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1
Claisse, Penny J., Jodi Binning, and Julia Potter. "Effect of Orthotic Therapy on Claw Toe Loading." Journal of the American Podiatric Medical Association 94, no. 3 (May 1, 2004): 246–54. http://dx.doi.org/10.7547/0940246.
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This study demonstrates the effect of orthotic therapy for toe deformity on toe and metatarsal head pressures using a new analysis method facilitated by an in-shoe pressure-measurement system’s ability to export detailed data. Plantar pressure–time integrals in 11 individuals (22 feet) with claw deformity of the lesser toes were measured with and without toe props. Differences in pressure–time integrals at every individual sensor unit were then calculated for the two conditions, and significance was tested using the paired t-test. Plantar surface charts with contours of equal significant pressure–time integral change showed significant reduction under 17 second toes (77%), 22 third toes (100%), 15 fourth toes (68%), 13 second metatarsal heads (59%), 16 third metatarsal heads (73%), and 16 fourth metatarsal heads (73%). All 22 feet showed increases under the prop in the area of the third toe sulcus. This innovative approach to plantar pressure analysis could improve access to data that show significant pressure–time integral changes and, therefore, could advance the clinical application of plantar pressure measurement. (J Am Podiatr Med Assoc 94(3): 246–254, 2004)
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Naraghi, Reza, Linda Slack-Smith, and Alan Bryant. "Plantar Pressure Measurements and Geometric Analysis of Patients With and Without Morton’s Neuroma." Foot & Ankle International 39, no. 7 (April 11, 2018): 829–35. http://dx.doi.org/10.1177/1071100718766553.
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Background: The purpose of this research was to see if there were any differences in peak pressure, contact time, pressure-time integrals, and geometric variables such as forefoot width, foot length, coefficient of spreading, and arch index between subjects with Morton’s neuroma (MN) and control subjects. Methods: Dynamic peak plantar pressure, contact time, pressure-time integral, and geometric data were extracted using the EMED-X platform in 52 subjects with MN and 31 control subjects. Differences in peak pressure, contact time, pressure-time integral, and geometric data between participants with and those without MN were determined using independent-samples t tests. There were no significant differences in age, weight, height, and body mass index between patients with MN and control subjects. Results: There were no significant differences in the peak pressures of all masked areas and pressure-time integrals under metatarsal 2 to 4 heads between patients with MN and control subjects. In addition, no significant differences were observed between patients with MN and control subjects in geometric measurements of forefoot length, width, coefficient of spreading, foot progression angle, and arch index. Conclusion: No relationship was found in this study between peak pressure, contact time, and pressure-time integral under the metatarsal heads, forefoot width, foot length, coefficient of spreading, and foot progression angle in a symptomatic MN group compared with a control group. The need to perform osteotomies to treat MN not associated with other lesser metatarsal phalangeal joint pathologies is questionable. Level of Evidence: Level III, Case-Control Study
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Tong, Jasper W. K., U. Rajendra Acharya, Kuang C. Chua, and Peck H. Tan. "In-shoe Plantar Pressure Distribution in Nonneuropathic Type 2 Diabetic Patients in Singapore." Journal of the American Podiatric Medical Association 101, no. 6 (November 1, 2011): 509–16. http://dx.doi.org/10.7547/1010509.
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Background: We sought to establish the in-shoe plantar pressure distribution during normal level walking in type 2 diabetic patients of Chinese, Indian, and Malay descent without clinical evidence of peripheral neuropathy. Methods: Thirty-five patients with type 2 diabetes mellitus without loss of tactile sensation and foot deformities and 38 nondiabetic individuals in a control group had in-shoe plantar pressures collected. Maximum peak pressure and peak pressure-time integral of each foot were analyzed as separate variables and were masked into 13 areas. Differences in pressure variables were assessed by analysis of covariance, adjusting for relevant covariates at the 95% confidence interval. Results: No significant differences were noted in maximum peak pressures after adjusting for sex, race, age, height, and body mass. However, patients with diabetes mellitus had significantly higher mean ± SD pressure-time integrals at the right whole foot (309.50 ± 144.17 kPa versus 224.06 ± 141.70 kPa, P < .05) and first metatarsal (198.65 ± 138.27 kPa versus 121.54 ± 135.91 kPa, P < .05) masked areas than did those in the control group after adjustment. Conclusions: Patients without clinical observable signs of foot deformity (implying absence of motor neuropathy) and sensory neuropathy had similar in-shoe maximum peak pressures as controls. This finding supported the notion that either component of neuropathy needs to be present before plantar pressures are elevated. Patients with diabetes mellitus demonstrated greater pressure-time integrals, implying that this variable might be the first clinical sign observable even before peripheral neuropathy could be tested. (J Am Podiatr Med Assoc 101(6): 509–516, 2011)
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Borg, Iona, Stephen Mizzi, and Cynthia Formosa. "Plantar Pressure Distribution in Patients with Diabetic Peripheral Neuropathy and a First-Ray Amputation." Journal of the American Podiatric Medical Association 108, no. 3 (May 1, 2018): 225–30. http://dx.doi.org/10.7547/16-021.
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Background: Elevated dynamic plantar pressures are a consistent finding in diabetic patients with peripheral neuropathy, with implications for plantar foot ulceration. This study aimed to investigate whether a first-ray amputation affects plantar pressures and plantar pressure distribution patterns in individuals living with diabetes and peripheral neuropathy. Methods: A nonexperimental matched-subject design was conducted. Twenty patients living with diabetes and peripheral neuropathy were recruited. Group 1 (n = 10) had a first-ray amputation and group 2 (n = 10) had an intact foot with no history of ulceration. Plantar foot pressures and pressure-time integrals were measured under the second to fourth metatarsophalangeal joints, fifth metatarsophalangeal joint, and heel using a pressure platform. Results: Peak plantar pressures under the second to fourth metatarsophalangeal joints were significantly higher in participants with a first-ray amputation (P = .008). However, differences under the fifth metatarsophalangeal joint (P = .734) and heel (P = .273) were nonsignificant. Pressure-time integrals were significantly higher under the second to fourth metatarsophalangeal joints in participants with a first-ray amputation (P = .016) and in the heel in the control group (P = .046). Conclusions: Plantar pressures and pressure-time integrals seem to be significantly higher in patients with diabetic peripheral neuropathy and a first-ray amputation compared with those with diabetic neuropathy and an intact foot. Routine plantar pressure screening, orthotic prescription, and education should be recommended in patients with a first-ray amputation.
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Štefan, Lovro, Mario Kasović, and Martin Zvonar. "Association between the levels of physical activity and plantar pressure in 6-14-year-old children." PeerJ 8 (February 14, 2020): e8551. http://dx.doi.org/10.7717/peerj.8551.
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Background The main purpose of the study was to determine whether lower levels of physical activity were associated with higher plantar pressure generated under each foot. Methods In this cross-sectional study, we recruited 641 children aged 6–14 years (agemean ± SD = 9.7 ± 2.4 years; heightmean ± SD = 143.6 ± 15.3 cm, weightmean ± SD = 37.6 ± 13.4 kg; body-mass indexmean ± SD = 17.6 ± 3.2 kg/m2; 44.2% girls). We used EMED –XL pressure platform to measure force time integral, pressure-time integral, contact-time and contact area, peak plantar pressure and mean plantar pressure of the right and the left foot during the gait analysis. The level of physical activity was measured by using The Physical Activity Questionnaire for Older Children (PAQ–C). The associations were calculated by using generalized estimating equations with linear regression models. Results Lower levels of physical activity were associated with higher force- and pressure-time integrals, longer contact time and higher peak and mean plantar pressures in both feet. Conclusion Our study shows that the level of physical activity is strongly and inversely associated with plantar pressure in a sample of 6–14 year olds.
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Chang, An-Hsiung, Ziad U. Abu-Faraj, Gerald F. Harris, Joe Nery, and Michael J. Shereff. "Multistep Measurement of Plantar Pressure Alterations Using Metatarsal Pads." Foot & Ankle International 15, no. 12 (December 1994): 654–60. http://dx.doi.org/10.1177/107110079401501205.
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Metatarsal pads are frequently prescribed for nonoperative management of metatarsalgia due to various etiologies. When appropriately placed, they are effective in reducing pressures under the metatarsal heads on the plantar surface of the foot. Despite the positive clinical reports that have been cited, there are no quantitative studies documenting the load redistribution effects of these pads during multiple step usage within the shoe environment. The objective of this study was to assess changes in plantar pressure metrics resulting from pad use. Ten normal adult male subjects were tested during a series of 400-step trials. Pressures were recorded from eight discrete plantar locations at the hindfoot, midfoot, and forefoot regions of the insole. Significant increases in peak pressures, contact durations, and pressure-time integrals were noted at the metatarsal shaft region with pad use ( P ≤ .05). Statistically significant changes in metric values were not seen at the other plantar locations, although metatarsal pad use resulted in mild decreases in mean peak pressures at the first and second metatarsal heads and slight increases laterally. Contact durations decreased at all metatarsal head locations, while pressure-time integrals decreased at the first, second, third, and fourth metatarsal heads. A slight increase in pressure-time integrals was seen at the fifth metatarsal head. The redistribution of plantar pressures tended to relate not only to the dimensions of the metatarsal pads, but also to foot size, anatomic foot configuration, and pad location. Knowledge of these parameters, along with careful control of pad dimensions and placement, allows use of the metatarsal pad as an effective orthotic device for redistributing forefoot plantar pressures.
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Prats, Michael, Lidia Lucely Meneses-P., Fernando Samaniego-V., and Ricardo Pacheco-V. "Pressure Buildup in a Well Produced at Constant Pressure." SPE Journal 25, no. 04 (May 20, 2020): 1578–98. http://dx.doi.org/10.2118/201111-pa.
