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1
Kozlov, Victor, Stanislav Subbotin, and Ivan Karpunin. "Supercritical Dynamics of an Oscillating Interface of Immiscible Liquids in Axisymmetric Hele-Shaw Cells." Fluids 8, no. 7 (July 12, 2023): 204. http://dx.doi.org/10.3390/fluids8070204.
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The oscillation of the liquid interface in axisymmetric Hele-Shaw cells (conical and flat) is experimentally studied. The cuvettes, which are thin conical layers of constant thickness and flat radial Hele-Shaw cells, are filled with two immiscible liquids of similar densities and a large contrast in viscosity. The axis of symmetry of the cell is oriented vertically; the interface without oscillations is axially symmetric. An oscillating pressure drop is set at the cell boundaries, due to which the interface performs radial oscillations in the form of an oscillating “tongue” of a low-viscosity liquid, periodically penetrating into a more viscous liquid. An increase in the oscillation amplitude leads to the development of a system of azimuthally periodic structures (fingers) at the interface. The fingers grow when the viscous liquid is forced out of the layer and reach their maximum in the phase of maximum displacement of the interface. In the reverse course, the structures decrease in size and, at a certain phase of oscillations, take the form of small pits directed toward the low-viscosity fluid. In a conical cell, a bifurcation of period doubling with an increase in amplitude is found; in a flat cell, it is absent. A slow azimuthal drift of finger structures is found. It is shown that the drift is associated with the inhomogeneity of the amplitude of fluid oscillations in different radial directions. The fingers move from the region of a larger to the region of a lower amplitude of the interface oscillations.
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Liu, Cheng, Guowei Cai, Deyou Yang, Zhenglong Sun, and Mingna Zhang. "The Online Identification of Dominated Inter-area Oscillations Interface Based on the Incremental Energy Function in Power System." Open Electrical & Electronic Engineering Journal 10, no. 1 (September 30, 2016): 88–100. http://dx.doi.org/10.2174/1874129001610010088.
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The online identification of power system dominated inter-area oscillations interface based on the incremental energy function method is proposed in this paper. The dominant inter-area oscillations interface can be obtained by calculating branch oscillation potential energy, which is tie-line concentrated by oscillations energy. To get the oscillation energy caused by the different mechanism (free oscillation and forced oscillation), different fault position, different oscillation source. Power system dominated inter-area oscillations interface can be effectively obtained by proposed method, at the same time, dominated inter-area oscillations clusters also can be obtained. Finally, damping property of power system is effectively improved by configurating series damping controller in the dominant oscillation profile. The accuracy of the dominant oscillation interface identification is verified in this paper. At the same time, the proposed approach can also provides the basis for the configuration of damping control based on line.
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Kozlov, Viktor, and Olga Vlasova. "Oscillatory dynamics of immiscible liquids with high viscosity contrast in a rectangular Hele–Shaw channel." Physics of Fluids 34, no. 3 (March 2022): 032121. http://dx.doi.org/10.1063/5.0084363.
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The dynamics of the interface of liquids with a high viscosity contrast, performing harmonic oscillations with zero mean in a straight slot channel, is experimentally investigated. The boundary is located across the channel and oscillates along the channel with a harmonic change in the flow rate of the fluid pumped through the channel. Owing to the high contrast of viscosities, the motion of the more viscous liquid obeys Darcy's law, while the low-viscosity liquid performs “inviscid” oscillations. The oscillations of the interface occur in the form of an oscillating flat tongue of low-viscosity liquid that periodically penetrates into the more viscous one. The interface oscillations lead to the manifestation of two effects. One of these consists of changes in the averaged shape of the interface and the liquid contact line. The interface in the cell plane takes the form of a “hill,” the dynamical equilibrium of which is maintained by oscillations, while the deformation of the boundary is proportional to the amplitude of the oscillations and vanishes in their absence. The second effect consists of the development of finger instability of the oscillating boundary, which manifests itself in the periodic development of fingers of low-viscosity liquid at part of a period. The instability develops in a threshold manner when the relative amplitude of the interface oscillations reaches a critical value. It is found that the instability has a local character and manifests itself in those regions of the interface where the amplitude of the oscillations reaches a critical value. The stability threshold decreases with the dimensionless frequency.
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Jian, Liu, and Gyung-Min Choi. "Using Amorphous CoB Alloy as Transducer to Detect Acoustic Propagation and Heat Transport at Interface." Applied Sciences 11, no. 11 (June 1, 2021): 5155. http://dx.doi.org/10.3390/app11115155.
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Acoustic oscillation provides useful information regarding the interfacial coupling between metal transducer layers and substrate materials. The interfacial coupling can be significantly reduced by a mechanically soft layer between the transducer and substrate. However, preserving a thin, soft layer at the interface during fabrication is often challenging. In this study, we demonstrate that an amorphous CoB alloy on top of a sapphire substrate can substantially amplify acoustic oscillations. By analyzing the attenuation of acoustic oscillations, we show that a thin, soft layer with a thickness of >2 ± 1 Å exists at the interface. The intermediate layer at the interface is further verified by investigating heat transport. By analyzing the slow decrease of the temperature of the transducer layer, we determine a thermal conductance of 35 ± 5 MW m−2 K−1 at the transducer/substrate interface. This low value supports the existence of a thin, soft layer at the interface. Our results demonstrate that an amorphous metal with B alloying effectively preserves the soft nature at the interface and detects the acoustic propagation and heat transport across it.
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Kovalchuk, Nina. "Spontaneous oscillations due to solutal Marangoni instability: air/water interface." Open Chemistry 10, no. 5 (October 1, 2012): 1423–41. http://dx.doi.org/10.2478/s11532-012-0083-5.
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AbstractSystems far from equilibrium are able to self-organize and often demonstrate the formation of a large variety of dissipative structures. In systems with free liquid interfaces, self-organization is frequently associated with Marangoni instability. The development of solutal Marangoni instability can have specific features depending on the properties of adsorbed surfactant monolayer. Here we discuss a general approach to describe solutal Marangoni instability and review in details the recent experimental and theoretical results for a system where the specific properties of adsorbed layers are crucial for the observed dynamic regimes. In this system, Marangoni instability is a result of surfactant transfer from a small droplet located in the bulk of water to air/water interface. Various dynamic regimes, such as quasi-steady convection with a monotonous decrease of surface tension, spontaneous oscillations of surface tension, or their combination, are predicted by numerical simulations and observed experimentally. The particular dynamic regime and oscillation characteristics depend on the surfactant properties and the system aspect ratio.
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Ganiev, R. F., D. A. Zhebynev, and A. M. Feldman. "EXCITATION OF NONLINEAR PRESSURE OSCILLATIONS IN LOW-PRESSURE FLUID FLOW USING A HIGH-PRESSURE HYDRODYNAMIC GENERATOR." Spravochnik. Inzhenernyi zhurnal, no. 280 (July 2020): 7–13. http://dx.doi.org/10.14489/hb.2020.07.pp.007-013.
