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1.
It was hypothesized that a crew's rowing performance was predictable based on their total propulsive power, synchrony (a real-time comparison of rower propulsive force magnitudes) and total drag contribution (a measure of the rowers' effect on shell drag forces during the recovery), quantities calculated from individual rower's force-time profiles and recovery kinematics. A rowing pair was equipped with transducers to gather shell velocity, propulsive blade force, oar angular position and seat displacement. Eight subjects (four port, four starboard) participated in two rounds of data collection. The first round pairings were random, while the second round pairings were assigned based on Round 1 results. Regression analysis and ANCOVA were used to test the validity of assumptions inherent in the predictive model and, if applicable, explore a linear model predicting rowing performance based on total propulsive power, synchrony and total drag contribution. Total propulsive power, synchrony and total drag contribution were correlated and further were affected by pairing, violating assumptions inherent in the linear model. The original hypothesis was not supported based on these violations. Important findings include (1) performance cannot be predicted using the simple linear model proposed, (2) rowers' force-time profiles are repeatable between trials, with some but not all rowers adapting their force-time profile dependent on their pair partner, presumably in an effort to increase the level of synchrony between the two, and (3) subtle biomechanical factors may play a critical role in performance.  相似文献   

2.
The present experiment evaluated a new approach to establish exercise intensity during hydraulic rowing ergometry. In contrast to the traditional approach where exercise intensity is augmented by systematically increasing workload, the new procedure increments the intensity of exercise while maintaining a constant percentage of maximum force output. Ten college females exercised on a hydraulic rower that allowed for control of rowing speed and resistance. The new method to establish work intensity was to row at a cadence of 30 c.min-1 at a force output equal to 50% of maximum rowing force at each setting determined dynamically prior to testing. Two protocols were used for the maximum tests on the hydraulic rower. Row 1 was a 17-min, six-stage, incremental continuous row test performed at increasingly difficult settings from easy (setting 1; 603 N) to difficult (setting 6; 893 N). Row 2 was identical to row 1 until 15 min when resistance was reduced to setting 2 (658 N) for "allout" effort during the last 2 min. During this time, cadence declined from 30 c.min-1 to 19.4 c.min-1 at dial setting 6 and increased to 35.4 c.min-1 at dial setting 2. Both rowing protocols were compared to maximal physiological responses during treadmill running (TM). Compared to TM, both rowing protocols elicited significantly lower maximum oxygen uptake (VO2max; P less than 0.05; row 1 = delta 29.0% and row 2 = delta 12.9%) and maximum heart rate (HRmax; P less than 0.05; row 1 = delta 12.9% and row 2 = delta 6.7%). Maximum ventilation (VEmax) during row 1 was also lower by 30.4% than TM (P less than 0.05).(ABSTRACT TRUNCATED AT 250 WORDS)  相似文献   

3.
Many marine invertebrates have planktonic larvae with cilia used for both propulsion and capturing of food particles. Hence, changes in ciliary activity have implications for larval nutrition and ability to navigate the water column, which in turn affect survival and dispersal. Using high-speed high-resolution microvideography, we examined the relationship between swimming speed, velar arrangements, and ciliary beat frequency of freely swimming veliger larvae of the gastropod Crepidula fornicata over the course of larval development. Average swimming speed was greatest 6 days post hatching, suggesting a reduction in swimming speed towards settlement. At a given age, veliger larvae have highly variable speeds (0.8–4 body lengths s−1) that are independent of shell size. Contrary to the hypothesis that an increase in ciliary beat frequency increases work done, and therefore speed, there was no significant correlation between swimming speed and ciliary beat frequency. Instead, there are significant correlations between swimming speed and visible area of the velar lobe, and distance between centroids of velum and larval shell. These observations suggest an alternative hypothesis that, instead of modifying ciliary beat frequency, larval C. fornicata modify swimming through adjustment of velum extension or orientation. The ability to adjust velum position could influence particle capture efficiency and fluid disturbance and help promote survival in the plankton.  相似文献   

