Ratio Of Path Length Research Articles

Changes in Gait Economy Between Full-Contact Custom-made Foot Orthoses and Prefabricated Inserts in Patients with Musculoskeletal Pain

Specific kinematic and kinetic outcomes have been used to detect biomechanical change while wearing foot orthoses; however, few studies demonstrate consistent effects. We sought to observe changes in walking economy in patients with musculoskeletal pain across 10 weeks while wearing custom-made foot orthoses and prefabricated shoe inserts. In this crossover randomized controlled trial, 40 participants wore custom-made orthoses and prefabricated inserts for 4 weeks each, consecutively. The path length ratio was used to quantify walking economy by comparing the undulating path of a point in the pelvis with its direct path averaged across multiple strides. For the prefab-custom group (n=27), significant decreases in path length ratio (improved economy of gait) were noted at the initial introduction of prefabricated inserts (P= .02) and custom orthoses (P= .02) but maintained a trend toward improved economy only while wearing custom orthoses (P= .08). For the custom-prefab group (n=13), there was worsening of the path length ratio that was significant after removing the custom-made orthoses for 4 weeks (P= .01). For patients with lower-extremity musculoskeletal pain, immediate improvements in economy of gait can be expected with both interventions. It seems, however, that only the custom-made orthoses maintain economy of gait for 4 weeks. Patients who begin wearing custom-made orthoses and then wear prefabricated insoles can expect a decrease in economy of gait.

Measurement Properties of Simple Biomechanical Measures of Walking Effort

A simple measure of overall walking effort would be valuable to patients and clinicians to select suitable treatment interventions and to monitor progress. In this paper, the reproducibility and responsiveness of seven potentially useful clinical measures of walking effort are presented. These walking effort outcomes were derived from a compass gait model and space curve displacement, acceleration and differential geometry theory. The walking effort outcomes were primarily calculated from the motion of a point on or in the rigid body pelvis as a patient walked cyclically. These motion data were collected from eight healthy volunteers who each walked on a treadmill for 4 min, at four different speeds, repeated twice. Four of the seven walking effort outcomes clearly had better measurement properties. The path length ratio, acceleration ratio, Frenet–Serret torsion and Frenet–Serret energy had excellent reproducibility (ICC>0.8) and responded to a small change in walking speed (< 0.03 m/s) compared to two versions of the biomechanical efficiency quotient and the Frenet–Serret curvature. The measurement properties of most outcomes were not consistently improved using a point in versus on the pelvis. This study presents four biomechanical walking effort outcomes that have good theoretical underpinnings, excellent reproducibility and responsiveness, are simple and easy to administer with relatively inexpensive equipment, and can be used in real world environments. However, future work must investigate the minimal clinically important change of these outcome measures before they can be used in clinical practice.

Continuous-time quantum walks on one-dimensional regular networks

In this paper, we consider continuous-time quantum walks (CTQWs) on a one-dimensional ring lattice of N nodes in which every node is connected to its 2m nearest neighbors ( m on either side). In the framework of the Bloch function ansatz, we calculate the space-time transition probabilities between two nodes of the lattice. We find that the transport of CTQWs between two different nodes is faster than that of the classical continuous-time random walks (CTRWs). The transport speed, which is defined by the ratio of the shortest path length and propagating time, increases with the connectivity parameter m for both CTQWs and CTRWs. For fixed parameter m , the transport of CTRWs gets slower with the increase of the shortest distance while the transport (speed) of CTQWs turns out to be a constant value. In the long-time limit, depending on the network size N and connectivity parameter m , the limiting probability distributions of CTQWs show various patterns. When the network size N is an even number, the probability of being at the original node differs from that of being at the opposite node, which also depends on the precise value of parameter m .

Photonic crystal enhanced light-trapping in thin film solar cells

We utilize photonic crystals to simulate enhanced light-trapping in a-Si:H thin film solar cells. A one dimensional photonic crystal or distributed Bragg reflector with alternating dielectric layers acts as low loss backreflector. A two dimensional photonic crystal between the absorber layer and the Bragg reflector diffracts light at oblique angles within the absorber. The photonic crystal geometry is optimized to obtain maximum absorption. The photonic crystal provides lossless diffraction of photons, increasing the photon path length within the absorber layer. The simulation predicts significantly enhanced photon harvesting between 600 and 775nm below the band edge, and an absorption increase by more than a factor of 10 near the band edge. The optical path length ratio can exceed the classical limit predicted for randomly roughened scattering surfaces at most wavelengths near the band edge. The optical modeling is performed with a rigorous scattering matrix approach where Maxwell’s equations are solved in Fourier space.

