Small-amplitude Oscillations Research Articles

Volume oscillations slow down a rising Taylor bubble

A gas volume rising in a vertical tube is called a Taylor bubble when its equivalent spherical diameter is greater than the diameter of the tube. Continuity dictates that the rising velocity of such bullet-shaped bubbles must be such that the drainage flow in the liquid film separating the gas from the tube wall equals the rate at which space is vacated by the bubble tail on its rise. The numerical simulations presented here show that, if the volume of the bubble is made to execute small-amplitude oscillations, this drainage flow can be markedly decreased so that the bubble slows down so much as to very nearly stop. The mechanism is a subtle nonlinear interplay between the upward flow imposed by the bubble expansion and the inertia of the falling liquid. Two manners of excitation are considered. In the first one the liquid column above the bubble is forced to oscillate sinusoidally, e.g. by a piston. In the second one, an oscillating pressure is imposed on the top liquid surface. With the first arrangement the bubble slows down during its entire ascent by an amount depending on the oscillation frequency and amplitude. With the second one, for a given frequency, the bubble slows down only in the neighbourhood of a certain resonant depth at which the volume oscillations are maximized, but is little affected at deeper and shallower depths.

Effect of thermal-oxidative and mechanical degradation of recycled LDPE on foaming

In this study, we investigated the effect of recycling process on the molecular structure, viscoelasticity and foaming behavior of low density polyethylene (LDPE). A series of LDPE samples with different recycling process was prepared by multiple extrusion using a twin-screw extruder. The molecular weight distribution (MWD) was characterized by gel permeation chromatography (GPC). Wider MWD indicated the generation of higher molecular weight products. Small-amplitude oscillation rheology showed reduced loss factors, indicating that the chain entanglement was more difficult to relax. Moreover, nonlinear viscoelasticity was investigated using elongational rheology and molecular stress function (MSF) model. The results showed a steeper strain hardening exhibited in recycled LDPE. The correlated parameter β in the MSF model indicated that the recycling did not significantly change the branches regularity in LDPE, while the increasing [Formula: see text], the other correlated parameter, indicated that the chain entanglement was enhanced, which was corresponded to the improvement of high molecular weight component. The foaming results revealed that the recycled LDPE had finer cellular structure and higher nucleation density. Moreover, despite adding PP and active CaCO3 to simulate the impurities, the foamability loss of these mixed samples was well restricted and still valuable. Recycled LDPE is instead better than its corresponding virgin one in foaming performance, exhibiting the application potential for further developments.

Simple pendulum: period dependent on amplitude of oscillation

In this study, with a pedagogical aim suited for the undergraduate, the differential equations of motion that characterize and determine the motion of a simple pendulum were obtained considering small and large amplitudes of oscillation. These differential equations were solved through differential equation solution methods, numerical, expansion of functions and integrations. The solutions obtained using the different methods were compared. It was possible to verify, both experimentally and theoretically, that for the oscillatory movement of the simple pendulum, its oscillation period increases and its angular frequency decreases with the increase of the oscillation amplitude. The validity range of the approximation for small ranges of motion was also determined. It was verified that the theoretical and experimental results present a good agreement for angles smaller than 55°. The experimental measurements were made with “a low-cost home-built” equipment.

Dynamics of localized waves in quasi-one-dimensional imbalanced binary Bose-Einstein condensates

In the framework of coupled Gross-Pitaevskii equations, we explore the dynamics of localized waves in quasi-1D imbalanced binary Bose-Einstein condensates where the intra-component interaction is repulsive, while the inter-component one is attractive. The existence regimes of stable self-trapped localized states in the form of symbiotic solitons have been analyzed. Imbalanced mixtures, where the number of atoms in one component exceeds the number of atoms in the other component, are considered in parabolic potential and box-like trap. A variational approach has been developed which allows us to find the stationary state of the system and frequency of small amplitude oscillations near the equilibrium. It is shown that the strength of inter-component coupling can be retrieved from the frequency of the localized state's vibrations. When all the intra-species and inter-species interactions are repulsive, we numerically find a new type of symbiotic solitons resembling dark-bright solitons. The motion of the minority component in the surrounding gas of the majority component with different velocities reveals its superfluid properties.

