Displacement Fluctuations Research Articles

Attenuation of centre-of-pressure trajectory fluctuations under the prosthetic foot when using an articulating hydraulic ankle attachment compared to fixed attachment

BackgroundDisruptions to the progress of the centre-of-pressure trajectory beneath prosthetic feet have been reported previously. These disruptions reflect how body weight is transferred over the prosthetic limb and are governed by the compliance of the prosthetic foot device and its ability to simulate ankle function. This study investigated whether using an articulating hydraulic ankle attachment attenuates centre-of-pressure trajectory fluctuations under the prosthetic foot compared to a fixed attachment. MethodsTwenty active unilateral trans-tibial amputees completed walking trials at their freely-selected, comfortable walking speed using both their habitual foot with either a rigid or elastic articulating attachment and a foot with a hydraulic ankle attachment. Centre-of-pressure displacement and velocity fluctuations beneath the prosthetic foot, prosthetic shank angular velocity during stance, and walking speed were compared between foot conditions. FindingsUse of the hydraulic device eliminated or reduced the magnitude of posteriorly directed centre-of-pressure displacements, reduced centre-of-pressure velocity variability across single-support, increased mean forward angular velocity of the shank during early stance, and increased freely chosen comfortable walking speed (P≤0.002). InterpretationThe attenuation of centre-of-pressure trajectory fluctuations when using the hydraulic device indicated bodyweight was transferred onto the prosthetic limb in a smoother, less faltering manner which allowed the centre of mass to translate more quickly over the foot.

Displacement Spectra Under Isometric Muscle Contraction

The purposes of this work were to detect the microscopic displacements accompanying isometric muscle tissue contraction under different external loads, to explore their spectral characteristics, and to develop physical models capable of explaining the experimental data obtained. By means of a spectral Doppler musculoskeletal ultrasound method, spectral characteristics of local isometric skeletal muscle tissue contraction were studied. In this method, the phased fluctuation (Doppler) algorithm is used to estimate tissue displacements within the given sample volume in real time, and the spectral characteristics of recorded displacements are determined. Observation of local isometric muscle contraction was conducted in the brachioradial muscle of the flexor digitorum profundus. Data obtained from 6 healthy volunteers during observation of muscle contraction in a relaxed state and under different static loads (2, 5, and 10 kg) were processed. The main difference in recorded displacements under different loads was in the displacement fluctuation values, whereas spectral characteristics were almost constant. Differences in the numbers and values of spectral maxima were also observed. These results are explained by a developed physical model assuming that the mechanochemical characteristics of crossbridges between actin and myosin filaments are the main factors influencing the spectral peculiarities of the Doppler response. Both the developed model of the Doppler response and the proposed dynamic model of sarcomere movement establish a link between macroscopic Doppler measurements and the biomechanical processes and behavior of sarcomeres at a subcellular level. The results of these pilot experiments demonstrate the suitability of this spectral Doppler method for a more detailed spectral study of biomechanical processes that occur under muscle contraction. The stability of the spectral characteristics under different loads also testifies to the value of this method as a reliable and valid diagnostic tool for diagnosing neuromuscular disorders.

Nanoscale fluctuations and surface tension measurements in droplets using phase-resolved low-coherence interferometry

A common-path interferometer was designed with rapidly tunable broadband swept laser source, which provides quantitative phase measurements of nanometer scale motions with very high sensitivity. With this setup, we are able to detect the thermal fluctuations in liquid droplets hanging at the end of an optical fiber. The measured nanoscale displacement fluctuations of various droplet surfaces were used to extract the surface tension. This newly developed technique proved the feasibility of noninvasive, fast, phase-resolved dynamic light scattering measurement of fluid mechanical properties.

Vortex formation and dissolution in sheared sands

Using digital image correlation, we track the displacement fluctuations within a persistent shear band in a dense sand specimen bounded by glass walls undergoing plane strain compression. The data evidences a clear, systematic, temporally recurring pattern of vortex formation, dissolution, and reformation throughout macroscopic softening and critical state regimes. During softening, locally affine deformation zones are observed at various locations along the shear band, which we argue to be kinematic signatures of semi-stable force chains. Force chain collapse then occurs, inducing vortex formation. Local jamming at the conflux of opposing displacements between adjacent vortices arrests the vortices, providing an avenue for potential new force chains to form amidst these jammed regions. The process repeats itself temporally throughout the critical state. The pattern further correlates with fluctuations in macroscopic shear stress. We characterize the nature of the observed vortices, as they are different in our sands comprised of irregular shaped particles, as compared to previous observations from experiments and numerical simulations which involved circular or rounded particles. The results provide an interesting benchmark for behavior of non-circular/non-spherical particles undergoing shear.