Sway ratio - a new measure for quantifying postural stability.

In the search of a reliable postural stability index, two sway time series: the center-of-mass (COM) and the center-of-foot pressure (COP) were recorded simultaneously in elderly subjects standing quiet with eyes open and with eyes closed. From a battery of commonly use sway measures, only the anteroposterior COM and the COP path lengths proved their high sensitivity and discriminative power to the imposed vision conditions. Based upon these indices, a new measure - sway ratio (SR) - was computed, as the COP-to-COM path length ratio. The measure can easily distinguish vision vs. no vision in the elderly. The SR can be successfully accessed base upon the COP signal only. In contrast to traditional sway indices, the SR as a relative measure is insensitive to the length of sampled record and to the signal sampling frequency. Its magnitude can be interpreted as an average amount of balance controlling motor activity that coincides with a unit COM displacement. The SR is recommended as a reliable measure that allows for assessment of postural stability.

Dynamic modelling of saturable reactor for HVDC applications

Experimental development of dynamic models for the saturable reactor for HVDC applications was made by taking account of the effects of the eddy-current, the air gap, and the nonlinear magnetisation of the cores of the 3% grain-oriented silicon steels used. The experimentally developed models were confirmed by comparing them to measurements with regard to step current, rate of change of the reactor current, and the current reversal as a result of the oscillations between the storage capacitance and the equivalent inductance of the saturable reactor. The magnetising inductances and the rules for approaching saturation of the cores were determined from actual static magnetisation curves, corrected according to the core geometry and the size of the air gaps used. The linear relationships between the mean magnetic polarisations and the eddy-current resistance factors, which correspond to the eddy-current resistance for a reactor with a 1-turn exciting coil and a unit core cross-sectional area-to-magnetic path length ratio, were established using a circuit representing the capacitance discharging in typical HVDC applications. The work presented simplifies the optimisation process, which aims to minimise the reactor cost and losses, but without compromising the safe protection of the semiconductors for HVDC applications.

Waveguiding properties of fiber-optic capillaries for chemical sensing applications

The optical properties of a novel fused silica fiber-optic capillary (FOCap) waveguide for absorbance spectroscopy were evaluated. Absorbance within the tubing was measured by optically coupling the FOCap to a spectrophotometer. The FOCap operated evanescently or as a liquid core waveguide (LCW) depending upon the refractive index of the solution within the capillary core. Evanescent absorbance was linear with concentration of a non-polar dye but non-linear with ionic dyes due to adsorption to the capillary wall. Evanescent absorbance was linear with FOCap length up to 50m. Evanescent field depth of penetration ratios determined from peak absorbances at λmax for a series of thiacyanine dyes show increasing penetration depth with increasing absorbance wavelength as predicted by theory. Evanescent absorbance measurements in 50, 150, and 250μm inner diameter (ID) FOCaps show that greater sensitivity is achieved in thinner-walled tubing with more internal reflections. The evanescent effective pathlength ratio (EPLR) of 150μm ID FOCaps is on the order of ∼10−6 to 10−5m/m of tubing length. FOCaps operating as LCWs have shorter effective pathlengths than conventional polyimide-coated glass capillaries. A FOCap that determines pH from the evanescent absorbance spectrum of immobilized fluorescein demonstrates the utility of the device as an optical chemical sensor.

Spatial orientation in the bushcricket Leptophyes punctatissima (Phaneropterinae; Orthoptera): II. Phonotaxis to elevated sound sources on a walking compensator

The ability of the bushcricket Leptophyes punctatissima to orient to elevated sound sources was investigated. Males were placed on a walking compensator and oriented in response to a synthetic female reply, which was broadcast via one of five loudspeakers placed at elevations of 0 degrees , 30 degrees , 60 degrees , 75 degrees and 90 degrees . Forward and backward movements were compensated, so that males remained at the same distance and elevation to the sound source. With increasing loudspeaker elevation, the males meandered more, and the ratio of the ideal path length to the actual path length decreased. The same was true for the correlation between stimulus angle and turn angle, and there were more turns to the wrong side with increasing loudspeaker elevation. Most males performed phonotaxis with a high acuity up to an elevation of 60 degrees . Individuals varied strongly in their performance especially at a source elevation of 75 degrees , where some were still very accurate in their approach, whereas the acuity of others decreased rapidly. We also describe a behaviour where males tilt their body axis to more anterior and sideward positions, both during walking and while calling on the spot. This behaviour is interpreted as a kind of directional scanning in order to actively induce changes in binaural cues.

