Small Oscillations Research Articles

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.

Drag on Cylinders Moving in Superfluid 3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3$$\\end{document}He-B as the Dimension Spans the Coherence Length

Vibrating probes when immersed in a fluid can provide powerful tools for characterising the surrounding medium. In superfluid 3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3$$\\end{document}He-B, a condensate of Cooper pairs, the dissipation arising from the scattering of quasiparticle excitations from a mechanical oscillator provides the basis of extremely sensitive thermometry and bolometry at sub-millikelvin temperatures. The unique properties of the Andreev reflection process in this condensate also assist by providing a significantly enhanced dissipation. While existing models for such damping on an oscillating cylinder have been verified experimentally, they are valid only for flows with scales much greater than the coherence length of 3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3$$\\end{document}He, which is of the order of a hundred nanometres. With our increasing proficiency in fabricating nanosized oscillators, which can be readily used in this superfluid, there is a pressing need for the development of new models that account for the modification of the flow around these smaller oscillators. Here we report preliminary results on measurements of the damping in superfluid 3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3$$\\end{document}He-B of a range of cylindrical nanosized oscillators with radii comparable to the coherence length and outline a model for calculating the associated drag.

Dynamical coupling of Keplerian orbits in a hierarchical four-body system: from the Galactic Centre to compact planetary systems

ABSTRACT This study focuses on the long-term evolution of two bodies in nearby initially coplanar orbits around a central dominant body perturbed by a fourth body on a distant Keplerian orbit. Our previous works that considered this setup enforced circular orbits by adding a spherical potential of extended mass, which dampens Kozai–Lidov oscillations; it led to two qualitatively different modes of the evolution of the nearby orbits. In one scenario, their mutual interaction exceeds the effect of differential precession caused by a perturbing body. This results in a long-term coherent evolution, with nearly coplanar orbits experiencing only small oscillations of inclination. We extend the previous work by (i) considering post-Newtonian corrections to the gravity of the central body, either instead of or in addition to the potential of extended mass, (ii) relaxing the requirement of strictly circular orbits, and (iii) removing the strict requirement of complete Kozai–Lidov damping. Thus, we identify the modes of interorbital interaction described for the zero eccentricity case in the more general situation, which allows for its applicability to a much broader range of astrophysical systems than considered initially. In this work, we scale the systems to the orbits of S-stars; we consider the clockwise disc to represent the perturbing body, with post-Newtonian corrections to the gravity of Sagittarius A* playing the role of damping potential. Considering post-Newtonian corrections, even stellar-mass central bodies in compact planetary systems can allow for the coupled evolution of Keplerian orbits.

Assembly procedure and tooling development plan for in-situ winding of ITER in-vessel vertical stability coils

The ITER in-vessel Vertical Stabilization (VS) coils, composed by the upper and lower VS coils, are designed to provide fast vertical stabilization of the plasma through a fast-current noise profile to compensate small plasma oscillations and to recover vertical displacement events.The VS coils are made by 4 continuous turns of Mineral Insulated Conductor (MIC) joined by Inconel ® 625 welded brackets, installed on rails on the inner wall of ITER Vacuum Vessel (VV). Thus, the coil turns winding/forming and the entire coils assembly have to be performed inside ITER VV, forcing the assembly procedure and tooling design to cope with the very limited space and strict constraints of ITER VV environment. The proposed procedure foresees that MIC conductor is un-spooled in the Neutral Beam (NB) port area and inserted into the ITER VV through a NB equatorial port, then a set of tooling is installed on a reinforced staging platform to wind, form and seal the conductor turns and finally to weld brackets under pre-compression. For this purpose, the tooling design including the reinforcement staging has been developed to meet the required tooling function, configuration optimization, assembly procedure and environmental constraints. The dedicated tools to be used for the assembly procedure of the VS coils are categorized into ex-vessel tools for unspooling and cleaning, in-vessel tools for winding and bump forming, bracket assembly tools for pre-compression and welding, termination and sealing tools, ancillary lifting tools and reinforcement staging platforms. This paper provides the overall assembly procedure and tooling development for the in-situ winding of VS coils.

