Velocity Amplitude Research Articles

Primitive and gravity modulation of periodical heat transfer along magnetic-driven porous cone with thermal conductivity and surface heat flux

The significant goal of present problem is to evaluate oscillating frequency and amplitude in heat and magnetic flux with thermal conductivity and heat flux effects across magnetized porous cone under lower gravitational region. To maintain heat transport efficiency, the thermal conductivity of conducting fluid is assumed as temperature dependent. The magnetic-driven cone is placed in lower gravitational region. To improve the heating rate across the magnetic-driven porous cone, the convective heating conditions are applied. The implications of thermal conductivity, surface heat flux, and reduced gravity on the periodic behavior of convective heat transfer characteristics of conducting fluid across porous gravity-driven cone is the novelty of this research. Using the appropriate non-dimensional variables, the model's nonlinear governing partial differential has been converted into a dimensionless form. The proposed model is solved later with the help of finite difference approach. The dimensionless form of the equations is reduced to the convenient form for numerical algorithm. The influence of adjusting parameters, such as thermal conductivity parameter ζ, reduced gravity parameter Rg, Biot number Bi, Prandtl number Pr, mixed convection parameter λ, porosity parameter Ω, magnetic prandtl number γ and some others stationary parameters has been highlighted. By using FORTRAN tool, the numerical outcomes are explored in graphs and tabular form. It is depicted that magnetic field enhances as Biot number decreases because magnetic field insulates the excessive heating across the magnetic-driven porous cone. It is noticed that significant amplitude in fluid velocity is noticed with prominent changes as reduced gravity increases. It is concluded that fluctuations in heat transport increases as parameter γ decreases under thermal conductivity because magnetic material insulates the extreme heat across the porous cone. The recent thermal conductivity and lowered gravity problem is significant in the fields of radioactive waste, cooling electronic components, storing nuclear, catalysts, heat exchangers, the underground storage of radioactive or nonnuclear materials, aircrafts and space vehicles.

Simultaneous Horizontal and Vertical Oscillation of a Quiescent Filament Observed by CHASE and SDO

In this paper, we present the imaging and spectroscopic observations of the simultaneous horizontal and vertical large-amplitude oscillation of a quiescent filament triggered by an extreme-ultraviolet (EUV) wave on 2022 October 2. Particularly, the filament oscillation involved winking phenomenon in Hα images and horizontal motions in EUV images. Originally, a filament and its overlying loops across AR 13110 and 13113 erupted with a highly inclined direction, resulting in an X1.0 flare and a non-radial coronal mass ejection. The fast lateral expansion of loops excited an EUV wave and the corresponding Moreton wave propagating northward. Once the EUV wave front arrived at the quiescent filament, the filament began to oscillate coherently along the horizontal direction, and the “winking filament” appeared concurrently in Hα images. The horizontal oscillation involved an initial amplitude of ∼10.2 Mm and a velocity amplitude of ∼46.5 km s−1, lasting for ∼3 cycles with a period of ∼18.2 minutes and a damping time of ∼31.1 minutes. The maximum Doppler velocities of the oscillating filament are 18 km s−1 (redshift) and −24 km s−1 (blueshift), which were derived from the spectroscopic data provided by the Chinese Hα Solar Explorer/Hα Imaging Spectrograph. The three-dimensional velocity of the oscillation is determined to be ∼50 km s−1 at an angle of ∼50° to the local photosphere plane. Based on the wave–filament interaction, the minimum energy of the EUV wave is estimated to be 2.7 × 1020 J. Furthermore, this event provides evidence that Moreton waves should be excited by the highly inclined eruptions.

