The force, power, and energy of the 100 meter sprint

At the 2008 Summer Olympics in Beijing, Usain Bolt broke the world record for the 100 m sprint. Just one year later, at the 2009 World Championships in Athletics in Berlin he broke it again. A few months after Beijing, Eriksen [Am. J. Phys. 77, 224-228 (2009)] studied Bolt's performance and predicted that Bolt could have run about one-tenth of a second faster, which was confirmed in Berlin. In this paper we extend the analysis of Eriksen to model Bolt's velocity time dependence for the Beijing 2008 and Berlin 2009 records. We deduce the maximum force, the maximum power, and the total mechanical energy produced by Bolt in both races. Surprisingly, we conclude that all of these values were smaller in 2009 than in 2008.

Power-law creep behavior of a semiflexible chain

Rheological properties of adherent cells are essential for their physiological functions, and microrheological measurements on living cells have shown that their viscoelastic responses follow a weak power law over a wide range of time scales. This power law is also influenced by mechanical prestress borne by the cytoskeleton, suggesting that cytoskeletal prestress determines the cell's viscoelasticity, but the biophysical origins of this behavior are largely unknown. We have recently developed a stochastic two-dimensional model of an elastically joined chain that links the power-law rheology to the prestress. Here we use a similar approach to study the creep response of a prestressed three-dimensional elastically jointed chain as a viscoelastic model of semiflexible polymers that comprise the prestressed cytoskeletal lattice. Using a Monte Carlo based algorithm, we show that numerical simulations of the chain's creep behavior closely correspond to the behavior observed experimentally in living cells. The power-law creep behavior results from a finite-speed propagation of free energy from the chain's end points toward the center of the chain in response to an externally applied stretching force. The property that links the power law to the prestress is the chain's stiffening with increasing prestress, which originates from entropic and enthalpic contributions. These results indicate that the essential features of cellular rheology can be explained by the viscoelastic behaviors of individual semiflexible polymers of the cytoskeleton.

Angular-planar CMB power spectrum

Gaussianity and statistical isotropy of the Universe are modern cosmology's minimal set of hypotheses. In this work we introduce a new statistical test to detect observational deviations from this minimal set. By defining the temperature correlation function over the whole celestial sphere, we are able to independently quantify both angular and planar dependence (modulations) of the CMB temperature power spectrum over different slices of this sphere. Given that planar dependence leads to further modulations of the usual angular power spectrum C(l), this test can potentially reveal richer structures in the morphology of the primordial temperature field. We have also constructed an unbiased estimator for this angular-planar power spectrum which naturally generalizes the estimator for the usual C(l)'s. With the help of a chi-square analysis, we have used this estimator to search for observational deviations of statistical isotropy in WMAP's 5 year release data set (ILC5), where we found only slight anomalies on the angular scales l = 7 and l = 8. Since this angular-planar statistic is model-independent, it is ideal to employ in searches of statistical anisotropy (e.g., contaminations from the galactic plane) and to characterize non-Gaussianities.

Finding Quasi-Optimal Network Topologies for Information Transmission in Active Networks

This work clarifies the relation between network circuit (topology) and behaviour (information transmission and synchronization) in active networks, e.g. neural networks. As an application, we show how one can find network topologies that are able to transmit a large amount of information, possess a large number of communication channels, and are robust under large variations of the network coupling configuration. This theoretical approach is general and does not depend on the particular dynamic of the elements forming the network, since the network topology can be determined by finding a Laplacian matrix (the matrix that describes the connections and the coupling strengths among the elements) whose eigenvalues satisfy some special conditions. To illustrate our ideas and theoretical approaches, we use neural networks of electrically connected chaotic Hindmarsh-Rose neurons.

The electromagnetics of light transmission through subwavelength slits in metallic films

By numerically calculating the relevant electromagnetic fields and charge current densities, we show how local charges and currents near subwavelength structures govern light transmission through subwavelength apertures in a real metal film. The illumination of a single aperture generates surface waves; and in the case of slits, generates them with high efficiency and with a phase close to - pi with respect to a reference standing wave established at the metal film front facet. This phase shift is due to the direction of induced charge currents running within the slit walls. The surface waves on the entrance facet interfere with the standing wave. This interference controls the profile of the transmission through slit pairs as a function of their separation. We compare the calculated transmission profile for a two-slit array to simple interference models and measurements [Phys. Rev. B 77(11), 115411 (2008)]. (C) 2011 Optical Society of America

Quantitative determination of optical transmission through subwavelength slit arrays in Ag films: Role of surface wave interference and local coupling between adjacent slits

Measurement of the transmitted intensity from a coherent monomode light source through a series of subwavelength slit arrays in Ag films, with varying array pitch and number of slits, demonstrates enhancement (suppression) by factors of as much as 6 (9) when normalized to the transmission efficiency of an isolated slit. Pronounced minima in the transmitted intensity are observed at array pitches corresponding to lambda(SPP), 2 lambda(SPP), and 3 lambda(SPP), where lambda(SPP) is the wavelength of the surface plasmon polariton (SPP). The position of these minima arises from destructive interference between incident propagating waves and pi-phase-shifted SPP waves. Increasing the number of slits to four or more does not increase appreciably the per-slit transmission intensity. A simple interference model fits well the measured transmitted intensity profile.

