Small Oscillations Research Articles

Transient rheology and morphology in sheared nanolayer polymer films

Abstract The rheology of coextruded layered films of polystyrene/poly(methyl methacrylate) (PS/PMMA) has been studied with small and large amplitude oscillations at a temperature above their glass transition. While the complex viscosity remains constant over the experimental time window for the micron-sized layered films, a decrease has been observed for the nanolayered films. The rheological behavior has then been correlated to the morphological evolution of the multilayer films while the nanolayers dewet. Layer breakup followed by retraction and coalescence leading to a lamellar-like blend morphology followed by a nodular-like morphology has been evidenced in the nanolayer films, for all compositions and conditions tested. The analysis of the microscopic images of the Lfilm cross-sections also provided the droplet size distribution. The nodular morphology is achieved more rapidly when the initial layers are the thinnest at low strains, while at high strains the formation of these droplets is prevented. Graphical abstract

Bimodal Photothermal-driven Self-sustained Oscillator Based on MXene Structure

Soft robots capable of autonomous, continuous, fast, and adjustable motion speeds under constant external stimuli have great potential in environmental, industrial, military, and medical fields. Aiming at the difficulties of existing self-oscillators, including small oscillation range, difficulty of achieving non-reciprocal motion, and the slow forward speed of the resulting self-sustained soft robots. In this paper, a sunlight-driven self-oscillator based on MXene is prepared. By employing a bimorph structure and thermal regulation process, the self-oscillator exhibits two distinct oscillation modes: 'elastic' and 'plastic' deformation. These modes can be modulated within the same film by varying the light power. A broader amplitude range (3.6-302.3°, 3.3 times that of the existing studies) is achieved by attaching a load to the film's end to enhance the inertial force of movement. Non-reciprocal motion in both modes and stable oscillations in sunlight are achieved. Finally, a light-driven sailboat model is developed. The sailboat can achieve autonomous light-forward motion with a speed of up to 12.8 body length per minute (2.1 times that of existing studies), with its propulsion mechanism further explained through numerical simulation results. This research provides new strategies for constructing fast and large-amplitude self-oscillators and demonstrates the potential for applications in speed-adjustable autonomous forward devices.

An active queue management method for multiple bottleneck networks based on distributed average tracking

The active queue management (AQM) is a key technology for the information infrastructure and the Internet. The AQM for multiple bottleneck networks is especially challenging than that for single-bottleneck networks because the stability analysis of multiple bottleneck networks is more complex. In this paper, the active queue management problem for multiple bottleneck networks is considered. A novel random early detection algorithm is designed based on distributed average tracking technology, which is used to estimate the global queue length and improve the network's performance. Sufficient conditions for global asymptotic stability of the closed-loop active queue management system are presented, and some simulation results with NS-2 are given. Compared with the RED algorithm, simulation results show that the presented algorithm has smaller oscillations at routers, which highlights its effectiveness.

Layer interface characteristics and adhesion of 3D printed cement-based materials exposed to post-printing temperature disturbance

The layer interface, which is vital for the performance and longevity of 3D printed cement-based materials (3DPCM), is very sensitive to the environmental conditions because of the lack of formwork. Nevertheless, the current limited understanding of how temperature affects the layer interface has restricted the application of 3D printing in different construction scenarios. Here, we revealed the effects of temperature on the multi-scale phase distribution features of the layer interface through mercury intrusion porosimetry, X-ray computed tomography, nanoindentation and scanning electron microscopy with energy dispersive spectroscopy techniques. Additionally, the interlayer bond strength of 3DPCM was evaluated via the splitting tensile test. Small amplitude oscillation, surface roughness and isothermal calorimetry measurements were employed for an in-depth analysis of the mechanisms. Results indicate that an increase in temperature post-printing reduces the discrepancies in aggregate volume fraction between the layer interface and bulk matrix due to the increasing structuration rate and the amount of cement paste at the interface due to the reduced settlement of aggregates. The porosity difference between the layer interface and bulk matrix decreased with increasing temperature due to the pore size refinement by faster filling with hydrates. In addition, a more concentrated distribution of atomic ratios and elastic modulus of hydrates were observed at the layer interface of 3DPCM hardened at higher temperatures. Increased curing temperature improves the interlayer bond strength of 3DPCM owing to the enhanced aggregate interlocking, reduced porosity and improved high-density CSH content.