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Summary Dimensionless analytic expressions of the well-pressure buildup resulting from shutting in a well after producing it at constant pressure were obtained, in both Laplace space and time, using different mathematical approaches to solve the pertinent differential equations, including the effects of both wellbore storage and skin damage. Such a pressure response is said to have been obtained at constant-pressure-buildup (CPBU) conditions. The well, represented by a cylindrical source of nonzero radius, produces a single compressible fluid from an infinite and homogeneous reservoir. For a vertical well, the reservoir flow is always radial and horizontal. For the first approach in Laplace space, the pressure distribution in the reservoir at the shut-in time was used as the initial condition to obtain the transient pressure response upon shutting in the well. In the second approach, the solution in Laplace space was inverted analytically, yielding an expression containing infinite integrals. Duhamel's principle was used in the third approach, yielding the same integrals as the second approach. Subject to the inherent numerical errors in the integration and inversion algorithms, all solutions gave the same numerical results over a wide range of the production period, the elapsed time since the well was shut in, the storage coefficients, and the skin damage. As required by material balance, all pressures are restored to the value of the initial reservoir pressure as the infinite reservoir eventually completely recharges the amount of fluid produced before the well being shut in. The pressure response divided by the production rate at the time the well is shut in is denoted as the specific pressure response and has the same units as the pressure response under constant rate buildup (CRBU) conditions. It is thus not surprising that the general trends of the specific pressure response and the specific pressure increment are somewhat similar for both producing conditions, and that a number of interpretation procedures developed for CRBU conditions using the exponential integrals are applicable under CPBU conditions, including use of Horner plots. The Laplace-space procedure used to obtain numerically inverted values of the pressure response under CPBU conditions can be formally extended to provide expressions for the shut-in pressure response for any rate or pressure history during the production period. Although the emphasis is on the description of the well pressure and the specific-well-pressure buildup after shut-in, and of their time derivatives, the paper also presents analytic Laplace-space expressions for the pressure and radial flow within the reservoir after the well is shut in.
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Maiwald, Christian, Stefan Grau, Inga Krauss, Marlene Mauch, Detlef Axmann, and Thomas Horstmann. "Reproducibility of Plantar Pressure Distribution Data in Barefoot Running." Journal of Applied Biomechanics 24, no. 1 (February 2008): 14–23. http://dx.doi.org/10.1123/jab.24.1.14.
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The aim of this study was to provide detailed information on rationales, calculations, and results of common methods used to quantify reproducibility in plantar pressure variables. Recreational runners (N = 95) performed multiple barefoot running trials in a laboratory setup, and pressure variables were analyzed in nine distinct subareas of the foot. Reproducibility was assessed by calculating intraclass correlation coefficients (ICC) and the root mean square error (RMSE). Intraclass correlation coefficients ranged from 0.58 to 0.99, depending on the respective variable and type of ICC. Root mean square errors ranged between 2.3 and 3.1% for relative force–time integrals, between 0.07 and 0.23 for maximum force (Fmax), and between 107 and 278 kPa for maximum pressure (Pmax), depending on the subarea of the foot. Force–time integral variables demonstrated the best within-subject reproducibility. Rear-foot data suffered from slightly increased measurement error and reduced reproducibility compared with the forefoot.
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Rome, Keith, David George Survepalli, Maria Lobo, Nicola Dalbeth, Fiona McQueen, and Peter J. McNair. "Evaluating Intratester Reliability of Manual Masking of Plantar Pressure Measurements Associated with Chronic Gout." Journal of the American Podiatric Medical Association 101, no. 5 (September 1, 2011): 424–29. http://dx.doi.org/10.7547/1010424.
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Background: Plantar pressure measurements are commonly used to evaluate foot function in chronic musculoskeletal conditions. However, manually identifying anatomical landmarks is a source of measurement error and can produce unreliable data. The aim of this study was to evaluate intratester reliability associated with manual masking of plantar pressure measurements in patients with gout. Methods: Twenty-five patients with chronic gout (mean disease duration, 22 years) were recruited from rheumatology outpatient clinics. Patients were excluded if they were experiencing an acute gout flare at the time of assessment, had lower-limb amputation, or had diabetes mellitus. Manual masking of peak plantar pressures and pressure-time integrals under ten regions of the foot were undertaken on two occasions on the same day using an in-shoe pressure measurement system. Test-retest reliability was assessed by using intraclass correlation coefficients, SEM, 95% limits of agreement, and minimal detectable change. Results: Mean peak pressure intraclass correlation coefficients ranged from 0.92 to 0.97, with SEM of 8% to 14%. The 95% limits of agreement ranged from−150.3 to 133.5 kPa, and the minimal detectable change ranged from 30.8 to 80.6 kPa. For pressure-time integrals, intraclass correlation coefficients were 0.86 to 0.94, and SEM were 5% to 29%, with the greater errors observed under the toes. The 95% limits of agreement ranged from −48.5 to 48.8 kPa/sec, and the minimal detectable change ranged from 6.8 to 21.0 kPa/sec. Conclusions: These findings provide clinicians with information confirming the errors associated with manual masking of plantar pressure measurements in patients with gout. (J Am Podiatr Med Assoc 101(5): 424–429, 2011)
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Coates, P. D., and R. G. Speight. "Towards Intelligent Process Control of Injection Moulding of Polymers." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 209, no. 5 (October 1995): 357–67. http://dx.doi.org/10.1243/pime_proc_1995_209_095_02.
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Steps towards process control of the complex, multi-variable injection moulding process are presented. In-process measurements, in particular melt and hydraulic pressures in the primary injection stage, are shown to provide a sensitive means of monitoring changes in the process and changes in the polymer feedstock. Correlations have been observed between real time process measurements, in the form of specific time integrals of melt and hydraulic pressure, and product quality measures, such as product weight or dimensions. The research has been validated in both scientific laboratory and factory studies, and for a range of polymers, injection moulding technologies and complexities of product. Such correlations, and the specific integrals upon which they are based, can therefore form the basis of meaningful statistical process control for injection moulding or a viable closed-loop control strategy.
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Borodin, Vladislav I., Alexandr V. Lun-Fu, Mikhail A. Bubenchikov, Alexey M. Bubenchikov, and Dmitriy V. Mamontov. "Exact solution of the fundamental equation of acoustics for a pressure wave developing in two directions." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 79 (2022): 5–13. http://dx.doi.org/10.17223/19988621/79/1.
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The authors proceed from the hyperbolic equation for acoustic pressure. Using the integral Fourier transform along the axial coordinate, an equation in partial derivatives for the kernel of this transformation is found. This equation contains only one spatial coordinate and time. Applying the integral Laplace transform in time to the last equation, we obtain an ordinary differential equation with respect to the radial coordinate for the corresponding image. It turns out that the solution of the last equation is the well-known Macdonald function. For this function, it was possible to find the original image according to Laplace. All this made it possible to write an integral formula for the pressure in a sound wave. If the function of the initial pressure distribution along the pipe axis is taken in the form of a Gaussian impulse, then the integrals included in the representation of the desired solution are taken explicitly. As a result, we obtain an explicit compact formula for the acoustic pressure distribution in the axisymmetric case. It is convenient to use this formula to analyze the distribution of sound disturbances both along the pipe axis and in the radial direction. Therefore, the results are presented as isobars in the (z, r) plane corresponding to different times.
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Klein, Erin E., Ryan T. Crews, Stephanie C. Wu, James S. Wrobel, and David G. Armstrong. "CLEAR Cleat: A Proof-of-Concept Trial of an Aerobic Activity Facilitator to Reduce Plantar Forefoot Pressures and Their Potential in Those with Foot Ulcers." Journal of the American Podiatric Medical Association 98, no. 4 (July 1, 2008): 261–67. http://dx.doi.org/10.7547/0980261.
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Background: Exercise has not been studied extensively in persons with active neuropathic diabetic foot wounds, primarily because a device does not exist that allows patients to exercise while sufficiently off-loading pressure at the ulcer site. The purpose of this project was to demonstrate a device that reduces cycling plantar forefoot pressure. Methods: Ten healthy participants rode a recumbent bicycle under three cycling conditions. While the left foot interaction remained constant with a standard gym shoe and pedal, the right foot was exposed to a control condition with standard gym shoe and pedal, gym shoe and specialized cleat, and gym shoe with an off-loading insole and specialized cleat. Pressure and contact area of the plantar aspect of the feet were recorded for a 10-sec interval once during each minute of each condition’s 7-min trial. Results: The off-loading insole and specialized cleat condition yielded significantly lower (P < .01) peak pressure, contact area, and pressure–time integral values in the forefoot than the specialized cleat condition with gym shoe, which yielded significantly lower values (P < .01) than the standard gym shoe and pedal. Conclusion: Modifications to footwear may alter plantar forefoot pressures, contact area, and pressure–time integrals while cycling. The CLEAR Cleat could play a significant role in the facilitation of fitness in patients with (or at high risk for) neuropathic wounds. (J Am Podiatr Med Assoc 98(4): 261–267, 2008)
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Otter, Simon J., Catherine Jane Bowen, and Adam K. Young. "Forefoot Plantar Pressures in Rheumatoid Arthritis." Journal of the American Podiatric Medical Association 94, no. 3 (May 1, 2004): 255–60. http://dx.doi.org/10.7547/0940255.
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We sought to investigate the magnitude and duration of peak forefoot plantar pressures in rheumatoid arthritis. The spatial and temporal characteristics of forefoot plantar pressures were measured in 25 patients with a positive diagnosis of rheumatoid arthritis of 5 to 10 years’ duration (mean, 8 years) and a comparison group using a platform-based pressure-measurement system. There were no significant differences between groups in the magnitude of peak plantar pressure in the forefoot region. Significant differences were, however, noted for temporal aspects of foot-pressure measurement. The duration of loading over sensors detecting peak plantar pressure was significantly longer in the rheumatoid arthritis group. In addition, the rheumatoid arthritis group demonstrated significantly greater force–time integrals. Significant increases in the temporal parameters of plantar pressure distribution, rather than those of amplitude, may be characteristic of the rheumatoid foot. (J Am Podiatr Med Assoc 94(3): 255–260, 2004)
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Chong, Thomas S. Y., William R. Paterson, and David M. Scott. "An Improved Method to Calculate the Conservation of Mass in the Simulation of Rapid Pressurization Depressurization in a Packed Bed." ASEAN Journal of Chemical Engineering 2, no. 1 (October 20, 2008): 30. http://dx.doi.org/10.22146/ajche.50800.
