechanism is the following: a solid plate supporting a liquid droplet is simultaneously subject to lateral and vertical harmonic oscillations. In this way the symmetry of the back-and-forth droplet movement along the substrate under inertial effects is broken and thus will induce a net driven motion of the drop. We study the dependency of the traveled distance on the oscillation parameters (forcing amplitude, frequency, and phase shift between the two perpendicular oscillations) via phase field simulations. The internal flow structure inside the droplet is also investigated. We make predictions on resonance frequencies for drops on a substrate with a varying wettability.}, language = {en} } @misc{PototskyBestehorn, author = {Pototsky, Andrey and Bestehorn, Michael}, title = {Faraday instability of a two-layer liquid film with a free upper surface}, series = {Physical Review Fluids}, volume = {1}, journal = {Physical Review Fluids}, number = {2}, issn = {2469-990X}, doi = {10.1103/PhysRevFluids.1.023901}, pages = {023901-1 -- 023901-18}, abstract = {We study the linear stability of a laterally extended flat two-layer liquid film under the influence of external vertical vibration. The first liquid layer rests on a vibrating solid plate and is overlaid by a second layer of immiscible fluid with deformable upper surface. Surface waves, excited as the result of the Faraday instability, can be characterized by a time-dependent relative amplitude of the displacements of the liquid-liquid and the liquid-gas interfaces. The in-phase displacements are associated with a zigzag (barotropic) mode and the antiphase displacement corresponds to the varicose thinning mode. We numerically determine the stability threshold in the vibrated two-layer film and compute the dispersion relation together with the decay rates of the surface waves in the absence of vibration. The in-phase and the antiphase displacements are strongly coupled in the vibrated system. The interplay between the Faraday and the Rayleigh-Taylor instabilities in the system with heavier fluid on top of a lighter fluid is analyzed.}, language = {en} } @misc{BestehornPototsky, author = {Bestehorn, Michael and Pototsky, Andrey}, title = {Faraday instability and nonlinear pattern formation of a two-layer system: A reduced model}, series = {Physical Review Fluids}, volume = {1}, journal = {Physical Review Fluids}, number = {6}, issn = {2469-990X}, doi = {10.1103/PhysRevFluids.1.063905}, pages = {063905-1 -- 063905-24}, abstract = {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.}, language = {en} } @misc{BorciaBorciaHelbigetal., author = {Borcia, Rodica and Borcia, Ion-Dan and Helbig, Markus and Meier, Martin and Egbers, Christoph and Bestehorn, Michael}, title = {Dancing drops over vibrating substrates}, series = {The European Physical Journal Special Topics}, volume = {226}, journal = {The European Physical Journal Special Topics}, number = {6}, issn = {1951-6355}, doi = {10.1140/epjst/e2016-60202-6}, pages = {1297 -- 1306}, language = {en} } @misc{RichterBestehorn, author = {Richter, Sebastian and Bestehorn, Michael}, title = {Thin-film Faraday patterns in three dimensions}, series = {The European Physical Journal Special Topics}, volume = {226}, journal = {The European Physical Journal Special Topics}, number = {6}, issn = {1951-6401}, doi = {10.1140/epjst/e2016-60234-4}, pages = {1253 -- 1261}, abstract = {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.}, language = {en} } @misc{StermanCohenBestehornOron, author = {Sterman-Cohen, Elad and Bestehorn, Michael and Oron, Alexander}, title = {Rayleigh-Taylor instability in thin liquid films subjected to harmonic vibration}, series = {Physics of Fluids}, volume = {29}, journal = {Physics of Fluids}, number = {5}, issn = {1089-7666}, doi = {10.1063/1.4984082}, pages = {052105-1 -- 052105-17}, abstract = {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.