Development and verification of a coupled DSMC–NS scheme using unstructured mesh

An efficient and accurate parallel coupled DSMC–NS method using three-dimensional unstructured grid topology is proposed and verified for the simulation of high-speed gas flows involving continuum and rarefied regimes. A domain overlapping strategy, taking advantage of unstructured data format, with Dirichlet–Dirichlet type boundary conditions based on two breakdown parameters is used iteratively to determine the choice of solvers in the spatial domain. The selected breakdown parameters for this study include: (1) a local maximum Knudsen number defined as the ratio of the local mean free path and local characteristic length based on property gradient and (2) a thermal non-equilibrium indicator defined as the ratio of the difference between translational and rotational temperatures to the translational temperature. A supersonic flow (M∞=4) over a quasi-2-D 25° wedge is employed as the first step in verifying the present coupled method. The results of simulation using the coupled method are in excellent agreement with those of the pure DSMC method, which is taken as the benchmark solution. Effects of the size of overlapping regions and the choice of breakdown parameters on the convergence history are discussed. Results show that the proposed iteratively coupled method predicts the results more accurately as compared to the “one-shot” coupled method, which has been often used in practice. Further, a realistic 3-D nitrogen flow, which two near-continuum parallel orifice jets underexpand into a near-vacuum environment, is simulated using the present coupled method to demonstrate its capability. Finally, developments in extending the present method are also outlined in this paper.

The determination of relative path length as a measure for tortuosity in compacts using image analysis

Tortuosity is defined as the ratio of the actual path length from start to goal through the pores to the Euclidean distance (shortest linear distance). However, traditional methods to calculate tortuosity, such as the calculation of tortuosity out of the results from dissolution experiments, do not determine path length directly. In this paper we describe the application of image analysis for direct measurement of path length in order to obtain quantitative information on tortuosity. Several planes in cubic sodium chloride compacts, made by uni-axial compression, were imaged using scanning electron microscopy (SEM). In these images the average path length from top-to-bottom and from left-to-right was calculated, using the gray-weighted distance transform (GDT). As the direct, straight forward path was defined as having a length of unity, the relative path length could be taken as a quantitative measure for the tortuosity. The relative path length through the pores was found to be 1.4–1.6 and the relative path length over the grains was significantly lower (1.0–1.2). In most cases, the relative path length through the pores was significantly higher for the compacts containing small particles than for the compacts made of large particles. The relative path length was also dependent on the direction of the measurement, i.e. in the direction of compression of the compact or perpendicular to it. This indicates anisotropy in structure with the pores preferentially oriented in the direction of compression. It was concluded that this method is a valuable tool for the determination of path length in compacts as a direct measure for tortuosity. It can also be used to evaluate the anisotropy in structure.

Analysis of fluid flow through micro‐fluidic devices using characteristic‐based‐split procedure

AbstractGas flow in micro‐electro‐mechanical systems can be considered as rarefied since the ratio of free molecular path length to the characteristic length of the device is high. It is possible to analyse these flows using a conventional Navier–Stokes solver with modified boundary conditions to account for temperature‐jump and slip‐velocity on solid walls. In this study, characteristic‐based‐split (CBS) algorithm is modified to account for slip‐velocity and temperature‐jump boundary conditions in order to perform compressible flow analysis for a micro sized geometry. The CBS algorithm is a split procedure which yields a unified solution method valid for both compressible and incompressible flows. To verify the modified CBS solver, straight micro channel and micro step duct geometries are selected as test cases. To reduce the size of the implicit part of the algorithm, pseudo‐quadratic velocity/linear pressure elements (pP2P1) are employed. The results obtained using CBS algorithm, are compared with other analytical and computational results available in the literature. It is shown that this implementation of the CBS algorithm is applicable and effective for micro gas flows. It is also shown that, increasing Knudsen number results in increased temperature‐jump and slip‐velocity. This effect, however, is limited, especially for high Mach number flows. Copyright © 2006 John Wiley & Sons, Ltd.