An experimental assessment of displacement fluctuations in a 2D granular material subjected to shear

In a granular material, a macroscopically homogeneous deformation does not correspond to a homogeneous displacement field when looking at the individual grains. The deviation of a grain displacement from the value dictated by the continuum field (referred to as ‘fluctuation’) is likely to hold valuable information about the characteristic length(s) involved in the grains' rearrangement, which is the principal mechanism of irreversible deformation for granular materials. This paper shows a selection of results from a series of shear tests on a two-dimensional analogue granular material. The route opened by the pioneering work of Radjaï and Roux is followed, and the same framework is used to analyse the experimental data on displacement fluctuations. Digital image correlation has been used to measure and characterise the displacement fluctuations. The analysis of their spatial organisation reveals the emergence of a minimum-length scale; that is, in the order of 10 times the mean particle size.

Performances of a balanced hydraulic motor with planetary gear train

The current research of a balanced hydraulic motor focuses on the characteristics of the motor with three planet gears. References of a balanced hydraulic motor with more than three planet gears are hardly found. In order to study the characteristics of a balanced hydraulic motor with planetary gear train that includes more than three planet gears, on the basis of analysis of the structure and working principle of a balanced hydraulic motor with planetary gear train, formulas are deduced for calculating the hydraulic motor’s primary performance indexes such as displacement, unit volume displacement, flowrate fluctuation ratio, etc. Influences of the gears’ tooth number on displacement and flowrate characteristics are analyzed. In order to guarantee the reliability of sealing capability, the necessary conditions that tooth number of the sun gear and the planet gears should satisfy are discussed. Selecting large unit volume displacement and small displacement fluctuation ratio as designing objectives, a balanced hydraulic motor with three planet gears and a common gear motor are designed under the conditions of same displacement, tooth addendum coefficien and clearance coefficient. By comparing the unit volume displacement and fluctuation ratio of the two motors, it can be seen that the balanced hydraulic motor with planetary gear train has the advantages of smaller fluctuation ratio and larger unit volume displacement. The results provide theoretical basis for choosing gear tooth-number of this kind of hydraulic motor.

Quasi-synchronous multi-parameter anomalies associated with the 2010–2011 New Zealand earthquake sequence

Abstract. Positive thermal anomalies about one month before the 3 September 2010 Mw = 7.1 New Zealand earthquake and "coincidental" quasi-synchronous fluctuations of GPS displacement were reported. Whether there were similar phenomena associated with the aftershocks? To answer it, the following was investigated: multiple parameters including surface and near-surface air temperature, surface latent heat flux, GPS displacement and soil moisture, using a long-term statistical analysis method. We found that local thermal and deformation anomalies appeared quasi-synchronously in three particular tectonic zones, not only about one month before the mainshock, but also tens of days before the 21 February 2011 Mw = 6.3 aftershock, and that the time series of soil moisture on the epicenter pixel had obvious peaks on most of the anomalous days. Based on local tectonic geology, hydrology and meteorology, the particular lithosphere-coversphere-atmosphere coupling mode is interpreted and four mechanisms (magmatic-hydrothermal fluids upwelling, soil moisture increasing, underground pore gases leaking, and positive holes activating and recombining) are discussed.

Dual Fractal Dimension and Long-Range Correlation of Chinese Stock Prices

The recently developed modified inverse random midpoint displacement (mIRMD) and conventional detrended fluctuation analysis (DFA) algorithms are used to analyze the tick-by-tick high-frequency time series of Chinese A-share stock prices and indexes. A dual-fractal structure with a crossover at about 10 min is observed. The majority of the selected time series show visible persistence within this time threshold, but approach a random walk on a longer time scale. The phenomenon is found to be industry-dependent, i.e., the crossover is much more prominent for stocks belonging to cyclical industries than for those belonging to noncyclical (defensive) industries. We have also shown that the sign series show a similar dual-fractal structure, while like generally found, the magnitude series show a much longer time persistence.