Heat source/sink impact on wave oscillations of thermal and concentration boundary layer along inclined plate under lower gravitational region

The force of attraction between two masses increases as gravity increases. Gravity is very important mechanism for mass transfer characteristics across the inclined shape. The significant purpose of current study is to examine amplitude in mass transfer under reduced gravity-driven flow. The impact of heat source/sink on periodic mixed convective gravity-driven flow across the inclined plate has been evaluated. The oscillatory characteristics of heat rate and mass transmission are explored at three inclined angles π/6, π/4 and π/3. The gravity is assumed under maximum temperature difference. The governing dimensional model is transformed into non-dimensional equations with appropriate scaling variables. The non-dimensional equations are again reduced in non-oscillatory, real and imaginary parts. For smooth coding, the primitive formulation is used with finite difference method to change non-dimensional forms in algebraic system. The algebraic equations are solved with Gaussian elimination scheme to display velocity field, temperature distribution and rate of concentration numerically. The impact of heat source/sink ±δ, reduced gravity Rg, buoyancy variable λT, modified buoyancy factor λC, Prandtl factor Pr, reduced gravitation factor Rg, and Schmidt variable Sc on the oscillating behavior of shear stress, rate of fluctuating heat transfer, and rate of fluctuating mass transfer is secured. It is found that the amplitude of fluid velocity and temperature increases for each parameter under heat source +δ=0.4. It can be seen that concentration distribution increases as reduced gravity Rg increases under heat sink −δ=0.3. It can be seen that amplitude of shearing stress and heat transfer increases as heat source +δ increases. It is obtained that oscillation in mass transfer increases as heat source/sink ±δ increases under reduced gravitation Rg=1.2.

Deep learning with soft attention mechanism for small-scale ground roll attenuation

Ground roll is a type of coherent noise with low frequency, low velocity, and high amplitude, which masks useful signals and decreases the quality of subsequent seismic data processing. It is a challenge for traditional signal processing methods to separate useful signals effectively when the ground roll and useful reflected signals overlap seriously in the low-frequency band. We develop a supervised-learning-based framework with soft attention residual learning mechanisms for suppressing the ground roll noise. To reduce the cost of manual labeling, the 2D patching technique is used to segment large-scale seismic data into a large number of small-scale patches for training. Our network includes a multibranch attention block that uses multiple branches with different kernel sizes to extract waveform features at different scales from input noisy patches. Then, we use the soft attention mechanism to select and fuse the feature maps of different branches. Our network can achieve encouraging ground roll attenuation performance by using a small number of training samples, which is demonstrated by synthetic and field data examples. Compared with one traditional method and two advanced deep-learning frameworks, our network has better abilities in preserving low-frequency useful signals and removing ground roll.

The magnetically quiet solar surface dominates HARPS-N solar RVs during low activity

ABSTRACT Using images from the Helioseismic and Magnetic Imager aboard the Solar Dynamics Observatory, we extract the radial velocity (RV) signal arising from the suppression of convective blueshift and from bright faculae and dark sunspots transiting the rotating solar disc. We remove these rotationally modulated magnetic-activity contributions from simultaneous RVs observed by the HARPS-N (High Accuracy Radial velocity Planet Searcher for the Northern hemisphere) solar feed to produce an RV time series arising from the magnetically quiet solar surface (the ‘inactive-region RVs’). We find that the level of variability in the inactive-region RVs remains constant over the almost 7-yr baseline and shows no correlation with well-known activity indicators. With an root-mean-square scatter of roughly 1 ${\rm m\, s}^{-1}$, the inactive-region RV time series dominates the total RV variability budget during the decline of solar cycle 24. Finally, we compare the variability amplitude and time-scale of the inactive-region RVs with simulations of supergranulation. We find consistency between the inactive-region RV and simulated time series, indicating that supergranulation is a significant contribution to the overall solar RV variability, and may be the main source of variability towards solar minimum. This work highlights supergranulation as a key barrier to detecting Earth twins.