}, language = {en} } @misc{StermanCohenBestehornOron, author = {Sterman-Cohen, Elad and Bestehorn, Michael and Oron, Alexander}, title = {Ratchet flow of thin liquid films induced by a two-frequency tangential forcing}, series = {Physics of Fluids}, volume = {30}, journal = {Physics of Fluids}, number = {2}, issn = {1089-7666}, doi = {10.1063/1.5010262}, pages = {022101-1 -- 022101-13}, abstract = {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.}, language = {en} } @misc{RaziVarlamovaReifetal., author = {Razi, Sepehr and Varlamova, Olga and Reif, J{\"u}rgen and Bestehorn, Michael and Varlamov, Sergej and Mollabashi, Mahmoud and Madanipour, Khosro and Ratzke, Markus}, title = {Birth of periodic Micro/Nano structures on 316L stainless steel surface following femtosecond laser irradiation; single and multi scanning study}, series = {Optics \& Laser Technology}, volume = {104}, journal = {Optics \& Laser Technology}, issn = {0030-3992}, doi = {10.1016/j.optlastec.2018.02.001}, pages = {8 -- 16}, abstract = {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.}, language = {en} } @book{Bestehorn, author = {Bestehorn, Michael}, title = {Hydrodynamik und Strukturbildung}, publisher = {Springer}, address = {Berlin [u.a.]}, isbn = {978-3-540-33796-6}, doi = {10.1007/3-540-33797-0}, pages = {XIV, 392}, abstract = {Das vorliegende Buch wendet sich an Studierende der Physik und der Ingenieurwissenschaften. Aufbauend auf den klassischen Problemstellungen der Hydrodynamik stellt es, {\"u}ber eine detaillierte Analyse hydrodynamischer Instabilit{\"a}ten, 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 Verst{\"a}ndnis erleichtern.}, language = {de} } @inproceedings{Bestehorn, author = {Bestehorn, Michael}, title = {IMA8 - Interfacial Fluid Dynamics and Process}, series = {The European Physical Journal Special Topics}, volume = {26}, booktitle = {The European Physical Journal Special Topics}, number = {6}, issn = {1951-6355}, doi = {10.1140/epjst/e2017-70057-9}, pages = {1151 -- 1153}, language = {en} } @incollection{Bestehorn, author = {Bestehorn, Michael}, title = {Fluid Dynamics and Pattern Formation}, series = {Encyclopedia of Complexity and Systems Science}, booktitle = {Encyclopedia of Complexity and Systems Science}, publisher = {Springer}, address = {New York, NY}, isbn = {978-0-387-75888-6}, doi = {10.1007/978-0-387-30440-3}, abstract = {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...}, language = {en} } @misc{PototskyBestehorn, author = {Pototsky, Andrey and Bestehorn, Michael}, title = {Shaping liquid drops by vibration}, series = {epl : a letters journal exploring the frontiers of physics}, volume = {121}, journal = {epl : a letters journal exploring the frontiers of physics}, number = {4}, issn = {1286-4854}, doi = {10.1209/0295-5075/121/46001}, pages = {46001-p1 -- 46001-p6}, abstract = {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.}, language = {en} } @misc{BorciaBestehornUhligetal., author = {Borcia, Rodica and Bestehorn, Michael and Uhlig, Sebastian and Gaudet, Matthieu and Schenk, Harald}, title = {Liquid pumping induced by transverse forced vibrations of an elastic beam: A lubrication approach}, series = {Physical Review Fluids}, volume = {3}, journal = {Physical Review Fluids}, number = {8}, issn = {2469-990X}, doi = {10.1103/PhysRevFluids.3.084202}, abstract = {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.