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The results of the study of the excitation process of nonlinear oscillations of finite amplitude pressure in a low-pressure (treated) fluid flow using a hydrodynamic oscillator of flow type, the working fluid of which has no direct contact with the fluid of the treated flow, are presented. It is shown that the oscillations from the hydrodynamic generator can be transmitted to the fluid flow through the interface (matching device) in the form of a disk with a certain acoustic resistance. It was found that resonant oscillations can be disturbed in the low-pressure flow processing chamber. The conditions of excitation of resonant oscillations in the processing chamber with a flowing liquid are found. Numerical values of the oscillation span and resonance frequencies are given.
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Ganiev, R. F., D. A. Zhebynev, and A. M. Feldman. "EXCITATION OF NONLINEAR PRESSURE OSCILLATIONS IN LOW-PRESSURE FLUID FLOW USING A HIGH-PRESSURE HYDRODYNAMIC GENERATOR." Spravochnik. Inzhenernyi zhurnal, no. 280 (July 2020): 7–13. http://dx.doi.org/10.14489/hb.2020.07.pp.007-013.
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The results of the study of the excitation process of nonlinear oscillations of finite amplitude pressure in a low-pressure (treated) fluid flow using a hydrodynamic oscillator of flow type, the working fluid of which has no direct contact with the fluid of the treated flow, are presented. It is shown that the oscillations from the hydrodynamic generator can be transmitted to the fluid flow through the interface (matching device) in the form of a disk with a certain acoustic resistance. It was found that resonant oscillations can be disturbed in the low-pressure flow processing chamber. The conditions of excitation of resonant oscillations in the processing chamber with a flowing liquid are found. Numerical values of the oscillation span and resonance frequencies are given.
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Soler, Roberto. "Exploring the Ideal MHD Quasi-Modes of a Plasma Interface with a Thick Nonuniform Transition." Physics 4, no. 4 (November 8, 2022): 1359–70. http://dx.doi.org/10.3390/physics4040087.
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Nonuniform plasma across an imposed magnetic field, such as those present in the solar atmosphere, can support collective Alfvénic oscillations with a characteristic damping time. The damped transverse oscillations of coronal loops are an example of this process. In ideal magnetohydrodynamics (MHD), these transient collective motions are associated with quasi-modes resonant in the Alfvén continuum. Quasi-modes live in a non-principal Riemann sheet of the dispersion relation, and so they are not true ideal MHD eigenmodes. The present study considers the illustrative case of incompressible surface MHD waves propagating on a nonuniform interface between two uniform plasmas with a straight magnetic field parallel to the interface. It is explored how the ideal quasi-modes of this configuration change when the width of the nonuniform transition increases. It is found that interfaces with wide enough transitions are not able to support truly collective oscillations. A quasi-mode that can be related with a resonantly damped surface MHD wave can only be found in interfaces with sufficiently thin transitions.
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DELOURME, BERANGERE, HOUSSEM HADDAR, and PATRICK JOLY. "ON THE WELL-POSEDNESS, STABILITY AND ACCURACY OF AN ASYMPTOTIC MODEL FOR THIN PERIODIC INTERFACES IN ELECTROMAGNETIC SCATTERING PROBLEMS." Mathematical Models and Methods in Applied Sciences 23, no. 13 (September 16, 2013): 2433–64. http://dx.doi.org/10.1142/s021820251350036x.
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We prove the well-posedness and stability properties of a parameter dependent problem that models the reflection and transmission of electromagnetic waves at a thin and rapidly oscillating interface. The latter is modeled using approximate interface conditions that can be derived using asymptotic expansion of the exact solution with respect to the small parameter (proportional to the periodicity length of oscillations and the width of the interface). The obtained uniform stability results are then used to prove the accuracy (with respect to the small parameter) of the proposed model.
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Adamatzky, Andrew, Claire Fullarton, Neil Phillips, Ben De Lacy Costello, and Thomas C. Draper. "Thermal switch of oscillation frequency in Belousov–Zhabotinsky liquid marbles." Royal Society Open Science 6, no. 4 (April 2019): 190078. http://dx.doi.org/10.1098/rsos.190078.
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External control of oscillation dynamics in the Belousov–Zhabotinsky (BZ) reaction is important for many applications including encoding computing schemes. When considering the BZ reaction, there are limited studies dealing with thermal cycling, particularly cooling, for external control. Recently, liquid marbles (LMs) have been demonstrated as a means of confining the BZ reaction in a system containing a solid–liquid interface. BZ LMs were prepared by rolling 50 μl droplets in polyethylene (PE) powder. Oscillations of electrical potential differences within the marble were recorded by inserting a pair of electrodes through the LM powder coating into the BZ solution core. Electrical potential differences of up to 100 mV were observed with an average period of oscillation ca 44 s. BZ LMs were subsequently frozen to −1°C to observe changes in the frequency of electrical potential oscillations. The frequency of oscillations reduced upon freezing to 11 mHz cf. 23 mHz at ambient temperature. The oscillation frequency of the frozen BZ LM returned to 23 mHz upon warming to ambient temperature. Several cycles of frequency fluctuations were able to be achieved.
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Fyrillas, Marios M., and Andrew J. Szeri. "Dissolution or growth of soluble spherical oscillating bubbles." Journal of Fluid Mechanics 277 (October 25, 1994): 381–407. http://dx.doi.org/10.1017/s0022112094002806.
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A new theoretical formulation is presented for mass transport across the dynamic interface associated with a spherical bubble undergoing volume oscillations. As a consequence of the changing internal pressure of the bubble that accompanies volume oscillations, the concentration of the dissolved gas in the liquid at the interface undergoes large-amplitude oscillations. The convection-diffusion equations governing transport of dissolved gas in the liquid are written in Lagrangian coordinates to account for the moving domain. The Henry's law boundary condition is split into a constant and an oscillating part, yielding the smooth and the oscillatory problems respectively. The solution of the oscillatory problem is valid everywhere in the liquid but differs from zero only in a thin layer of the liquid in the neighbourhood of the bubble surface. The solution to the smooth problem is also valid everywhere in the liquid; it evolves via convection-enhanced diffusion on a slow timescale controlled by the Péclet number, assumed to be large. Both the oscillatory and smooth problems are treated by singular perturbation methods: the oscillatory problem by boundary-layer analysis, and the smooth problem by the method of multiple scales in time. Using this new formulation, expressions are developed for the concentration field outside a bubble undergoing arbitrary nonlinear periodic volume oscillations. In addition, the rate of growth or dissolution of the bubble is determined and compared with available experimental results. Finally, a new technique is described for computing periodically driven nonlinear bubble oscillations that depend on one or more physical parameters. This work extends a large body of previous work on rectified diffusion that has been restricted to the assumptions of infinitesimal bubble oscillations or of threshold conditions, or both. The new formulation represents the first self-consistent, analytical treatment of the depletion layer that accompanies nonlinear oscillating bubbles that grow via rectified diffusion.
