Bubble extinction in Hele-Shaw flow with surface tension and kinetic undercooling regularisation

We perform an analytic and numerical study of an inviscid contracting bubble in a two-dimensional Hele-Shaw cell, where the effects of both surface tension and kinetic undercooling on the moving bubble boundary are not neglected. In contrast to expanding bubbles, in which both boundary effects regularise the ill-posedness arising from the viscous (Saffman-Taylor) instability, we show that in contracting bubbles the two boundary effects are in competition, with surface tension stabilising the boundary, and kinetic undercooling destabilising it. This competition leads to interesting bifurcation behaviour in the asymptotic shape of the bubble in the limit it approaches extinction. In this limit, the boundary may tend to become either circular, or approach a line or "slit" of zero thickness, depending on the initial condition and the value of a nondimensional surface tension parameter. We show that over a critical range of surface tension values, both these asymptotic shapes are stable. In this regime there exists a third, unstable branch of limiting self-similar bubble shapes, with an asymptotic aspect ratio (dependent on the surface tension) between zero and one. We support our asymptotic analysis with a numerical scheme that utilises the applicability of complex variable theory to Hele-Shaw flow.

Insights into the nature of the coupling interactions between uracil corrosion inhibitors and copper : a DFT and molecular dynamics study

In this study, the nature of the coupling interactions between copper and uracil as well as its several derivatives has been systematically investigated employing the atoms in molecules (AIM) theory and energy decomposition analyses. The whole interaction process has been investigated through the analyses of the radial distribution functions of the Cu⋯X (X = S and O) contact on the basis of the ab initio molecular dynamics. No direct relationship between the adsorption strengths and inhibition efficiencies of the inhibitors has been observed. Additionally, the possibility of the methyl-substituted dithiouracil species to act as copper corrosion inhibitors has been tested.

An accurate numerical scheme for the contraction of a bubble in a Hele-Shaw cell

We report on an accurate numerical scheme for the evolution of an inviscid bubble in radial Hele-Shaw flow, where the nonlinear boundary effects of surface tension and kinetic undercooling are included on the bubble-fluid interface. As well as demonstrating the onset of the Saffman-Taylor instability for growing bubbles, the numerical method is used to show the effect of the boundary conditions on the separation (pinch-off) of a contracting bubble into multiple bubbles, and the existence of multiple possible asymptotic bubble shapes in the extinction limit. The numerical scheme also allows for the accurate computation of bubbles which pinch off very close to the theoretical extinction time, raising the possibility of computing solutions for the evolution of bubbles with non-generic extinction behaviour.

The interplay between chondrocyte redifferentiation pellet size and oxygen concentration

Chondrocytes dedifferentiate during ex vivo expansion on 2-dimensional surfaces. Aggregation of the expanded cells into 3-dimensional pellets, in the presence of induction factors, facilitates their redifferentiation and restoration of the chondrogenic phenotype. Typically 1×105–5×105 chondrocytes are aggregated, resulting in “macro” pellets having diameters ranging from 1–2 mm. These macropellets are commonly used to study redifferentiation, and recently macropellets of autologous chondrocytes have been implanted directly into articular cartilage defects to facilitate their repair. However, diffusion of metabolites over the 1–2 mm pellet length-scales is inefficient, resulting in radial tissue heterogeneity. Herein we demonstrate that the aggregation of 2×105 human chondrocytes into micropellets of 166 cells each, rather than into larger single macropellets, enhances chondrogenic redifferentiation. In this study, we describe the development of a cost effective fabrication strategy to manufacture a microwell surface for the large-scale production of micropellets. The thousands of micropellets were manufactured using the microwell platform, which is an array of 360×360 µm microwells cast into polydimethylsiloxane (PDMS), that has been surface modified with an electrostatic multilayer of hyaluronic acid and chitosan to enhance micropellet formation. Such surface modification was essential to prevent chondrocyte spreading on the PDMS. Sulfated glycosaminoglycan (sGAG) production and collagen II gene expression in chondrocyte micropellets increased significantly relative to macropellet controls, and redifferentiation was enhanced in both macro and micropellets with the provision of a hypoxic atmosphere (2% O2). Once micropellet formation had been optimized, we demonstrated that micropellets could be assembled into larger cartilage tissues. Our results indicate that micropellet amalgamation efficiency is inversely related to the time cultured as discreet microtissues. In summary, we describe a micropellet production platform that represents an efficient tool for studying chondrocyte redifferentiation and demonstrate that the micropellets could be assembled into larger tissues, potentially useful in cartilage defect repair.