}, language = {en} } @inproceedings{BorciaBorciaBestehornetal., author = {Borcia, Ion-Dan and Borcia, Rodica and Bestehorn, Michael and Xu, Wenchao and Harlander, Uwe}, title = {Surface waves generated by libration in a circular channel}, series = {The 12th European Fluid Mechanics Conference, 9 September 2018 - 13 September 2018, Vienna, Austria}, booktitle = {The 12th European Fluid Mechanics Conference, 9 September 2018 - 13 September 2018, Vienna, Austria}, pages = {1}, language = {en} } @misc{BorciaBorciaBestehornetal., author = {Borcia, Rodica and Borcia, Ion-Dan and Bestehorn, Michael and Varlamova, Olga and Hoefner, Kevin and Reif, J{\"u}rgen}, title = {Drop Behavior Influenced by the Correlation Length on Noisy Surfaces}, series = {Langmuir}, volume = {35}, journal = {Langmuir}, doi = {10.1021/acs.langmuir.8b03878}, pages = {928 -- 934}, language = {en} } @book{Bestehorn, author = {Bestehorn, Michael}, title = {Computational Physics : With Worked Out Examples in FORTRAN and MATLAB}, edition = {1. Auflage}, publisher = {De Gruyter}, address = {Berlin}, isbn = {978-3-11-051513-8}, pages = {320}, abstract = {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.}, language = {en} } @misc{RichterBestehorn, author = {Richter, Sebastian and Bestehorn, Michael}, title = {Direct numerical simulations of liquid films in two dimensions under horizontal and vertical external vibrations}, series = {Physical Review Fluids}, volume = {4}, journal = {Physical Review Fluids}, number = {4}, issn = {2469-990X}, doi = {10.1103/PhysRevFluids.4.044004}, pages = {044004-1 -- 044004-21}, abstract = {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)].}, language = {en} } @misc{StermanCohenBestehornOron, author = {Sterman-Cohen, Elad and Bestehorn, Michael and Oron, Alexander}, title = {Driving mechanisms of ratchet flow in thin liquid films under tangential two-frequency forcing}, series = {Physics of Fluids}, volume = {31}, journal = {Physics of Fluids}, number = {7}, doi = {10.1063/1.5098941}, pages = {14}, abstract = {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.}, language = {en} } @misc{BorciaBorciaBestehornetal., author = {Borcia, Ion-Dan and Borcia, Rodica and Bestehorn, Michael and Richter, Stefan and Xu, Wenchao and Harlander, Uwe}, title = {Horizontal Faraday instability and parametric excitation in a circular channel}, series = {GAMM 2019, 90th Annual Meeting of the International Assoociation of Applied Mathematics and Mechanics, February 18-22, 2019, Vienna, Austria}, journal = {GAMM 2019, 90th Annual Meeting of the International Assoociation of Applied Mathematics and Mechanics, February 18-22, 2019, Vienna, Austria}, publisher = {TU Verlag}, address = {Wien}, isbn = {978-3-903024-84-7}, pages = {338}, language = {en} } @misc{BestehornTyvandMichelitsch, author = {Bestehorn, Michael and Tyvand, Peder A. and Michelitsch, Thomas M.}, title = {Dimension-Reduced Model for Deep-Water Waves}, series = {Journal of Applied Mathematics and Physics}, volume = {7}, journal = {Journal of Applied Mathematics and Physics}, number = {1}, issn = {2327-4379}, doi = {10.4236/jamp.2019.71007}, pages = {72 -- 92}, abstract = {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.}, language = {en} } @misc{BorciaBorciaRichteretal., author = {Borcia, Ion-Dan and Borcia, Rodica and Richter, Sebastian and Xu, Wenchao and Bestehorn, Michael and Harlander, Uwe}, title = {Horizontal Faraday instability in a circular channel}, series = {Proceedings in Applied Mathematics and Mechanics (PAMM)}, volume = {19}, journal = {Proceedings in Applied Mathematics and Mechanics (PAMM)}, number = {1}, issn = {1617-7061}, doi = {10.1002/pamm.201900242}, pages = {2}, abstract = {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.}, language = {en} } @misc{BorciaBorciaXuetal., author = {Borcia, Ion-Dan and Borcia, Rodica and Xu, Wenchao and Bestehorn, Michael and Richter, Sebastian and Harlander, Uwe}, title = {Undular bores in a large circular channel}, series = {European Journal of Mechanics - B/Fluids}, volume = {79}, journal = {European Journal of Mechanics - B/Fluids}, issn = {0997-7546}, doi = {10.1016/j.euromechflu.2019.09.003}, pages = {67 -- 73}, abstract = {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.