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Bracker, G. P., and R. W. Hyers. "The effects of the excitation pulse on flow in electromagnetic levitation experiments." High Temperatures-High Pressures 52, no. 2 (2023): 111–22. http://dx.doi.org/10.32908/hthp.v52.1301.
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Oscillating drop experiments allow the surface tension and viscosity of high temperature and highly reactive melts to be measured without an interface contacting the surface of the molten sample. Surface oscillations are induced by varying the electromagnetic field. The oscillations are measured to determine the surface tension and viscosity from the frequency and damping of the oscillations, respectively. The damping of the oscillations is, however, sensitive to the flow conditions within the melt. Recent advances have allowed transient magnetohydrodynamic models to calculate changes in the internal flow in response to variations in the magnetic field, much like those used to induce surface oscillations. These models show that the excitation pulse drives rapid acceleration within the melt. While the fluid flow may accelerate to speeds above the laminar-turbulent transition, the flow speeds are not sustained for sufficient time periods to allow turbulent flow to develop. Following the excitation pulse, the flow rapidly slows and quickly returns to the conditions present before the excitation pulse.
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Ma, Xiaolei, and Justin C. Burton. "Self-organized oscillations of Leidenfrost drops." Journal of Fluid Mechanics 846 (May 4, 2018): 263–91. http://dx.doi.org/10.1017/jfm.2018.294.
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In the Leidenfrost effect, a thin layer of evaporated vapour forms between a liquid and a hot solid. The complex interactions between the solid, liquid and vapour phases can lead to rich dynamics even in a single Leidenfrost drop. Here we investigate the self-organized oscillations of Leidenfrost drops that are excited by a constant flow of evaporated vapour beneath the drop. We show that for small Leidenfrost drops, the frequency of a recently reported ‘breathing mode’ (Caswell, Phys. Rev. E, vol. 90, 2014, 013014) can be explained by a simple balance of gravitational and surface tension forces. For large Leidenfrost drops, azimuthal star-shaped oscillations are observed. Our previous work showed how the coupling between the rapid evaporated vapour flow and the vapour–liquid interface excites the star-shaped oscillations (Ma et al., Phys. Rev. Fluids, vol. 2, 2017, 031602). In our experiments, star-shaped oscillation modes of $n=2{-}13$ are observed in different liquids, and the number of observed modes depends sensitively on the viscosity of the liquid. Here we expand on this work by directly comparing the oscillations with theoretical predictions, as well as show how the oscillations are initiated by a parametric forcing mechanism through pressure oscillations in the vapour layer. The pressure oscillations are driven by the capillary waves of a characteristic wavelength beneath the drop. These capillary waves can be generated by a large shear stress at the liquid–vapour interface due to the rapid flow of evaporated vapour. We also explore potential effects of thermal convection in the liquid. Although the measured Rayleigh number is significantly larger than the critical Rayleigh number, the frequency (wavelength) of the oscillations depends only on the capillary length of the liquid, and is independent of the drop radius and substrate temperature. Thus convection seems to play a minor role in Leidenfrost drop oscillations, which are mostly hydrodynamic in origin.
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Phillips, Leon F. "Local-mode oscillations at a liquid interface." Chemical Physics Letters 330, no. 1-2 (November 2000): 15–20. http://dx.doi.org/10.1016/s0009-2614(00)01064-2.
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Win, Ko Ko, and A. N. Temnov. "A THEORETICAL STUDY OF OSCILLATIONS OF TWO IMMISCIBLE FLUIDS IN A LIMITED TANK." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 69 (2021): 97–113. http://dx.doi.org/10.17223/19988621/69/8.
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In the paper, the nonlinear oscillations of a two-layer fluid that completely fills a limited tank are theoretically studied. To determine any smooth function on the deflected interface, the Taylor series expansions are considered using the values of the function and its normal derivatives on the undisturbed interface of the fluids. Using two fundamental asymmetric harmonics, which are generated in two mutually perpendicular planes, the differential equations of nonlinear oscillations of the two-layer fluid interface are investigated. As a result, the frequency-response characteristics are presented and the instability regions of the forced oscillations of the two-layer fluid in the cylindrical tank are plotted, as well as the parametric resonance regions for different densities of the upper and lower fluids. The Bubnov-Galerkin method is used to plot instability regions for the approximate solution to nonlinear differential equations. At the final stage of the work, the nonlinear effects resulting from the interaction of fluids with a rigid tank that executes harmonic oscillations at the interface of the fluids are theoretically studied.
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Reddy, R. V., and G. S. Lakhina. "Shear flow instabilities in the Earth's magnetotail." Annales Geophysicae 14, no. 8 (August 31, 1996): 786–93. http://dx.doi.org/10.1007/s00585-996-0786-z.
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Abstract. Shear flow instability is studied in the Earth's magnetotail by treating plasma as compressible. A dispersion relation is derived from the linearized MHD equations using the oscillating boundary conditions at the inner central plasma sheet/outer central plasma sheet (OCPS) interface and OCPS/plasma-sheet boundary layer (PSBL) interface, whereas the surface-mode boundary condition is used at the PSBL/lobe interface. The growth rates and the real frequencies are obtained numerically for near-Earth (∣X∣~10–15 RE) and far-Earth (∣X∣~100 RE) magnetotail parameters. The periods and wavelengths of excited modes depend sensitively on the value of plasma-sheet half thickness, L, which is taken as L=5 RE for quiet time and L=1 RE for disturbed time. The plasma-sheet region is found to be stable for constant plasma flows unless MA3>1.25, where MA3 is the Alfvén Mach number in PSBL. For near-Earth magnetotail, the excited oscillations have periods of 2–20 min (quiet time) and 0.5–4 min (disturbed time) with typical transverse wavelengths of 2–30 RE and 0.5–6.5 RE, respectively; whereas for distant magnetotail, the analysis predicts the oscillation periods of ~8–80 min for quiet periods and 2–16 min for disturbed periods.
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Savotchenko, S. E. "Nonlinear surface waves propagating along the composite waveguide consisting of self-focusing slab between defocusing media separated by interfaces with nonlinear response." Journal of Nonlinear Optical Physics & Materials 28, no. 04 (December 2019): 1950039. http://dx.doi.org/10.1142/s0218863519500395.
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The model of the composite symmetric waveguide consisting of self-focusing slab between defocusing nonlinear media separated by interfaces characterized by own nonlinearity response is proposed. Two new types of nonlinear surface waves propagating along it with anti-phase amplitude oscillations at interface planes are found. The frequencies of the nonlinear surface waves existing near the interfaces with the nonlinear response only are calculated analytically. The conditions of the surface wave existence are found. The frequencies and localization distances of the surface waves in dependence on nonlinearity waveguide parameters, slab width and interface characteristics are analyzed.
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Kuzmin M.V. and Mittsev M.A. "Effect of Friedel Oscillations on the Work Function of Ytterbium Nanofilms." Physics of the Solid State 65, no. 6 (2023): 1036. http://dx.doi.org/10.21883/pss.2023.06.56121.48.