Topological ordering during flexible to rigid transitions in disordered networks

This contribution focuses on the structural origin of flexible to rigid transitions and the possible underlying intermediate phase which have been reported to occur in a variety of network glasses such as chalcogenides or modified oxides. Here, using molecular dynamics simulations of densified glass-forming liquids, 2SiO 2 -Na 2 O, which are known to display a numerical reversibility window as a signature of an intermediate phase, we focus on structural functions emphasizing topological ordering using the Bhatia–Thornton formalism. Results not only reveal that densified silicates display topological ordering on lengthscales of about 25 Å, but also display obvious threshold behaviors close to the isostatic condition when the network undergoes a flexible to rigid transition. The mechanical constraint count of the atomic network structure reveals that a typical lengthscale characterizing the decay of topological correlations emerges for stressed rigid systems at ≃3.5 Å, whereas small wavevector oscillations are found to be minimal when the isostatic condition is merely satisfied. An additional analysis building on diffusivity and liquid entropy suggests that the locus of flexible to rigid transitions has also connections with water-like anomalies of densified tetrahedral liquids.

Numerical integrator for highly oscillatory differential equations based on the Neumann series

AbstractWe propose a third-order numerical integrator based on the Neumann series and the Filon quadrature, designed mainly for highly oscillatory partial differential equations. The method can be applied to equations that exhibit small or moderate oscillations; however, counter-intuitively, large oscillations increase the accuracy of the scheme. With the proposed approach, the convergence order of the method can be easily improved. Error analysis of the method is also performed. We consider linear evolution equations involving first- and second-time derivatives that feature elliptic differential operators, such as the heat equation or the wave equation. Numerical experiments consider the case in which the space dimension is greater than one and confirm the theoretical study.

Study on the mechanism of interaction between cations and the surface of nano-SiO2 particle in the salt solution by using molecular dynamics simulation

Nano-SiO2 solution has great potential for application in the field of oil and gas exploration and development. However, its application is restricted due to the aggregation of nano-SiO2 in stratum water. This paper studies the process of interaction between nano-SiO2 particles and salt solutions by using the molecular dynamics simulation experiments, including the characteristics of transportation and diffusion of cations around the nano SiO2, the effect of cations on the recombination and destruction of hydrogen bonds, the interaction energy between cations and nano SiO2. The main results are as follows. During the transportation and diffusion of cations in the solution, the hydrogen bonds of water molecules are broken, so that the hydrogen bonds can be rearranged, and a stable solvated layer can be formed. In the solvated layer, the repulsive force of solvation can prevent the charge exchange between cation and the charged surface of nano SiO2 particle. Compared with the monovalent salt solution, more divalent cations can break through the solvation layer to generate the charge exchange on the surface of nano-SiO2 particle. More divalent cations can conduct small amplitude oscillation movement near the surface of nano-SiO2 particle due to the strong electrostatic effect. When the concentration of salt solution is increased (3000 mg/L → 7000 mg/L) and the valence of cations is increased (monovalent → bivalent), the hydrogen bond is easier to break through the solvation layer to gather on the surface of nano SiO2 particles, which is unfavorable to the stability of nano SiO2 particles. When the cations transport to the position of 7 Å away from the surface of nano-SiO2 particles, the short-range force (including hydrogen bond force, van der Waals force, and electrostatic force) begins to affect the movement of cations. When the cations transport to the position of 2 ∼ 3 Å away from the surface of nano-SiO2 particles, the charge exchange occurs between cations and the surface of nano SiO2 particle, so that the local energy is increased and the cation continues to oscillate. In summary, with the increasing of concentration of salt solution and the valence state, more cations can break through the solvation layer to be adsorbed on the surface of nano SiO2 particle, showing that the ability of transportation and diffusion of cations is weakened, the interaction energy between nano SiO2 particle and salt solution molecules is enhanced. The electrostatic force is the main force to destroy the stability of nano SiO2 particle. The conclusions can provide a certain theoretical basis for the efficient application of nano-SiO2 materials in the field of oil and gas exploration and development and other interrelated industry.