A comparison of magneto-responsive particles and testing protocols for active rheology control of cementitious materials

Magneto-responsive cementitious materials with magnetic interventions enable on-demand and real-time adjustment of rheology. This research aims to elaborate the early-stage magneto response of cement pastes using different types of Fe3O4 particles and carbonyl iron particles. A series of methods to evaluate the magnetorheological response of cementitious materials were established. The magneto-responsive cement pastes were tested by shear test and small amplitude oscillatory shear test at constant and time-varying magnetic fields. The increase of static yield stress and storage modulus after applying a magnetic field was a time-dependent process, while the decrease of static yield stress and storage modulus was an instant process at the moment of removing magnetic fields. Such a procedure can be reversibly controlled in real time. The cement pastes containing different magneto-responsive particles showed significant difference in the onset of flow and structural build-up. With the intervention of a magnetic field, the static yield stress and storage modulus of mixtures with carbonyl iron particles were able to increase with one order of magnitude. Compared with the particle size distribution and particle morphology, the magnetic parameters of magneto-responsive particles dominated the magnetorheological properties of cementitious materials. Shear tests were found the most effective to evaluate the magneto response of cement pastes with the intervention of a magnetic field.

Linear and nonlinear viscoelasticity of edible o/w emulsions used as saturated fat replacers

A recent strategy for controlling saturated fat intake consists on the design of vegetable oil-based emulsions. The aim was to characterize the linear and nonlinear viscoelastic properties of o/w emulsions formulated with two types of cellulose: MX (methylcellulose, MC) and F4M (hydroxypropyl methylcellulose, HPMC). The emulsions were characterized by steady flow curves and frequency sweeps in SAOS (Small Amplitude Oscillatory Shear) regime. In order to evaluate linear and non-linear response, strain sweeps were performed from 0.01 to 1000% strain amplitude at different frequencies (0.1, 1 and 5 Hz). Fourier Transform rheology and orthogonal stress decomposition were applied and LAOS (Large Amplitude Oscillatory Shear) parameters (G’M, G’L, ηM’, ηL’, S and T) were analysed. The type of cellulose ether significantly affected both flow behaviour and internal structure of the samples. MX emulsion presented greater consistency at rest and higher gel strength in SAOS regime with a lower frequency dependence than F4M emulsion. However, both emulsions presented similar properties at large deformations, showing shear thinning and strain stiffening behaviour. Nonlinear viscoelastic analysis allows to improve the textural characterization of emulsions, providing complementary useful information for establishing the most suitable formulation in experimental conditions closer to real applications and processes.

Effect of a Conical Extension on Aerosol Sedimentation in the Case of Acoustic Small-Amplitude Oscillations in a Tube

Effect of a Conical Extension on Aerosol Sedimentation in the Case of Acoustic Small-Amplitude Oscillations in a Tube

Role of asymmetry and external noise in the development and synchronization of oscillations in the analog Hopfield neural networks with time delay.

The analog Hopfield neural network with time delay and random connections has been studied for its similarities in activity to human electroencephalogram and its usefulness in other areas of the applied sciences such as speech recognition, image analysis, and electrocardiogram modeling. Our goal here is to understand the mechanisms that affect the rhythmic activity in the neural network and how the addition of a Gaussian noise contributes to the network behavior. The neural network studied is composed of ten identical neurons. We investigated the excitatory and inhibitory networks with symmetric (square matrix) and asymmetric (triangular matrix) connections. The differential equations that model the network are solved numerically using the stochastic second-order Runge-Kutta method. Without noise, the neural networks with symmetric and asymmetric matrices possessed different synchronization properties: fully connected networks were synchronized both in time and in amplitude, while asymmetric networks were synchronized in time only. Saturation outputs of the excitatory neural networks do not depend on the time delay, whereas saturation oscillation amplitudes of inhibitory networks increase with the time delay until the steady state. The addition of the Gaussian noise is shown to significantly amplify small-amplitude oscillations, dramatically accelerates the rate of amplitude growth to saturation, and changes synchronization properties of the neural network outputs.