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The effect of standing waves of charge density (Friedel oscillations) generated by an interface of the metallic ytterbium nanofilm single-crystal silicon substrate type on the work function of ytterbium nanolayers has been studied. It is shown that in the range of nanofilm thicknesses from 0 to 8 monatomic layers, the work function has an oscillating character. This feature of the dependence of the work function on the nanofilm thickness is a consequence of the fact that the standing waves change nonmonotonically the power (momentum) of the electric double layer, which exists on the metal surface and affects the work function of the metal. This ultimately determines the oscillating nature of the dependence of the work function on the thickness of the nanofilms. Keywords: surface, nanofilm, work function, Friedel oscillations, electric double layer, ytterbium.
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Nourgaliev, R. R., T. N. Dinh, and T. G. Theofanous. "The Characteristics-Based Matching (CBM) Method for Compressible Flow With Moving Boundaries and Interfaces." Journal of Fluids Engineering 126, no. 4 (July 1, 2004): 586–604. http://dx.doi.org/10.1115/1.1778713.
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Recently, Eulerian methods for capturing interfaces in multi-fluid problems become increasingly popular. While these methods can effectively handle significant deformations of interface, the treatment of the boundary conditions in certain classes of compressible flows are known to produce nonphysical oscillations due to the radical change in equation of state across the material interface. One promising recent development to overcome these problems is the Ghost Fluid Method (GFM). The present study initiates a new methodology for boundary condition capturing in multifluid compressible flows. The method, named Characteristics-Based Matching (CBM), capitalizes on recent developments of the level set method and related techniques, i.e., PDE-based re-initialization and extrapolation, and the Ghost Fluid Method (GFM). Specifically, the CBM utilizes the level set function to capture interface position and a GFM-like strategy to tag computational nodes. In difference to the GFM method, which employs a boundary condition capturing in primitive variables, the CBM method implements boundary conditions based on a characteristic decomposition in the direction normal to the boundary. In this way overspecification of boundary conditions is avoided and we believe so will be spurious oscillations. In this paper, we treat (moving or stationary) fluid-solid interfaces and present numerical results for a select set of test cases. Extension to fluid-fluid interfaces will be presented in a subsequent paper.
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Zhu, Zhi-Cheng, Hao-Ran Liu, and Hang Ding. "Buoyancy-driven bubbles in a constricted vertical capillary." Physics of Fluids 34, no. 3 (March 2022): 032102. http://dx.doi.org/10.1063/5.0083160.
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We numerically study the dynamics of buoyancy-driven bubbles in a constricted vertical capillary in which a throat with an arc shape is present. To investigate at what conditions and how the bubble would be entrapped at the capillary throat, a diffuse-interface immersed-boundary method is used in numerical simulations. Axisymmetric simulations are performed for various bubble and throat sizes, represented by the diameter ratio of the throat to the bubble, η ([Formula: see text]), the Bond number ([Formula: see text]), and the Reynolds number ([Formula: see text]). We find that small bubbles have insignificant deformation and, thus, cannot pass through a throat with [Formula: see text], while relatively large bubbles encounter noticeable interface oscillations at their lower part when approaching the throat. In particular, the interface oscillations are composed of a standing wave arising from buoyancy and a capillary wave propagating radially. A phase diagram is presented regarding the eventual bubble morphology: pass-through and entrapment. For the critical diameter ratio ηc at the onset of bubble entrapment, we proposed two scaling laws based on the analysis of the deformability and oscillation of the bubble, i.e., [Formula: see text] for Bo < 1 and [Formula: see text] for Bo > 1. These theoretical predictions are in good agreement with our numerical results.
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Chevrychkina A. A., Bessonov N. M., and Korzhenevskii A. L. "Calculation of the dynamics of the amorphous phase-crystal interface during solid-phase explosive crystallization." Physics of the Solid State 63, no. 13 (2022): 1788. http://dx.doi.org/10.21883/pss.2022.13.52323.162.
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The nonlinear differential equation described a dynamics of solid-phase explosive crystallization front in a much larger parameters domain in comparison with the theoretical results available in literature was obtained. The features of the self-oscillating mode transition of the front motion to the mode of its self-propagation with a constant velocity was numerically studied in detail. Ketwords: Explosive crystallization, self-oscillations of the interface glass-crystal, self-propagating front.
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Niu, Wei, Zhenqi Wu, Yongda Chen, Yulin Gan, Yequan Chen, Hongqi Hu, Xiaoqian Zhang, et al. "Evidence of the nontrivial Berry phase at γ-Al2O3/SrTiO3 heterointerfaces." Applied Physics Letters 121, no. 10 (September 5, 2022): 101601. http://dx.doi.org/10.1063/5.0093903.
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The nontrivial Berry phase in correlated oxide heterostructures has been highly attractive due to the Rashba spin–orbit interactions originating from the inversion symmetry breaking at the heterointerfaces. Despite the theoretically predicated nontrivial π Berry phase in Rashba systems, its experimental detection among all Rashba oxide interfaces remains elusive. Here, we report a nontrivial Berry phase at the interface between γ-Al2O3 and SrTiO3 as evidenced by the quantum oscillations. Analysis of transport properties under the high magnetic field up to 32 T reveals the weak anti-localization (WAL) effect and Shubnikov–de Haas (SdH) oscillations. Both the WAL effect and the nontrivial π Berry phase extracted from the SdH oscillations manifest the significance of the Rashba spin–orbit coupling in γ-Al2O3/SrTiO3. Physical quantities concerning the Fermi surface, such as effective mass, scattering time, etc., are experimentally accessed as well. Our work provides insights into the nontrivial Berry phase in correlated oxide interfaces.
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Maksimov, A. O., and Yu A. Polovinka. "Oscillations of a gas inclusion near an interface." Acoustical Physics 63, no. 1 (January 2017): 26–32. http://dx.doi.org/10.1134/s1063771016060099.
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Blanco-Coronas, Angela M., Maria L. Calvache, Manuel López-Chicano, Crisanto Martín-Montañés, Jorge Jiménez-Sánchez, and Carlos Duque. "Salinity and Temperature Variations near the Freshwater-Saltwater Interface in Coastal Aquifers Induced by Ocean Tides and Changes in Recharge." Water 14, no. 18 (September 9, 2022): 2807. http://dx.doi.org/10.3390/w14182807.
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The temperature distribution of shallow sectors of coastal aquifers are highly influenced by the atmospheric temperature and recharge. However, geothermal heat or vertical fluxes due to the presence of the saline wedge have more influence at deeper locations. In this study, using numerical models that account for variable density, periodic oscillations of temperature have been detected, and their origin has been attributed to the influence exerted by recharge and tides. The combined analysis of field data and numerical models showed that the alternation of dry and wet periods modifies heat distribution in deep zones (>100 m) of the aquifer. Oscillations with diurnal and semidiurnal frequencies have been detected for groundwater temperature, but they show differences in terms of amplitudes and delay with electrical conductivity (EC). The main driver of the temperature oscillations is the forward and backward displacement of the freshwater–saltwater interface, and the associated thermal plume generated by the upward flow from the aquifer basement. These oscillations are amplified at the interfaces between layers with different hydraulic conductivity, where thermal contours are affected by refraction.