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The work described here forms part of a project to model rapid pressure swing adsorption (RPSA), which is a single-bed process used for air separation. We have earlier identified a form of model and boundary conditions for an axially dispersed plug flow model that conserves mass. We solve the RPSA models numerically by spatially discretizing the partial differential equations to a system of ordinary differential equations (ODEs), which are then integrated over time. Although the formulation of our models conserves mass, our numerical simulations, however, do not perfectly conserve mass because of discretization error and rounding error. The discrepancy in the conservation of mass is computed as a guide to the numerical accuracy of the calculations. The computation of the conservation error requires the evaluation of time integrals of molar flowrates in and out of the bed. Since the velocity at the feed end of the bed changes rapidly with time, the application of quadrature to evaluate the time integrals does not provide the accuracy required. In this paper, the inadequacy is demonstrated using a simple problem, i.e. pressurization and depressurization into a non-adsorptive bed. An improved method is proposed. By transforming equations involving time integrals into ODEs, excellent accuracy is obtained. Further, this transformation minimizes the number of decision parameters that need to be specified by the users of the computer programs. Keywords: rapid pressure swing adsorption, modelling and simulation, packed bed.
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Wegener, Caleb, Joshua Burns, Stefania Penkala, and Grad Dip Ex Spr Sc. "Effect of Neutral-Cushioned Running Shoes on Plantar Pressure Loading and Comfort in Athletes with Cavus Feet." American Journal of Sports Medicine 36, no. 11 (June 24, 2008): 2139–46. http://dx.doi.org/10.1177/0363546508318191.
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Background High injury rates observed in athletes with cavus feet are thought to be associated with elevated plantar pressure loading. Neutral-cushioned running shoes are often recommended to manage and prevent such injuries. Purpose To investigate in-shoe plantar pressure loading and comfort during running in 2 popular neutral-cushioned running shoes recommended for athletes with cavus feet. Study Design Controlled laboratory study. Methods Plantar pressures were collected using the in-shoe Novel Pedar-X system during overground running in 22 athletes with cavus feet in 2 neutral-cushioned running shoes (Asics Nimbus 6 and Brooks Glycerin 3) and a control condition (Dunlop Volley). Comfort was measured using a validated visual analog scale. Results Compared with the control, both neutral-cushioned running shoes significantly reduced peak pressure and pressure-time integrals by 17% to 33% ( P < .001). The Brooks Glycerin most effectively reduced pressure beneath the whole foot and forefoot ( P < .01), and the Asics Nimbus most effectively reduced rearfoot pressure ( P < .01). Both neutral-cushioned running shoes reduced force at the forefoot by 6% and increased it at the midfoot by 12% to 17% ( P < .05). Contact time and area increased in both neutral-cushioned running shoes ( P < .01). The Asics Nimbus was the most comfortable, although both neutral-cushioned running shoes were significantly more comfortable than the control ( P < .001). Conclusion Two popular types of neutral-cushioned running shoes were effective at reducing plantar pressures in athletes with cavus feet. Clinical Relevance Regional differences in pressure reduction suggest neutral-cushioned running shoe recommendation should shift from being categorical in nature to being based on location of injury or elevated plantar pressure.
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Afinogentov, Alexander A., and Yulia A. Tychinina. "Analytical solution of the boundary value problem of mathematical modeling for non-stationary oil flows through the trunk pipeline in the presence of internal pressure sources." Vestnik of Samara State Technical University. Technical Sciences Series 30, no. 4 (February 1, 2023): 6–19. http://dx.doi.org/10.14498/tech.2022.4.1.
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The main oil pipeline, due to its spatial extent, can be considered as a control object with distributed parameters (ODP). The dependences on time and coordinates of the flow velocity and pressure in the pipeline are considered as controlled output values of the ODP. The boundary value problem of mathematical modeling of the process of pipeline transportation of oil in the standard form is presented in the form of a linear partial differential equation of the second order. The paper presents a solution to the boundary value problem of mathematical modeling of unsteady oil flow through a trunk pipeline in the presence of internal concentrated pressure sources in the form of functions describing the dependences on time and spatial coordinates of pressures and average cross-section pipeline oil flow rates. To represent the solution of the boundary value problem in the form of convolution integrals, Green's functions and standardizing functions are obtained, which makes it possible to use non-smooth (discontinuous) dependencies to describe programs for changing the values of internal concentrated pressure sources over time. The solutions obtained make it possible to use the methods of the theory of optimal control of systems with distributed parameters to solve the problems of optimal control of the process of pipeline transportation of oil.
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Sacco, Isabel C. N., Tatiana Almeida Bacarin, Maíra Grizzo Canettieri, and Ewald M. Hennig. "Plantar Pressures During Shod Gait in Diabetic Neuropathic Patients with and without a History of Plantar Ulceration." Journal of the American Podiatric Medical Association 99, no. 4 (July 1, 2009): 285–94. http://dx.doi.org/10.7547/0980285.
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Background: Diabetic neuropathy leads to progressive loss of sensation, lower-limb distal muscle atrophy, autonomic impairment, and gait alterations that overload feet. This overload has been associated with plantar ulcers even with consistent daily use of shoes. We sought to investigate and compare the influence of diabetic neuropathy and plantar ulcers in the clinical history of diabetic neuropathic patients on plantar sensitivity, symptoms, and plantar pressure distribution during gait while patients wore their everyday shoes. Methods: Patients were categorized into three groups: a control group (CG; n = 15), diabetic patients with a history of neuropathic ulceration (DUG; n = 8), and diabetic patients without a history of ulceration (DG; n = 10). Plantar pressure variables were measured by Pedar System shoe insoles in five plantar regions during gait while patients wore their own shoes. Results: No statistical difference between neuropathic patients with and without a history of plantar ulcers was found in relation to symptoms, tactile sensitivity, and duration of diabetes. Diabetic patients without ulceration presented the lowest pressure–time integral under the heel (72.1 ± 16.1 kPa × sec; P = .0456). Diabetic patients with a history of ulceration presented a higher pressure–time integral at the midfoot compared to patients in the control group (59.6 ± 23.6 kPa × sec × 45.8 ± 10.4 kPa × sec; P = .099), and at the lateral forefoot compared to diabetic patients without ulceration (70.9 ± 17.7 kPa sec × 113.2 ± 61.1 kPa × sec, P = .0193). Diabetic patients with ulceration also presented the lowest weight load under the hallux (0.06 ± 0.02%, P = .0042). Conclusions: Although presenting a larger midfoot area, diabetic neuropathic patients presented greater pressure–time integrals and relative loads over this region. Diabetic patients with ulceration presented an altered dynamic plantar pressure pattern characterized by overload even when wearing daily shoes. Overload associated with a clinical history of plantar ulcers indicates future appearance of plantar ulcers. (J Am Podiatr Med Assoc 99(4): 285–294, 2009)
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CHOU, YOU-LI, SHIUH-SHENG SHI, GWO-FENG HUANG, and TING-SHENG LIN. "INTERFACE PRESSURE AND GAIT ANALYSIS IN DIFFERENT WALKING SPEEDS AND ON THE BELOW-KNEE AMPUTEES WITH MULTIPLE AXIS PROSTHETIC FOOT PROSTHESIS." Biomedical Engineering: Applications, Basis and Communications 15, no. 05 (October 25, 2003): 207–11. http://dx.doi.org/10.4015/s1016237203000316.
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Interface stresses are an important consideration in stump and socket for a prosthetic limb to a person with transtibial amputation. During stance phase of the gait cycle, the prosthetic socket is expected to support and distribute the entire body weight of the patient. Excessive stresses between stump and socket will induce pain, discomfort and breakdown of soft tissues. The objectives of this study are to investigate the differences of gait, the maximum forces and pressures between stump and socket during different walking speed. Motion analysis system was applied to investigate the kinematics and kinetics of the gait and the Pedar system was used to measure the maximum forces and pressures between stump and socket during different walking speeds. Fifteen male subjects with transtibial amputation were collected in this research. These subjects were required to walk in three different speeds (85 steps/min, 95 steps/min, 115 steps/min). The maximum force, pressure and forcetime integrals in head of fibula, patellar ligament, medial condyle of tibia, tibial end and fibular end were recorded. The results showed that, the range of motion and the moment in hip, knee and ankle joint increased as the walking speed. Maximum forces and pressures in the measured areas had no significant difference in multiple axis prosthetic foot when the walking speed increased. The distributions of the force-time integrals were the same when compared with maximum force and the pain scale of subjects' subjective feeling. Walking speed would not influence the maximum force and pressure when subjects were in single axis prosthetic foot. This study provided the objective and subjective data for prosthetist or physician when applied on amputees.
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Azmoudeh, S., H. Zamani, and K. Shelesh-Nezhad. "Influence of Injection Molding Parameters on the Consistency of Molding Process." Applied Mechanics and Materials 446-447 (November 2013): 398–402. http://dx.doi.org/10.4028/www.scientific.net/amm.446-447.398.
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The existence of variations in the injection molding process conditions leads to the inconsistency of molded parts quality during the molding cycles. In this research, the variations of cavity pressure-time profiles integrals over the molding cycles were accounted as the molded parts quality variations. Thereafter, the correlations between injection molding process settings and the degree of consistency of molding process were investigated by applying cavity pressure measurement, Taguchi design of experiments approach and signal to noise ratio. The results derived from experiments indicated that an increase approximately as high as five times in the capability of injection molding may be achieved. Under the best setting condition, the cavity pressure profiles were relatively smooth and similar. Low screw rotational speed, high injection speed and short packing time led to the inconsistency elevation of injection molding.
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Khokhlov, A. V. "EXACT SOLUTION FOR THE STRESS RELAXATION PROBLEM IN A THICKWALLED TUBE OF A NONLINEAR VISCOELASTIC MATERIAL OBEYING THE RABOTNOV CONSTITUTIVE EQUATION." Problems of Strength and Plasticity 84, no. 2 (2022): 168–91. http://dx.doi.org/10.32326/1814-9146-2022-84-2-168-191.