A Study on Oscillatory Micropolar Flow Beyond a Contaminated Micropolar Fluid Sphere

In this paper, the hypothesis of the axisymmetric rectilinear oscillatory flow beyond a micropolar tainted fluid sphere particle in an incompressible non-Newtonian fluid and also the axisymmetric rectilinear oscillatory flow over a viscous tainted fluid sphere particle in an incompressible Newtonian fluid with small amplitude oscillations have been investigated. The velocity field is exhibited in terms of stream functions, and a slip condition is considered on the boundary. The fluid velocities and microrotation components were derived through analytical procedure. The drag force acting on the particle was also computed and verified for special cases. The real drag and imaginary drag values are numerically extracted for varying slip parameter i.e., 2≤s≤30, micro polarity i.e., 8≤e≤32 , and viscosity ratio i.e., 5≤μ≤20 at a fixed parameter values k=0.1,ρ=0.6,ω=0.6,t=0.6. Graphs and tables are used to display the numerical results. It was observed that there was an inverse proportion between slip parameter values, real drag and direct proportion between slip parameter and imaginary drag, for different viscosity ratio and micro polarity values.

Experimental investigation of the period-adding bifurcation route to chaos in plasma.

Since the characteristic timescales of the various transport processes inside the discharge plasma span several orders of magnitude, it can be regarded as a typical fast-slow system. Interestingly, in this work, a special kind of complex oscillatory dynamics composed of a series of large-amplitude relaxation oscillations and small-amplitude near-harmonic oscillations, namely, mixed-mode oscillations (MMOs), was observed. By using the ballast resistance as the control parameter, a period-adding bifurcation sequence of the MMOs, i.e., from L^{s} to L^{s+1}, was obtained in a low-pressure DC glow discharge system. Meanwhile, a series of intermittently chaotic regions caused by inverse saddle-node bifurcation was embedded between the two adjacent periodic windows. The formation mechanism of MMOs was analyzed, and the results indicated that the competition between electron production and electron loss plays an important role. Meanwhile, the nonlinear time series analysis technique was used to study the dynamic behavior quantitatively. The attractor in the reconstructed phase space indicated the existence of the homoclinic orbits of type Γ^{-}. In addition, by calculating the largest Lyapunov exponent (LLE), the chaotic nature of these states was confirmed and quantitatively characterized. With the decrease in the ballast resistance, the return map of the chaotic state gradually changed from the nearly one-dimensional single-peak structure to the multibranch structure, which indicates that the dissipation of the system decreased. By further calculating the correlation dimension, it was shown that the complexity of the strange attractors increased for higher-order chaotic states.

External factors affecting the linear and nonlinear rheological behavior of oleogel-based emulsions

This study reported oleogel-based emulsions (OGEs, W/O) stabilized by carnauba wax. The effects of different external factors (heating temperature, crystallization temperature, and shear application during crystallization) on the microstructure and linear/nonlinear rheological properties of OGEs were investigated. Microstructural observation suggested that the OGEs had a uniform droplet distribution, and the carnauba wax crystals trapped oil in the continuous phase. The gelatinized oil phase allowed the OGEs to have a solid appearance and typical yielding behavior. The small amplitude oscillation shear analysis showed that lower heating temperature, higher crystallization temperature, and suitable shear application resulted in a stronger, more stable, and tighter packed network structure and better resistance to deformation of the OGEs. For nonlinear behavior, the elastic dominant behavior of OGEs transformed into viscous dominant behavior at large strain amplitudes, accompanied by more energy dissipation, strain stiffening, and a transition from shear thickening to shear thinning.

