A Dynamical Systems Approach to Stability Tracking of Treadmill Running

2008 ◽  
Author(s):  
Christopher S. Adam ◽  
Ian R. Berry ◽  
Kevin M. Short ◽  
Diana I. Saly
Keyword(s):  
Dynamical Systems ◽  
Nearest Neighbor ◽  
Systems Approach ◽  
Three Dimensional ◽  
Low Frequency ◽  
Temporal Variations ◽  
Gait Pattern ◽  
Treadmill Running ◽  
Reference Orbit ◽  
The Mean

Traditional analysis of running gait utilizes averaged biomechanical data from several strides to generate a mean curve. This curve is then used to define the average picture of a runners gait. However, such measures are frequently accompanied by time normalization, which results in a loss of temporal variations in the gait patterns. An examination of stability requires analysis of both time and position, therefore loss of such information makes stability analysis difficult. On the contrary, the use of a dynamical systems approach for gait analysis allows for a better understanding of how variations in gait pattern change over time. In the current study runners ran on a treadmill, with both a flat and uneven surface, at a self selected speed. Three-dimensional position data was captured for 11 different anatomical locations at a frequency of 120 Hz using a Qualysis motion capture system. The data was first shifted to a lumbar coordinate system to account for low frequency drift attributed to the subjects’ drift on the treadmill. Since all of the markers were rigidly connected, via the subject, the movements and variations of certain components of the 33-dimensional measurements were not independent. As a result, it was possible to reduce the dimensionality of the transformed data using singular value decomposition techniques. The primary components were then analyzed using the method of delay embeddings to extract geometric information, revealing the natural structure found in the data as a result of the periodicity of each running stride. A nearest neighbor mean stride orbit was then computed to create a reference orbit, so that deviations from the mean stride orbit can be measured. The expectation was that a more stable running configuration would lead to smaller deviations from the mean stride orbit. On-going work that will be reported includes: (i) analysis of running stability related to the reference stride comparator, (ii) compensation of lumbar centroid dynamics, (iii) reconstructions using one dimension from the lumbar centroid transformed data, and (iv) consideration of transients, fatigue, adaptation, etc.

scholarly journals Temporal Variations of the Turbulence Profiles at the Sayan Solar Observatory Site

Atmosphere ◽  
2019 ◽  
Vol 10 (9) ◽  
pp. 499 ◽  
Author(s):  
Artem Shikhovtsev ◽  
Pavel Kovadlo ◽  
Vladimir Lukin
Keyword(s):  
Atmospheric Turbulence ◽  
Temporal Variability ◽  
Low Frequency ◽  
Temporal Variations ◽  
Solar Observatory ◽  
Vertical Profiles ◽  
Spatial And Temporal Scales ◽  
Atmospheric Disturbances ◽  
Wide Range ◽  
The Mean

The paper focuses on the development of the method to estimate the mean characteristics of the atmospheric turbulence. Using an approach based on the shape of the energy spectrum of atmospheric turbulence over a wide range of spatial and temporal scales, the vertical profiles of optical turbulence are calculated. The temporal variability of the vertical profiles of turbulence under different low-frequency atmospheric disturbances is considered.

Coherent structures and dominant frequencies in a turbulent three-dimensional diffuser

2012 ◽  
Vol 699 ◽  
pp. 320-351 ◽  
Author(s):  
Johan Malm ◽  
Philipp Schlatter ◽  
Dan S. Henningson
Keyword(s):  
Coherent Structures ◽  
Large Scale ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Low Frequency ◽  
Bulk Velocity ◽  
Time Signal ◽  
Mean Flow ◽  
The Mean ◽  
Dominant Frequencies

AbstractDominant frequencies and coherent structures are investigated in a turbulent, three-dimensional and separated diffuser flow at $\mathit{Re}= 10\hspace{0.167em} 000$ (based on bulk velocity and inflow-duct height), where mean flow characteristics were first studied experimentally by Cherry, Elkins and Eaton (Intl J. Heat Fluid Flow, vol. 29, 2008, pp. 803–811) and later numerically by Ohlsson et al. (J. Fluid Mech., vol. 650, 2010, pp. 307–318). Coherent structures are educed by proper orthogonal decomposition (POD) of the flow, which together with time probes located in the flow domain are used to extract frequency information. The present study shows that the flow contains multiple phenomena, well separated in frequency space. Dominant large-scale frequencies in a narrow band $\mathit{St}\equiv fh/ {u}_{b} \in [0. 0092, 0. 014] $ (where $h$ is the inflow-duct height and ${u}_{b} $ is the bulk velocity), yielding time periods ${T}^{\ensuremath{\ast} } = T{u}_{b} / h\in [70, 110] $, are deduced from the time signal probes in the upper separated part of the diffuser. The associated structures identified by the POD are large streaks arising from a sinusoidal oscillating motion in the diffuser. Their individual contributions to the total kinetic energy, dominated by the mean flow, are, however, small. The reason for the oscillating movement in this low-frequency range is concluded to be the confinement of the flow in this particular geometric set-up in combination with the high Reynolds number and the large separated zone on the top diffuser wall. Based on this analysis, it is shown that the bulk of the streamwise root mean square (r.m.s.) value arises due to large-scale motion, which in turn can explain the appearance of two or more peaks in the streamwise r.m.s. value. The weak secondary flow present in the inflow duct is shown to survive into the diffuser, where it experiences an imbalance with respect to the upper expanding corners, thereby giving rise to the asymmetry of the mean separated region in the diffuser.