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We constructed and studied analytically the exact solution of the quasi-static boundary value problem for a hollow cylinder (a tube) made of physically nonlinear homogeneous isotropic viscoelastic material obeying the Rabotnov constitutive equation with two arbitrary material functions (a creep compliance and a function which governs physical nonlinearity). A time-dependent displacement and zero shear stresses are given on the inside cylinder surface, a pressure (normal stress) is given on outside surface and zero axial displacements and zero shear stresses are preset on the end cross sections of the tube (thus, cylinder stress and plain strain are realized in a tube). We supposed that a material is incompressible and that given boundary displacement and pressure vary slowly enough with time to neglect inertia terms in the equilibrium equations. We obtained explicit expressions for strains and stresses at any point via the ratio of a tube radii, given external pressure and integral operators involving composition of two material functions of the constitutive relation and displacement preset on the internal cylindrical surface. In particular, assuming given boundary displacement and pressure are constant we considered the stress relaxation problem. For arbitrary material functions, we calculated all the hereditary integrals involved in the general representation for the stress field and reduced it to simple algebraic formulas convenient for analysis and use. We studied analytically general properties of the stress relaxation curves at any point of a tube and features of stress distributions along radius. We proved that the first material function (relaxation modulus) of the constitutive equation governs completely stresses dependence on time and the second one (non-linearity function) governs only stresses dependence on radial coordinate and found out that hoop stress and axial stress can change sign and can increase, decrease and be non-monotone with respect to radial coordinate. In case of zero external pressure, we proved that all stress relaxation curves at any point of a tube are proportional to each other (ratio of stresses at different points doesn't depend on time), decrease with time and have no flexure points. We also calculated integral mean values of axial and hoop stresses and discovered that their ratio depends on thickness/radius ratio only and doesn't depend on time and material functions although mean stresses do.
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Khokhlov, A. V. "THE EXACT SOLUTION FOR STRAINS AND STRESSES IN A HOLLOW CYLINDER OF NON-LINEAR VISCOELASTIC MATERIAL SUBJECT TO INTERNAL AND EXTERNAL PRESSURES IN THE CASE OF POWER MATERIAL FUNCTION GOVERNING NON-LINEARITY." Problems of strenght and plasticity 82, no. 2 (2020): 225–43. http://dx.doi.org/10.32326/1814-9146-2020-82-2-225-243.
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We study analytically the exact solution of the quasi-static problem for a thick-walled tube of physically non-linear viscoelastic material obeying the Rabotnov constitutive equation with two arbitrary material functions (a creep compliance and a function which governs physical non-linearity). We suppose that a material is homogeneous, isotropic and incompressible and that a tube is loaded with time-dependent internal and external pressures (varying slowly enough to neglect inertia terms in the equilibrium equations) and that a plain strain state is realized, i.e. zero axial displacements are given on the edge cross sections of the tube. We previously have obtained the closed form expressions for displacement, strain and stress fields via the single unknown function of time and integral operators involving this function, two arbitrary material functions of the constitutive relation, preset pressure values and radii of the tube and derive functional equation to determine this unknown resolving function. Assuming creep complience is arbitrary and choosing the material function governing non-linearity to be power function with a positive exponent, we construct exact solution of the resolving non-linear functional equation, calculate all the convolution integrals involved in the general representation for strain and stress fields and reduce it to simple algebraic formulas convenient for analysis and use. Strains evolution in time is characterized by creep compliance function and loading history. The stresses in this case depend on the current magnitudes of pressures only, they don't depend on creep compliance (i.e. viscoelastic properties of a material) and on loading history. The stress field coincides with classical solution for non-linear elastic material or elastoplastic material with power hardening (for non-decreasing pressure difference). We obtain criteria for increase, decrease or constancy of stresses with respect to radial coordinate in form of inequalities for the exponent value and for difference of pressures. Assuming creep compliance is arbitrary, we study analytically properties of strain and stress fields in a tube under internal pressure growing with constant rate and properties of corresponding stress-strain curves implying measurement of strains at a surface point of a tubular specimen.
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Zhang, Hui, Xin Zhang, Yi Shang, Giri Kattel, and Lijuan Miao. "Continuously Vegetation Greening over Inner Mongolia for the Past Three Decades." Remote Sensing 13, no. 13 (June 23, 2021): 2446. http://dx.doi.org/10.3390/rs13132446.
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The warming climate has rapidly altered vegetation growth in drylands, and consequently, has put great pressure on sustainable livelihoods. Various datasets have been applied from local to global scale to study vegetation dynamics and there is a lack of solid comparison among multiple datasets. Note that vegetation growth might shift over time and the greening and browning components over a long-time span might be masked by a linear trend. Here, we aim to monitor the long-term and nonlinear dynamics in vegetation greenness for Inner Mongolia (an important part of dryland Asia). As a useful tool that indicates vegetation greenness, NDVI (Normalized Difference Vegetation Index) and LAI (Leaf Area Index) integrals derived from the GIMMS (Global Inventory Modelling and Mapping Studies) NDVI3g and the GIMMS LAI3g products are applied. During the period of 1982-2016, NDVI/LAI integrals have an overall acceptable consistency in characterizing the trends of vegetation greenness, with NDVI large/small integrals and LAI large/small integrals increase at a rate of 0.96, 1.72, 2.23, and 3.13 per decade, respectively. Inner Mongolia experienced a noticeable greening process (71% and 82% greening area in NDVI large/small integrals, 67% and 73% greening area in LAI large/small integrals), despite the fragmentally distributed browning trends in eastern and partial northern Inner Mongolia. As inferred from nonlinear trend analysis, we found the greening process is still prevalent. The browning of eastern Inner Mongolia under the linear analysis was actually transferring from browning to greening, while the greening trend in northern Inner Mongolia was changing to browning. Increased occurrences in the frequency of breakpoints after 1999 suggest that previously stable vegetation ecology is more sensitive to external disturbances such as altered climatic impact and anthropogenic intervention.
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Vypasnyak, Ihor, Bogdan Mytskan, Serhiy Popel, Tetyana Mytskan, Iryna Ivanyshyn, Volodymyr Banakh, Lyubov Levandovska, and Viktoria Gryb. "Non-medicinal Correction of Motor Disorders of the Valley of the Foot in Multiple Sclerosis." Acta Balneologica 63, no. 1 (2021): 26–32. http://dx.doi.org/10.36740/abal202101104.
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Introduction: Analysis of motor disorders peculiarities in multiple sclerosis and assessment of non-drug correction and rehabilitation procedures impact on them will help to form new approaches in studying the motor disorders mechanisms, expand diagnostic capabilities and optimize physical therapy programs, which determines the relevance of our study. Aim: To analyze gait disorders in patients with multiple sclerosis associated with increased skeletal muscle tone, which form the anterior and posterior myofascial kinematic leg chain and to carry out their non-drug correction. Material and Methods: Gait pecularities analysis was performed in 95 patients with multiple sclerosis using the method of computer podography on the instrumental complex “DIERS FAMUS” (Germany). The study performed visual diagnosis of optimal statics, manual testing and bilateral stabilography. Anthropometric examination was supplemented by electroneuromyographic examination using the device “Neuro-EMG-Micro”. (Russia) Muscles involved in myofascial kinematic tibia chains were studied. A group of patients with increased muscle tone in the myofascial kinematic tibia chains received a cryotherapy course and muscle relaxation exercises. Results: After physical therapy, there was a probable reduction of whole foot contact time, as well as in almost all anatomical foot areas, which led to body weight transfer speed increasing. At the same time there was observed a reduction of the maximum force and the integral “force-time” under the foot ; integrals “pressure-time” and “force-time” under the second and lateral surfaces of fingers; integral “pressure-time” under the heel, which can be explained by contact time decrease between the foot and the surface of the toes while walking. Conclusions: Local cryotherapy use and relaxation exercises for patients with multiple sclerosis provides muscle tone decrease and, as a result, walking speed increase.
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Marston, Philip L., Timothy D. Daniel, Auberry R. Fortuner, Ivars P. Kirsteins, and Ahmad T. Abawi. "Amplitude and time-dependence of ultrasonic radiation force on modulation frequency computed from specular reflection contributions." Journal of the Acoustical Society of America 151, no. 4 (April 2022): A89. http://dx.doi.org/10.1121/10.0010749.
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Ever since the late 1970s, there has been interest in the modulated radiation pressure of double sideband suppressed carrier (DSSC) ultrasound, because the associated radiation pressure oscillates at a single low frequency. Recent research considers situations, where the radius of curvature of the illuminated objects greatly exceeds the wavelength at the implicit carrier frequency of the ultrasonic illumination [Marston et al., J. Acoust. Soc. Am. 149, 3042–3051 (2021); 150, 25–28 (2021)]. Furthermore, the objects of interest, cylinders, and spheres in water are taken to be sufficiently highly reflecting that the radiation force can be shown to be dominated by contributions associated with specular reflection. In such cases, it is helpful to geometrically analyze the amplitude and time dependence of the oscillatory radiation force for perfectly reflecting objects, where the relevant integrals of the stress projections can be carried out analytically. The results are expressed using Bessel and Struve functions. They explain how the amplitude and phase of the force depends on the DSSC modulation frequency in agreement with partial-wave-series based calculations. The approach is relevant in other situations. [Work supported by the U. S. Office of Naval Research.]
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Guenette, Jordan A., Lee M. Romer, Jordan S. Querido, Romeo Chua, Neil D. Eves, Jeremy D. Road, Donald C. McKenzie, and A. William Sheel. "Sex differences in exercise-induced diaphragmatic fatigue in endurance-trained athletes." Journal of Applied Physiology 109, no. 1 (July 2010): 35–46. http://dx.doi.org/10.1152/japplphysiol.01341.2009.
