A radiological method to determine the accuracy of motion capture marker placement on palpable anatomical landmarks through a shoe

The accuracy of marker placement on palpable surface anatomical landmarks is an important consideration in biomechanics. Although marker placement reliability has been studied in some depth, it remains unclear whether or not the markers are accurately positioned over the intended landmark in order to define the static position and orientation of the segment. A novel method using commonly available X-ray imaging was developed to identify the accuracy of markers placed on the shoe surface by palpating landmarks through the shoe. An anterior–posterior and lateral–medial X-ray was taken on 24 participants with a newly developed marker set applied to both the skin and shoe. The vector magnitude of both skin- and shoe-mounted markers from the anatomical landmark was calculated, as well as the mean marker offset between skin- and shoe-mounted markers. The accuracy of placing markers on the shoe relative to the skin-mounted markers, accounting for shoe thickness, was less than 5mm for all markers studied. Further, when using the developed guidelines provided in this study, the method was deemed reliable (Intra-rater ICCs¼0.50–0.92). In conclusion, the method proposed here can reliably assess marker placement accuracy on the shoe surface relative to chosen anatomical landmarks beneath the skin.

The effect of exercise intensity on fat oxidation and non-exercise activity thermogenesis in overweight/obese men

It is frequently reported that the actual weight loss achieved through exercise interventions is less than theoretically expected. Amongst other compensatory adjustments that accompany exercise training (e.g., increases in resting metabolic rate and energy intake), a possible cause of the less than expected weight loss is a failure to produce a marked increase in total daily energy expenditure due to a compensatory reduction in non-exercise activity thermogenesis (NEAT). Therefore, there is a need to understand how behaviour is modified in response to exercise interventions. The proposed benefits of exercise training are numerous, including changes to fat oxidation. Given that a diminished capacity to oxidise fat could be a factor in the aetiology of obesity, an exercise training intensity that optimises fat oxidation in overweight/obese individuals would improve impaired fat oxidation, and potentially reduce health risks that are associated with obesity. To improve our understanding of the effectiveness of exercise for weight management, it is important to ensure exercise intensity is appropriately prescribed, and to identify and monitor potential compensatory behavioural changes consequent to exercise training. In line with the gaps in the literature, three studies were performed. The aim of Study 1 was to determine the effect of acute bouts of moderate- and high-intensity walking exercise on NEAT in overweight and obese men. Sixteen participants performed a single bout of either moderate-intensity walking exercise (MIE) or high-intensity walking exercise (HIE) on two separate occasions. The MIE consisted of walking for 60-min on a motorised treadmill at 6 km.h-1. The 60-min HIE session consisted of walking in 5-min intervals at 6 km.h-1 and 10% grade followed by 5-min at 0% grade. NEAT was assessed by accelerometer three days before, on the day of, and three days after the exercise sessions. There was no significant difference in NEAT vector magnitude (counts.min-1) between the pre-exercise period (days 1-3) and the exercise day (day 4) for either protocol. In addition, there was no change in NEAT during the three days following the MIE session, however NEAT increased by 16% on day 7 (post-exercise) compared with the exercise day (P = 0.32). During the post-exercise period following the HIE session, NEAT was increased by 25% on day 7 compared with the exercise day (P = 0.08), and by 30-33% compared with the pre-exercise period (day 1, day 2 and day 3); P = 0.03, 0.03, 0.02, respectively. To conclude, a single bout of either MIE or HIE did not alter NEAT on the exercise day or on the first two days following the exercise session. However, extending the monitoring of NEAT allowed the detection of a 48 hour delay in increased NEAT after performing HIE. A longer-term intervention is needed to determine the effect of accumulated exercise sessions over a week on NEAT. In Study 2, there were two primary aims. The first aim was to test the reliability of a discontinuous incremental exercise protocol (DISCON-FATmax) to identify the workload at which fat oxidation is maximised (FATmax). Ten overweight and obese sedentary male men (mean BMI of 29.5 ¡Ó 4.5 kg/m2 and mean age of 28.0 ¡Ó 5.3 y) participated in this study and performed two identical DISCON-FATmax tests one week apart. Each test consisted of alternate 4-min exercise and 2-min rest intervals on a cycle ergometer. The starting work load of 28 W was increased every 4-min using 14 W increments followed by 2-min rest intervals. When the respiratory exchange ratio was consistently >1.0, the workload was increased by 14 W every 2-min until volitional exhaustion. Fat oxidation was measured by indirect calorimetry. The mean FATmax, ƒtV O2peak, %ƒtV O2peak and %Wmax at which FATmax occurred during the two tests were 0.23 ¡Ó 0.09 and 0.18 ¡Ó 0.08 (g.min-1); 29.7 ¡Ó 7.8 and 28.3 ¡Ó 7.5 (ml.kg-1.min-1); 42.3 ¡Ó 7.2 and 42.6 ¡Ó 10.2 (%ƒtV O2max) and 36.4 ¡Ó 8.5 and 35.4 ¡Ó 10.9 (%), respectively. A paired-samples T-test revealed a significant difference in FATmax (g.min-1) between the tests (t = 2.65, P = 0.03). The mean difference in FATmax was 0.05 (g.min-1) with the 95% confidence interval ranging from 0.01 to 0.18. Paired-samples T-test, however, revealed no significant difference in the workloads (i.e. W) between the tests, t (9) = 0.70, P = 0.4. The intra-class correlation coefficient for FATmax (g.min-1) between the tests was 0.84 (95% confidence interval: 0.36-0.96, P < 0.01). However, Bland-Altman analysis revealed a large disagreement in FATmax (g.min-1) related to W between the two tests; 11 ¡Ó 14 (W) (4.1 ¡Ó 5.3 ƒtV O2peak (%)).These data demonstrate two important phenomena associated with exercise-induced substrate oxidation; firstly, that maximal fat oxidation derived from a discontinuous FATmax protocol differed statistically between repeated tests, and secondly, there was large variability in the workload corresponding with FATmax. The second aim of Study 2 was to test the validity of a DISCON-FATmax protocol by comparing maximal fat oxidation (g.min-1) determined by DISCON-FATmax with fat oxidation (g.min-1) during a continuous exercise protocol using a constant load (CONEX). Ten overweight and obese sedentary males (BMI = 29.5 ¡Ó 4.5 kg/m2; age = 28.0 ¡Ó 4.5 y) with a ƒtV O2max of 29.1 ¡Ó 7.5 ml.kg-1.min-1 performed a DISCON-FATmax test consisting of alternate 4-min exercise and 2-min rest intervals on a cycle ergometer. The 1-h CONEX protocol used the workload from the DISCON-FATmax to determine FATmax. The mean FATmax, ƒtV O2max, %ƒtV O2max and workload at which FATmax occurred during the DISCON-FATmax were 0.23 ¡Ó 0.09 (g.min-1); 29.1 ¡Ó 7.5 (ml.kg-1.min-1); 43.8 ¡Ó 7.3 (%ƒtV O2max) and 58.8 ¡Ó 19.6 (W), respectively. The mean fat oxidation during the 1-h CONEX protocol was 0.19 ¡Ó 0.07 (g.min-1). A paired-samples T-test revealed no significant difference in fat oxidation (g.min-1) between DISCON-FATmax and CONEX, t (9) = 1.85, P = 0.097 (two-tailed). There was also no significant correlation in fat oxidation between the DISCON-FATmax and CONEX (R=0.51, P = 0.14). Bland- Altman analysis revealed a large disagreement in fat oxidation between the DISCONFATmax and CONEX; the upper limit of agreement was 0.13 (g.min-1) and the lower limit of agreement was ¡V0.03 (g.min-1). These data suggest that the CONEX and DISCONFATmax protocols did not elicit different rates of fat oxidation (g.min-1). However, the individual variability in fat oxidation was large, particularly in the DISCON-FATmax test. Further research is needed to ascertain the validity of graded exercise tests for predicting fat oxidation during constant load exercise sessions. The aim of Study 3 was to compare the impact of two different intensities of four weeks of exercise training on fat oxidation, NEAT, and appetite in overweight and obese men. Using a cross-over design 11 participants (BMI = 29 ¡Ó 4 kg/m2; age = 27 ¡Ó 4 y) participated in a training study and were randomly assigned initially to: [1] a lowintensity (45%ƒtV O2max) exercise (LIT) or [2] a high-intensity interval (alternate 30 s at 90%ƒtV O2max followed by 30 s rest) exercise (HIIT) 40-min duration, three times a week. Participants completed four weeks of supervised training and between cross-over had a two week washout period. At baseline and the end of each exercise intervention,ƒtV O2max, fat oxidation, and NEAT were measured. Fat oxidation was determined during a standard 30-min continuous exercise bout at 45%ƒtV O2max. During the steady state exercise expired gases were measured intermittently for 5-min periods and HR was monitored continuously. In each training period, NEAT was measured for seven consecutive days using an accelerometer (RT3) the week before, at week 3 and the week after training. Subjective appetite sensations and food preferences were measured immediately before and after the first exercise session every week for four weeks during both LIT and HIIT. The mean fat oxidation rate during the standard continuous exercise bout at baseline for both LIT and HIIT was 0.14 ¡Ó 0.08 (g.min-1). After four weeks of exercise training, the mean fat oxidation was 0.178 ¡Ó 0.04 and 0.183 ¡Ó 0.04 g.min-1 for LIT and HIIT, respectively. The mean NEAT (counts.min-1) was 45 ¡Ó 18 at baseline, 55 ¡Ó 22 and 44 ¡Ó 16 during training, and 51 ¡Ó 14 and 50 ¡Ó 21 after training for LIT and HIIT, respectively. There was no significant difference in fat oxidation between LIT and HIIT. Moreover, although not statistically significant, there was some evidence to suggest that LIT and HIIT tend to increase fat oxidation during exercise at 45% ƒtV O2max (P = 0.14 and 0.08, respectively). The order of training treatment did not significantly influence changes in fat oxidation, NEAT, and appetite. NEAT (counts.min-1) was not significantly different in the week following training for either LIT or HIIT. Although not statistically significant (P = 0.08), NEAT was 20% lower during week 3 of exercise training in HIIT compared with LIT. Examination of appetite sensations revealed differences in the intensity of hunger, with higher ratings after LIT compared with HIIT. No differences were found in preferences for high-fat sweet foods between LIT and HIIT. In conclusion, the results of this thesis suggest that while fat oxidation during steady state exercise was not affected by the level of exercise intensity, there is strong evidence to suggest that intense exercise could have a debilitative effect on NEAT.