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Si, Nan, Jinwon Park, and Alan J. Brown. "A Direct Ghost Fluid Method for Modeling Explosive Gas and Water Flows." Shock and Vibration 2022 (April 16, 2022): 1–19. http://dx.doi.org/10.1155/2022/1627382.
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This work presents a Direct Ghost Fluid Method (DGFM) as part of a two-fluid numerical framework suitable to model explosive gas and water flows resulting from underwater explosion (UNDEX). Due to the presence of explosive gas and water with shock waves in the modeling domain, classic Eulerian methods with inherent diffusion may not be effective. Numerical diffusion occurs due to nonphysical diffused density at material interfaces, which creates spurious pressure oscillations and significantly degrades the quality of the numerical results. To eliminate or minimize numerical diffusion, sharp interface methods having no mixed elements may be used in multifluid flow computations. The Direct Ghost Fluid Method (DGFM) described in this paper uses direct extrapolation of density (vice pressure) and tangential velocity from real to ghost fluid. The spurious pressure oscillations near the material interface are therefore minimized. One-, two-, and three-dimensional computational fluid dynamics (CFD) solvers that have DGFM as an essential part in their framework to model UNDEX interface conditions are developed, explored, and applied to the simulation of a series of benchmark problems. Excellent agreement is obtained among the simulations, the analytical solutions, and the experiments.
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Gañán-Calvo, A. M. "Oscillations of liquid captive rotating drops." Journal of Fluid Mechanics 226 (May 1991): 63–89. http://dx.doi.org/10.1017/s002211209100229x.
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A linear analysis of the free oscillations of captive drops or bubbles is discussed. The drop is surrounded by an immiscible liquid or gas and undergoes rotation as a rigid body in the presence of gravity. Using spectral analytical methods, we provide a general formulation for both elliptic and hyperbolic oscillation regimes of the frequency spectrum, for any combination of the Weber and Bond numbers. The method uses a Green function to reduce the inviscid Navier–Stokes equations and boundary conditions to an eigenvalue problem. Both the Green function and normal velocities at the interface are expanded in the orthogonal functional space generated by the Sturm–Liouville problem associated to the interface equation. The effect on the vibration modes of the density and geometrical parameters of the captive drop and surrounding medium is analysed. We present a complete analysis of the low-frequency spectra in the elliptic regime of a set of floating liquid zones and captive drops for a continuous range of Weber and Bond numbers. It is shown that, depending on the geometrical parameters of the system, the elliptic vibration spectrum presents a sui generis modal interaction for low wavenumbers and certain ranges of Weber number.
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De los Santos, Hannah, Emily J. Collins, Catherine Mann, April W. Sagan, Meaghan S. Jankowski, Kristin P. Bennett, and Jennifer M. Hurley. "ECHO: an application for detection and analysis of oscillators identifies metabolic regulation on genome-wide circadian output." Bioinformatics 36, no. 3 (August 6, 2019): 773–81. http://dx.doi.org/10.1093/bioinformatics/btz617.
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Abstract Motivation Time courses utilizing genome scale data are a common approach to identifying the biological pathways that are controlled by the circadian clock, an important regulator of organismal fitness. However, the methods used to detect circadian oscillations in these datasets are not able to accommodate changes in the amplitude of the oscillations over time, leading to an underestimation of the impact of the clock on biological systems. Results We have created a program to efficaciously identify oscillations in large-scale datasets, called the Extended Circadian Harmonic Oscillator application, or ECHO. ECHO utilizes an extended solution of the fixed amplitude oscillator that incorporates the amplitude change coefficient. Employing synthetic datasets, we determined that ECHO outperforms existing methods in detecting rhythms with decreasing oscillation amplitudes and in recovering phase shift. Rhythms with changing amplitudes identified from published biological datasets revealed distinct functions from those oscillations that were harmonic, suggesting purposeful biologic regulation to create this subtype of circadian rhythms. Availability and implementation ECHO’s full interface is available at https://github.com/delosh653/ECHO. An R package for this functionality, echo.find, can be downloaded at https://CRAN.R-project.org/package=echo.find. Supplementary information Supplementary data are available at Bioinformatics online.
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Abi Chebel, Nicolas, Jiří Vejražka, Olivier Masbernat, and Frédéric Risso. "Shape oscillations of an oil drop rising in water: effect of surface contamination." Journal of Fluid Mechanics 702 (May 30, 2012): 533–42. http://dx.doi.org/10.1017/jfm.2012.205.
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AbstractInertial shape oscillations of heptane drops rising in water are investigated experimentally. Diameters from 0.59 to 3.52 mm are considered, corresponding to a regime where the rising motion should not affect shape oscillations for pure immiscible fluids. The interface, however, turns out to be contaminated. The drag coefficient is considerably increased compared to that of a clean drop due to the well-known Marangoni effect resulting from a gradient of surfactant concentration generated by the fluid motion along the interface. Thanks to the decomposition of the shape into spherical harmonics, the eigenfrequencies and the damping rates of oscillation modes $n= 2$, 3, 4 and 5 have been measured. Frequencies are not affected by contamination, while damping rates are increased by a considerable amount that depends neither on drop instantaneous velocity nor on diameter. This augmentation, however, depends on the mode number: it is maximum for mode two (multiplied by 2.4) and then relaxes towards the value of a clean drop as $n$ increases. A previous similar investigation of a drop attached to a capillary has not revealed such an increase of the damping rates, indicating that the coupling between rising motion and surface contamination is responsible for this effect.
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Farsoiya, Palas Kumar, Y. S. Mayya, and Ratul Dasgupta. "Axisymmetric viscous interfacial oscillations – theory and simulations." Journal of Fluid Mechanics 826 (August 15, 2017): 797–818. http://dx.doi.org/10.1017/jfm.2017.443.
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We study axisymmetric, free oscillations driven by gravity and surface tension at the interface of two viscous, immiscible, radially unbounded fluids, analytically and numerically. The interface is perturbed as a zeroth-order Bessel function (in space) and its evolution is obtained as a function of time. In the linearised approximation, we solve the initial value problem (IVP) to obtain an analytic expression for the time evolution of wave amplitude. It is shown that a linearised Bessel mode temporally evolves in exactly the same manner as a Fourier mode in planar geometry. We obtain novel analytical expressions for the time varying vorticity and pressure fields in both fluids. For small initial amplitudes, our analytical results show excellent agreement with those obtained from solving the axisymmetric Navier–Stokes equations numerically. We also compare our results with the normal mode approximation and find the latter to be an accurate representation at very early and late times. The deviation between the normal mode approximation and the IVP solution is found to increase as a function of viscosity ratio. The vorticity field has a jump discontinuity at the interface and we find that this jump depends on the viscosity and the density ratio of the two fluids. Upon increasing the initial perturbation amplitude in the simulations, nonlinearity produces qualitatively new features not present in the analytical IVP solution. Notably, a jet is found to emerge at the axis of symmetry rising to a height greater than the initial perturbation amplitude. Increasing the perturbation amplitude further causes the jet to undergo end pinch off, giving birth to a daughter droplet. This can happen either for an advancing or a receding jet, depending on the viscosity ratio. A relation is found between the maximum jet height and the perturbation amplitude. Hankel transform of the interface demonstrates that at large perturbation amplitudes higher wavenumbers emerge, sharing some of the energy of the lowest mode. When these additional higher modes are present, the interface has pointed crests and rounded troughs.