Visual attention predictive model of built colonial heritage based on visual behaviour and subjective evaluation

Although physiological measurements, subjective evaluation and other methods have been applied to visual attention research, architects still lack a systematic quantitative classification method when assessing the visual attention to built colonial heritage. This study aimed to investigate the relationship between people’s visual behaviour and subjective evaluation when observing built colonial heritage and to construct a prediction model based on eye-movement metrics and subjective evaluation indicators to distinguish the visual attention to built colonial heritage. This study recorded data from 54 participants while observing five scenes of built colonial heritage, and the results showed that participants had different visual behaviours and subjective evaluations when viewing built colonial heritage in different scenes. And visual attention to built colonial heritage was negatively correlated with the average saccades peak velocity and average saccades amplitude and positively correlated with the average pupil diameter; visual attention was correlated with 12 subjective evaluation indicators. The eye-movement metrics and subjective evaluation indicators with correlation to visual attention were used as input variables to construct a prediction model of visual attention to built colonial heritage based on the BP neural network. Different built colonial heritage’s low, middle and high visual attention were identified with high accuracy (74.46%). This quantitative method can help architects to measure the visual attention to built colonial heritage to develop conservation and renewal strategies.

Time-periodic electroosmotic analysis of couple stress fluid in nanofluidic channels with slippages

This paper investigates the electroosmotic flow of an incompressible couple stress fluid squeezed between two prolonged channels with slippage. An analytical solution is provided for two cases: Poiseuille flow and Couette flow. It investigated how dimensionless parameters affect electroosmotic velocities and volume flow rates, such as slippages, couple stress, frequency, wall zeta potential, and electrokinetic width parameters. In the results, the electroosmotic ‎velocity amplitudes, and volume flow rates decay to zero when the couple stress ‎parameter is zero. The effects of slip parameters, electrokinetic width, characteristic speed, and frequency on the electroosmotic velocity are similar to a Newtonian fluid. Nevertheless, there is a complex relationship between electroosmotic velocity and some of the abovementioned parameters. Previous literature has already resolved the Newtonian and non-Newtonian fluid versions of this problem. In this study, a novel issue involving electroosmotic flow in a couple stress fluid was addressed.

Detecting a disc bending wave in a barred-spiral galaxy at redshift 4.4

ABSTRACT The recent discovery of barred spiral galaxies in the early Universe (z > 2) poses questions of how these structures form and how they influence galaxy evolution in the early Universe. In this study, we investigate the morphology and kinematics of the far-infrared (FIR) continuum and [C ii] emission in BRI1335-0417 at z ≈ 4.4 from ALMA observations. The variations in position angle and ellipticity of the isophotes show the characteristic signature of a barred galaxy. The bar, $3.3^{+0.2}_{-0.2}$ kpc long in radius and bridging the previously identified two-armed spiral, is evident in both [C ii] and FIR images, driving the galaxy’s rapid evolution by channelling gas towards the nucleus. Fourier analysis of the [C ii] velocity field reveals an unambiguous kinematic m = 2 mode with a line-of-sight velocity amplitude of up to ∼30–40 km s−1; a plausible explanation is the disc’s vertical bending mode triggered by external perturbation, which presumably induced the high star formation rate and the bar/spiral structure. The bar identified in [C ii] and FIR images of the gas-rich disc galaxy (≳ 70 per cent of the total mass within radius R ≈ 2.2 disc scale lengths) suggests a new perspective of early bar formation in high redshift gas-rich galaxies – a gravitationally unstable gas-rich disc creating a star-forming gaseous bar, rather than a stellar bar emerging from a pre-existing stellar disc. This may explain the prevalent bar-like structures seen in FIR images of high-redshift submillimeter galaxies.