The acute response of tendon to loading: implications for rehabilitation

Achilles tendinopathy is a common disorder involving physically active and sedentary individuals alike. Although the processes underlying its development are poorly understood, tendinopathy is widely regarded as an ‘overuse’ injury in which the tendon fails to adapt to prevalent loading conditions. Paradoxically, there is emerging evidence that heavy eccentric loading of the Achilles tendon may be an effective conservative approach for treatment of tendinopathy, with success rates of 60–80% reported. Interestingly, loading exercises involving other forms of muscle action, such as concentric activation, have been shown to be less effective treatment options. However, little is known about the acute response of tendon to exercise at present, and there are few plausible explanatory mechanisms for the observed beneficial effects of eccentric exercise, as opposed to other forms of strain stimuli. This paper presents the findings from a series of experiments undertaken to evaluate the effect of various strain stimuli on the time-dependent response of human Achilles tendon in vivo. It was shown for the first time, that heavy resistive ankle plantarflexion/ dorsiflexion exercises induced an immediate and significant decrease in Achilles tendon thickness (~15%). While thickness returned to pre-exercise levels within 24 hours, the recovery was exponential, with primary recovery occurring in less than 6 hours post-exercise. We proposed that such a diametral strain response with tensile loading reflects collagen realignment, Poison’s effects and radial extrusion of water from the tendon core. With unloading, the recovery of tendon dimensions likely reflects the re-diffusion of water via osmotic and/or inflammatory driven processes. Interestingly, prolonged walking was found to induce a similar diametral strain response. In subsequent studies, we demonstrated that eccentric exercise resulted in a greater reduction (-21%) in Achilles tendon thickness than isolated concentric exercise alone (-5%), despite a similar loading impulse. These novel findings, coupled with observations of a reduced diametral strain response with tendon pathology, highlight the importance of fluid movement to tendon function, nutrition and health. They also provide new insights into potential mechanisms underlying Achilles tendinopathy that impact rehabilitation strategies.

Design optimisation of ironless motors based on magnet selection

This paper considers the design of a radial flux permanent magnet iron less core brushless DC motor for use in an electric wheel drive with an integrated epicyclic gear reduction. The motor has been designed for a continuous output torque of 30 Nm and peak rating of 60 Nm with a maximum operating speed of 7000 RPM. In the design of brushless DC motors with a toothed iron stator the peak air-gap magnetic flux density is typically chosen to be close to that of the remanence value of the magnets used. This paper demonstrates that for an ironless motor the optimal peak air-gap flux density is closer to the maximum energy product of the magnets used. The use of a radial flux topology allows for high frequency operation and can be shown to give high specific power output while maintaining a relatively low magnet mass. Two-dimensional finite element analysis is used to predict the air-gap flux density. The motor design is based around commonly available NdFeB bar magnet size