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Savotchenko, S. E. "Localized states in symmetric three-layered structure consisting of linear layer between focusing media separated by interfaces with nonlinear response." Modern Physics Letters B 33, no. 11 (April 18, 2019): 1850127. http://dx.doi.org/10.1142/s0217984919501276.
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We analyze the localization in three-layered symmetric structure consisting of linear layer between focusing nonlinear media separated by nonlinear interfaces. The mathematical formulation of the model is a one-dimensional boundary value problem for the nonlinear Schrödinger equation. We find nonlinear localized states of two types of symmetry. We derive the energies of obtained stationary states in explicit form. We obtain the localization energies as exact solutions of dispersion equations choosing the amplitude of the interface oscillations as a free parameter. We analyze the conditions of their existence depending on the combination of signs of interface parameters.
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Sadeghi, Rayhane, and Ehsan Tavabi. "Characteristics of chromospheric oscillation periods in magnetic bright points." Monthly Notices of the Royal Astronomical Society 512, no. 3 (April 6, 2022): 4164–70. http://dx.doi.org/10.1093/mnras/stac574.
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ABSTRACT In this investigation, oscillation periods in Mg ii k-line intensity, brightness temperature, and Doppler velocity obtained above magnetic bright points (MBPs) are investigated. For this purpose, data from the Interface Region Imaging Spectrometer (IRIS) observing the higher chromosphere and transition region (TR) were analysed, together with imaging and magnetogram data obtained by the Solar Dynamics Observatory(SDO). The MBPs were identified by combining Si iv 1403-Å slit-jaw images with magnetogram information from the Heliospheric and Magnetic Imager (HMI). A time-slice analysis followed by a wavelet inspection were carried out on the Mg ii k (2796-Å and 10 000 K) resonance lines for the detection of the oscillation period. Finally, a power spectrum analysis was performed to characterize the oscillations. It was found that the network points feature a typical intensity, temperature, and velocity oscillation period of about 300 s. The internetwork points have a mean intensity oscillation period of about 180 s, a mean temperature oscillation period of about 202 s, and a mean velocity oscillation period of about 202 s. In addition, one BP that was analysed in detail demonstrates intensity oscillation periods with a value of 500 s, which are obviously not related to the common 3- or 5-min oscillations typically found elsewhere in chromospheric/photospheric structures.
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Cui, Naitao, Shiyong Zhao, Chao Wang, and Shenhao Chen. "A study of periodic current oscillations of iron in nitric acid solutions." Journal of the Serbian Chemical Society 66, no. 8 (2001): 563–69. http://dx.doi.org/10.2298/jsc0108563c.
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The periodic current oscillations of Fe/HNO3 are presented in this paper. The effects of HNO3 concentration and imposed potential were investigated. The dropping method was used to change the local pH of the Fe/electrolyte interface, creating environments that favor the occurrence of current oscillations. Some interesting results were obtained and an explanation of the current oscillations is suggested.
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Kunin, Mikhail, Yasuhiro Osaki, Bernard Cohen, and Theodore Raphan. "Rotation Axes of the Head During Positioning, Head Shaking, and Locomotion." Journal of Neurophysiology 98, no. 5 (November 2007): 3095–108. http://dx.doi.org/10.1152/jn.00764.2007.
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Static head orientations obey Donders’ law and are postulated to be rotations constrained by a Fick gimbal. Head oscillations can be voluntary or generated during natural locomotion. Whether the rotation axes of the voluntary oscillations or during locomotion are constrained by the same gimbal is unknown and is the subject of this study. Head orientation was monitored with an Optotrak (Northern Digital). Human subjects viewed visual targets wearing pin-hole goggles to achieve static head positions with the eyes centered in the orbit. Incremental rotation axes were determined for pitch and yaw by computing the velocity vectors during head oscillation and during locomotion at 1.5 m/s on a treadmill. Static head orientation could be described by a generalization of the Fick gimbal by having the axis of the second rotation rotate by a fraction, k, of the angle of the first rotation without a third rotation. We have designated this as a k-gimbal system. Incremental rotation axes for both pitch and yaw oscillations were functions of the pitch but not the yaw head positions. The pivot point for head oscillations was close to the midpoint of the interaural line. During locomotion, however, the pivot point was considerably lower. These findings are well explained by an implementation of the k-gimbal model, which has a rotation axis superimposed on a Fick-gimbal system. This could be realized physiologically by the head interface with the dens and occipital condyles during head oscillation with a contribution of the lower spine to pitch during locomotion.
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Ansini, Nadia, Andrea Braides, and Valeria Chiadò Piat. "Gradient theory of phase transitions in composite media." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 133, no. 2 (April 2003): 265–96. http://dx.doi.org/10.1017/s0308210500002390.
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We study the behaviour of non-convex functionals singularly perturbed by a possibly oscillating inhomogeneous gradient term, in the spirit of the gradient theory of phase transitions. We show that a limit problem giving a sharp interface, as the perturbation vanishes, always exists, but may be inhomogeneous or anisotropic. We specialize this study when the perturbation oscillates periodically, highlighting three types of regimes, depending on the frequency of the oscillations. In the two extreme cases, a separation of scales effect is described.
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Kuzma-Kichta, Yury, and Valery Bondur. "Interface oscillations investigation in chaotic processes. Overview of investigations." Thermal processes in engineering 12, no. 11 (2020): 503–14. http://dx.doi.org/10.34759/tpt-2020-12-11-503-514.
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Hugelmann, Martin, and Werner Schindler. "Tunnel barrier height oscillations at the solid/liquid interface." Surface Science 541, no. 1-3 (September 2003): L643—L648. http://dx.doi.org/10.1016/s0039-6028(03)00923-3.
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Pu, Yi, Douglas Cheyne, Yanan Sun, and Blake W. Johnson. "Theta oscillations support the interface between language and memory." NeuroImage 215 (July 2020): 116782. http://dx.doi.org/10.1016/j.neuroimage.2020.116782.
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de Souza, J. Pedro, Alexei A. Kornyshev, and Martin Z. Bazant. "Polar liquids at charged interfaces: A dipolar shell theory." Journal of Chemical Physics 156, no. 24 (June 28, 2022): 244705. http://dx.doi.org/10.1063/5.0096439.