A DYNAMICAL SYSTEMS APPROACH TO MEMBRANE PHENOMENA UNDERLYING CARDIAC ARRHYTHMIAS

1995 ◽  
Vol 05 (01) ◽  
pp. 75-88 ◽  
Author(s):  
RICHARD P. KLINE ◽  
B. MITCHELL BAKER
Keyword(s):  
Dynamical Systems ◽  
Action Potential ◽  
Systems Approach ◽  
Chaotic Behavior ◽  
Three Dimensional ◽  
Quantitative Agreement ◽  
Current Activation ◽  
Patterns Of Behavior ◽  
On Line ◽  
Considerable Detail

A model is constructed for cardiac rhythmic response to stimulation via a family of continuous time dynamical systems. Starting with experimentally observed properties common to the kinetics of both repolarizing membrane currents and cardiac action potential responses to sudden changes in cycle length, extremely elementary dynamical assumptions are made concerning current activation and decay, and repolarization threshold. A two-parameter family of one-dimensional dynamical systems emerges. The resulting systems are analytically tractable in considerable detail generating restitution curves, bifurcation schemes, rhythmic responses and chaotic behavior for a representative cardiac cell. The excellent qualitative and quantitative agreement with experimental data reported for several cardiac preparations is discussed. The two-dimensional analog produces unexpected basin behavior which could be of clinical significance in explaining how a single extra beat or a pause could alter subsequent action potential behavior and cause dispersion of refractoriness across the ventricle increasing the risks for arrhythmias. By having a manageable number of parameters, analytically defined patterns of behavior, and computational ease, this dynamical system has the potential to be used in computer simulations to study the effects of antiarrhythmic drugs on complex two- and three-dimensional reentrant substrates, or used on line by an interactive pacemaker.

Propagation of Low Frequency Elastic Disturbances in a Three-Dimensional Composite Material

1975 ◽  
Vol 42 (1) ◽  
pp. 159-164 ◽  
Author(s):  
W. Kohn
Keyword(s):  
Secular Equation ◽  
Displacement Vector ◽  
Three Dimensional ◽  
Low Frequency ◽  
Three Dimensions ◽  
Low Frequencies ◽  
One Dimensional ◽  
Coupled Partial Differential Equations ◽  
Constant Coefficients ◽  
The Mean

This paper is a generalization to three dimensions of an earlier study for one-dimensional composites. We show here that in the limit of low frequencies the displacement vector ui(r,t) can be written in the form ui (r,t) = (∂ij + vijl (r) ∂/∂xl + …) Uj (r,t). Here Uj (r,t) is a slowly varying vector function of r and t which describes the mean displacement of each cell of the composite. Its components satisfy a set of three coupled partial differential equations with constant coefficients. These coefficients are obtainable from the three-by-three secular equation which yields the low-lying normal mode frequencies, ω(k). Information about local strains is contained in the function vijl(r), which is characteristic of static deformations, and is discussed in detail. Among applications of this method is the structure of the head of a pulse propagating in an arbitrary direction.

scholarly journals Scattering Transform Framework for Unmixing of Hyperspectral Data

2019 ◽  
Vol 11 (23) ◽  
pp. 2868 ◽  
Author(s):  
Zeng ◽  
Ritz ◽  
Zhao ◽  
Lan
Keyword(s):  
Nearest Neighbor ◽  
Hyperspectral Image ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Low Frequency ◽  
Hyperspectral Data ◽  
Training Data ◽  
K Nearest Neighbor ◽  
Scattering Transform ◽  
Scattering Transforms

The scattering transform, which applies multiple convolutions using known filters targeting different scales of time or frequency, has a strong similarity to the structure of convolution neural networks (CNNs), without requiring training to learn the convolution filters, and has been used for hyperspectral image classification in recent research. This paper investigates the application of the scattering transform framework to hyperspectral unmixing (STFHU). While state-of-the-art research on unmixing hyperspectral data utilizing scattering transforms is limited, the proposed end-to-end method applies pixel-based scattering transforms and preliminary three-dimensional (3D) scattering transforms to hyperspectral images in the remote sensing scenario to extract feature vectors, which are then trained by employing the regression model based on the k-nearest neighbor (k-NN) to estimate the abundance of maps of endmembers. Experiments compare performances of the proposed algorithm with a series of existing methods in quantitative terms based on both synthetic data and real-world hyperspectral datasets. Results indicate that the proposed approach is more robust to additive noise, which is suppressed by utilizing the rich information in both high-frequency and low-frequency components represented by the scattering transform. Furthermore, the proposed method achieves higher accuracy for unmixing using the same amount of training data with all comparative approaches, while achieving equivalent performance to the best performing CNN method but using much less training data.