Spectroscopic Detection of Alfvénic Waves in the Chromospheric Fibrils of a Solar-quiet Region

We report the detection of transverse magnetohydrodynamic waves, also known as Alfvénic waves, in the chromospheric fibrils of a solar-quiet region. Unlike previous studies that measured transversal displacements of fibrils in imaging data, we investigate the line-of-sight (LOS) velocity oscillations of the fibrils in spectral data. The observations were carried out with the Fast Imaging Solar Spectrograph of the 1.6 m Goode Solar Telescope at the Big Bear Solar Observatory. By applying spectral inversion to the Hα and Ca ii 8542 Å line profiles, we determine various physical parameters, including the LOS velocity in the chromosphere of the quiet Sun. In the Hα data, we select two adjacent points along the fibrils and analyze the LOS velocities at those points. For the time series of the velocities that show high cross-correlation between the two points and do not exhibit any correlation with intensity, we interpret them as propagating Alfvénic wave packets. We identify a total of 385 Alfvénic wave packets in the quiet-Sun fibrils. The mean values of the period, velocity amplitude, and propagation speed are 7.5 minutes, 1.33 km s−1, and 123 km s−1, respectively. We find that the detected waves are classified into three groups based on their periods, namely, 3, 5, and 10 minute bands. Each group of waves exhibits distinct wave properties, indicating a possible connection to their generation mechanism. Based on our results, we expect that the identification of Alfvénic waves in various regions will provide clues to their origin and the underlying physical processes in the solar atmosphere.

Decayless low-amplitude transverse oscillations in short coronal loops as manifestations of driven slow modes

ABSTRACT A recent theoretical study of slow magnetoacoustic oscillations in a curved magnetic slab shows that the principal slow mode causes both dominant longitudinal motions and radial (transverse) kink-like motions of a slab. This modification of wave properties occurs due to the violation of the symmetry of wave motions with respect to the waveguide axis and the slow to fast wave interaction in curved magnetic configurations. In this work, we carry out a comprehensive investigation of the principal slow mode depending on the model parameters. It is shown that the dominance of longitudinal motions in the principal slow mode decreases as both the internal plasma-β and slab aspect ratio increase. The results are used to explain the observed small amplitude decayless transverse oscillations in short coronal loops. In particular, these phenomena are interpreted as direct manifestation of slow mode oscillations in curved coronal loops excited at the footpoints by compressible oscillations of the underlying atmospheric layers. Numerical calculations have shown that the observed velocity range of V = 0.6–5 km s−1 corresponds to radial velocity amplitudes in the principal slow mode, provided that the plasma-β inside the short loops is in the range of βi= 0.3–0.5 and the loop aspect ratio 0.15 ≤ a/R ≤ 0.25. These parameters appear to be typical for low-lying small coronal loops extending from the transition region to the lower corona.

Path instabilities and drag in the settling of single spheres

The settling behavior of individual spheres in a quiescent fluid was studied experimentally. The dynamics of the spheres was analyzed in the parameter space of particle-to-fluid density ratio (Γ) and Galileo number (Ga), with Γ∈(1.1,7.9) and Ga∈(100,340). The experimental results showed for the first time that the mean trajectory angle with the vertical exhibits a complex behavior as Ga and Γ are varied. Numerically predicted regimes such as Vertical Periodic for low Γ values, and Planar Rotating for high Γ values were validated. In particular, for the denser spheres, a clear transition from planar to non-planar trajectories was observed, accompanied by the emergence of semi-helical trajectories corresponding to the Planar Rotating Regime. The spectra of trajectory oscillations were also quantified as a function of Ga, confirming the existence of oblique oscillating regimes at both low and high frequencies. The amplitudes of the perpendicular velocities in these regimes were also quantified and compared with numerical simulations in the literature. The terminal velocity and drag of the spheres were found to depend on the particle-to-fluid density ratio, and correlations between the drag coefficient and particle Reynolds number (Rep) as a function of Ga were established, allowing for the estimation of drag and settling velocity using Ga, a control parameter, rather than the response parameter Rep.