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The structure of polar liquids and electrolytic solutions, such as water and aqueous electrolytes, at interfaces underlies numerous phenomena in physics, chemistry, biology, and engineering. In this work, we develop a continuum theory that captures the essential features of dielectric screening by polar liquids at charged interfaces, including decaying spatial oscillations in charge and mass, starting from the molecular properties of the solvent. The theory predicts an anisotropic dielectric tensor of interfacial polar liquids previously studied in molecular dynamics simulations. We explore the effect of the interfacial polar liquid properties on the capacitance of the electrode/electrolyte interface and on hydration forces between two plane-parallel polarized surfaces. In the linear response approximation, we obtain simple formulas for the characteristic decay lengths of molecular and ionic profiles at the interface.
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Grebenakova, Elena, and Stojan Manolev. "Demonstration of Damped Electrical Oscillations." Natural Science and Advanced Technology Education 30, no. 1 (March 1, 2021): 26–33. http://dx.doi.org/10.53656/nat2021-1.02.
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Introducing mechanical oscillations in schools is a fairly simple and easy experimental feasible task. To demonstrate electromagnetic oscillations, we have difficulty in understanding by students. The explanation of electromagnetic circuits is more abstract. We offered an experiment where we make electromagnetic oscillations obvious and understandable to students. In our experiment we used the software and interface of the AMSTEL Institute (AMSTEL Institute – Amsterdam Mathematics, Science and Technology Education Laboratory) as well as elements from the sets of experimental tasks from the Physics Olympiads organized by the Sofia branch of physicists.
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Nguyen, Phuc Nghia, Mariam Veschgini, Motomu Tanaka, Gilles Waton, Thierry Vandamme, and Marie Pierre Krafft. "Counteracting the inhibitory effect of proteins towards lung surfactant substitutes: a fluorocarbon gas helps displace albumin at the air/water interface." Chem. Commun. 50, no. 78 (2014): 11576–79. http://dx.doi.org/10.1039/c3cc47840h.
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Leguillon, Dominique, and Sébastien Murer. "A Criterion for Crack Kinking Out of an Interface." Key Engineering Materials 385-387 (July 2008): 9–12. http://dx.doi.org/10.4028/www.scientific.net/kem.385-387.9.
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Cotterell and Rice theory (1980) on the kinking of a crack submitted to a biaxial loading in a homogeneous material has been recently revisited (Leguillon and Murer 2008). The mixed criterion for fracture which involves both an energetic and a stress condition (Leguillon 2002) allows defining a positive threshold of the T-stress below which no branching can occur (Selvarathinam and Goree 1998). This analysis enters within a more general mixed-mode analysis (I+II+T-stress). Despite the complex terms and the oscillations, results extend to interfacial cracks. The assumption of a crack jump as a consequence of the energy balance allows getting rid of the problem brought by the oscillations due to these complex terms. This approach brings a new insight on the prediction of crack kinking out of a bimaterial interface.
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Kashina, M. A., and A. A. Alabuzhev. "The deformed oblate drop’s free translational oscillations." Journal of Physics: Conference Series 2317, no. 1 (July 1, 2022): 012017. http://dx.doi.org/10.1088/1742-6596/2317/1/012017.
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Abstract Free translational oscillations of deformable liquid droplet are considered. It is placed into a vessel filled with another liquid. This droplet has an equilibrium revolution shape. The revolution axis of this form is perpendicular two parallel solid plates – floor and cover of vessel. The arbitrary equilibrium contact angle between the interface and the solid substrate can take arbitrary values in the range 0 and π. A contact line velocity is linearly proportional to contact angle deviation from its initial position. Proportionality coefficients (Hocking’s parameters) are individual for any substrate. They characterize individual dissipation coefficient, but whole system’s dissipation is proportional to a sum of all coefficients. There are three characteristic natural frequency intervals for the case of small aspect ratio. High frequencies are the capillary wave frequencies at the interface. The middle frequency is the fundamental or main one. Low frequencies correspond to the drop oscillations with a stationary contact angle. The cylindrical droplet has the highest frequency.
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Iwata, Nobuyuki, Yuta Watabe, Yoshito Tsuchiya, Kento Norota, Takuya Hashimoto, Mark Huijben, Guus Rijnders, Dave H. A. Blank, and Hiroshi Yamamoto. "Growth and Evaluation of [AFeOx/REFeO3] (A=Ca, Sr, RE=La, Bi) Superlattices by Pulsed Laser Deposition Method Using High Density Targets Prepared by Pechini Method." MRS Proceedings 1454 (2012): 161–66. http://dx.doi.org/10.1557/opl.2012.1235.
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ABSTRACTThe LaFeO3 and CaFeOX layers are grown using highly dense target prepared by Pechini method, with which accurate growth rate is achieved. Since the LaFeO3demonstrates the obvious RHEED oscillation until the end of growth, constant growth rate, and the step-terraces structure, the LFO is employed as a buffer and/or reference layer to determine the required pulses to deposit the thickness we desire in the superlattice. Superlattices show the clear satellite peaks and Laue oscillation in the XRD spectra as well as the oscillations caused by the film thickness with a flat surface and superstructure with a flat interface in the x-ray reflection spectrum. The streaky RHEED patterns and step-terraces surface are consistent with the results of spectra using x-ray.
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Mao, Xinyu, Wei Liu, Yuanzhi Ni, and Valentin L. Popov. "Limiting shape of profile due to dual-mode fretting wear in contact with an elastomer." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, no. 9 (December 2, 2015): 1417–23. http://dx.doi.org/10.1177/0954406215619450.
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We consider fretting wear due to superimposed normal and tangential oscillations of two contacting bodies, one of which is an elastomer with a linear rheology. Similarly to the contact of elastic bodies, at small oscillation amplitudes, the wear occurs only in a circular slip zone at the border of the contact area and the wear profile tends to a limiting form, in which no further wear occurs. It is shown that under assumption of a constant coefficient of friction at the contact interface, the limiting form of the wear profile does depend neither on the particular wear criterion nor on the rheology of the elastomer and can be calculated analytically in a general form. The general calculation procedure and explicit analytic solutions for two initial forms, parabolic and conical, are presented for various combinations of frequencies and phases of normal and tangential oscillations as well as for various linear rheologies of the elastomer.
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Najem, Joseph, Myles Dunlap, Sergei Sukharev, and Donald J. Leo. "Mechanosensitive Channels Activity in a Droplet Interface Bilayer System." MRS Proceedings 1621 (2014): 171–76. http://dx.doi.org/10.1557/opl.2014.64.