A Simple Model for the Emergence of Relaxation‐Oscillator Convection

AbstractEarth's tropics are characterized by quasi‐steady precipitation with small oscillations about a mean value, which has led to the hypothesis that moist convection is in a state of quasi‐equilibrium (QE). In contrast, very warm simulations of Earth's tropical convection are characterized by relaxation‐oscillator‐like (RO) precipitation, with short‐lived convective storms and torrential rainfall forming and dissipating at regular intervals with little to no precipitation in between. We develop a model of moist convection by combining a zero‐buoyancy model of bulk‐plume convection with a QE heat engine model, and we use it to show that QE is violated at high surface temperatures. We hypothesize that the RO state emerges when the equilibrium condition of the convective heat engine is violated, that is, when the heating rate times a thermodynamic efficiency exceeds the rate at which work can be performed. We test our hypothesis against one‐ and three‐dimensional numerical simulations and find that it accurately predicts the onset of RO convection. The proposed mechanism for RO emergence from QE breakdown is agnostic of the condensable, and can be applied to any planetary atmosphere undergoing moist convection. To date, RO states have only been demonstrated in three‐dimensional convection‐resolving simulations, which has made it seem that the physics of the RO state requires simulations that can explicitly resolve the three‐dimensional interaction of cloudy plumes and their environment. We demonstrate that RO states also exist in single‐column simulations of radiative‐convective equilibrium with parameterized convection, albeit in a different surface temperature range and with much longer storm‐free intervals.

Projective Synchronization for Uncertain Fractional Reaction-Diffusion Systems via Adaptive Sliding Mode Control Based on Finite-Time Scheme.

In this article, the projective synchronization of uncertain fractional-order (FO) reaction-diffusion systems is studied for the first time via the fractional adaptive sliding mode control (SMC) method. A FO integral type switching function is designed, and corresponding adaptive SMC laws are derived which ensure the FO sliding mode surface (SMS) is reachable after a finite time interval. The improved version of these control laws which have smaller oscillation and better control performance are also derived. A new lemma for proving the finite-time reachability of the FO SMS is developed. At last, numerical examples are provided to verify the effectiveness of our theories.

Research on sedimentation characteristics of squirmer in a power-law fluid.

Sedimentation characteristics of a squirmer in a power-law fluid within a vertical channel are studied numerically using the two-dimensional lattice Boltzmann method. The effects of swimming type (- 5 ≤ β ≤ 5), self-propelling strength (0.5 ≤ α ≤ 1.1), power-law indexes (0.5 ≤ n ≤ 1.5), and the density ratio of the squirmer to the fluid (γ = 1.01, 1.5 and 2.3) on the sedimentation of the squirmer are analyzed. Four settlement patterns are identified: steady falling in the center, downward along the wall, oscillating with large amplitude and oscillating around the centerline. The squirmer in the channel exhibits more fluctuations in shear-thinning (n < 1) and Newtonian (n = 1) fluids compared to shear-thickening fluids (n > 1). Additionally, a puller (β > 0) settles faster than a pusher (β < 0) in shear-thinning and Newtonian fluids. Puller generates flow towards their head and away from their tail, exhibiting small amplitude oscillations. Pushers exhibit higher amplitude oscillations throughout the channel, creating flow towards their tail and away from their head. At lower γ, the fluctuation of the squirmer is less pronounced compared to higher γ.