4.
Why do some animals swim by rowing appendages back and forthwhile others fly by flapping them up and down? One hypothesissuggests the answer lies in the sharply divergent physical environmentsencountered by small, slow animals, and large, fast animals.Flapping appendages allow large animals to move through a fluidenvironment quickly and efficiently. As size and speed decrease,however, viscous drag increasingly dominates the force balance,with negative consequences for both rowing and flapping appendages.Nevertheless, comparative data suggest that flapping does notoccur in animals at Reynolds numbers (Re) less than about 15.I used a computer simulation experiment to address the question,"Below what Re is rowing more effective than flapping?" Thesimulation, which employed a simple quasi-steady, blade-elementmodel of virtual oscillating appendages, has several importantresults. First, the mechanical efficiency of both rowing andflapping decrease dramatically with scale. Second, the performanceof rowing can increase substantially by taking advantage ofseveral dynamic shape modifications, including area and spanreduction during the recovery stroke. Finally, the relativeperformance of rowing and flapping is dependent on the advanceratio, which is a function of the travel speed relative to theoscillation frequency. The model predicts that rowing is moreefficient than flapping at Re < 20 for animals moving throughoutthe range of typically observed advance ratios.  相似文献   

5.
Hybrid functional electrical stimulation (FES) rowing has positive effects on cardiovascular fitness, producing significantly greater aerobic power than either upper body or FES exercise alone. However, there is minimal information on the kinematics, kinetics, and mechanical efficiency of FES-rowing in the spinal cord injured (SCI) population. This study examined the biomechanics of FES-rowing to determine how motions, forces, and aerobic demand change with increasing intensity. Six individuals with SCI and six able-bodied subjects performed a progressive aerobic capacity rowing test. Differences in kinematics (motion profiles), kinetics (forces produced by the feet and arms), external mechanical work, and mechanical efficiency (work produced/volume of oxygen consumed) were compared in able-bodied rowing vs. SCI FES-rowing at three comparable subpeak workloads. With increasing exercise intensity (measured as wattage), able-bodied rowing increased stroke rate by decreasing recovery time, while FES-rowing maintained a constant stroke rate, with no change in drive or recovery times. While able-bodied rowers increased leg and arm forces with increasing intensity, FES-rowers used only their arms to achieve a higher intensity with a constant and relatively low contribution of the legs. Oxygen consumption increased in both groups, but more so in able-bodied rowers, resulting in able-bodied rowers having twice the mechanical efficiency of FES-rowers. Our results suggest that despite its ability to allow for whole body exercise, the total force output achievable with FES-rowing results in only modest loading of the legs that affects overall rowing performance and that may limit forces applied to bone.  相似文献   

6.
Power requirements of swimming: do new methods resolve old questions?   总被引:3,自引:0,他引:3  
A recurring question in the study of fish biomechanics and energeticsis the mechanical power required for tail-swimming at the highspeeds seen among aquatic vertebrates. The quest for answershas been driven by conceptual advances in fluid dynamics, startingwith ideas on the boundary layer and drag initiated by Prandtl,and in measurement techniques starting with force balances focussingon drag and thrust. Drag (=thrust) from measurements on physicalmodels, carcasses, kinematics as inputs to hydromechanical models,and physiological power sources vary from less than that expectedfor an equivalent rigid reference to over an order of magnitudegreater. Estimates of drag and thrust using recent advanceslargely made possible by increased computing power have notresolved the discrepancy. Sources of drag and thrust are notseparable in axial undulatory self propulsion, are open to interpretationand Froude efficiency is zero. Wakes are not easily interpreted,especially for thrust evaluation. We suggest the best measuresof swimming performance are velocity and power consumption forwhich 2D inviscid simulations can give realistic predictions.Steady swimming power is several times that required for towingan equivalent flat plate at the same speed.  相似文献   

7.
In rowing, motor learning may be facilitated by augmented feedback that displays the ratio between actual mean boat velocity and maximal achievable mean boat velocity. To provide this ratio, the aim of this work was to develop and evaluate an algorithm calculating an individual maximal mean boat velocity. The algorithm optimised the horizontal oar movement under constraints such as the individual range of the horizontal oar displacement, individual timing of catch and release and an individual power–angle relation. Immersion and turning of the oar were simplified, and the seat movement of a professional rower was implemented. The feasibility of the algorithm, and of the associated ratio between actual boat velocity and optimised boat velocity, was confirmed by a study on four subjects: as expected, advanced rowing skills resulted in higher ratios, and the maximal mean boat velocity depended on the range of the horizontal oar displacement.  相似文献   