Comparison of three generations of ActiGraph (TM) activity monitors in children and adolescents

In this study, we evaluated agreement among three generations of ActiGraph (TM) accelerometers in children and adolescents. Twenty-nine participants (mean age = 14.2 +/- 3.0 years) completed two laboratory-based activity sessions, each lasting 60 min. During each session, participants concurrently wore three different models of the ActiGraph (TM) accelerometers (GT1M, GT3X, GT3X+). Agreement among the three models for vertical axis counts, vector magnitude counts, and time spent in moderate-to-vigorous physical exercise (MVPA) was evaluated by calculating intraclass correlation coefficients and Bland-Altman plots. The intraclass correlation coefficient for total vertical axis counts, total vector magnitude counts, and estimated MVPA was 0.994 (95% CI = 0.989-0.996), 0.981 (95% CI = 0.969-0.989), and 0.996 (95% CI = 0.989-0.998), respectively. Inter-monitor differences for total vertical axis and vector magnitude counts ranged from 0.3% to 1.5%, while inter-monitor differences for estimated MVPA were equal to or close to zero. On the basis of these findings, we conclude that there is strong agreement between the GT1M, GT3X, and GT3X+ activity monitors, thus making it acceptable for researchers and practitioners to use different ActiGraph (TM) models within a given study.