Coarse nodal count and topological persistence

Courant’s theorem implies that the number of nodal domains of a Laplace eigenfunction is controlled by the corresponding eigenvalue. Over the years, there have been various attempts to find an appropriate generalization of this statement in different directions. We propose a new take on this problem using ideas from topological data analysis. We show that if one counts the nodal domains in a coarse way, basically ignoring small oscillations, Courant’s theorem extends to linear combinations of eigenfunctions, to their products, to other operators, and to higher topological invariants of nodal sets. We also obtain a coarse version of the Bézout estimate for common zeros of linear combinations of eigenfunctions. We show that our results are essentially sharp and that the coarse count is necessary, since these extensions fail in general for the standard count. Our approach combines multiscale polynomial approximation in Sobolev spaces with new results in the theory of persistence modules and barcodes.

Short-Term Influence of Water Ingress on Wear in Pitch Bearings of Wind Turbines

The pitch bearings of wind turbines are slowly oscillating, grease-lubricated slewing bearings. They facilitate the pitching movements of blades which control aerodynamic loads. These bearings have diameters of several meters, their blade-side sealings can face the environment, bending moment loads can cause radial deformation of the bearing rings, and their highly variable operating temperatures can facilitate condensation of water inside them. All of this makes water ingress into the lubricant possible. There is limited public knowledge with regards to the maximum water content for safe operation in this application. This work presents the results of a series of scaled wind turbine time series tests with both ‘dry’ (no water contamination) and ‘wet’ (10 mass % demineralized water added) greases. A set of four commercially available greases were tested. The time series were scaled from wind turbine operation and represented a 13.7 h worst-case scenario of operation with small oscillation amplitudes and no longer lubrication runs in between. Three of the greases showed reduced friction and no or limited raceway damage in the wet condition, whereas one showed increased friction and raceway damages.

The role of the dynamic pressure in the behavior of an oscillating gas bubble

The paper contains a preliminary study on the role that dynamic pressure might play in the dynamics of a gas bubble oscillating in a liquid. To this aim, we introduce a mathematical model, proposed under the homobaricity hypothesis and deduced from the 14-moment theory of rational extended thermodynamics through significant simplifications, that makes the equations easily integrable over long time intervals. In the presence of a gas with high bulk viscosity, relevant effects can be observed in different physical conditions: isothermal or adiabatic regimes, small amplitude oscillations, non-linear oscillations, resonances, and sonoluminescence. To make the study more realistic, we always refer to carbon dioxide gas, which on the one hand could present high values of bulk viscosity and on the other hand is known for its peculiar behaviors in the framework of cavitation and gas bubbles.

Schauder and Cordes–Nirenberg estimates for nonlocal elliptic equations with singular kernels

AbstractWe study integro‐differential elliptic equations (of order ) with variable coefficients, and prove the natural and most general Schauder‐type estimates that can hold in this setting, both in divergence and non–divergence form. Furthermore, we also establish Hölder estimates for general elliptic equations with no regularity assumption on , including for the first‐time operators like , provided that the coefficients have “small oscillation.”

Microwave field mapping for EPR-on-a-chip experiments.

Electron paramagnetic resonance-on-a-chip (EPRoC) devices use small voltage-controlled oscillators (VCOs) for both the excitation and detection of the EPR signal, allowing access to unique sample environments by lifting the restrictions imposed by resonator-based EPR techniques. EPRoC devices have been successfully used at multiple frequencies (7 to 360 gigahertz) and have demonstrated their utility in producing high-resolution spectra in a variety of spin centers. To enable quantitative measurements using EPRoC devices, the spatial distribution of the B1 field produced by the VCOs must be known. As an example, the field distribution of a 12-coil VCO array EPRoC operating at 14 gigahertz is described in this study. The frequency modulation-recorded EPR spectra of a "point"-like and a thin-film sample were investigated while varying the position of both samples in three directions. The results were compared to COMSOL simulations of the B1-field intensity. The EPRoC array sensitive volume was determined to be ~19 nanoliters. Implications for possible EPR applications are discussed.