8.
Reynolds number and thus body size may potentially limit aerodynamic force production in flying insects due to relative changes of viscous forces on the beating wings. By comparing four different species of fruit flies similar in shape but with different body mass, we have investigated how small insects cope with changes in fluid mechanical constraints on power requirements for flight and the efficiency with which chemical energy is turned into aerodynamic flight forces. The animals were flown in a flight arena in which stroke kinematics, aerodynamic force production, and carbon dioxide release were measured within the entire working range of the flight motor. The data suggest that during hovering performance mean lift coefficient for flight is higher in smaller animals than in their larger relatives. This result runs counter to predictions based on conventional aerodynamic theory and suggests subtle differences in stroke kinematics between the animals. Estimates in profile power requirements based on high drag coefficient suggest that among all tested species of fruit flies elastic energy storage might not be required to minimize energetic expenditures during flight. Moreover, muscle efficiency significantly increases with increasing body size whereas aerodynamic efficiency tends to decrease with increasing size or Reynolds number. As a consequence of these two opposite trends, total flight efficiency tends to increase only slightly within the 6-fold range of body sizes. Surprisingly, total flight efficiency in fruit flies is broadly independent of different profile power estimates and typically yields mean values between 2–4%.  相似文献   

9.
Recent developments in the design and propulsion of biomimetic autonomous underwater vehicles (AUVs) have focused on boxfish as models (e.g. Deng and Avadhanula 2005 Biomimetic micro underwater vehicle with oscillating fin propulsion: system design and force measurement Proc. 2005 IEEE Int. Conf. Robot. Auto. (Barcelona, Spain) pp 3312-7). Whilst such vehicles have many potential advantages in operating in complex environments (e.g. high manoeuvrability and stability), limited battery life and payload capacity are likely functional disadvantages. Boxfish employ undulatory median and paired fins during routine swimming which are characterized by high hydromechanical Froude efficiencies (approximately 0.9) at low forward speeds. Current boxfish-inspired vehicles are propelled by a low aspect ratio, 'plate-like' caudal fin (ostraciiform tail) which can be shown to operate at a relatively low maximum Froude efficiency (approximately 0.5) and is mainly employed as a rudder for steering and in rapid swimming bouts (e.g. escape responses). Given this and the fact that bioinspired engineering designs are not obligated to wholly duplicate a biological model, computer chips were developed using a multilayer perception neural network model of undulatory fin propulsion in the knifefish Xenomystus nigri that would potentially allow an AUV to achieve high optimum values of propulsive efficiency at any given forward velocity, giving a minimum energy drain on the battery. We envisage that externally monitored information on flow velocity (sensory system) would be conveyed to the chips residing in the vehicle's control unit, which in turn would signal the locomotor unit to adopt kinematics (e.g. fin frequency, amplitude) associated with optimal propulsion efficiency. Power savings could protract vehicle operational life and/or provide more power to other functions (e.g. communications).  相似文献   

10.
Summary Power input measurements are carried out in a production bioreactor with a liquid volume up to 25 m3. The results show that the cavity formation principle is applicable to reactors at this scale. It can also be observed that empirical correlations are not useful to predict gassed power input accurately. It is found that at gas flow rates for normal production conditions (NQ =0.1), the gassed power input is about 30–40 % of the non gassed power input.Nomenclature Cp specific heat J/kgK - D impeller diameter m - Db1 impeller blade diameter m - d baffle diameter m - Fr Froude number - - g gravitation m/s2 - h impeller clearance m - H liquid height m - N stirrer speed s-1 - Np power number - - NQ gas flow (aeration) number - - NQ * critical gasflow number for 3 cavity formation - - Po ungassed power consumption W - Pg gassed power consumption W - Q gas flow rate (273 K, 105 N/m2) m3/s - Re Reynolds number - - T tankdiameter m temperature K - t time s - V liquid volume m3 - Vtip impeller tip speed m/s - Vs impeller correlated superficial gas flow rate m/s - W impeller blade width m - density kg/m3  相似文献   