Improved soil hydraulic conductivity function based on specific liquid–vapour interfacial area around the soil particles

Improvement in the prediction of soil hydraulic conductivity function is a major concern in soil physics. Zand-Parsa and Sepaskhah (2004) [Zand-Parsa, Sh., Sepaskhah, A.R., 2004. Soil hydraulic conductivity function based on specific liquid–vapour interfacial area around the soil particles. Geoderma 119, 143–157] proposed a new method for the prediction of soil hydraulic conductivity function [ K( h) or K( θ) (where h and θ are soil water pressure head and water content, respectively] based on specific liquid–vapour interfacial area around the soil particles (SLVIA). In the present paper, the SLVIA method was improved as follows: (i) a more straightforward and efficient numerical technique for the prediction of K( θ) function was proposed instead of the analytical method in Zand-Parsa and Sepaskhah; (ii) saturated soil hydraulic conductivity ( K s) was predicted by assumption of a linear relationship between K( θ) and θ for very small θ ranges near saturated soil water content; (iii) the value of soil tortuosity (ratio of actual path length to the straight path length of flow) factor ( Tr) was estimated by using the Newton–Raphson method, by minimizing the difference between predicted and measured saturated soil hydraulic conductivity. The K( θ) curve was predicted by soil water characteristic curve and measured saturated soil hydraulic conductivity. Soil water characteristic curve was predicted by the van Genuchten method with four required soil parameters [ α, n, residual soil water content ( θ r), and saturated soil water content ( θ sat) [van Genuchten, M.Th., 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soil. Soil Sci. Soc. Am. J. 44, 892–898]. A computer program (UNSATK model) written in VISUAL BASIC was used to predict the K( h) or K( θ) curve. The utility of the UNSATK model was tested for three soil types (sandy, loamy, and clayey textures) selected from the literature. The uniqueness of model outputs for each selected soil was checked by different input Tr values. Model predictions yielded reasonable agreement with measured soil hydraulic conductivity data and compared favorably with the widely applied Mualem–van Genuchen method.

Soil hydraulic conductivity function based on specific liquid–vapor interfacial area around the soil particles

Water in soils flows through a tortuous path which depends on the specific liquid–vapor interfacial area around the soil particles ( A ws) and tortuosity factor ( ξ). This specific area is defined as the area of liquid–vapor interfacial around the soil particles per unit bulk volume of soil. The objective of this study was to develop a new approach for determining unsaturated hydraulic conductivity using soil water characteristic function based on the specific liquid–vapor interfacial area around the soil particles. In this study, the capillary rise equation has been modified by A ws. The A ws was determined from the soil water retention curve. Tortuosity factor or the ratio of actual path length to the straight path length of flow was estimated based on A ws by trail and error procedure from soil water retention curve and measurement of saturated soil hydraulic conductivity. Therefore, a new soil hydraulic conductivity function ( K– θ) was derived based on soil water retention curve, A ws and ξ in laminar flow conditions. In this approach, variable liquid viscosity near the soil particles was considered and a tortuous undulating wide-open channel with small and variable water depth was assumed. The resulted curves of K– θ by derived equations were compared with experimental K– θ data for 19 different soils from sandy to clayey textures obtained from literature. The results of comparison show that the estimated K– θ and D– θ ( D is soil hydraulic diffusivity) relationships are very close to those reported in literature for the 19 selected soils.

Rotation Measure and Opacity Asymmetry in 2134+004

AbstractBased on the free–free absorption (FFA) model of gigahertz peaked spectrum (GPS) sources, we explain both Faraday rotation asymmetry and opacity asymmetry consistently between two components of a GPS quasar 2134+004. The FFA model assumes dense plasma around the central core to produce FFA, and the difference of path lengths in the plasma toward each component could cause these asymmetries. The component that is closer to the observer has a shorter path length, and consequently, smaller opacity of FFA and lower Faraday rotation. In a simple case, the ratio of Faraday rotation between two components is a function of the ratio of path length, and is the same as the ratio of opacity. Then these two ratios are shown to be essentially the same by our observations. We could thus distinguish between near-side and far-side components by the asymmetries.

A Technique for Processing Undisturbed Marine Sand Sediments and Reconstructing Fabric and Porometry

ABSTRACT Study of marine sediment pore fluid pathways and porometry requires careful analysis of the fabric of undisturbed sediment samples. A novel solution to the preservation of the interstitial organic material and the in situ fabric or sedimentary structure is the application, with little modification, of well-established biological techniques employing agar infiltration. The solidified agar preserves fabric during subsequent epoxy impregnation. Once impregnated, porosity of the samples can be measured using image analysis of polished surfaces of the microfabric and/or a gravimetric-volumetric technique. Porosity was about 10% higher with image analysis, apparently because of problems in visualizing carbonates and edges of grains. Tortuosity was measured as a function of pathlength ratios taken in stacked planes of microfabric images. The technique allowed us to detect variability in directional tortuosity as a function of orthogonal pathlength ratios. Three-dimensional stacking of digitally acquired wireframe images of sequential planes through the microfabric allows visualization of long continuous pores, some with 2.6 mm length.