Complex dynamics in nonlinear small time-delayed optoelectronic oscillator and application in fast reservoir computing and pulse generation

We investigated a time-delayed optoelectronic oscillator (OEO) that displays a wide range of complex dynamic behavior under small time delay. The phase-space trajectory distributions in different dynamic regimes were compared which brings a new perspective on the underlying mechanism of the transition process. It was found that bifurcation is always possible no matter how small the time delay is even if the universal adiabatic approximation model is invalid. Hereby we proposed a versatile simple oscillator which has a potential capacity as memory carrier and high-dimensional state spatial mapping ability that brings 1000 times computing-efficiency improvements of reservoir computing over the large time delay one. Furthermore, we demonstrated a new approach for a tunable optoelectronic pulse generator (repetition rate at 0.2 MHz and 0.25 GHz) which depends critically on time-delayed input electrical pulse. The proposed oscillator is also a promising system for the applications of fast chaos-based communication.

Mixed convective heat transfer in a square cavity filled with power‐law fluids under active flow modulation

AbstractThe current study presents a computational investigation of mixed convective heat transfer in a square enclosure containing power‐law fluid. An active flow modulator is employed in the form of a flat plate with negligible thickness, and the mixed convection is achieved through clockwise rotation of the plate. The rotation of the plate is modeled by incorporating a moving mesh technique. The solution is then obtained by applying the Finite Element Technique under the arbitrary Lagrangian–Eulerian framework. Numerical validation is performed with contemporary research studies consisting of rotating plates to justify the accuracy of the present study. The study is conducted at constant Prandtl number Pr = 1.0 and Reynolds number Re = 500 while varying the power‐law index (0.6 ≤ n ≤ 1.4) and the Richardson number (0.1 ≤ Ri ≤ 10.0). The results have been presented in terms of the flow and thermal fields, spatially averaged Nusselt number, spatially averaged power consumption by the plate, and the velocity and temperature profile in the enclosure. The numerical findings indicate that a higher Richardson number encourages heat transfer. For the shear‐thinning fluid, a 37% thermal augmentation is observed in comparison to the Newtonian fluid at Ri = 10. However, in the case of shear‐thickening fluid, thermal performance was reduced by 21.13%. Small thermal oscillations are observed in naturally dominated mixed convection for shear‐thinning fluids, but none are observed for shear‐thickening or Newtonian fluids. In addition, the findings demonstrate that the flow modulator has a positive impact on heat transfer for the shear‐thickening fluids (n &gt; 1) and an adverse effect for the shear‐thinning fluids (n &lt; 1). Furthermore, the power consumption decreases as Ri increases, and it becomes negative beyond Ri = 1.0 due to the increase in natural convection strength.

Investigating viscoelastic properties and structural stability mechanisms of oil bodies emulsion gels: Role of non-intrinsic protein

This research aims to investigate the mechanism of the effect of intrinsic and non-intrinsic protein content on the stability of oil bodies (OBs) emulsion gels. We employed small amplitude oscillation shear (SAOS) and large amplitude oscillation shear (LAOS) to measure the linear and nonlinear rheological properties of the OBs emulsion gels. The SAOS test indicated that an increase in non-intrinsic protein content weakened the interaction between OBs, decreasing their storage modulus (G'). The LAOS test demonstrated that the increase in non-intrinsic protein content affected the structural recombination and destruction behavior of OBs emulsion gels under large strains. Overall, the content of non-intrinsic protein during the extraction process is a crucial factor affecting the stability of OBs emulsion gels. These findings provide insights into the potential strategies for improving oil extraction efficiency and offer a foundation for further investigation into the functional properties of OBs.