Drag reduction in turbulent boundary layers by spanwise traveling waves with wall deformation

The drag-reducing effect of a spanwise-traveling wave with wall deformation on a zero-pressure-gradient turbulent boundary layer over a flexible sheet was investigated. The test plate placed in the wind tunnel consisted of a flexible sheet section, where the traveling wave motion was generated by a vibration device with a crank via upstream and downstream smooth rigid wall sections. Streamwise and wall-normal velocity components were measured by single and cross hot-wire anemometers. Amplitude and frequency of the spanwise-traveling-wave motion were measured using two laser displacement sensors. The drag reduction ratio was estimated from the friction coefficients through the growth rate of the momentum thickness of the turbulent boundary layer over the flexible sheet section. A maximum drag reduction ratio of up to 13% was obtained. The relations between sheet displacement and streamwise and wall-normal velocity fluctuations were compared at a large (DR=8%) and at a very small (), which was almost the same as the no drag reduction case, taking into account the experimental uncertainty. For the larger drag reduction, a slow-velocity fluctuation with large amplitude appeared further away from the flexible sheet. Quadrant analysis of streamwise and wall-normal velocity fluctuations revealed that the drag reduction was attributed to a reduction in the sweep event and an increase in the negative contribution of the inward-interaction event to the Reynolds shear stress due to the sheet displacement fluctuation.

Stochastic rolling of a rigid sphere in weak adhesive contact with a soft substrate

We study the rolling motion of a small solid sphere on a fibrillated rubber substrate in an external field in the presence of a Gaussian noise. From the nature of the drift and the evolution of the displacement fluctuation of the ball, it is evident that the rolling is controlled by a complex non-linear friction at a low velocity and a low noise strength (K), but by a linear kinematic friction at a high velocity and a high noise strength. This transition from a non-linear to a linear friction control of motion can be discerned from another experiment in which the ball is subjected to a periodic asymmetric vibration in conjunction with a random noise. Here, as opposed to that of a fixed external force, the rolling velocity decreases with the strength of the noise suggesting a progressive fluidization of the interface. A state (K) and rate (V) dependent friction model is able to explain both the evolution of the displacement fluctuation as well as the sigmoidal variation of the drift velocity with K. This research sets the stage for studying friction in a new way, in which it is submitted to a noise and then its dynamic response is studied using the tools of statistical mechanics. Although more works would be needed for a fuller realization of the above-stated goal, this approach has the potential to complement direct measurements of friction over several decades of velocities and other state variables. It is striking that the non-Gaussian displacement statistics as observed with the stochastic rolling is similar to that of a colloidal particle undergoing Brownian motion in contact with a soft microtubule.

Non-Gaussian Fluctuations Resulting from Power-Law Trapping in a Lipid Bilayer

Anomalous diffusion in lipid bilayers is usually attributed to viscoelastic behavior. We compute the scaling exponent of relative fluctuations of the time-averaged mean square displacement in a lipid bilayer, by using a molecular dynamics simulation. According to the continuous time random walk theory, this exponent indicates non-Gaussian behavior caused by a power-law trapping time. Our results provide the first evidence that a lipid bilayer has not only viscoelastic properties but also trapping times distributed according to a power law.

Quantum kinetics of squeezed lattice displacement generated by phonon down conversion

We study the fluctuation properties of longitudinal acoustic (LA) phonons generated by the anharmonic decay of coherent longitudinal optical phonons in a bulk semiconductor and a quantum dot. This process is comparable to the down conversion of photons, which is well known to generate squeezed photons. We use a quantum kinetic model to calculate the fluctuations of lattice displacement and momentum. This allows us to analyze the strength and the spatial distribution of the fluctuations. It is shown that the fluctuations may fall below their vacuum value, i.e., squeezing occurs. The squeezing only persists for short times due to fast dephasing of the different LA phonon modes and the increasing LA phonon population. In the quantum dot case, it is found that although LA phonon wave packets travel out of the quantum dot, the squeezing does not leave the vicinity of the dot but remains confined.