}, language = {en} } @misc{GrangerMichelitschBestehornetal., author = {Granger, T{\´e}o and Michelitsch, Thomas M. and Bestehorn, Michael and Riascos, Alejandro P. and Collet, Bernard A.}, title = {Stochastic Compartment Model with Mortality and Its Application to Epidemic Spreading in Complex Networks}, series = {Entropy}, volume = {26}, journal = {Entropy}, number = {5}, issn = {1099-4300}, doi = {10.3390/e26050362}, abstract = {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 Barab{\´a}si-Albert (BA), Erd{\"o}s-R{\´e}nyi (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.}, language = {en} } @misc{BorciaRichterBorciaetal., author = {Borcia, Ion-Dan and Richter, Sebastian and Borcia, Rodica and Sch{\"o}n, Franz-Theo and Harlander, Uwe and Bestehorn, Michael}, title = {Wave propagation in a circular channel: sloshing and resonance}, series = {The European Physical Journal Special Topics}, volume = {Vol. 232}, journal = {The European Physical Journal Special Topics}, number = {4}, issn = {1951-6401}, doi = {10.1140/epjs/s11734-023-00790-z}, pages = {461 -- 468}, abstract = {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}, language = {en} } @misc{SchoenBestehorn, author = {Sch{\"o}n, Franz-Theo and Bestehorn, Michael}, title = {Instabilities and pattern formation in viscoelastic fluids}, series = {The European Physical Journal Special Topics}, volume = {Vol. 232}, journal = {The European Physical Journal Special Topics}, number = {4}, issn = {1951-6401}, doi = {10.1140/epjs/s11734-023-00792-x}, pages = {375 -- 383}, language = {en} } @misc{GrangerMichelitschBestehornetal., author = {Granger, T{\´e}o and Michelitsch, Thomas M. and Bestehorn, Michael and Riascos, Alejandro P. and Collet, Bernard A.}, title = {Four-compartment epidemic model with retarded transition rates}, series = {Physical Review E}, volume = {107}, journal = {Physical Review E}, number = {4}, issn = {2470-0045}, doi = {10.1103/PhysRevE.107.044207}, pages = {044207-1 -- 044207-15}, abstract = {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.}, language = {en} } @misc{BestehornRiascosMichelitschetal., author = {Bestehorn, Michael and Riascos, Alejandro P. and Michelitsch, Thomas M. and Collet, Bernard A.}, title = {A Markovian random walk model of epidemic spreading}, series = {Continuum Mechanics and Thermodynamics}, volume = {33}, journal = {Continuum Mechanics and Thermodynamics}, number = {4}, issn = {1432-0959}, doi = {10.1007/s00161-021-00970-z}, pages = {1207 -- 1221}, abstract = {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.}, language = {en} } @misc{PototskyOronBestehorn, author = {Pototsky, Andrey and Oron, Alexander and Bestehorn, Michael}, title = {Equilibrium shapes and floatability of static and vertically vibrated heavy liquid drops on the surface of a lighter fluid}, series = {Journal of Fluid Mechanics}, volume = {922}, journal = {Journal of Fluid Mechanics}, issn = {1469-7645}, doi = {10.1017/jfm.2021.546}, pages = {A31-1 -- A31-21}, abstract = {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.}, language = {en} } @misc{PirizPirizTahiretal., author = {Piriz, S. A. and Piriz, Antonio R. and Tahir, Naeem A. and Richter, Sebastian and Bestehorn, Michael}, title = {Rayleigh-Taylor instability in elastic-plastic solid slabs bounded by a rigid wall}, series = {Physical Review E}, volume = {103}, journal = {Physical Review E}, number = {2}, issn = {2470-0045}, doi = {10.1103/PhysRevE.103.023105}, pages = {023105-1 -- 023105-12}, abstract = {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)].}, language = {en} }