Mean flow and turbulence in unsteady canopy layers

Non-stationarity is the rule in the atmospheric boundary layer (ABL). Under such conditions, the flow may experience departures from equilibrium with the underlying surface stress, misalignment of shear stresses and strain rates, and three-dimensionality in turbulence statistics. Existing ABL flow theories are primarily established for statistically stationary flow conditions and cannot predict such behaviours. Motivated by this knowledge gap, this study analyses the impact of time-varying pressure gradients on mean flow and turbulence over urban-like surfaces. A series of large-eddy simulations of pulsatile flow over cuboid arrays is performed, programmatically varying the oscillation amplitude $\alpha$ and forcing frequency $\omega$ . The analysis focuses on both longtime-averaged and phase-dependent flow dynamics. Inspection of longtime-averaged velocity profiles reveals that the aerodynamic roughness length $z_0$ increases with $\alpha$ and $\omega$ , whereas the displacement height $d$ appears to be insensitive to these parameters. In terms of oscillatory flow statistics, it is found that $\alpha$ primarily controls the oscillation amplitude of the streamwise velocity and Reynolds stresses, but has a negligible impact on their wall-normal structure. On the other hand, $\omega$ determines the size of the region affected by the unsteady forcing, which identifies the so-called Stokes layer thickness $\delta _s$ . Within the Stokes layer, phase-averaged resolved Reynolds stress profiles feature substantial variations during the pulsatile cycle, and the turbulence is out of equilibrium with the mean flow. Two phenomenological models have been proposed that capture the influence of flow unsteadiness on $z_0$ and $\delta _s$ , respectively.

Anatomy of Mode-1 Internal Solitary Waves Derived From Seaglider Observations in the Northern South China Sea

Abstract Observations from a Seaglider, two pressure-sensor-equipped inverted echo sounders (PIESs), and a thermistor chain (T-chain) mooring were used to determine the waveform and timing of internal solitary waves (ISWs) over the continental slope east of Dongsha Atoll. The Korteweg–de Vries (KdV) and Dubreil–Jacotin–Long (DJL) equations supplemented the data from repeated profiling by the glider at a fixed position (depth ∼1017 m) during 19–24 May 2019. The glider-recorded pressure perturbations were used to compute the rarely measured vertical velocity (w) with a static glider flight model. After removing the internal tide–caused vertical velocity, the w of the eight mode-1 ISWs ranged from −0.35 to 0.36 m s−1 with an uncertainty of ±0.005 m s−1 due to turbulent oscillations and measurement error. The horizontal velocity profiles, wave speeds, and amplitudes of the eight ISWs were further derived from the KdV and DJL equations using the glider-observed w and potential density profiles. The mean speed of the corresponding ISW from the PIES deployed at ∼2000 m depth to the T-chain moored at 500 m depth and the 19°C isotherm displacement computed from the T-chain were used to validate the waveform derived from KdV and DJL. The validation suggests that the DJL equation provides reasonably representative wave speed and amplitude for the eight ISWs compared to the KdV equation. Stand-alone glider data provide near-real-time hydrography and vertical velocities for mode-1 ISWs and are useful for characterizing the anatomy of ISWs and validating numerical simulations of these waves. Significance Statement Internal solitary waves (ISWs), which vertically displace isotherms by approximately 100 m, considerably affect nutrient pumping, turbulent mixing, acoustic propagation, underwater navigation, bedform generation, and engineering structures in the ocean. A complete understanding of their anatomy and dynamics has many applications, such as predicting the timing and position of mode-1 ISWs and evaluating their environmental impacts. To improve our understanding of these waves and validate the two major theories based on the Korteweg–de Vries (KdV) and Dubreil–Jacotin–Long (DJL) equations, the hydrography data collected from stand-alone, real-time profiling of an autonomous underwater vehicle (Seaglider) have proven to be useful in determining the waveform of these transbasin ISWs in deep water. The solutions to the DJL equation show good agreement with the properties of mode-1 ISWs obtained from the rare in situ data, whereas the solutions to the KdV equation underestimate these properties. Seaglider observations also provide in situ data to evaluate the performance of numerical simulations and forecasting of ISWs in the northern South China Sea.