Accelerometer validity and placement for detection of changes in physical activity in dogs under controlled conditions on a treadmill

The objective of the research was to determine the optimal location and method of attachment for accelerometer-based motion sensors, and to validate their ability to differentiate rest and increases in speed in healthy dogs moving on a treadmill. Two accelerometers were placed on a harness between the scapulae of dogs with one in a pouch and one directly attached to the harness. Two additional accelerometers were placed (pouched and not pouched) ventrally on the dog's collar. Data were recorded in 1. s epochs with dogs moving in stages lasting 3. min each on a treadmill: (1) at rest, lateral recumbency, (2) treadmill at 0% slope, 3. km/h, (3) treadmill at 0% slope, 5. km/h, (4) treadmill at 0% slope, 7. km/h, (5) treadmill at 5% slope, 5. km/h, and; (6) treadmill at 5% slope, 7. km/h. Only the harness with the accelerometer in a pouch along the dorsal midline yielded statistically significant increases (P< 0.05) in vector magnitude as walking speed of the dogs increased (5-7. km/h) while on the treadmill. Statistically significant increases in vector magnitude were detected in the dogs as the walking speed increased from 5 to 7. km/h, however, changes in vector magnitude were not detected when activity intensity was increased as a result of walking up a 5% grade. Accelerometers are a valid and objective tool able to discriminate between and monitor different levels of activity in dogs in terms of speed of movement but not in energy expenditure that occurs with movement up hill.

Decision trees for detection of activity intensity in youth with cerebral palsy

PURPOSE To develop and test decision tree (DT) models to classify physical activity (PA) intensity from accelerometer output and Gross Motor Function Classification System (GMFCS) classification level in ambulatory youth with cerebral palsy (CP); and 2) compare the classification accuracy of the new DT models to that achieved by previously published cut-points for youth with CP. METHODS Youth with CP (GMFCS Levels I - III) (N=51) completed seven activity trials with increasing PA intensity while wearing a portable metabolic system and ActiGraph GT3X accelerometers. DT models were used to identify vertical axis (VA) and vector magnitude (VM) count thresholds corresponding to sedentary (SED) (<1.5 METs), light PA (LPA) (>/=1.5 and <3 METs) and moderate-to-vigorous PA (MVPA) (>/=3 METs). Models were trained and cross-validated using the 'rpart' and 'caret' packages within R. RESULTS For the VA (VA_DT) and VM decision trees (VM_DT), a single threshold differentiated LPA from SED, while the threshold for differentiating MVPA from LPA decreased as the level of impairment increased. The average cross-validation accuracy for the VC_DT was 81.1%, 76.7%, and 82.9% for GMFCS levels I, II, and III, respectively. The corresponding cross-validation accuracy for the VM_DT was 80.5%, 75.6%, and 84.2%, respectively. Within each GMFCS level, the decision tree models achieved better PA intensity recognition than previously published cut-points. The accuracy differential was greatest among GMFCS level III participants, in whom the previously published cut-points misclassified 40% of the MVPA activity trials. CONCLUSION GMFCS-specific cut-points provide more accurate assessments of MVPA levels in youth with CP across the full spectrum of ambulatory ability.

A Medium-Voltage Inverter-Fed IM Drive Using Multilevel 12-Sided Polygonal Vectors, With Nearly Constant Switching Frequency Current Hysteresis Controller

In this paper, a current error space vector (CESV)-based hysteresis current controller for a multilevel 12-sided voltage space vector-based inverter-fed induction motor (IM) drive is proposed. The proposed controller gives a nearly constant switching frequency operation throughout different speeds in the linear modulation region. It achieves the elimination of 6n +/- 1, n = odd harmonics from the phase voltages and currents in the entire modulation range, with an increase in the linear modulation range. It also exhibits fast dynamic behavior under different transient conditions and has a simple controller implementation. Nearly constant switching frequency is obtained by matching the steady-state CESV boundaries of the proposed controller with that of a constant switching frequency SVPWM-based drive. In the proposed controller, the CESV reference boundaries are computed online, using the switching dwell time and voltage error vector of each applied vector. These quantities are calculated from estimated sampled reference phase voltages. Vector change is decided by projecting the actual current error along the computed hysteresis space vector boundary of the presently applied vector. The estimated reference phase voltages are found from the stator current error ripple and the parameters of the IM.