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There is evidence that female athletes may be more susceptible to exercise-induced arterial hypoxemia and expiratory flow limitation and have greater increases in operational lung volumes during exercise relative to men. These pulmonary limitations may ultimately lead to greater levels of diaphragmatic fatigue in women. Accordingly, the purpose of this study was to determine whether there are sex differences in the prevalence and severity of exercise-induced diaphragmatic fatigue in 38 healthy endurance-trained men ( n = 19; maximal aerobic capacity = 64.0 ± 1.9 ml·kg−1·min−1) and women ( n = 19; maximal aerobic capacity = 57.1 ± 1.5 ml·kg−1·min−1). Transdiaphragmatic pressure (Pdi) was calculated as the difference between gastric and esophageal pressures. Inspiratory pressure-time products of the diaphragm and esophagus were calculated as the product of breathing frequency and the Pdi and esophageal pressure time integrals, respectively. Cervical magnetic stimulation was used to measure potentiated Pdi twitches (Pdi,tw) before and 10, 30, and 60 min after a constant-load cycling test performed at 90% of peak work rate until exhaustion. Diaphragm fatigue was considered present if there was a ≥15% reduction in Pdi,tw after exercise. Diaphragm fatigue occurred in 11 of 19 men (58%) and 8 of 19 women (42%). The percent drop in Pdi,tw at 10, 30, and 60 min after exercise in men ( n = 11) was 30.6 ± 2.3, 20.7 ± 3.2, and 13.3 ± 4.5%, respectively, whereas results in women ( n = 8) were 21.0 ± 2.1, 11.6 ± 2.9, and 9.7 ± 4.2%, respectively, with sex differences occurring at 10 and 30 min ( P < 0.05). Men continued to have a reduced contribution of the diaphragm to total inspiratory force output (pressure-time product of the diaphragm/pressure-time product of the esophagus) during exercise, whereas diaphragmatic contribution in women changed very little over time. The findings from this study point to a female diaphragm that is more resistant to fatigue relative to their male counterparts.
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Zhang, Guoxin, Duo Wai-Chi Wong, Ivy Kwan-Kei Wong, Tony Lin-Wei Chen, Tommy Tung-Ho Hong, Yinghu Peng, Yan Wang, Qitao Tan, and Ming Zhang. "Plantar Pressure Variability and Asymmetry in Elderly Performing 60-Minute Treadmill Brisk-Walking: Paving the Way towards Fatigue-Induced Instability Assessment Using Wearable In-Shoe Pressure Sensors." Sensors 21, no. 9 (May 6, 2021): 3217. http://dx.doi.org/10.3390/s21093217.
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Evaluation of potential fatigue for the elderly could minimize their risk of injury and thus encourage them to do more physical exercises. Fatigue-related gait instability was often assessed by the changes of joint kinematics, whilst planar pressure variability and asymmetry parameters may complement and provide better estimation. We hypothesized that fatigue condition (induced by the treadmill brisk-walking task) would lead to instability and could be reflected by the variability and asymmetry of plantar pressure. Fifteen elderly adults participated in the 60-min brisk walking trial on a treadmill without a pause, which could ensure that the fatigue-inducing effect is continuous and participants will not recover halfway. The plantar pressure data were extracted at baseline, the 30th minute, and the 60th minute. The median of contact time, peak pressure, and pressure-time integrals in each plantar region was calculated, in addition to their asymmetry and variability. After 60 min of brisk walking, there were significant increases in peak pressure at the medial and lateral arch regions, and central metatarsal regions, in addition to their impulses (p < 0.05). In addition, the variability of plantar pressure at the medial arch was significantly increased (p < 0.05), but their asymmetry was decreased. On the other hand, the contact time was significantly increased at all plantar regions (p < 0.05). The weakened muscle control and shock absorption upon fatigue could be the reason for the increased peak pressure, impulse, and variability, while the improved symmetry and prolonged plantar contact time could be a compensatory mechanism to restore stability. The outcome of this study can facilitate the development of gait instability or fatigue assessment using wearable in-shoe pressure sensors.
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Escobar, Freddy Humberto, Javier Andrés Martínez, and Matilde Montealegre M. "PRESSURE AND PRESSURE DERIVATIVE ANALYSIS FOR INJECTION TESTS WITH VARIABLE TEMPERATURE WITHOUT TYPE-CURVE MATCHING." CT&F - Ciencia, Tecnología y Futuro 3, no. 4 (December 31, 2008): 83–91. http://dx.doi.org/10.29047/01225383.464.
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The analysis of injection tests under nonisothermic conditions is important for the accurate estimation of the reservoir permeability and the well's skin factor; since previously an isothermical system was assumed without taking into account a moving temperature front which expands with time plus the consequent changes in both viscosity and mobility between the cold and the hot zone of the reservoir which leads to unreliable estimation of the reservoir and well parameters. To construct the solution an analytical approach presented by Boughrara and Peres (2007) was used. That solution was initially introduced for the calculation of the injection pressure in an isothermic system. It was later modified by Boughrara and Reynolds (2007) to consider a system with variable temperature in vertical wells. In this work, the pressure response was obtained by numerical solution of the anisothermical model using the Gauss Quadrature method to solve the integrals, and assuming that both injection and reservoir temperatures were kept constant during the injection process and the water saturation is uniform throughout the reservoir. For interpretation purposes, a technique based upon the unique features of the pressure and pressure derivative curves were used without employing type-curve matching (TDS technique). The formulation was verified by its application to field and synthetic examples. As expected, increasing reservoir temperature causes a decrement in the mobility ratio, then estimation of reservoir permeability is some less accurate from the second radial flow, especially, as the mobility ratio increases.
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Petrov, A. N., and M. V. Grigoryev. "NUMERICAL MODELLING OF DYNAMIC RESPONSE OF A PARTIALLY SATURATED POROELASTIC HALF-SPACE IN CASE OF A LOAD ACTING INSIDE A CUBIC CAVITY." Problems of strenght and plasticity 82, no. 4 (2020): 507–23. http://dx.doi.org/10.32326/1814-9146-2020-82-4-507-523.
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Computer modeling based on the boundary element method is performed for the problem of loading in terms of the Heaviside step function inside a cubic cavity located in a partially saturated poroelastic half-space. A poroelastic medium is represented by a heterogeneous material-based model consisting of an elastic matrix phase and two phases of fillers – liquid and gas filling the pore system. The material model corresponds to a three-component medium. The constitutive relations of poroelastic medium written in terms skeleton displacements and pore pressures of fillers are considered. The original initial-boundary value problem is reduced to a boundary value problem by using the formal application of the Laplace transform. The research technique is based on the direct approach boundary integral equations of 3D isotropic linear theory of poroelasticity. Boundary integral equations corresponding to the boundary value problem are solved by the boundary element method in combination with the collocation method. In this study 8-noded elements have been adopted to discretize the boundary of poroelastic half-space. It is assumed that the element is linear with respect to displacements and pore pressures, while only one central node is used to represent tractions and fluxes. Algorithms for eliminating singularities, decreasing the order and subdividing elements are employed to compute the integral coefficients of a discrete analogue of the boundary integral equation. Regular integrals are calculated using the Gauss quadrature formula. The solution in time is obtained by numerical inversion of the Laplace transform. The numerical inversion method relies on quadrature formulas for computing the convolution integral. The time dependences of unknown displacement functions and pore pressures at points on the surface of the half-space and the cavity are plotted. The corresponding graphs are given. The influence of the cavity depth and degree of saturation on dynamic responses is investigated. The solution obtained by using the model of a fully saturated poroelastic material is compared to that of partially saturated poroelastic material. It is noted that the model used for solving this problem leads to an underestimation of displacement and overestimation of pore pressure estimates.
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Hughes, Chris W., Shane Elipot, Miguel Ángel Morales Maqueda, and John W. Loder. "Test of a Method for Monitoring the Geostrophic Meridional Overturning Circulation Using Only Boundary Measurements." Journal of Atmospheric and Oceanic Technology 30, no. 4 (April 1, 2013): 789–809. http://dx.doi.org/10.1175/jtech-d-12-00149.1.
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Abstract Measurements of ocean bottom pressure, particularly on the continental slope, make an efficient means of monitoring large-scale integrals of the ocean circulation. However, direct pressure measurements are limited to monitoring relatively short time scales (compared to the deployment period) because of problems with sensor drift. Measurements are used from the northwest Atlantic continental slope, as part of the Rapid Climate Change (RAPID)–West Atlantic Variability Experiment, to demonstrate that the drift problem can be overcome by using near-boundary measurements of density and velocity to reconstruct bottom pressure differences with accuracy better than 1 cm of water (100 Pa). This accuracy permits the measurement of changes in the zonally integrated flow, below and relative to 1100 m, to an accuracy of 1 Sv (1 Sv ≡ 106 m3 s−1) or better. The technique employs the “stepping method,” a generalization of hydrostatic balance for sloping paths that uses geostrophic current measurements to reconstruct the horizontal component of the pressure gradient.
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Venner, C. H., W. E. ten Napel, and R. Bosma. "Advanced Multilevel Solution of the EHL Line Contact Problem." Journal of Tribology 112, no. 3 (July 1, 1990): 426–31. http://dx.doi.org/10.1115/1.2920277.
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The application of multilevel multi-integration to the calculation of the elastic deformation integrals and the use of an alternative relaxation process in the multilevel solution of the governing equations have resulted in an algorithm solving the EHL line contact problem in O(n ln n) operations, also for highly loaded situations. The reduction in computing time thus obtained was used to solve the problem using large numbers of nodal points and to study the pressure spike. The presented algorithm will enable fast and accurate solution of surface roughness and transient problems.
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VanZant, R. Scott, Thomas G. McPoil, and Mark W. Cornwall. "Symmetry of Plantar Pressures and Vertical Forces in Healthy Subjects During Walking." Journal of the American Podiatric Medical Association 91, no. 7 (July 1, 2001): 337–42. http://dx.doi.org/10.7547/87507315-91-7-337.
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The purpose of this study was to determine the degree of symmetry for in-shoe plantar pressure and vertical force patterns between the left and right feet of healthy subjects during walking. Thirty subjects with a mean age of 29.6 years participated in the study. Each subject walked a distance of 8 m three times while in-shoe plantar pressure and vertical force data were collected. A total of 12 steps were analyzed for both feet, and maximum vertical force, peak pressure, and pressure-time integrals were calculated for four plantar regions of the foot. No differences in the three variables were noted between male and female subjects. Plantar pressure and vertical force patterns were found to be symmetrical between the left and right feet, except for two of the four plantar regions studied. Only the forefoot and rearfoot regions were found to show significant differences between the left and right feet for plantar pressure and vertical force, respectively. The degree of asymmetry for these two plantar regions in the same foot, however, was minimal. (J Am Podiatr Med Assoc 91(7): 337-342, 2001)
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SJÖGREN, TORBJÖRN, and ARNE V. JOHANSSON. "Measurement and modelling of homogeneous axisymmetric turbulence." Journal of Fluid Mechanics 374 (November 10, 1998): 59–90. http://dx.doi.org/10.1017/s0022112098002511.