Thixo-elastoviscoplastic modeling of human blood

We propose an enhanced model for the rheological characterization of human blood that accounts for thixotropy, viscoelasticity, and yield-stress. Blood plasma is assumed to act as a Newtonian solvent. We introduce a scalar variable, λ, to macroscopically describe the structure of blood. The temporal evolution of λ is governed by an equation that accounts for aggregation of red blood cells and breakdown of rouleaux structures. We introduce a Gaussian function that qualitatively describes experimental findings on rouleaux restructuring and the expression that was proposed by Stephanou and Georgiou for the breakdown term. The constitutive equation for stresses is based on the elastoviscoplastic formalism by Saramito. However, the max term of the viscoplastic deformation rate has been replaced by a continuous function of λ to account for smooth solid-fluid transition, following the experimental evidence. The continuous yielding description provides improved rheological predictions, especially in small amplitude oscillatory shear. The model predicts finite viscous dissipation at small amplitude oscillation, as we would expect from a gel material-like human blood. Overall, it has nine adjustable parameters that are fitted simultaneously to experimental data by nonlinear regression. The model can accurately predict numerous flow conditions: steady shear, step shear, hysteresis loops, and oscillatory shear. We compare this model (TEVP 9) to our previous formulation for human blood (TEVP 11), and we show that the predictions of the new model are more accurate, despite using fewer parameters. We provide additional predictions for uniaxial elongation, which include finite normal stress difference, extensional hardening at large values of the extensional rate, and extensional thinning at extremely large extensional rates.

Investigation of the wake flow and the oscillation process of two free-to-rotate tandem cylinders due to a flow disturbance

This paper presents an exploratory analysis of the oscillation process of a set of two circular cylinders (D = 25 mm) mounted with a fixed pitch-to-diameter ratio P/D = 1.26 and attached to a free-to-rotate circular table submitted to a turbulent crossflow in a wind tunnel. Measurements were performed with hot wire anemometers placed in the wake of the cylinders synchronized with a high-speed digital camera. Flow visualizations with static cylinders in a water channel were performed to investigate the wake formation around the cylinders. The analysis of the results was made through Fourier and wavelet transforms. The main objective is to address the observed phenomenon with its causing physical mechanism. Wind tunnel results showed that, depending on the imposed mean flow velocity, the set starts oscillating with a low steady amplitude. When the flow is disturbed, an increase in the oscillation amplitude is observed, remaining in this steady regime even after removing the disturbance. Although the interaction between the flow and cylinder set generates two stable states, the properties of the oscillation phenomena (frequency and amplitude) remained the same, pointing out an intrinsic property of the dynamical system. The vortex shedding is identified to be the primary mechanism responsible for initiating the small amplitude oscillation, while the flow passing through the gap between the cylinders is the cause of the high amplitude oscillation. The flow visualization corroborated the wake analysis described in the wind tunnel experiments. No evidence of coherence between the vortex shedding from the first cylinder and the oscillation process was identified. Considering the results in the present work, the configuration analyzed may work as a vortex-shedding suppressor.

Effect of a Conical Extension on Aerosol Sedimentation in the Case of Acoustic Small-Amplitude Oscillations in a Tube

The effect of acoustic low-intensity oscillations in a homogeneous tube and in a tube with a conical extension is experimentally investigated for the same resonator volumes. The resonator shape is shown to have an effect on the oscillation spectrum and intensity and the pressure wave shape at constant values of the resonance frequency and the piston displacement amplitude. An increase in the resonator Q-factor is observable, when the resonator has a conical extension. An accelerated aerosol sedimentation in tubes is revealed in the case of acoustic oscillation with the resonance frequency. In the presence of a conical extension the aerosol drop concentration is reduced by a factor of 1.2 more rapidly than in the case of a uniform tube and three times more rapidly as compared with natural sedimentation. The results obtained can be used for increasing the efficiency of acoustic methods of gas purification from the disperse phase