On the unstable stacking criterion for ideal and cracked copper-crystals

The unstable stacking criteria for an ideal copper crystal under homogeneous shearing and for a cracked copper crystal under pure mode II loading are analysed. For the ideal crystal under homogeneous shearing, the unstable stacking energy gamma(us) defined by Rice in 1992 results from shear with no relaxation in the direction normal to the slip plane. For the relaxed shear configuration, the critical condition for unstable stacking does not correspond to the relative displacement Delta = b(p)/2, where b(p) is the Burgers vector magnitude of the Shockley partial dislocation, but to the maximum shear stress. Based on this result, the unstable stacking energy Gamma(us) is defined for the relaxed lattice. For the cracked crystal under pure mode II loading, the dislocation configuration corresponding to Delta = b(p)/2 is a stable state and no instability occurs during the process of dislocation nucleation. The instability takes place at approximately Delta = 3b(p)/4. An unstable stacking energy Pi(us) is defined which corresponds to the unstable stacking state at which the dislocation emission takes place. A molecular dynamics method is applied to study this in an atomistic model and the results verify the analysis above.

Inverse Class-E Amplifier With Transmission-Line Harmonic Suppression

This paper reports on the design methodology and experimental characterization of the inverse Class-E power amplifier. A demonstration amplifier with excellent second and third harmonic-suppression levels has been designed, constructed, and measured. The circuit fabricated using a 1.2-min gate-width GaAs MESFET is shown to be able to deliver 22-dBm output power at 2.3 GHz. The amplifier achieves a peak power-added efficiency of 64 % and drain efficiency of 69 %, and exhibits 11.6 dB power gain when operated from a 3-V supply voltage. Comparisons of simulated and measured results are given with good agreement between them being obtained. Experimental results are presented for the amplifier's response to Gaussian minimum shift keying modulation, where a peak error vector modulation value of 0.6% is measured.

Necessary and sufficient condition for generalized passivity, passification and application to multivariable adaptive systems

Recently, a generalized passivity concept for linear multivariable systems was obtained which allows circumventing the restrictiveness of the usual passivity concept. The latter is associated with the classical SPR (Strictly Positive Real) condition whereas the new concept of passivity is associated with the so called WSPR condition and its advantage in multivariable systems is that it does not require a restrictive symmetry condition of SPR systems. As a result, it allows the design of multivariable adaptive control that, unlike some existing factorization approaches, does not imply in additional overparameterization of the adaptive controller. In this paper, we complete a previously established WSPR sufficient condition and prove that it is also necessary. We also propose some methods of passification by either premultiplying the system output tracking error vector or the system input vector by an adequate passifying matrix multiplier, so that the resulting input/output transfer function becomes WSPR. The efficiency of our proposals are illustrated by simulation utilizing a well known robotics adaptive visual servoing problem. © 2011 IFAC.

Assessment of physical activity by accelerometer and IPAQ-short version in patients with chronic kidney disease undergoing hemodialysis

To compare the short version of International Physical Activity Questionnaire (IPAQ) and the accelerometer measurement of physical activity (PA) in patients undergoing hemodialysis. Sample consisted of 40 patients (19 men) aged 45 ± 16 years. Patients reported their PA using the IPAQ during a face-to-face interview, and wore an Actigraph GT3-X accelerometer for 1 week to obtain minutes per day of light PA, moderate-to-vigorous PA (MVPA) and total PA as well as raw counts per day (vector magnitude). All PA-related variables were significantly correlated among instruments (r = 0.34-0.47) when analyzed as a group. However, when analyzed separately by gender, the relationships were present for women only (r = 0.46-0.62). IPAQ significantly underestimated light PA (IPAQ vs. accelerometer: 180.0 vs. 251.1 min/day, p = 0.019), but no differences were found between methods for MVPA and total PA. Modest correlations were found between self-reported PA time by IPAQ (short version) and accelerometer, but only in women. However, the IPAQ may underestimate light PA, which is the main form of PA in this population.