11.
Propulsive efficiency is a key indicator of propulsive performance, but it can be difficult to measure when the propulsion system is integrated into the vehicle body because the average rate of useful work done propelling the vehicle (Wu) and/or the average mechanical power expended propelling the vehicle (Pmech) is not known directly. A general approach would be to determine either or both of (Wu) and (Pmech) from the vehicle wake. The present discussion demonstrates that only (Pmech) can be determined from the flow crossing a plane a fixed (average) distance downstream of the vehicle. A method for measuring (Pmech) is presented using the observation that the power required to tow a permeable obstruction behind the vehicle depends on (Pmech). Several methods for evaluating propulsive performance using [Formula: see text] are proposed, including the definition of an equivalent jet velocity and corresponding Froude efficiency if the time-averaged mass flow rate through the propulsion system is known. If only (Pmech) is known, the recommended measure of propulsive performance is a power coefficient defined analogous to a drag coefficient.  相似文献   

12.
BackgroundIt has been suggested that a higher intra-individual variability benefits the motor learning of wheelchair propulsion. The present study evaluated whether feedback-induced variability on wheelchair propulsion technique variables would also enhance the motor learning process. Learning was operationalized as an improvement in mechanical efficiency and propulsion technique, which are thought to be closely related during the learning process.Methods17 Participants received visual feedback-based practice (feedback group) and 15 participants received regular practice (natural learning group). Both groups received equal practice dose of 80 min, over 3 weeks, at 0.24 W/kg at a treadmill speed of 1.11 m/s. To compare both groups the pre- and post-test were performed without feedback. The feedback group received real-time visual feedback on seven propulsion variables with instruction to manipulate the presented variable to achieve the highest possible variability (1st 4-min block) and optimize it in the prescribed direction (2nd 4-min block). To increase motor exploration the participants were unaware of the exact variable they received feedback on. Energy consumption and the propulsion technique variables with their respective coefficient of variation were calculated to evaluate the amount of intra-individual variability.ResultsThe feedback group, which practiced with higher intra-individual variability, improved the propulsion technique between pre- and post-test to the same extent as the natural learning group. Mechanical efficiency improved between pre- and post-test in the natural learning group but remained unchanged in the feedback group.ConclusionThese results suggest that feedback-induced variability inhibited the improvement in mechanical efficiency. Moreover, since both groups improved propulsion technique but only the natural learning group improved mechanical efficiency, it can be concluded that the improvement in mechanical efficiency and propulsion technique do not always appear simultaneously during the motor learning process. Their relationship is most likely modified by other factors such as the amount of the intra-individual variability.  相似文献   

13.
Extremely fast animal actions are accomplished with mechanisms that reduce the duration of movement. This process is known as power amplification. Although many studies have examined the morphology and performance of power‐amplified systems, little is known about their development and evolution. Here, we examine scaling and modularity in the powerful predatory appendages of a mantis shrimp, Gonodactylaceus falcatus (Crustacea, Stomatopoda). We propose that power‐amplified systems can be divided into three units: an engine (e.g., muscle), an amplifier (e.g., spring), and a tool (e.g., hammer). We tested whether these units are developmentally independent using geometric morphometric techniques that quantitatively compare shapes. Additionally, we tested whether shape and several mechanical features are correlated with size and sex. We found that the morphological regions that represent the engine, amplifier, and tool belong to independent developmental modules. In both sexes, body size was positively correlated with the size of each region. Shape, however, changed allometrically with appendage size only in the amplifier (both sexes) and tool (males). These morphological changes were correlated with strike force and spring force (amplifier), but not spring stiffness (amplifier). Overall, the results indicate that each functional unit belongs to different developmental modules in a power‐amplified system, potentially allowing independent evolution of the engine, amplifier, and tool.  相似文献   