Groundwater electromagnetic imaging in complex geological and topographical regions: A case study of a tectonic boundary in the French Alps

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1048-1060 ◽  
Author(s):  
Sophie Hautot ◽  
Pascal Tarits ◽  
Frédéric Perrier ◽  
Corinne Tarits ◽  
Michael Trique
Keyword(s):  
Water Chemistry ◽  
Three Dimensional ◽  
Low Frequency ◽  
Temporal Variations ◽  
Circulation System ◽  
Water Geochemistry ◽  
French Alps ◽  
Electromagnetic Imaging ◽  
Groundwater Circulation ◽  
East West

Very‐low‐frequency (VLF), audiomagnetotelluric (AMT), and water geochemistry surveys were performed on the Sur‐Frêtes Ridge in the French Alps to evaluate the groundwater circulation system within the ridge. At this site, temporal variations of the electric field have been observed in association with water‐level variations of neighboring artificial lakes. The Sur‐Frêtes Ridge is 1 km wide and trends east–west. Water samples were collected at 52 points distributed throughout the area. VLF soundings were carried out along three parallel east–west profiles, and 7 AMT soundings were carried out along an east–west profile on the top of the ridge. This site is characterized by a rugged topography of the ridge where geological and topographic trends are almost perpendicular, making the structure fully three dimensional. We constructed a 2‐D resistivity model of the ridge from 2‐D and 3‐D analyses of the VLF and AMT data, associating geology and topography models. When combined with the water chemistry data, a model is proposed for groundwater percolation below the ridge across the geological contacts. This study demonstrates that electromagnetic imaging in a highly heterogeneous context can be combined with water chemistry to map groundwater circulation at the kilometer scale. The approach is relevant for hydrogeological and environmental applications.

On the Dynamic Response of Disordered Composites

1973 ◽  
Vol 40 (2) ◽  
pp. 511-517 ◽  
Author(s):  
J. J. McCoy
Keyword(s):  
Material Properties ◽  
Mass Density ◽  
Mean Field ◽  
Low Frequency ◽  
Temporal Variations ◽  
Spatial Variations ◽  
Inertia Effects ◽  
Long Wavelength ◽  
The Mean ◽  
Statistical Sample

A formulation is obtained that is to be satisfied by the mean (i.e., statistical averaged) field quantities in a statistical sample of heterogeneous, linearly elastic solids. Inertia effects are included in the analysis. A low frequency-long wavelength theory is extracted from the general formulation as an approximation to be used when spatial variations of the mean field quantities are slow relative to spatial variations of the material properties of the inhomogeneous solids. The temporal variations are restricted to slow variations on a time scale defined by the spatial variations of material properties and a characteristic wave speed. The predictions of the low frequency-long wavelength theory can be given a purely deterministic interpretation. Some aspects of the latter formulation are investigated. In particular, it is shown that the infinite wavelength limit reduces to an effective modulus theory. The effective elastic moduli tensor is identical to one that is obtained on ignoring inertia effects from the outset; the mass density to be used is the “averaged” mass density. By retaining correction terms it is then shown that elastic wave propagation will always exhibit both dispersion and decay over large enough propagation distances.

Electron Holographic Nano-Characterization of Gold Catalyst at Interface

2002 ◽  
Vol 727 ◽  
Author(s):  
S. Ichikawa ◽  
T. Akita ◽  
M. Okumura ◽  
M. Haruta ◽  
K. Tanaka
Keyword(s):  
Contact Angle ◽  
Titanium Oxide ◽  
Gold Catalyst ◽  
Three Dimensional ◽  
High Resolution Electron Microscopy ◽  
Electron Holography ◽  
Gold Particles ◽  
Oxide Support ◽  
The Mean ◽  
A Charge

AbstractThe catalytic properties of nanostructured gold catalyst are known to depend on the size of the gold particles and to be activated when the size decreases to a few nanometers. We investigated the size dependence of the three-dimensional nanostructure on the mean inner potential of gold catalysts supported on titanium oxide using electron holography and high-resolution electron microscopy (HREM). The contact angle of the gold particles on the titanium oxide tended to be over 90° for gold particles with a size of over 5 nm, and below 90° for a size of below 2 nm. This decreasing change in the contact angle (morphology) acts to increase the perimeter and hence the area of the interface between the gold and titanium oxide support, which is considered to be an active site for CO oxidation. The mean inner potential of the gold particles also changed as their size decreased. The value of the inner potential of gold, which is approximately 25 V in bulk state, rose to over 40 V when the size of the gold particles was less than 2 nm. This phenomenon indicates the existence of a charge transfer at the interface between gold and titanium oxide. The 3-D structure change and the inner potential change should be attributed to the specific electronic structure at the interface, owing to both the “nano size effect” and the “hetero-interface effect.”

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