Laser cooling of a nanomechanical oscillator into its quantum ground state

The simple mechanical oscillator, canonically consisting of a coupled mass-spring system, is used in a wide variety of sensitive measurements, including the detection of weak forces and small masses. On the one hand, a classical oscillator has a well-defined amplitude of motion; a quantum oscillator, on the other hand, has a lowest-energy state, or ground state, with a finite-amplitude uncertainty corresponding to zero-point motion. On the macroscopic scale of our everyday experience, owing to interactions with its highly fluctuating thermal environment a mechanical oscillator is filled with many energy quanta and its quantum nature is all but hidden. Recently, in experiments performed at temperatures of a few hundredths of a kelvin, engineered nanomechanical resonators coupled to electrical circuits have been measured to be oscillating in their quantum ground state. These experiments, in addition to providing a glimpse into the underlying quantum behaviour of mesoscopic systems consisting of billions of atoms, represent the initial steps towards the use of mechanical devices as tools for quantum metrology or as a means of coupling hybrid quantum systems. Here we report the development of a coupled, nanoscale optical and mechanical resonator formed in a silicon microchip, in which radiation pressure from a laser is used to cool the mechanical motion down to its quantum ground state (reaching an average phonon occupancy number of 0.85 ± 0.08). This cooling is realized at an environmental temperature of 20 K, roughly one thousand times larger than in previous experiments and paves the way for optical control of mesoscale mechanical oscillators in the quantum regime.

Coastal cliff ground motions from local ocean swell and infragravity waves in southern California

[1] Ground motions atop a southern California, USA coastal cliff are compared with water level fluctuations observed at the cliff base, and with ground motions observed 10 km inland. At high tide, cliff top ground motions in three frequency bands were generated locally by ocean waves at the cliff base: (1) high-frequency (>0.3 Hz) “shaking” caused by waves impacting the cliff, and (2) gravitational loading-induced “swaying” at the frequency of the incident sea swell waves (0.05–0.1 Hz), and (3) slow “swaying” at infragravity frequencies (0.006–0.05 Hz). At high tide, at infragravity and incident sea swell wave frequencies, cliff top vertical ground displacement and cliff base water level fluctuations are coherent and oscillate in phase (with occasional deviation at sea swell frequencies), and spectral levels at the cliff top are much higher than at the inland seismometer. In contrast, at “double frequencies” (0.1–0.3 Hz) spectral levels of vertical motions are nearly identical inland and at the cliff top, consistent with a common (distant or spatially distributed) source. At low tide, when ocean waves did not reach the cliff base, power levels of vertical ground motions at the cliff top decreased to inland levels at incident wave frequencies and higher, and only infragravity-band motions were noticeably forced by local ocean waves.

Dynamic Peculiarity of Piezoelectric-Stack Displacement-Amplifying Actuator

In order to find out the dynamic peculiarity of piezoelectric-stack displacement-amplifying actuator, three methods: harmonic response analysis, impedance test and dynamic grating projection are used to analyze it. Experimental results indicate that the displacement-amplifying mechanism can provide large output torque; its response time is less than 0.3ms; its mutation time of displacement is less than 0.5ms, the fluctuation of displacement is less than 5um, and the change of displacement vs. voltage is linearity variety; its dynamic displacement is smooth, when discharging. After analyzing the actuator, some virtues of dynamic response peculiarity are shown: rapidly responding, tiny displacement fluctuates, fine displacement linearity, higher precision, large output torque, etc. Therefore it can be abroad applied in many micro-displacement control and drive systems, which need high precision and large displacement. Its application prospect is worth to expect.

Multiscale analysis of laminated plates with integrated piezoelectric fiber composite actuators