14.
BackgroundUltramarathon is a high endurance exercise associated with a wide range of exercise-related problems, such as acute kidney injury (AKI). Early recognition of individuals at risk of AKI during ultramarathon event is critical for implementing preventative strategies.ObjectivesTo investigate the impact of speed variability to identify the exercise-related acute kidney injury anticipatively in ultramarathon event.MethodsThis is a prospective, observational study using data from a 100 km ultramarathon in Taipei, Taiwan. The distance of entire ultramarathon race was divided into 10 splits. The mean and variability of speed, which was determined by the coefficient of variation (CV) in each 10 km-split (25 laps of 400 m oval track) were calculated for enrolled runners. Baseline characteristics and biochemical data were collected completely 1 week before, immediately post-race, and one day after race. The main outcome was the development of AKI, defined as Stage II or III according to the Acute Kidney Injury Network (AKIN) criteria. Multivariate analysis was performed to determine the independent association between variables and AKI development.Results26 ultramarathon runners were analyzed in the study. The overall incidence of AKI (in all Stages) was 84.6% (22 in 26 runners). Among these 22 runners, 18 runners were determined as Stage I, 4 runners (15.4%) were determined as Stage II, and none was in Stage III. The covariates of BMI (25.22 ± 2.02 vs. 22.55 ± 1.96, p = 0.02), uric acid (6.88 ± 1.47 vs. 5.62 ± 0.86, p = 0.024), and CV of speed in specific 10-km splits (from secondary 10 km-split (10th – 20th km-split) to 60th – 70th km-split) were significantly different between runners with or without AKI (Stage II) in univariate analysis and showed discrimination ability in ROC curve. In the following multivariate analysis, only CV of speed in 40th – 50th km-split continued to show a significant association to the development of AKI (Stage II) (p = 0.032).ConclusionsThe development of exercise-related AKI was not infrequent in the ultramarathon runners. Because not all runners can routinely receive laboratory studies after race, variability of running speed (CV of speed) may offer a timely and efficient tool to identify AKI early during the competition, and used as a surrogate screening tool, at-risk runners can be identified and enrolled into prevention trials, such as adequate fluid management and avoidance of further NSAID use.  相似文献   

15.
Cerebrospinal fluid (CSF) analysis is an important tool in the diagnostic work-up of many neurological disorders, but reference ranges for CSF glucose, CSF/plasma glucose ratio and CSF lactate based on studies with large numbers of CSF samples are not available. Our aim was to define age-specific reference values. In 1993 The Nijmegen Observational CSF Study was started. Results of all CSF samples that were analyzed between 1993 and 2008 at our laboratory were systematically collected and stored in our computerized database. After exclusion of CSF samples with an unknown or elevated erythrocyte count, an elevated leucocyte count, elevated concentrations of bilirubin, free hemoglobin, or total protein 9,036 CSF samples were further studied for CSF glucose (n = 8,871), CSF/plasma glucose ratio (n = 4,516) and CSF lactate values (n = 7,614). CSF glucose, CSF/plasma glucose ratio and CSF lactate were age-, but not sex dependent. Age-specific reference ranges were defined as 5–95th percentile ranges. CSF glucose 5th percentile values ranged from 1.8 to 2.9 mmol/L and 95th percentile values from 3.8 to 5.6 mmol/L. CSF/plasma glucose ratio 5th percentile values ranged from 0.41 to 0.53 and 95th percentile values from 0.82 to 1.19. CSF lactate 5th percentile values ranged from 0.88 to 1.41 mmol/L and 95th percentile values from 2.00 to 2.71 mmol/L. Reference ranges for all three parameters were widest in neonates and narrowest in toddlers, with lower and upper limits increasing with age. These reference values allow a reliable interpretation of CSF results in everyday clinical practice. Furthermore, hypoglycemia was associated with an increased CSF/plasma glucose ratio, whereas hyperglycemia did not affect the CSF/plasma glucose ratio.  相似文献   

16.
The unsteady hydrodynamics of a biomimetic fin attached to a cylindrical body has been studied numerically using a computational fluid dynamic (CFD) simulator based on an in-house solver of the Navier-Stokes equations, combined with a recently developed multi-block, overset grid method. The fin-body CFD model is based on a mechanical pectoral fin device, which consists of a cylindrical body and an asymmetric fin and can mimic flapping, rowing and feathering motions of the pectoral fins in fishes. First the multi-block, overset grid method incorporated into the NS solver was verified through an extensive study of unsteady flows past a single fin undergoing rowing and feathering motion. Then unsteady flows past the biomimetic fin-body model undergoing the same motions were computed and compared with the measurements of forces of the mechanical pectoral fin, which shows good agreement in both time-varying and time-averaged hydrodynamic forces. The relationship between force generation and vortex dynamics points to the importance of the match in fin kinematics between power and recovery strokes and implies that an optimal selection of parameters of phase lags between and amplitudes of rowing and feathering motions can improve the performance of labriform propulsion in terms of either maximum force generation or minimum mechanical power.  相似文献   