Mass transfer characteristics of artificial lungs.

An artificial lung is used during cardiopulmonary bypass to oxygenate blood and control blood temperature. The oxygen transfer rate-flow rate characteristics of three hollow fiber membrane artificial lungs (Sarns Turbo 440, Cobe Optima, Dideco Compactflo) were determined in vitro to characterize design features. Results are presented as a unique dimensionless relationship between Sherwood number, NSh (ratio of convective to diffusive mass transfer), Schmidt number, NSc (ratio of momentum to diffusive transport), and Reynolds number, NRe (ratio of inertial to viscous forces). This relationship is a function of device porosity, epsilon, and characteristic device length, xi, defined as the ratio of the mean blood path and manifold length: Nsh/NSc(1/3) x xi(1/2) = phi x (epsilon(1/m) x NRe)(m) where phi = 0.26 and m = 1.00 for NPe < 3,200 and phi = 0.47 and m = 0.64 for NPe > 3,200 where NPe is the dimensionless Péclet number defined as NRe x NSc. We found good correspondence between the model predictions and in vitro blood oxygen transfer rates. We conclude that this dimensionless approach allows us (1) to compare artificial lungs independently, (2) to relate water tests to blood, and (3) to predict the oxygen transfer rate of a new artificial lung design.

A new “geometric” mapping function for the hydrostatic delay at GPS frequencies

The hydrostatic mapping function, m(ε), is a dimensionless factor which describes the elevation angle dependence of the hydrostatic path delay and relates the line of sight delay to the zenith delay. We have developed a simple “geometric” mapping function where the only free parameter (besides the elevation angle, ε) is the climatological pressure scale height. The value of m(ε) is given by the ratio of the straight-line ray path length within the first two scale heights above the surface and the “effective height” defined by these first two scale heights. We used simulated neutral delays at GPS frequencies derived from high resolution ECMWF (European Centre for Medium-Range Weather Forecasts) atmospheric analysis fields (T213L50, T213L60) at different latitudes to compare the new mapping function with others currently in use (we compare with the Niell and the Davis mapping function, respectively, most frequently encountered in literature).At elevations > 6° the geometric mapping function displays, without involving any meteorological data, comparable or better accuracy and precision than the other mapping functions.

Hydrodynamic characteristics of artificial lungs.

An artificial lung is used during cardiopulmonary bypass to oxygenate blood and to control blood temperature. The pressure drop-flow rate characteristics of the membrane compartment in three hollow fiber membrane oxygenators were determined in vitro to characterize design features. Results are presented in a unique dimensionless relationship between Euler number, N(Eu) (ratio of pressure drop to kinetic energy), and Reynolds number, N(Re) (ratio of inertial to viscous forces), and are a function of the device porosity, epsilon, and a characteristic device length, xi, defined as the ratio of the mean blood path and manifold length: [equation in text]. This dimensionless approach allows us (1) to compare oxygenators independently, and (2) to relate water tests to blood.

Markov paths on the Poisson-Delaunay graph with applications to routeing in mobile networks

Consider the Delaunay graph and the Voronoi tessellation constructed with respect to a Poisson point process. The sequence of nuclei of the Voronoi cells that are crossed by a line defines a path on the Delaunay graph. We show that the evolution of this path is governed by a Markov chain. We study the ergodic properties of the chain and find its stationary distribution. As a corollary, we obtain the ratio of the mean path length to the Euclidean distance between the end points, and hence a bound for the mean asymptotic length of the shortest path.We apply these results to define a family of simple incremental algorithms for constructing short paths on the Delaunay graph and discuss potential applications to routeing in mobile communication networks.

Markov paths on the Poisson-Delaunay graph with applications to routeing in mobile networks

Consider the Delaunay graph and the Voronoi tessellation constructed with respect to a Poisson point process. The sequence of nuclei of the Voronoi cells that are crossed by a line defines a path on the Delaunay graph. We show that the evolution of this path is governed by a Markov chain. We study the ergodic properties of the chain and find its stationary distribution. As a corollary, we obtain the ratio of the mean path length to the Euclidean distance between the end points, and hence a bound for the mean asymptotic length of the shortest path. We apply these results to define a family of simple incremental algorithms for constructing short paths on the Delaunay graph and discuss potential applications to routeing in mobile communication networks.