Random forest-based multi-hazard loss estimation using hypothetical data at seismic and tsunami monitoring networks

This article presents a novel approach to estimate multi-hazard loss in a post-event situation, resulting from cascading earthquake and tsunami events with machine learning for the first time. The proposed methodology combines the power of random forest (RF) with data that are simulated at seismic and tsunami monitoring locations. The RF model is well-suited for predicting highly nonlinear multi-hazard loss because of its nonparametric regression and ensemble learning capabilities. The study targets the cities of Iwanuma and Onagawa in Tohoku, Japan, where seismic and tsunami monitoring networks have been deployed. To encompass a diverse range of future multi-hazard loss estimation, an RF model is constructed based on 4000 simulated earthquake events with peak ground velocity and tsunami wave amplitude captured at ground-motion monitoring sites and offshore wave monitoring sensors, respectively. The incorporation of 10 ground-motion monitoring sites and five offshore wave monitoring sensors significantly enhances the model’s forecasting power, leading to a notable 60% decrease in mean squared error and 20% increase in the R 2 value compared to scenarios where no monitoring sensors are utilized. By harnessing the capabilities of RF and leveraging detailed sensing data, RF achieves R 2 values over 90%, which can contribute to enhanced disaster risk management.

Environmental filtering and biotic interactions act on different facets of the diversity of benthic assemblages associated with eelgrass.

Eelgrass supports diverse benthic communities that ensure a variety of ecosystem functions. To better understand the ecological processes that shape community composition in eelgrass at local and regional scales, taxonomic and functional α- and β-diversity were quantified for communities inhabiting five meadows in France. The extent to which environmental factors affected local and regional benthic communities was quantified by considering their direct and indirect effects (through morphological traits of eelgrass) using piecewise structural equation modeling (pSEM). Communities supported by eelgrass had higher species abundances, as well as taxonomic and functional diversity compared to nearby bare sediments. No significant differences were found between communities from the center relative to the edges of meadows, indicating that both habitats provide similar benefits to biodiversity. The presence of a few abundant species and traits suggests moderate levels of habitat filtering and close associations of certain species with eelgrass. Nevertheless, high turnover of a large number of rare species and traits was observed among meadows, resulting in meadows being characterized by their own distinct communities. High turnover indicates that much of the community is not specific to eelgrass, but rather reflects local species pools. pSEM showed that spatial variation in community composition (β-diversity) was primarily affected by environmental conditions, with temperature, current velocity, and tidal amplitude being the most significant explanatory variables. Local richness and abundance (α-diversity) were affected by both environment and morphological traits. Importantly, morphological traits of Zostera marina were also influenced by environmental conditions, revealing cascading effects of the environment on assemblages. In sum, the environment exerted large effects on community structure at both regional and local scales, while plant traits were only pertinent in explaining local diversity. This complex interplay of processes acting at multiple scales with indirect effects should be accounted for in conservation efforts that target the protection of biodiversity.

What is the Resonance of a Linear Mechanical Resonator, Peak Amplitude of Displacement or Peak Amplitude of Velocity?

What is the Resonance of a Linear Mechanical Resonator, Peak Amplitude of Displacement or Peak Amplitude of Velocity?

Observation and imitation of object-directed hand movements in Parkinson’s disease

Action observation and imitation may facilitate movement in Parkinson’s disease (PD). People with PD have been found to imitate intransitive actions similarly to neurologically healthy older adults, but their imitation of object-directed hand movements has not previously been investigated using kinematic measures. The present study examined observation and imitation of object-directed hand movements in 18 participants with PD and 21 neurologically healthy age-matched control participants. Participants observed and immediately imitated sequences showing a human hand reaching for and transferring an object between horizontal positions. Both groups significantly modulated their finger movements, showing higher vertical amplitude when imitating elevated compared to direct trajectories. In addition, movements were lower in vertical amplitude and higher in velocity when imitating the reaching segment than the transfer segment. Eye-tracking revealed that controls made smaller saccades when observing predictable than unpredictable elevated movements, but no effects of predictability on eye movements were found for the PD group. This study provides quantitative evidence that people with mild to moderate PD can imitate object-directed hand movement kinematics, although their prediction of such movements may be reduced. These findings suggest that interventions targeting object-directed actions may capitalize on the ability of people with PD to imitate kinematic parameters of a demonstrated movement.