Development and validation of GT3X accelerometer cut-off points in 5- to 9-year-old children based on indirect calorimetry measurements

The ActiGraph accelerometer is commonly used to measure physical activity in children. Count cut-off points are needed when using accelerometer data to determine the time a person spent in moderate or vigorous physical activity. For the GT3X accelerometer no cut-off points for young children have been published yet. The aim of the current study was thus to develop and validate count cut-off points for young children. Thirty-two children aged 5 to 9 years performed four locomotor and four play activities. Activity classification into the light-, moderate- or vigorous-intensity category was based on energy expenditure measurements with indirect calorimetry. Vertical axis as well as vector magnitude cut-off points were determined through receiver operating characteristic curve analyses with the data of two thirds of the study group and validated with the data of the remaining third. The vertical axis cut-off points were 133 counts per 5 sec for moderate to vigorous physical activity (MVPA), 193 counts for vigorous activity (VPA) corresponding to a metabolic threshold of 5 MET and 233 for VPA corresponding to 6 MET. The vector magnitude cut-off points were 246 counts per 5 sec for MVPA, 316 counts for VPA - 5 MET and 381 counts for VPA - 6 MET. When validated, the current cut-off points generally showed high recognition rates for each category, high sensitivity and specificity values and moderate agreement in terms of the Kappa statistic. These results were similar for vertical axis and vector magnitude cut-off points. The current cut-off points adequately reflect MVPA and VPA in young children. Cut-off points based on vector magnitude counts did not appear to reflect the intensity categories better than cut-off points based on vertical axis counts alone.

Sedimentology of ODP Leg 126 deep-water volcaniclastics

Three sites were drilled in the Izu-Bonin forearc basin during Ocean Drilling Program (ODP) Leg 126. High-quality formation microscanner (FMS) data from two of the sites provide images of part of a thick, volcaniclastic, middle to upper Oligocene, basin-plain turbidite succession. The FMS images were used to construct bed-by-bed sedimentary sections for the depth intervals 2232-2441 m below rig floor (mbrf) in Hole 792E, and 4023-4330 mbrf in Hole 793B. Beds vary in thickness from those that are near or below the resolution of the FMS tool (2.5 cm) to those that are 10-15 m thick. The bed thicknesses are distributed according to a power law with an exponent of about 1.0. There are no obvious upward thickening or thinning sequences in the bed-by-bed sections. Spaced packets of thick and very thick beds may be a response to (1) low stands of global sea level, particularly at 30 Ma, (2) periods of increased tectonic uplift, or (3) periods of more intense volcanism. Graded sandstones, most pebbly sandstones, and graded to graded-stratified conglomerates were deposited by turbidity currents. The very thick, mainly structureless beds of sandstone, pebbly sandstone, and pebble conglomerate are interpreted as sandy debris-flow deposits. Many of the sediment gravity flows may have been triggered by earthquakes. Long recurrence intervals of 0.3-1 m.y. for the very thickest beds are consistent with triggering by large-magnitude earthquakes (M = 9) with epicenters approximately 10-50 km away from large, unstable accumulations of volcaniclastic sand and ash on the flanks of arc volcanoes. Paleocurrents were obtained from the grain fabric of six thicker sandstone beds, and ripple migration directions in about 40 thinner beds; orientations were constrained by the FMS images. The data from ripples are very scattered and cannot be used to specify source positions. They do, however, indicate that the paleoenvironment was a basin plain where weaker currents were free to follow a broad range of flow paths. The data from sandstone fabric are more reliable and indicate that turbidity currents flowed toward 150? during the time period from 28.9 to 27.3 Ma. This direction is essentially along the axis of the forearc basin, from north to south, with a small component of flow away from the western margin of the basin.