Experimental study on the slip evolution of planar fractures subjected to cyclic normal stress

The frictional rupture mechanisms of rock discontinuities considering the dynamic load disturbance still remain unclear. This paper investigates the transitional behaviors of slip events happened on a planar granite fracture under cyclic normal stress with different oscillation amplitudes. The experimental results show that the activations of fast slips always correlate with unloading of normal stress. Besides, the intensive normal stress oscillation can weaken the shear strength which is recoverable when the normal stress return to constant. The rupture patterns are quantified by stress drop, slip length and slip velocity. With the effect of small oscillation amplitudes, the slip events show chaotic shapes, compared to the regular and predictable style under constant normal stress. When the amplitude is large enough, the big and small slip events emerge alternately, showing a compound slip style. Large amplitude of the cyclic normal stress also widens the interval differences of the slip events. This work provides experimental supports for a convincible link between the dynamic stress disturbance and the slip behavior of rock fractures.

Inertial wave attractors in librating cuboids

Perturbed rapidly rotating flows are dominated by inertial oscillations, with restricted group velocity directions, due to the restorative nature of the Coriolis force. In containers with some boundaries oblique to the rotation axis, the inertial oscillations may focus upon reflections, whereby their energy increases whilst their wavelength decreases and their trajectories focus onto attractor regions. In a linear inviscid setting, these attractors are Delta-like distributions. The linear inviscid setting is obtained formally by setting both Ekman number ${E}$ (ratio of inertial to viscous time scales) and Rossby number ${Ro}$ (non-dimensional amplitude of the forcing that drives the inertial oscillations) to zero. These settings raise fundamental questions, in particular concerning the nature of energy dissipation in the vanishing Ekman number regime. Here, we consider a simple container geometry, a rectangular cuboid, in which the direction of the rotation axis is oblique to four of its walls, subject to librational forcing (small-amplitude harmonic oscillations of the rotation rate). This geometry allows for accurate and efficient direct numerical simulations of the three-dimensional incompressible Navier–Stokes equations with no-slip boundary conditions using a spectral-Galerkin spatial discretisation along with a third-order temporal discretisation. Solutions with Ekman and Rossby numbers as small as ${E}={Ro}=10^{-8}$ reveal many details of how the inertial oscillations focus, at the libration frequency considered, onto attractors, and how the focusing leads to increased localised nonlinear and dissipative processes as ${E}$ and ${Ro}$ are reduced. Even for extremely small forcing amplitudes, nonlinear effects have important dynamic consequences for the attractors.

Soft Actor–Critic-Based Computation Offloading in Multiuser MEC-Enabled IoT—A Lifetime Maximization Perspective

This paper studies the network lifetime optimization problem in a multi-user mobile edge computing (MEC)-enabled Internet of things (IoT) system comprising an access point (AP), a MEC server, and a set of K mobile devices (MDs) with limited battery capacity. Considering the residual battery energy at the MDs, stochastic task arrivals, and time-varying wireless fading channels, a soft actor-critic (SAC)-based deep reinforcement learning (DRL) lifetime maximization, called DeepLM, is proposed to jointly optimize the task splitting ratio, the local CPU-cycle frequencies at the MDs, the bandwidth allocation, and the CPU-cycle frequency allocation at the MEC server subject to the task queuing backlogs constraint, the bandwidth constraint, and maximum CPU-cycle frequency constraints at the MDs and the MEC server. Our results reveal that DeepLM enjoys a fast convergence rate and a small oscillation amplitude. We also compare the performance of DeepLM with three benchmark offloading schemes, namely, fully edge computing (FEC), fully local computing (FLC), and random computation offloading (RCO). DeepLM increases the network lifetime by 496% and 229% compared to the FLC and RCO schemes. Interestingly, it achieves such a colossal lifetime improvement when its non-backlog probability is 0.99, while that of FEC, FLC, and RCO is 0.69, 0.53, and 0.25, respectively, showing a significant performance gain of 30%, 46%, and 74%.