On the stability of prestressed beams undergoing nonlinear flexural free oscillations

We study the nonlinear free undamped motions of a hinged-hinged beam exhibiting geometric stretching-induced nonlinearity and arbitrary initial conditions. We treat the governing integral-partial-differential equation of motion as an infinite dimensional Hamiltonian system. We analytically obtain a quantitative Birkhoff Normal Form via a nonlinear coordinate transformation that yields the reduced (modulation) equations describing the free oscillations to within a certain nonlinear order with an estimate of the reminder. The obtained solutions provide a very precise description of small amplitude oscillations over large time scales. The analytical optimization of the involved estimates yields time stability results obtained for plausible values of the physical quantities and of the perturbation parameter. The role played by internal resonances in determining the time stability of the solution is highlighted and discussed. We show that initial conditions with a finite number of eigenfunctions yield bounded solutions living on invariant subspaces of the involved modes at all times. Conversely, initial conditions comprising the full (infinite) spectrum of eigenfunctions provide solutions for which time stability for all times cannot be stated.

Numerical investigation of the interaction between an interface and a decaying Lamb–Oseen vortex

The present study investigates the dynamics of the interface in the presence of a decaying Lamb–Oseen vortex, and four distinct wave patterns are observed: non-breaking waves with small periodic oscillations, plunging breakers, depression breakers, and gravity–capillary waves. The deformation of the interface is induced by a two-dimensional Lamb–Oseen vortex, and the study examines the influence of vortex strength and surface tension on the resulting flow. The wave dynamics are characterized as a function of the Reynolds and Weber numbers, and a phase diagram is presented in terms of (Re, We) to distinguish the different wave patterns. To ensure accurate reconstruction of the interface, the numerical methods used in this study feature a mass and momentum consistent advection method, high-order interpolation schemes, and a block-structured adaptive mesh refinement strategy. The study presents the characteristics of the air cavity entrained at the moment of wave impact for each wave pattern. Furthermore, the results provide insight into the nature of bubble entrainment within a vortex and reveals the bubble entrainment process via a breakup cascade. Meanwhile, it is also shown that the entrainment of bubble results in significant vortex distortion. Overall, this research contributes to enhance our understanding of wave dynamics and the intricate interaction between vortices and interfaces.

A Method for Detecting Small Oscillations Based on Homodyne Demodulation with a Tandem Low-Coherence Interferometer

A Method for Detecting Small Oscillations Based on Homodyne Demodulation with a Tandem Low-Coherence Interferometer

Bubble thermodynamics in cryogenic fluids under ultrasonic field excitation: Theoretical analysis and numerical calculation

In the study of cavitation in room-temperature fluids, the heat transfer between gas and liquid in bubble oscillation is usually assumed to be an adiabatic process for simplification. However, this heat transfer and thermodynamic mechanism is not yet understood in cryogenic fluids, especially under small amplitude oscillation conditions excited by ultrasonic field. This article studies bubble thermodynamic model under an external ultrasonic field based on the heat transfer equation for cryogenic fluids. The temperature changes inside bubbles are calculated, and the heat transfer mechanism is briefly analyzed. The results indicate that the heat transfer mechanism of bubbles depends on the relationship between ultrasonic frequency and bubble resonance frequency. By analyzing two special cases of dual-bubble and high-pressure environment, it is believed that heat transfer can be approximated as an adiabatic process under high-pressure conditions with ultrasonic frequency far from the resonance frequency. This conclusion can provide a theoretical basis for subsequent accurate calculation of heat-transfer polytropic coefficient, or void faction measurement in cryogenic two-phase flow.

Point-set games and functions with the hereditary small oscillation property

Given a metric space X, we consider certain families of functions f:X→R having the hereditary oscillation property HSOP and the hereditary continuous restriction property HCRP on large sets. When X is Polish, among them there are families of Baire measurable functions, μ‾-measurable functions (for a finite nonatomic Borel measure μ on X) and Marczewski measurable functions. We obtain their characterizations using a class of equivalent point-set games. In similar aspects, we study cliquish functions, SZ-functions and countably continuous functions.