Design optimisation of ironless motors based on magnet selection

This paper considers the design of a radial flux permanent magnet ironless core brushless DC motor for use in an electric wheel drive with an integrated epicyclic gear reduction. The motor has been designed for a continuous output torque of 30 Nm and peak rating of 60 Nm with a maximum operating speed of 7000 RPM. In the design of brushless DC motors with a toothed iron stator the peak air-gap magnetic flux density is typically chosen to be close to that of the remanence value of the magnets used. This paper demonstrates that for an ironless motor the optimal peak air-gap flux density is closer to the maximum energy product of the magnets used. The use of a radial flux topology allows for high frequency operation and can be shown to give high specific power output while maintaining a relatively low magnet mass. Two-dimensional finite element analysis is used to predict the airgap flux density. The motor design is based around commonly available NdFeB bar magnet size

Choroidal thickness in childhood

Purpose To examine choroidal thickness (ChT) and its spatial distribution across the posterior pole in pediatric subjects with normal ocular health and minimal refractive error. Methods ChT was assessed using spectral domain optical coherence tomography (OCT) in 194 children aged between 4-12 years, with spherical equivalent refractive errors between +1.25 and -0.50 DS. A series of OCT scans were collected, imaging the choroid along 4 radial scan lines centered on the fovea (each separated by 45°). Frame averaging was used to reduce noise and enhance chorio-scleral junction visibility. The transverse scale of each scan was corrected to account for magnification effects associated with axial length. Two independent masked observers manually segmented the OCT images to determine ChT at foveal centre, and averaged across a series of perifoveal zones over the central 5 mm. Results The average subfoveal ChT was 330 ± 65 µm (range 189-538 µm), and was significantly influenced by age (p=0.04). The ChT of the 4 to 6 year old age group (312 ± 62 µm) was significantly thinner compared to the 7 to 9 year olds (337 ± 65 µm, p<0.05) and bordered on significance compared to the 10 to 12 year olds (341 ± 61 µm, p=0.08). ChT also exhibited significant variation across the posterior pole, being thicker in more central regions. The choroid was thinner nasally and inferiorly compared to temporally and superiorly. Multiple regression analysis revealed age, axial length and anterior chamber depth were significantly associated with subfoveal ChT (p<0.001). Conclusions ChT increases significantly from early childhood to adolescence. This appears to be a normal feature of childhood eye growth.

Interocular corneal symmetry in refractive error groups

Purpose: To examine between eye differences in corneal higher order aberrations and topographical characteristics in a range of refractive error groups. Methods: One hundred and seventy subjects were recruited including; 50 emmetropic isometropes, 48 myopic isometropes (spherical equivalent anisometropia ≤ 0.75 D), 50 myopic anisometropes (spherical equivalent anisometropia ≥ 1.00 D) and 22 keratoconics. The corneal topography of each eye was captured using the E300 videokeratoscope (Medmont, Victoria, Australia) and analyzed using custom written software. All left eye data were rotated about the vertical midline to account for enantiomorphism. Corneal height data were used to calculate the corneal wavefront error using a ray tracing procedure and fit with Zernike polynomials (up to and including the eighth radial order). The wavefront was centred on the line of sight by using the pupil offset value from the pupil detection function in the videokeratoscope. Refractive power maps were analysed to assess corneal sphero-cylindrical power vectors. Differences between the more myopic (or more advanced eye for keratoconics) and the less myopic (advanced) eye were examined. Results: Over a 6 mm diameter, the cornea of the more myopic eye was significantly steeper (refractive power vector M) compared to the fellow eye in both anisometropes (0.10 ± 0.27 D steeper, p = 0.01) and keratoconics (2.54 ± 2.32 D steeper, p < 0.001) while no significant interocular difference was observed for isometropic emmetropes (-0.03 ± 0.32 D) or isometropic myopes (0.02 ± 0.30 D) (both p > 0.05). In keratoconic eyes, the between eye difference in corneal refractive power was greatest inferiorly (associated with cone location). Similarly, in myopic anisometropes, the more myopic eye displayed a central region of significant inferior corneal steepening (0.15 ± 0.42 D steeper) relative to the fellow eye (p = 0.01). Significant interocular differences in higher order aberrations were only observed in the keratoconic group for; vertical trefoil C(3,-3), horizontal coma C(3,1) secondary astigmatism along 45 C(4, -2) (p < 0.05) and vertical coma C(3,-1) (p < 0.001). The interocular difference in vertical pupil decentration (relative to the corneal vertex normal) increased with between eye asymmetry in refraction (isometropia 0.00 ± 0.09, anisometropia 0.03 ± 0.15 and keratoconus 0.08 ± 0.16 mm) as did the interocular difference in corneal vertical coma C (3,-1) (isometropia -0.006 ± 0.142, anisometropia -0.037 ± 0.195 and keratoconus -1.243 ± 0.936 μm) but only reached statistical significance for pair-wise comparisons between the isometropic and keratoconic groups. Conclusions: There is a high degree of corneal symmetry between the fellow eyes of myopic and emmetropic isometropes. Interocular differences in corneal topography and higher order aberrations are more apparent in myopic anisometropes and keratoconics due to regional (primarily inferior) differences in topography and between eye differences in vertical pupil decentration relative to the corneal vertex normal. Interocular asymmetries in corneal optics appear to be associated with anisometropic refractive development.