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A new method for determining the slow and rapid pressure-strain rate terms directly from wind-tunnel experiments has been developed with the aid of a newly developed theoretical description of the kinematics of homogeneous axisymmetric turbulence. Both the straining and the return-to-isotropy process of homogeneous axisymmetric turbulence are studied with the aim of improving Reynolds stress closures. Direct experimental determination of the different terms in the transport equation for the Reynolds stress tensor plays a major role in the validation and development of turbulence models. For the first time it is shown that the pressure{strain correlation can be determined with good accuracy without balancing it out from the Reynolds stress transport equation (and without measuring the pressure). Instead it is determined through evaluation of integrals containing second- and third-order two-point velocity correlations. All the terms in the Reynolds stress equations are measured directly and balance is achieved.
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Ogbue, M. C., and E. Steve Adewole. "Theoretical Investigation of Factors Affecting Water Breakthrough Time in a Horizontal Well Subject to Bottom Water Drive." Advanced Materials Research 824 (September 2013): 394–400. http://dx.doi.org/10.4028/www.scientific.net/amr.824.394.
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Water breakthrough marks end of economic life of a reservoir. It has negative influence on recovery, operations, and economics. This means that delaying the encroachment and production of water is a means of maximizing the ultimate oil recovery, operating at higher efficiency and maximizing profit. This theoretical research is aimed at solving for time water will breakthrough a horizontal well placed in bottom-water reservoir. And subsequently, suggest ways to delay the water breakthrough time. Thus the model herein is a repository of three aims of reservoir modeling; predict, optimize and monitor oil production. Well modifications strategies were suggested to achieve significant delay of water breakthrough. The well in a bottom-water reservoir, which is much longer than the well, experiences four flow regimes, namely, early-time radial flow, early-time linear flow, late time pseudo radial flow and late-time linear flow period within which water breakthrough occurred. Each flow regime was represented mathematically. The resulting integrals were evaluated numerically. From the mathematical model, factors affecting water breakthrough were chiefly wellbore, reservoir fluid and reservoir properties. Their effects are evident in computed dimensionlesss pressure,, end of early radial flow, tDe, and dimensionless flow time, tD. Water breakthrough was evidenced by constant PD value. Delayed water breakthrough is favoured by narrow well, shorter well, low viscous fluid, low flow rate and high horizontal permeability relative to vertical permeability. Viscosity of oil can be reduced by gaslifting, EOR thermal process, etc. Higher values of and tDe can be achieved by increasing the horizontal permeability,kh, while vertical permeability,kv, is reduced. Suitable stimulation process can achieve improved permeability.Special functionserf error function =Ei exponential integral function Ei(x) = [
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Belevtsov, N. S. "On a Space-Fractional Generalization of the Black Oil Model." Mathematics and Mathematical Modeling, no. 6 (April 28, 2021): 13–27. http://dx.doi.org/10.24108/mathm.0620.0000228.
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Classical multiphase filtration models, which are based on Darcy's law, are well studied and actively used in modern oil engineering. However, such models do not allow efficient describing of processes with power-law memory effects or with spatial non-locality effects. In recent years, there has been a significantly increasing interest in models with fractional derivatives and integrals that allow such effects to be taken into account.The article considers the space-fractional generalization of the two-phase Black Oil model. This model is built on the basis of a fractional modification of the Darcy’s law with the Riesz potential, which is one of the possible generalizations of a fractional integral to the case of a multidimensional space. The use of such a modification of Darcy's law allows efficient describing of filtration processes in heterogeneous fractured porous media with the effects of spatial non-locality.For the numerical solution of the system of equations from the obtained model, the use of the IMPES method is proposed. For this purpose, from the presented system of equations, one equation is selected that describes the evolution of pressure. This equation is written provided that the capillary pressure variation within the time step is neglected.A special case of the pressure equation with the Riesz potential of radial function is considered, which describes the pressure variation in the case of a radial plane flow. For this equation, a self-similar solution is constructed using the Mellin integral transform method. A representation of this solution in the form of the Mellin-Barnes contour integral was obtained, which made it possible to write it in terms of the Fox functions. It is shown that in the limiting case of a zero degree of the Riesz potential, this solution coincides with the self-similar solution of the classical heat equation. The constructed self-similar solution can be further used in the software implementation of the numerical solution of the model presentedThe main line of further research is to develop and implement a software computing system based on the proposed fractional generalization of the two-phase Black Oil model.
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Vasconcelos, Ivan. "Source-receiver, reverse-time imaging of dual-source, vector-acoustic seismic data." GEOPHYSICS 78, no. 2 (March 1, 2013): WA123—WA145. http://dx.doi.org/10.1190/geo2012-0300.1.
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Novel technologies in seismic data acquisition allow for recording full vector-acoustic (VA) data: pointwise recordings of pressure and its multicomponent gradient, excited by pressure only as well as dipole/gradient sources. Building on recent connections between imaging and seismic interferometry, we present a wave-equation-based, nonlinear, reverse-time imaging approach that takes full advantage of dual-source multicomponent data. The method’s formulation relies on source-receiver scattering reciprocity, thus making proper use of VA fields in the wavefield extrapolation and imaging condition steps in a self-consistent manner. The VA imaging method is capable of simultaneously focusing energy from all in- and outgoing waves: The receiver-side up- and downgoing (receiver ghosts) fields are handled by the VA receiver extrapolation, whereas source-side in- and outgoing (source ghosts) arrivals are accounted for when combining dual-source data at the imaging condition. Additionally, VA imaging handles image amplitudes better than conventional reverse-time migration because it properly handles finite-aperture directivity directly from dual-source, 4C data. For nonlinear imaging, we provide a complete source-receiver framework that relies only on surface integrals, thus being computationally applicable to practical problems. The nonlinear image can be implicitly interpreted as a superposition of several nonlinear interactions between scattering components of data with those corresponding to the extrapolators (i.e., to the model). We demonstrate various features of the method using synthetic examples with complex subsurface features. The numerical results show, e.g., that the dual-source, VA image retrieves subsurface features with “super-resolution”, i.e., with resolution higher than the limits of Born imaging, but at the cost of introducing image artifacts not present in the linear image. Although the method does not require any deghosting as a preprocessing step, it can use separated up- and downgoing fields to generate independent subsurface images.
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Wong, Sen, and Manwai Yuen. "Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions." Scientific World Journal 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/580871.
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We study, in the radial symmetric case, the finite time life span of the compressible Euler or Euler-Poisson equations inRN. For timet≥0, we can define a functionalH(t)associated with the solution of the equations and some testing functionf. When the pressure functionPof the governing equations is of the formP=Kργ, whereρis the density function,Kis a constant, andγ>1, we can show that the nontrivialC1solutions with nonslip boundary condition will blow up in finite time ifH(0)satisfies some initial functional conditions defined by the integrals off. Examples of the testing functions includerN-1ln(r+1),rN-1er,rN-1(r3-3r2+3r+ε),rN-1sin((π/2)(r/R)), andrN-1sinh r. The corresponding blowup result for the 1-dimensional nonradial symmetric case is also given.
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Markvart, Jakob, Eva Rosenqvist, Helle Sørensen, Carl-Otto Ottosen, and Jesper M. Aaslyng. "Canopy Photosynthesis and Time-of-day Application of Supplemental Light." HortScience 44, no. 5 (August 2009): 1284–90. http://dx.doi.org/10.21273/hortsci.44.5.1284.
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There is increasing use of electricity for supplemental lighting in the northern European greenhouse industry. One reason for this may be to secure a high growth rate during low-light periods by an attempt to increase net photosynthesis. We wanted to clarify which period of the day resulted in the best use of a 5-h supplemental light period for photosynthesis and growth. The periods tested were supplemental light during the night, day, morning, and evening. The experiments were carried out in daylight climate chambers measuring canopy gas exchange. The air temperature was 25 °C and the CO2 level ≈900 ppm. Vegetative chrysanthemum was used, because this species responds quickly to change in light level. The leaf areas of the plant canopies were nondestructively measured each week during the 4-week experimental period. The fact that the quantum yield of photosynthesis is greater at low than at high light intensities favors the use of supplemental light during the dark period, but growth measured as dry weight of the treated plants at the end of the experiments was not significantly different given identical light integrals of the treatments. However, one experiment indicated that increased time with dark hours during day and night (24 h) might decrease net photosynthesis. The assimilation per unit leaf area was approximately the same during times of sunlight through a diffusing screen at 100 μmol·m−2·s−1 of photosynthetic photon flux (PPF) as during times of supplemental (direct) light application at PPF of 200 μmol·m−2·s−1 by high-pressure sodium lamps. We conclude that during the winter and periods of low light intensities, the daily carbon gain does not depend on the time of supplemental light application, but is linked to the total light integral. However, extended time with dark hours during day and night (24 h) might be a disadvantage because of longer periods with dark respiration and subsequent loss of carbon. Our results indicate that during times of low light conditions, it is not necessary to include factors such as the timing of supplemental lighting application to achieve higher net photosynthesis in climate control strategies.
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Ostrikov, N. N., and E. M. Zhmulin. "Vortex dynamics of viscous fluid flows. Part 1. Two-dimensional flows." Journal of Fluid Mechanics 276 (October 10, 1994): 81–111. http://dx.doi.org/10.1017/s0022112094002478.
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The method of product integration is applied to the vortex dynamics of two-dimensional incompressible viscous media. In the cases of both unbounded and bounded flows under the no-slip boundary condition, the analytic solutions of the Cauchy problem are obtained for the Helmholtz equation in the form of linear and nonlinear product integrals. The application of product integrals allows the generalization in a natural way of the vortex dynamics concept to the case of viscous flows. However, this new approach requires the reconsideration of some traditional notions of vortex dynamics. Two lengthscales are introduced in the form of a micro- and a macro-scale. Elementary ‘vortex objects’ are defined as two types of singular vortex filaments with equal but opposite intensities. The vorticity is considered as the macro-value proportional to the concentration of elementary vortex filaments inhabiting the micro-level. The vortex motion of a viscous medium is represented as the stochastic motion of an infinite set of elementary vortex filaments on the micro-level governed by the stochastic differential equations, where the stochastic velocity component of every filament simulates the viscous diffusion of vorticity, and the regular component is the macro-value induced according to the Biot–Savart law and simulates the convective transfer of vorticity.In flows with boundaries, the production of elementary vortex filaments at the boundary is introduced to satisfy the no-slip condition. This phenomenon is described by the application of the generalized Markov processes theory. The integral equation for the production intensity of elementary vortex filaments is derived and solved using the no-slip condition reformulated in terms of vorticity. Additional conditions on this intensity are determined to avoid the many-valuedness of the pressure in a multi-connected flow domain. This intensity depends on the vorticity in the flow and the boundary velocity at every time instant, together with boundary acceleration.As a result, the successive and accurate application of the product-integral method allows the study of vortex dynamics in a viscous fluid according to the concepts of Helmholtz and Kelvin.