17.
Push-rim wheelchair propulsion is biomechanically inefficient and physiologically stressful to the musculoskeletal structure of human body. This study focuses to obtain a new, optimized propulsion shape for wheelchair users, which is within the ergonomic ranges of joint motion, thus reducing the probability of injuries. To identify the propulsion movement, forward dynamic optimization was performed on a 3D human musculoskeletal model linked to a handle based propulsion mechanism, having shape and muscle excitations as optimization variables. The optimization resulted in a handle path shape with a circularity ratio of 0.95, and produced a net propulsion power of 34.7 watts for an isokinetic propulsion cycle at 50?rpm. Compared to push-rim propulsion, the compact design of the new propulsion mechanism along with the ergonomically optimized propulsion shape may help to reduce the risk of injuries and thus improve the quality of life for wheelchair users.  相似文献   

18.
Manual wheelchair propulsion places considerable physical demand on the upper extremity and is one of the primary activities associated with the high prevalence of upper extremity overuse injuries and pain among wheelchair users. As a result, recent effort has focused on determining how various propulsion techniques influence upper extremity demand during wheelchair propulsion. However, an important prerequisite for identifying the relationships between propulsion techniques and upper extremity demand is to understand how individual muscles contribute to the mechanical energetics of wheelchair propulsion. The purpose of this study was to use a forward dynamics simulation of wheelchair propulsion to quantify how individual muscles deliver, absorb and/or transfer mechanical power during propulsion. The analysis showed that muscles contribute to either push (i.e., deliver mechanical power to the handrim) or recovery (i.e., reposition the arm) subtasks, with the shoulder flexors being the primary contributors to the push and the shoulder extensors being the primary contributors to the recovery. In addition, significant activity from the shoulder muscles was required during the transition between push and recovery, which resulted in increased co-contraction and upper extremity demand. Thus, strengthening the shoulder flexors and promoting propulsion techniques that improve transition mechanics have much potential to reduce upper extremity demand and improve rehabilitation outcomes.  相似文献   

19.
M. S. Awan 《BioControl》1990,35(2):203-210
Three species of hemipteran predators preyed differently upon 1st instarHeliothis punctiger Wallengren larvae.Cermatulus nasalis consumed more larvae thanOechalia schellenbergii which consumed more larvae thanTropiconabis nigrolineatus. All the species consumed significantly less 1st instar larvae on plants than what they consumed in Petri-dishes. Fifth instar predators showed significant differences in terms of prey consumption due to sex independent of searching conditions. Only 4th and 5th instars ofT. nigrolineatus attacked and captured 2nd instars ofH. punctiger larvae. The other 2 species however readily attacked and consumed 2nd instarH. punctiger larvae. Their prey consumption was similar in Petri-dishes and on plants. Only 5th instars ofT. nigrolineatus could subdue and capture 3rd instarH. punctiger larvae. Second instar pentatomids captured just one 3rd instar larva but older instars killed and ate more. Fourth instarH. punctiger larvae were immune to attacks by allT. nigrolineatus and younger pentatomids due to their defense ploys but 5th instar pentatomids could subdue and capture them. None of the predators captured 5th instarH. punctiger larvae except few 5th instar females ofC. naslis andO. schellenbergii.   相似文献   

20.
In this work, a single tablet model and a discrete element method (DEM) computer simulation are developed to obtain the angular circulation speed of tablets in a vibratory tablet coating pan for range of vibration frequencies and amplitudes. The models identify three important dimensionless parameters that influence the speed of the tablets: the dimensionless amplitude ratio (a/R), the Froude number ( 2/g), and the tablet–wall friction coefficient, where a is the peak vibration amplitude at the drum center, ω is the vibration angular frequency, R is the drum radius, and g is the acceleration due to gravity. The models predict that the angular circulation speed of tablets increases with an increase in each of these parameters. The rate of increase in the angular circulation speed is observed to decrease for larger values of a/R. The angular circulation speed reaches an asymptote beyond a tablet–wall friction coefficient value of about 0.4. Furthermore, it is found that the Froude number should be greater than one for the tablets to start circulating. The angular circulation speed increases as Froude number increases but then does not change significantly at larger values of the Froude number. Period doubling, where the motion of the bed is repeated every two cycles, occurs at a Froude number larger than five. The single tablet model, although much simpler than the DEM model, is able to predict the maximum circulation speed (the limiting case for a large value of tablet–wall friction coefficient) as well as the transition to period doubling.  相似文献   

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