A RBF meshless approach for modeling a fractal mobile/immobile transport model

A fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBFs) to discretize the space variable. In contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example which is presented to describe a fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating fractional differential equations, and it has good potential in the development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

Differential pathologic variables and outcomes across the spectrum of adenocarcinoma of the esophagogastric junction

Background Adenocarcinoma of the esophagogastric junction (AEG) as described by Siewert et al. is classified as one entity in the latest (7th Edition) American Joint Cancer Committee/International Union Against Cancer (AJCC/UICC) manual, compared with the previous mix of esophageal and gastric staging systems. The origin of AEG tumors, esophageal or gastric, and their biology remain controversial, particularly for AEG type II (cardia) tumors. Methods We adapted a large prospective database (n = 520: 180 type I, 182 type II, 158 type III) to compare AEG tumors under the new TNM system Pathological variables associated with prognosis were compared (pT, pN, stage, differentiation, R status, lymphovascular invasion, perineural involvement, number of positive nodes, percent of positive nodes, and tumor length), as well as overall survival. Results Compared with AEG type I tumors, type II and type III tumors had significantly (p\0.05) more advanced pN stages, greater number and percentage of positive nodes, poorer differentiation, more radial margin involvement, and more perineural invasion. In AEG type I, 14/180 patients (8%) had[6 involved nodes (pN3), compared with 16 and 30% of patients classified type II and III, respectively. Median survival was significantly (p = 0.03) improved for type I patients (38 months) compared with those with tumors classified as type II (28 months) and type III (24 months). In multivariate analysis node positivity and pN staging but not AEG site had an impact on survival. Conclusions In this series AEG type I is associated with more favorable pathologic features and improved outcomes compared with AEG type II and III. This may reflect earlier diagnosis, but an alternative possibility, that type I may be a unique paradigm with more favorable biology, requires further study. © Société Internationale de Chirurgie 2010.

How transit route passenger load and distance can together influence quality of service

This paper investigates quality of service and resource productivity implications of transit route passenger loading and travel distance. Weekday Automatic Fare Collection data for a premium radial bus route in Brisbane, Australia, is used to investigate correlation between load factor and distance factor. Relationships between boardings and transit work indicate that distance factor generally increases with load factor. Time series analysis is then presented by examining each direction on an hour by hour basis. Inbound correlation is medium to strong across the entire span of service and strong for daytime services up to 19:30, while outbound correlation is strong across the entire span. Passengers tend to be making longer distance, peak direction commuter trips under the least comfortable conditions under stretched peak schedules than off-peak. Therefore productivity gains may be possible by adjusting fleet utilization during off-peak times. Weekday profiles by direction are established for a composite load-distance factor. A threshold corresponding to standing passengers on the Maximum Load Segment reveals that on-board loading and travel distance combined are more severe during the morning inbound peak than evening outbound peak, although the sharpness of the former suggests that encouraging shoulder peak travel during the morning would be more effective than evening peak. Further research suggested includes: consideration of travel duration factor, relating noise within hour to Peak Hour Factor, profiling load-distance factor across a range of case studies, and relating load-distance factor threshold to line length.