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Pagel, Paul S., Douglas A. Hettrick, Judy R. Kersten, Dermot Lowe, and David C. Warltier. "Cardiovascular Effects of Propofol in Dogs with Dilated Cardiomyopathy." Anesthesiology 88, no. 1 (January 1, 1998): 180–89. http://dx.doi.org/10.1097/00000542-199801000-00026.
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Background The authors tested the hypothesis that propofol improves left ventricular diastolic function in dogs with dilated cardiomyopathy by reducing left ventricular preload and afterload. Methods Seven dogs were instrumented for left ventricular and aortic pressures, aortic blood flow, and subendocardial segment length. Left ventricular afterload and contractility were quantified with aortic input impedance and preload recruitable stroke work, respectively. Diastolic function was evaluated with a time constant of left ventricular relaxation (tau); segment-lengthening velocities and time-velocity integrals during early left ventricular filling (dL/dtE and TVI-E, respectively) and atrial systole (dL/dtA and TVI-A, respectively); and a regional chamber stiffness constant (K). Dogs were paced at 240 beats/min for 18 +/- 3 days, and hemodynamics were recorded in sinus rhythm in the conscious state. Anesthesia was induced with propofol (5 mg/kg) and maintained with propofol infusions at 25, 50, and 100 mg x kg-1 x h-1, and hemodynamics were recorded after 15 min of equilibration at each dose. Results Propofol decreased mean arterial pressure, left ventricular end-diastolic pressure, and K but did not change heart rate. Propofol reduced total arterial resistance and increased total arterial compliance derived from aortic input impedance. Propofol also reduced preload recruitable stroke work. The lowest dose of propofol decreased tau. Propofol decreased dL/dtE and TVI-E and reduced the dL/dt-E/A and TVI-E/A ratios. Conclusions Propofol reduces left ventricular preload, afterload, and regional chamber stiffness, causes direct negative inotropic effects, and impairs early-diastolic left ventricular filling in dogs with dilated cardiomyopathy.
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Zhang, Zhiwang, Yu Zhang, Weijie Fu, Zhen Wei, Jiayi Jiang, and Lin Wang. "Plantar Loads of Habitual Forefoot Strikers during Running on Different Overground Surfaces." Applied Sciences 10, no. 7 (March 26, 2020): 2271. http://dx.doi.org/10.3390/app10072271.
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The objective of this study is to investigate plantar loads characteristics of habitual forefoot strike runners while running on different surfaces. Twenty-six runners (age: 28.2 ± 6.8 y, height: 172.9 ± 4.1 cm, weight: 67.7 ± 9.6 kg, BMI (body mass index): 22.6 ± 2.8 kg/m2, running age: 5.0 ± 4.2 y, running distance per week: 14.6 ± 11.7 km) with habitual forefoot strike participated in the study. Runners were instructed to run at 3.3 ± 0.2 m/s on three surfaces: grass, synthetic rubber and concrete. An in-shoe pressure measurement system was used to collect and analyze plantar loads data. Running on the synthetic rubber surface produced a lower plantar pressure in the lateral forefoot (256.73 kPa vs. 281.35 kPa, p = 0.006) than running on concrete. Compared with the concrete surface, lower pressure–time integrals were shown at the central forefoot (46.71 kPa⋅s vs. 50.73 kPa⋅s, p = 0.001) and lateral forefoot (36.13 kPa⋅s vs. 39.36 kPa⋅s, p = 0.004) when running on the synthetic rubber surface. The different surfaces influence plantar loads of habitual forefoot strikers and runners should choose appropriate overground surface to reduce the risk of lower extremity musculoskeletal injuries.
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Hope, Sarah A., David B. Tay, Ian T. Meredith, and James D. Cameron. "Comparison of generalized and gender-specific transfer functions for the derivation of aortic waveforms." American Journal of Physiology-Heart and Circulatory Physiology 283, no. 3 (September 1, 2002): H1150—H1156. http://dx.doi.org/10.1152/ajpheart.00216.2002.
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Arterial transfer functions have been promoted for the derivation of central aortic waveform characteristics not usually accessible noninvasively, but possibly of prognostic significance. The utility of generalized rather than gender-specific transfer functions has not been assessed. Invasive central aortic and noninvasive radial (Millar Mikro-tip tonometer) blood pressure waveforms were recorded simultaneously in 78 subjects (61 male and 17 female). Average transfer functions were obtained for the whole group and for each gender by two methods. Reverse transformation was performed with the use of each transfer function. Measured aortic waveform parameters were compared with those derived using average, gender-appropriate, and gender-inappropriate transfer functions. Differences in central waveform characteristics were demonstrated between men and women. Derived waveform parameters were significantly different from measured values [e.g., subendocardial viability index and augmentation index ( P < 0.001)]. A gender-appropriate transfer function significantly improved the derivation of some parameters, including systolic pressure and systolic and diastolic pressure time integrals ( P < 0.05). Generalized arterial transfer functions may not be universally applicable across all waveform parameters of potential interest, and gender-specific transfer functions may be more appropriate.
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Pagel, Paul S., Dermot Lowe, Douglas A. Hettrick, Iyad N. Jamali, Judy R. Kersten, John P. Tessmer, and David C. Warltier. "Isoflurane, but Not Halothane, Improves Indices of Diastolic Performance in Dogs with Rapid Ventricular, Pacing-induced Cardiomyopathy." Anesthesiology 85, no. 3 (September 1, 1996): 644–54. http://dx.doi.org/10.1097/00000542-199609000-00025.
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Background The left ventricular (LV) mechanical effects of isoflurane and halothane were examined in dogs with rapid LV pacing-induced cardiomyopathy. These experiments tested the hypothesis that isoflurane and halothane differentially enhance indices of diastolic performance in dogs with moderate LV dysfunction. Methods Eight dogs were chronically instrumented for measurement of LV and aortic pressures, subendocardial segment length, and cardiac output. Contractility was quantified by preload recruitable stroke work (Mw). Diastolic function was evaluated with a time constant of isovolumic relaxation (tau), segment lengthening velocities and time-velocity integrals during early filling (dL/dtE and TVI-E) and atrial systole (dL/dtA and TVI-A), and a regional chamber stiffness constant (Kp). Hemodynamics and LV function were recorded in the conscious state before pacing. The left ventricles of the dogs were then continuously paced at ventricular rates between 220 and 240 beats.min-1 for 10 +/- 1 days and monitored on a daily basis. After the development of moderate LV dysfunction, pacing was temporarily discontinued, and dogs were studied in sinus rhythm in the conscious state and after 20 min equilibration at 1.1, 1.4, and 1.7 minimum alveolar concentration isoflurane and halothane on separate days. Results Chronic rapid pacing increased baseline (sinus rhythm) heart rate, LV end-diastolic pressure, and end-diastolic segment length and decreased mean arterial pressure, LV systolic pressure, and cardiac output. Mw decreased and tau and Kp increased, consistent with LV systolic and diastolic dysfunction. Reductions in dL/dtE/dL/dtA and TVI-E/A occurred, which indicated that LV filling was more dependent on atrial systole. In dogs with cardiomyopathy, isoflurane and halothane increased heart rate and decreased mean arterial pressure, LV systolic pressure, LV end-diastolic pressure, cardiac output, Mw, and Kp. Decreases in LV end-diastolic pressure were more pronounced in dogs anesthetized with 1.1 minimum alveolar concentration isoflurane compared with halothane. Halothane-induced decreases Mw were greater than those observed with equi-minimum alveolar concentration isoflurane. A reduction in tau and increases in TVI-E/TVI-A and the ratio of early to total LV filling were observed with isoflurane. In contrast, halothane caused dose-related reductions in dL/dtE, dL/dtA, TVI-E, and TVI-A, and did not improve the ratios of these variables. Conclusions Isoflurane, but not halothane, improved several indices of diastolic performance in dogs with pacing-induced LV dysfunction, despite producing simultaneous negative inotropic effects. These findings can probably be attributed to favorable reductions in LV preload and not to direct lusitropic effects. Improvement of filling dynamics may partially offset the decrement in LV systolic function by isoflurane in the setting of LV dysfunction.
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Liu, Shuangbiao, Michael J. Rodgers, Qian Wang, and Leon M. Keer. "A Fast and Effective Method for Transient Thermoelastic Displacement Analyses." Journal of Tribology 123, no. 3 (June 29, 2000): 479–85. http://dx.doi.org/10.1115/1.1308010.
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Frictional heating due to the relative motion of contacting surfaces causes temperature rise and thermal distortion, which in turn affects the contact geometry and pressure distribution. A fast and effective method is presented for the calculation of the normal surface displacement of an elastic halfspace due to arbitrary transient surface heating. The method uses Fourier-transformed Green’s functions (frequency response functions), found in the closed form by using the approach of Seo and Mura and the heat conduction analyses of Carslaw and Jaeger. The frequency response functions are shown analytically to be the frequency domain representations of the Green’s functions given by Barber. The formulation for the surface normal displacement is in the form of three-dimensional convolution integrals (over surface and time) of the arbitrary transient heat flux and the Green’s functions. Fourier transforms of these convolution integrals are taken, avoiding the Green’s-function singularities and giving a simple multiplication between the transformed heat flux and the (known) frequency response functions. The discrete convolution–fast Fourier transform (DC-FFT) algorithm is applied for accurate and efficient calculations of the normal surface displacement from the frequency response functions for an arbitrary transient heat input. The combination of the frequency-domain formulation and the DC-FFT algorithm makes the solution of transient thermoelastic deformation extremely fast and convenient.