Asymptotic theory for damped dynamics of gas-filled bubbles

The small-amplitude damped oscillations of a gas-filled spherical bubble surrounded by a viscous liquid is studied analytically using a symbolically computable version of the two-time scale expansion (“two-timing”) technique. The developed uniformly valid asymptotic expansions have closed analytical forms under arbitrary specifications for the ideal gas polytropic exponent and the damping coefficient. Heretofore, a comparable level of analytical tractability has been afforded only by a linearized mass-spring-damper model; the corresponding regular perturbation expansion is, however, nonuniform for weak damping. Predictions from the two-timing and the mass-spring-damper models are compared with the full-scale numerical solution of the Rayleigh-Plesset equation. The two-scale analysis resolves several characteristics of the numerical data, such as the disparately large/small acceleration of the bubble wall near the most compressed/expanded states of the bubble, which the linearized model does not. The predictions of the two-scale model are shown to perform favorably against experimental data from the literature. New asymptotic predictions, which are very accurate for overdamped settings, are also developed by extending the mass-spring-damper model.

Early structural build‐up behavior, setting mechanism, and nanostructure of alkali‐activated GGBFS mixtures

AbstractThe initial changes in the microstructure of alkali‐activated slag cement (AAS) characterize the rheological behavior, initial structuration, and setting times of the mixture. In this study, the relationships among the rheological behavior, solidification process, and nanostructure changes of sodium hydroxide‐activated slag (NH–AAS) and sodium silicate‐activated slag (SS–AAS) pastes over time are investigated by small amplitude oscillation shear test, isothermal calorimetry, scanning electron microscopy analyses, and 1H–29Si cross‐polarization magic‐angle spinning nuclear magnetic resonance spectroscopy (CP MAS NMR) and 29Si MAS NMR spectroscopy. Test results showed that the NH–AAS reaches its initial setting time following a continuously proceeding structuration process, whereas the SS–AAS reaches its initial setting with an abrupt increase in the structuration process. At their initial setting times, the NH–AAS and SS–AAS mixtures release similar heat and reach a similar reaction degree. The SS–AAS mixture had more N–A–S–H formation than C–A–S–H at the initial setting time. On the other hand, the amount of C–A–S–H was similar to N–A–S–H in the NH–AAS mixture. The gradual N–A–S–H gel degradation to form C–A–S–H was observed during the acceleration period for the SS–AAS mixture.

Route to mixed-mode oscillations via step-shaped sharp transition of equilibria in a nonlinear gyroscope oscillator

Sharp transitions in relation to the variation of system parameters are frequently encountered in many multiple-timescale systems, and they have been found to be an important factor related to the generation of mixed-mode oscillations (MMOs). The present paper aims to report a novel type of sharp transition, referred to as step-shaped sharp transition, in a nonlinear gyroscope oscillator with multiple-frequency excitations, and investigate the resulting MMOs. We show that step-shaped sharp quantitative changes in relation to the variation of system parameters can be observed in the equilibrium branch, which yields the step-shaped sharp transition. In particular, with the increase of the frequency ratio between the parametric and external excitations, more step-shaped sharp transitions appear in the equilibrium branches, which evolve into the ones displaying different structures. Based on this, the rectangular-pulse-shaped explosion of equilibria is created. Furthermore, these sharp transitions can form active areas for the MMOs, leading to the alternations between large-amplitude and small-amplitude oscillations, and finally the route to MMOs is created. Our findings have significant implications for understanding the fast-slow dynamics of the nonlinear gyroscope oscillator, contributing to the exploration of new routes to MMOs. Thus, the results could provide theoretical support for the potential application of gyroscopes.