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ABSTRACTThis paper presents the first attempts to study the large conductance mechano-sensitive channel (MscL) activity in an artificial droplet interface bilayer (DIB) system. A novel and simple technique is developed to characterize the behavior of an artificial lipid bilayer interface containing mechano-sensitive (MS) channels. The experimental setup is assembled on an inverted microscope and consists of two micropipettes filled with PEG-DMA hydrogel and containing Ag/AgCl wires, a cylindrical oil reservoir glued on top of a thin acrylic sheet, and a piezoelectric oscillator actuator. By using this technique, dynamic tension can be applied by oscillating axial motion of one droplet, producing deformation of both droplets and area changes of the DIB interface. The tension in the artificial membrane will cause the MS channels to gate, resulting in an increase in the conductance levels of the membrane. The results show that the MS channels are able to gate under an applied dynamic tension. Moreover, it can be concluded that the response of channel activity to mechanical stimuli is voltage-dependent and highly related to the frequency and amplitude of oscillations.
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Zimasova, Alsu, and Victor Kozlov. "Dynamics of two liquids in a non-uniformly rotating horizontal cylinder." E3S Web of Conferences 402 (2023): 14002. http://dx.doi.org/10.1051/e3sconf/202340214002.
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Controlling the shape of the interfacial boundary is an important technological task. The effect of rotation velocity modulation on the interface between light viscous and denser low viscosity fluid in a rotating horizontal cylinder is studied experimentally. Liquids are characterized by a high contrast of viscosities, these are glycerin and a low-viscosity (denser) fluorinert FC-40. Glycerin is stained with rhodamine, which makes it possible to study the shape of the interface by photo registration with high accuracy when illuminating liquids with a green laser, which causes rhodamine fluorescence. Experiments are carried out in the centrifuged state of liquids when the gravity field has no effect while varying the rotation speed, as well as the amplitude and frequency of librations. It is found that librations qualitatively change the shape of the interface near the ends of the cavity without affecting the cylindrical interface in the middle cavity part. It is shown that this is due to different "viscous" interactions of liquids with the ends of the oscillating cavity, as a result of which the interface near the ends performs radial oscillations with a frequency of librations, and the latter leads to an averaged radial displacement of the wetting boundary of the ends, which increases with the modulation amplitude. At certain amplitudes, the contact line reaches the outer boundary of the cavity. It is shown that the dynamic equilibrium of the interface between liquids of different densities is determined by the averaged interaction of liquids of different viscosity with the oscillating ends.
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Basaran, Osman A. "Nonlinear oscillations of viscous liquid drops." Journal of Fluid Mechanics 241 (August 1992): 169–98. http://dx.doi.org/10.1017/s002211209200199x.
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A fundamental understanding of nonlinear oscillations of a viscous liquid drop is needed in diverse areas of science and technology. In this paper, the moderate- to large-amplitude axisymmetric oscillations of a viscous liquid drop, which is immersed in dynamically inactive surroundings, are analysed by solving the free boundary problem comprised of the Navier–Stokes system and appropriate interfacial conditions at the drop–ambient fluid interface. The means are the Galerkin/finite-element technique, an implicit predictor-corrector method, and Newton's method for solving the resulting system of nonlinear algebraic equations. Attention is focused here on oscillations of drops that are released from an initial static deformation. Two dimensionless groups govern such nonlinear oscillations: a Reynolds number, Re, and some measure of the initial drop deformation. Accuracy is attested by demonstrating that (i) the drop volume remains virtually constant, (ii) dynamic response to small-and moderate-amplitude disturbances agrees with linear and perturbation theories, and (iii) large-amplitude oscillations compare well with the few published predictions made with the marker-and-cell method and experiments. The new results show that viscous drops that are released from an initially two-lobed configuration spend less time in prolate form than inviscid drops, in agreement with experiments. Moreover, the frequency of oscillation of viscous drops released from such initially two-lobed configurations decreases with the square of the initial amplitude of deformation as Re gets large for moderate-amplitude oscillations, but the change becomes less dramatic as Re falls and/or the initial amplitude of deformation rises. The rate at which these oscillations are damped during the first period rises as initial drop deformation increases; thereafter the damping rate is lower but remains virtually time-independent regardless of Re or the initial amplitude of deformation. The new results also show that finite viscosity has a much bigger effect on mode coupling phenomena and, in particular, on resonant mode interactions than might be anticipated based on results of computations incorporating only an infinitesimal amount of viscosity.
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Capitanelli, Raffaela, and Cristina Pocci. "Periodic homogenization for quasi-filling fractal layers." Communications in Contemporary Mathematics 20, no. 08 (December 2018): 1750088. http://dx.doi.org/10.1142/s0219199717500882.
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In this paper, we study the periodic homogenization of the stationary heat equation in a domain with two connected components, separated by an oscillating interface defined on prefractal Koch type curves. The problem depends both on the parameter [Formula: see text], which is the index of the prefractal iteration, and [Formula: see text], that defines the periodic structure of the composite material. First, we study the limit as [Formula: see text] goes to infinity, giving rise to a limit problem defined on a domain with fractal interface. Then, we compute the limit as [Formula: see text] vanishes, showing that the homogenized problem is strictly dependent on the amplitude of the oscillations and the parameter appearing in the transmission condition. Finally, we discuss about the commutative nature of the limits in [Formula: see text] and [Formula: see text].
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Chai, Yi, Dale E. Gary, Kevin P. Reardon, and Vasyl Yurchyshyn. "A Study of Sunspot 3 Minute Oscillations Using ALMA and GST." Astrophysical Journal 924, no. 2 (January 1, 2022): 100. http://dx.doi.org/10.3847/1538-4357/ac34f7.
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Abstract Waves and oscillations are important solar phenomena, not only because they can propagate and dissipate energy in the chromosphere, but also because they carry information about the structure of the atmosphere in which they propagate. The nature of the 3 minute oscillations observed in the umbral region of sunspots is considered to be an effect of propagation of magnetohydrodynamic waves upward from below the photosphere. We present a study of sunspot oscillations and wave propagation in NOAA Active Region 12470 using an approximately 1 hr long data set acquired on 2015 December 17 by the Atacama Large Millimeter/submillimeter Array (ALMA), the Goode Solar Telescope (GST) operating at the Big Bear Solar Observatory, the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory, and the Interface Region Imaging Spectrograph. The ALMA data are unique in providing a time series of direct temperature measurements in the sunspot chromosphere. The 2 s cadence of ALMA images allows us to well resolve the 3 minute periods typical of sunspot oscillations in the chromosphere. Fourier analysis is applied to ALMA Band 3 (∼100 GHz, ∼3 mm) and GST Hα data sets to obtain power spectra as well as oscillation phase information. We analyzed properties of the wave propagation by combining multiple wavelengths that probe physical parameters of solar atmosphere at different heights. We find that the ALMA temperature fluctuations are consistent with that expected for a propagating acoustic wave, with a slight asymmetry indicating nonlinear steepening.
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McKay, Rebecca, Theodore Kolokolnikov, and Paul Muir. "Interface oscillations in reaction-diffusion systems above the Hopf bifurcation." Discrete & Continuous Dynamical Systems - B 17, no. 7 (2012): 2523–43. http://dx.doi.org/10.3934/dcdsb.2012.17.2523.
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