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WEBB, G. M., G. P. ZANK, R. H. BURROWS, and R. E. RATKIEWICZ. "Alfvén simple waves." Journal of Plasma Physics 77, no. 1 (February 4, 2010): 51–93. http://dx.doi.org/10.1017/s0022377809990596.
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AbstractMulti-dimensional Alfvén simple waves in magnetohydrodynamics (MHD) are investigated using Boillat's formalism. For simple wave solutions, all physical variables (the gas density, pressure, fluid velocity, entropy, and magnetic field induction in the MHD case) depend on a single phase function ϕ, which is a function of the space and time variables. The simple wave ansatz requires that the wave normal and the normal speed of the wave front depend only on the phase function ϕ. This leads to an implicit equation for the phase function and a generalization of the concept of a plane wave. We obtain examples of Alfvén simple waves, based on the right eigenvector solutions for the Alfvén mode. The Alfvén mode solutions have six integrals, namely that the entropy, density, magnetic pressure, and the group velocity (the sum of the Alfvén and fluid velocity) are constant throughout the wave. The eigenequations require that the rate of change of the magnetic induction B with ϕ throughout the wave is perpendicular to both the wave normal n and B. Methods to construct simple wave solutions based on specifying either a solution ansatz for n(ϕ) or B(ϕ) are developed.
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GUO, Y. P. "Application of the Ffowcs Williams/Hawkings equation to two-dimensional problems." Journal of Fluid Mechanics 403 (January 25, 2000): 201–21. http://dx.doi.org/10.1017/s0022112099006989.
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This paper discusses the application of the Ffowcs Williams/Hawkings equation to two-dimensional problems. A two-dimensional version of this equation is derived, which not only provides a very efficient way for numerical implementation, but also reveals explicitly the features of the source mechanisms and the characteristics of the far-field noise associated with two-dimensional problems. It is shown that the sources can be interpreted, similarly to those in three-dimensional spaces, as quadrupoles from turbulent flows, dipoles due to surface pressure fluctuations on the bodies in the flow and monopoles from non-vanishing normal accelerations of the body surfaces. The cylindrical spreading of the two-dimensional waves and their far-field directivity become apparent in this new version. It also explicitly brings out the functional dependence of the radiated sound on parameters such as the flow Mach number and the Doppler factor due to source motions. This dependence is shown to be quite different from those in three-dimensional problems. The two-dimensional version is numerically very efficient because the domains of the integration are reduced by one from the three-dimensional version. The quadrupole integrals are now in a planar domain and the dipole and monopole integrals are along the contours of the two-dimensional bodies. The calculations of the retarded-time interpolation of the integrands, a time-consuming but necessary step in the three-dimensional version, are completely avoided by making use of fast Fourier transform. To demonstrate the application of this, a vortex/airfoil interaction problem is discussed, which has many practical applications and involves important issues such as vortex shedding from the trailing edge.
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Liu, Shuangbiao, and Qian Wang. "Transient Thermoelastic Stress Fields in a Half-Space." Journal of Tribology 125, no. 1 (December 31, 2002): 33–43. http://dx.doi.org/10.1115/1.1501087.
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Computing the thermoelastic stress field of a material subjected to frictional heating is essential for component failure prevention and life prediction. However, the analysis for three-dimensional thermoelastic stress field for tribological problems is not well developed. Furthermore, the pressure distribution due to rough surface contact is irregular; hence the frictional heating can hardly be described by an analytical expression. This paper presents a novel set of frequency-domain expressions (frequency response functions) of the thermoelastic stress field of a uniformly moving three-dimensional elastic half-space subjected to arbitrary transient frictional heating, where the velocity of the half-space, its magnitude and direction, can be an arbitrary function of time. General formulas are expressed in the form of time integrals, and important expressions for constant velocities are given for the transient-instantaneous, transient-continuous, and steady-state cases. The thermoelastic stress field inside a translating half-space with constant velocities are illustrated and discussed by using the discrete convolution and fast Fourier transform method when a parabolic type or an irregularly distributed heat source is applied.
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Darbani, Mohsen. "The Meshfree Finite Element Method for Fluids with Large Deformations." Defect and Diffusion Forum 326-328 (April 2012): 176–80. http://dx.doi.org/10.4028/www.scientific.net/ddf.326-328.176.
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The shallow water equations (SWE) is often simulated by using Eulerian descriptions. These phenomena may give rise to strong gradients and lead to large distortion of grids meshes. Hence classical finite elements methods may fall in simulating such problems. In this paper we present a meshless method, based on the natural element nethod (NEM). In a geometrical domain of a cloud of nodes, NEM uses the Voronoi cells and then its dual, namely Delaunay triangulation. Its main advantage lies in shape function of the natural neighbour interpolation, such that the position of natural neighbours is enough to its construction. To avoid the nonlinear term, the time material derivative term is discretized by a Lagrangian procedure. We also used an appropriate nodal integration technique to estimate integrals related to the diffusion, pressure and Coriolis terms because NEM shape functions are not polynomials and they are rational. For the diffusion term, the method of stabilized conforming nodal integration (SCNI) is proposed while for pressure and Coriolis terms a geometrical method will transform the integration over the cells domain to the integration over the edges. The method was successfully used to simulate dam-break flows by solving the fully 2D shallow water equations (SWE) by using an implicit scheme under a transient flow.
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QUÉGUINER, CHRISTOPHE, and DOMINIQUE BARTHÈS-BIESEL. "Axisymmetric motion of capsules through cylindrical channels." Journal of Fluid Mechanics 348 (October 10, 1997): 349–76. http://dx.doi.org/10.1017/s0022112097006587.
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A boundary integral method is used to model the flow of capsules into pores. An axisymmetric configuration is considered where the capsule and the pore axis coincide. The channel is a cylinder with hyperbolic entrance and exit regions. The capsule has a discoidal unstressed shape, is filled with a Newtonian liquid and is enclosed by a very thin membrane with various elastic properties (neo-Hookean or area-incompressible). The motion of the internal capsule liquid and of the suspending fluid is governed by the Stokes equations whose solution is expressed as boundary integrals. Those are computed by a collocation technique, where points are distributed on the capsule interface, on the channel walls and on the entrance and exit sections of the flow domain. The capsule interface mechanics follow the theory of large deformations of elastic membranes. The numerical model uses a forward time-stepping method, where the position and the deformation of the capsule are computed at each time step.The model allows the study of the effect of a number of parameters (capsule size and geometry, membrane elastic properties) on the flow. The entrance length in the pore, the steady additional pressure drop at equilibrium and the capsule deformed profiles are determined. It is found that the entrance of a capsule into a pore is not sensitive to downstream conditions; but the length of tube necessary to reach steady conditions depends strongly on capsule size and membrane behaviour. Bursting of capsules with a neo-Hookean membrane is predicted to occur through a phenomenon of continuous elongation. The flow of a capsule with a membrane that resists area dilatation depends strongly on particle size and shape.
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ISAZA, JUAN C., and LANCE R. COLLINS. "On the asymptotic behaviour of large-scale turbulence in homogeneous shear flow." Journal of Fluid Mechanics 637 (September 17, 2009): 213–39. http://dx.doi.org/10.1017/s002211200999053x.
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The asymptotic behaviour of large-scale velocity statistics in an homogeneous turbulent shear flow is investigated using direct numerical simulations (DNS) of the incompressible Navier–Stokes equations on a 5123 grid, and with viscous rapid distortion theory (RDT). We use a novel pseudo-spectral algorithm that allows us to set the initial value of the shear parameter in the range 3–30 without the shortcomings of previous numerical approaches. We find there is an explicit dependence of the early-time behaviour on the initial value of the shear parameter. Moreover, the long-time asymptotes of large-scale quantities such as the ratio of the turbulent kinetic energy production rate over dissipation rate, the Reynolds stress anisotropic tensor and the shear parameter itself depend sensitively on the initial value of the shear parameter over the range of Reynolds number we could achieve (26 ≤ Rλ ≤ 63) with the stringent resolution requirements that were satisfied. To gain further insight into the matter, we analyse the full viscous RDT. While inviscid RDT has received a great deal of attention, viscous RDT has not been fully analysed. Our motivation for considering viscous RDT is so that the energy dissipation rate enters the problem, enabling the shear parameter to be defined. We show asymptotic expansions for the short-time behaviour and numerically evaluate the integrals to determine the long-time prediction of viscous RDT. The results are in quantitative agreement with DNS for short times; however, at long times viscous RDT predicts the turbulent energy decays to zero. Through an analysis of the pressure–strain terms, we show that the nonlinear ‘slow’ terms are essential for rearranging turbulent energy from the streamwise direction to the mean shear direction, and this sustains the indefinite growth of the kinetic energy at long times. In effect, the nonlinear pressure–strain correlation maintains the three-dimensionality of the turbulence, countering the tendency of the mean shear to project the turbulence onto the two-dimensional plane of the mean-flow streamlines. We postulate that the predictions of viscous RDT at long times could be improved by introducing a model for the ‘slow’ pressure–strain term, along the lines of the Rotta model.
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Khanal and Weijermars. "Modeling Flow and Pressure Fields in Porous Media with High Conductivity Flow Channels and Smart Placement of Branch Cuts for Variant and Invariant Complex Potentials." Fluids 4, no. 3 (August 9, 2019): 154. http://dx.doi.org/10.3390/fluids4030154.
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A long overdue distinction between so-called variant and invariant complex potentials is proposed here for the first time. Invariant complex potentials describe physical flows where a switch of the real and imaginary parts of the function will still describe the same type of physical flow (but only rotated by π/2). Such invariants can be formulated with Euler’s formula to depict the same flow for any arbitrary orientation with respect to the coordinate system used. In contrast, variant complex potentials, when swapping their real and imaginary parts, will result in two fundamentally different physical flows. Next, we show that the contour integrals of the real and imaginary part of simple variant and invariant complex potentials generally do not generate any discernable branch cut problems. However, complex potentials due to the multiple superpositions of simple flows, even when invariant, may involve many options for selecting the branch cut locations. Examples of such branch cut choices are given for so-called areal doublets and areal dipoles, which are powerful tools to describe the streamlines and pressure fields for flow in porous media with enhanced permeability flow channels. After a discussion of the branch cut solutions, applications to a series of synthetic and field examples with enhanced permeability flow channels are given with examples of the streamline and pressure field solutions.