Choroidal thickness in myopic and non-myopic children assessed with enhanced depth imaging optical coherence tomography

Purpose To examine choroidal thickness (ChT) and its topographical variation across the posterior pole in myopic and non-myopic children. Methods One hundred and four children aged 10-15 years of age (mean age 13.1 ± 1.4 years) had ChT measured using enhanced depth imaging optical coherence tomography (OCT). Forty one children were myopic (mean spherical equivalent -2.4 ± 1.5 D) and 63 non-myopic (mean +0.3 ± 0.3 D). Two series of 6 radial OCT line scans centred on the fovea were assessed for each child. Subfoveal ChT and ChT across a series of parafoveal zones over the central 6mm of the posterior pole were determined through manual image segmentation. Results Subfoveal ChT was significantly thinner in myopes (mean 303 ± 79 µm) compared to non-myopes (mean 359 ± 77 µm) (p<0.0001). Multiple regression analysis revealed both refractive error (r = 0.39, p<0.001) and age (r = 0.21, p = 0.02) were positively associated with subfoveal ChT. ChT also exhibited significant topographical variations, with the choroid being thicker in more central regions. The thinnest choroid was typically observed in nasal (mean 286 ± 77 µm) and inferior-nasal (306 ± 79 µm) locations, and the thickest in superior (346 ± 79 µm) and superior-temporal (341 ± 74 µm) locations. The difference in ChT between myopic and non-myopic children was significantly greater in central foveal regions compared to more peripheral regions (>3 mm diameter) (p<0.001). Conclusions Myopic children have significantly thinner choroids compared to non-myopic children of similar age, particularly in central foveal regions. The magnitude of difference in choroidal thickness associated with myopia appears greater than would be predicted by a simple passive choroidal thinning with axial elongation.

Stability of corneal topography and wavefront aberrations in young Singaporeans

Purpose To investigate the differences between and variations across time in corneal topography and ocular wavefront aberrations in young Singaporean myopes and emmetropes. Methods We used a videokeratoscope and wavefront sensor to measure the ocular surface topography and wavefront aberrations of the total eye optics in the morning, mid-day and late afternoon on two separate days. Topography data were used to derive the corneal surface wavefront aberrations. Both the corneal and total wavefronts were analysed up to the 4th radial order of the Zernike polynomial expansion, and were centred on the entrance pupil (5 mm). The participants included 12 young progressing myopes, 13 young stable myopes and 15 young age-matched emmetropes. Results For all subjects considered together there were significant changes in some of the aberrations terms across the day, such as spherical aberration ( ) and vertical coma ( ) (repeated measures ANOVA, p<0.05). The magnitude of positive spherical aberration ( ) was significantly lower in the progressing myope group than that of the stable myopes (p=0.04) and emmetrope group (p=0.02). There were also significant interactions between refractive group and time of day for with/against-the-rule astigmatism ( ). Significantly lower 4th order RMS of ocular wavefront aberrations were found in the progressing myope group compared with the stable myopes and emmetropes (p<0.01). Conclusions These differences and variations in the corneal and total aberrations may have significance for our understanding of refractive error development and for clinical applications requiring accurate wavefront measurements.

Load leveling in LV network using coordianted Energy Storage Units

This paper proposes a new distributed coordination approach to make load leveling, using Energy Storage Units (ESUs) in LV network. The proposed distributed control strategy is based on consensus algorithm which shares the required active power equally among the ESUs with respect to their rating. To show the effectiveness of the proposed approach, a typical radial LV network is simulated as a case study.