Ripple migration directions and grain fabric measurements on ODP Hole 210-1276A sediments

Albian turbidites and intercalated shales were cored from ~1145 to 1700 meters below seafloor at Site 1276 in the Newfoundland Basin. Strata at this level dip ~2.5° seaward (toward an azimuth of ~130°) based on seismic profiles. In contrast, beds dip an average of ~10° in the cores. This higher apparent dip is the sum of the ~2.5° seaward dip and a measured hole deviation of 7.43°, which must be essentially in the same seaward direction. Using the maximum dip direction in the cores as a reference direction, paleocurrents were measured from 11 current-ripple foresets and 11 vector means of grain fabric in planar-laminated sandstones. Five of the planar-laminated sandstone samples have a grain imbrication 8°, permitting specification of a unique flow direction rather than just the line-of-motion of the current. Both ripples and grain fabric point to unconfined flow toward the north-northeast. There is considerable spread in the data so that some paleoflow indicators point toward the northwest, whereas others point southeast. Nevertheless, the overall pattern of paleoflow suggests a source for the turbidity currents on the southeastern Grand Banks, likely from the long-emergent Avalon Uplift in that area. On average, turbidity currents apparently flowed axially in the young Albian rift, toward the north. This is opposite to what might be expected for a northward-propagating rift and a young ocean opening in a zipperlike fashion from south to north.

Microstructure-based inherent anisotropy of asphalt mixtures

Asphalt mixtures have been demonstrated to be anisotropic materials in both laboratory and field tests. The anisotropy of asphalt mixtures consists of inherent anisotropy and stress-induced anisotropy. In previous work, the inherent anisotropy of asphalt mixtures was quantified by using only the inclination angles of the coarse aggregate particles in the asphalt mixtures. However, the inclination of fine aggregates also has a contribution to the inherent anisotropy. Moreover, the contribution to the inherent anisotropy of each aggregate may not be the same as in the previous work but will depend on the size, orientation, and sphericity of the aggregate particle. This paper quantifies the internal microstructure of the aggregates in asphalt mixtures by using an aggregate-related geometric parameter, the vector magnitude. The original formulation of the vector magnitude, which addresses only the orientation of coarse aggregates, is modified to account for not only the coarse aggregate orientation, but also the size, orientation, and sphericity of coarse and fine aggregates. This formulation is applied to cylindrical lab-mixed lab-compacted asphalt mixture specimens varying in asphalt binder type, air void content, and aging period. The vertical modulus and the horizontal modulus are also measured by using nondestructive tests. A relationship between the modified vector magnitude and the modulus ratio of the vertical modulus to the horizontal modulus is developed to quantify the influence of the inherent microstructure of the aggregates on the anisotropy of the mixtures. The modulus ratio is found to depend solely on the aggregate characteristics including the inclination angle, size, and sphericity, and it is independent of the asphalt binder type, air void content, and aging period. The inclination angle, itself, proves to be insufficient to quantify the inherent anisotropy of the asphalt mixtures. © 2011 American Society of Civil Engineers.

GPU accelerated algorithms for computing matrix function vector products with applications to exponential integrators and fractional diffusion

The efficient computation of matrix function vector products has become an important area of research in recent times, driven in particular by two important applications: the numerical solution of fractional partial differential equations and the integration of large systems of ordinary differential equations. In this work we consider a problem that combines these two applications, in the form of a numerical solution algorithm for fractional reaction diffusion equations that after spatial discretisation, is advanced in time using the exponential Euler method. We focus on the efficient implementation of the algorithm on Graphics Processing Units (GPU), as we wish to make use of the increased computational power available with this hardware. We compute the matrix function vector products using the contour integration method in [N. Hale, N. Higham, and L. Trefethen. Computing Aα, log(A), and related matrix functions by contour integrals. SIAM J. Numer. Anal., 46(5):2505–2523, 2008]. Multiple levels of preconditioning are applied to reduce the GPU memory footprint and to further accelerate convergence. We also derive an error bound for the convergence of the contour integral method that allows us to pre-determine the appropriate number of quadrature points. Results are presented that demonstrate the effectiveness of the method for large two-dimensional problems, showing a speedup of more than an order of magnitude compared to a CPU-only implementation.