This study is concerned with the detailed analysis of fiber-reinforced composite plates with integrated piezoceramic fiber composite actuators. A multiscale framework based on the asymptotic expansion homogenization method is used to couple the microscale and macroscale field variables. The microscale fluctuations in the mechanical displacement and electric potential are related to the macroscale deformation and electric fields through 36 distinct characteristic functions. The local mechanical and charge equilibrium equations yield a system of partial differential equations for the characteristic functions that are solved using the finite element method. The homogenized electroelastic properties of a representative material element are computed using the characteristic functions and the material properties of the fiber and matrix. The three-dimensional macroscopic equilibrium equations for a laminated piezoelectric plate are solved analytically using the Eshelby–Stroh formalism. The formulation admits different boundary conditions at the edges and is applicable to thick and thin laminated plates. The microscale stresses and electric displacement in the fibers and matrix are computed from the macroscale fields through interscale transfer operators. The multiscale analysis procedure is illustrated using two model problems. In the first model problem, a simply-supported sandwich plate consisting of a piezoceramic fiber composite shear actuator embedded between two graphite/polymer layers is studied. The second model problem concerns a cantilever graphite/polymer substrate with segmented piezoceramic fiber composite extension actuators attached to its top and bottom surfaces. Results are presented for the homogenized material properties, macroscale deformation, macroscale average stresses and microscale stress distributions.

TH-A-220-01: An Automated Optimal ROI Discovery Method for Real-Time 3D Surface Image Monitoring of Head Motion

Purpose: To increase image registration accuracy, and to remove the time‐ consuming manual region‐of‐interest (ROI) selection process for patient monitoring 3D surface imaging systems (AlignRT,VisionRT,UK), a method was developed to adaptively define an optimal ROI based on discovering topographically stable surfaces over time. Methods: Our method calculates the displacement and velocity of 3D surface points between a series of images captured in real‐time and the reference image. Using a set of selection criteria, the algorithm adaptively constructs a ROI by including only facial surfaces that move rigidly with the target and excludes surfaces that fluctuate locally such as the mandible regions and eyes. Data for five volunteers were acquired over various facial surface and motion types. A total of 27 data sets were analyzed, with 2–7 data sets for each volunteer and each data set contained consecutively captured 40–120 real‐time images. Results: The adaptive ROI selection algorithm correspondingly detected surfaces affected by different types of facial movement independent of target motions. It interpreted the eyes, eyebrows and mandible motions shown in the real‐time 3D images as independent of target motion even when AlignRT misinterpreted them, and excluded them from the final ROI. For 3D images taken with substantial facial motions, either most of the facial areas were excluded or only small areas with random patterns were included in the final ROI. The algorithm excluded the upper side and nose where the view of the cameras was blocked, and thus surface was not well‐ reconstructed in many of real‐time 3D images when couch was rotated greater than 40°. Conclusion: The method successfully located suitable ROI surfaces undergoing minimal displacement and temporal fluctuation. By automating the ROI selection process, the time and complexity of current ROI definition can be reduced, together with user‐dependent registration errors.

Intrinsic randomness of transport coefficient in subdiffusion with static disorder

Fluctuations in the time-averaged mean-square displacement for random walks on hypercubic lattices with static disorder are investigated. It is analytically shown that the diffusion coefficient becomes a random variable as a manifestation of weak ergodicity breaking. For two- and higher- dimensional systems, the distribution function of the diffusion coefficient is found to be the Mittag-Leffler distribution, which is the same as for the continuous-time random walk, whereas for one-dimensional systems a different distribution (a modified Mittag-Leffler distribution) arises. We also present a comparison of these two distributions in terms of an ergodicity-breaking parameter and show that the modified Mittag-Leffler distribution has a larger deviation from ergodicity. Some remarks on similarities between these results and observations in biological experiments are presented.

QUANTUM EFFECTS OF A DOMAIN WALL IN THE FERROMAGNETIC SYSTEM

Starting from the classical equation of the motion of a domain wall in the ferromagnetic systems, the quantum energy levels of the wall and the corresponding eigenfunctions in the case of considering damping term are given by using the canonical quantization method and unitary transformation. The quantum fluctuations of displacement and momentum of the moving wall has also been given as well as the uncertain relation.

Electromagnetically induced transparency from two-phonon processes in quadratically coupled membranes

We describe how electromagnetically induced transparency can arise in quadratically coupled optomechanical systems. Due to quadratic coupling the underlying optical process involves a two phonon process in optomechanical system and this two phonon process makes the mean amplitude, which plays the role of atomic coherence in traditional EIT, zero. We show how the fluctuation in displacement can play a role similar to atomic coherence and can lead to EIT-like effects in quadratically coupled optomechanical systems. We show how such effects can be studied using the existing optomechanical systems.