Design of a dynamic measurement system for Bl factor spatial distribution of resonant blood viscoelastic sensor

Bl factor is a key system parameter of the resonant blood viscoelastic sensor. In this paper, a dynamic measurement system for the spatial distribution of Bl factor based on velocity amplitude and motional impedance was designed. The system extracted the velocity amplitude and motional impedance of the coil under the dynamic condition of driving the sensor to generate simple harmonic oscillations using laser displacement and impedance analysis combined with in-phase/quadrature demodulation algorithm, and controlled the equilibrium position of the coil by adjusting the direct current component of the excitation current to realize the position scanning. In the position interval of [-240, 240] μm, the maximum coefficient of variation of the measurement results was 0.077 3%, and the maximum relative error to the simulation results was 2.937 9%, with a linear fitting correlation coefficient R 2 = 0.996 8. The system can be used to accurately measure the spatial distribution of Bl factor of the resonant blood viscoelastic sensor, which provides a technical support for the verification of the design of the sensor magnetic circuit.

Internal shear layers in librating spherical shells: the case of attractors

Following our previous work on periodic ray paths (He et al., J. Fluid Mech., vol. 939, 2022, A3), we study asymptotically and numerically the structure of internal shear layers for very small Ekman numbers in a three-dimensional spherical shell and in a two-dimensional cylindrical annulus when the rays converge towards an attractor. We first show that the asymptotic solution obtained by propagating the self-similar solution generated at the critical latitude on the librating inner core describes the main features of the numerical solution. The internal shear layer structure and the scaling for its width and velocity amplitude in $E^{1/3}$ and $E^{1/12}$ , respectively, are recovered. The amplitude of the asymptotic solution is shown to decrease to $E^{1/6}$ when it reaches the attractor, as is also observed numerically. However, some discrepancies are observed close to the particular attractors along which the phase of the wave beam remains constant. Another asymptotic solution close to those attractors is then constructed using the model of Ogilvie (J. Fluid Mech., vol. 543, 2005, pp. 19–44). The solution obtained for the velocity has an $O(E^{1/6})$ amplitude, but a self-similar structure different from the critical-latitude solution. It also depends on the Ekman pumping at the contact points of the attractor with the boundaries. We demonstrate that it reproduces correctly the numerical solution. Surprisingly, the numerical solution close to an attractor with phase shift (that is, an attractor touching the axis in three or two dimensions with a symmetric forcing) is also found to be $O(E^{1/6})$ , but its amplitude is much weaker. However, its asymptotic structure remains a mystery.

Study on the motion of single particle chain in the magnetorheological fluid under the action of traveling magnetic field

Magnetorheological fluid (MRF) is a widely used intelligent material that can quickly respond to external magnetic fields. To effectively control the motion of the particle chain inside the MRF, this paper combines the traveling magnetic field (TMF) with the MRF to study the movement of the single particle chain in the MRF under the action of the TMF for the first time and discusses the influence of the moving velocity of the TMF and the magnetic induction intensity on the motion displacement and the velocity of the single particle chain, determines the adjustable range of the single particle chain motion parameters, and builds an experimental platform to observe the motion of the single particle chain. The results show that under the action of the TMF, the single particle chain makes a variable velocity reciprocating motion, and the displacement amplitude of the single particle chain is inversely proportional to the moving velocity of the TMF but directly proportional to the magnetic induction intensity of the TMF. The single particle chain velocity amplitude is only proportional to the magnetic induction intensity and is unrelated to the moving velocity of the TMF. This study shows that adjusting the TMF parameters can effectively control the displacement and velocity of single particle chain motion. This study provides a compelling new method to control the motion pattern of single particle chains in MRF.