Expression of genes related to muscle plasticity after strength and power training regimens

The purpose of our study was to compare the effects of 8-week progressive strength and power training regimens on strength gains and muscle plasticity [muscle fiber hypertrophy and phenotype shift, mammalian target of rapamycin (mTOR), regulatory-associated protein of mTOR (RAPTOR), rapamycin-insensitive companion of m-TOR (RICTOR), calcineurin and calcipressin gene expression]. Twenty-nine physically active subjects were divided into three groups: strength training (ST), power training (PT) and control (C). Squat 1 RM and muscle biopsies were obtained before and after the training period. Strength increased similarly for both ST and PT groups (P < 0.001). Fiber types I, IIa and IIb presented hypertrophy main time effect (P < 0.05). Only type IIb percentage decreased from pre- to post-test (main time effect, P < 0.05). mTOR and RICTOR mRNA expression increased similarly from pre- to post-test (P < 0.01). RAPTOR increased after training for both groups (P < 0.0001), but to a greater extent in the ST (P < 0.001) than in the PT group. 4EBP-1 decreased after training when the ST and PT groups were pooled (P < 0.05). Calcineurin levels did not change after training, while calcipressin increased similarly from pre- to post-test (P < 0.01). In conclusion, our data indicate that these training regimens produce similar performance improvements; however, there was a trend toward greater hypertrophy-related gene expression and muscle fiber hypertrophy in the ST group.

Is acute static stretching able to reduce the time to exhaustion at power output corresponding to maximal oxygen uptake?

Samogin Lopes, FA, Menegon, EM, Franchini, E, Tricoli, V, and de M. Bertuzzi, RC. Is acute static stretching able to reduce the time to exhaustion at power output corresponding to maximal oxygen uptake? J Strength Cond Res 24(6): 1650-1656, 2010-This study analyzed the effect of an acute static stretching bout on the time to exhaustion (T(lim)) at power output corresponding to (V) over dotO(2)max. Eleven physically active male subjects (age 22.3 +/- 2.8 years, (V) over dotO(2)max 2.7 +/- 0.5 L . min(-1)) completed an incremental cycle ergometer test, 2 muscle strength tests, and 2 maximal tests to exhaustion at power output corresponding to (V) over dotO(2)max with and without a previous static stretching bout. The T(lim) was not significantly affected by the static stretching (164 +/- 28 vs. 150 +/- 26 seconds with and without stretching, respectively, p = 0.09), but the time to reach (V) over dotO(2)max (118 +/- 22 vs. 102 +/- 25 seconds), blood-lactate accumulation immediately after exercise (10.7 +/- 2.9 vs. 8.0 +/- 1.7 mmol . L(-1)), and oxygen deficit (2.4 +/- 0.9 vs. 2.1 +/- 0.7 L) were significantly reduced (p <= 0.02). Thus, an acute static stretching bout did not reduce T(lim) at power output corresponding to (V) over dotO(2)max possibly by accelerating aerobic metabolism activation at the beginning of exercise. These results suggest that coaches and practitioners involved with aerobic dependent activities may use static stretching as part of their warm-up routines without fear of diminishing high-intensity aerobic exercise performance.

Evaluation of an innovative critical power model in intermittent vertical jump

The aim of this study was to test if the critical power model can be used to determine the critical rest interval (CRI) between vertical jumps. Ten males performed intermittent countermovement jumps on a force platform with different resting periods (4.1 +/- 0.3 s, 5.0 +/- 0.4 s, 5.9 +/- 0.6 s). Jump trials were interrupted when participants could no longer maintain 95% of their maximal jump height. After interruption, number of jumps, total exercise duration and total external work were computed. Time to exhaustion (s) and total external work (J) were used to solve the equation Work = a + b . time. The CRI (corresponding to the shortest resting interval that allowed jump height to be maintained for a long time without fatigue) was determined dividing the average external work needed to jump at a fixed height (J) by b parameter (J/s). in the final session, participants jumped at their calculated CRI. A high coefficient of determination (0.995 +/- 0.007) and the CRI (7.5 +/- 1.6 s) were obtained. In addition, the longer the resting period, the greater the number of jumps (44 13, 71 28, 105 30, 169 53 jumps; p<0.0001), time to exhaustion (179 +/- 50, 351 +/- 120, 610 +/- 141, 1,282 +/- 417 s; p<0.0001) and total external work (28.0 +/- 8.3, 45.0 +/- 16.6, 67.6 +/- 17.8, 111.9 +/- 34.6 kJ; p<0.0001). Therefore, the critical power model may be an alternative approach to determine the CRI during intermittent vertical jumps.

Time course of strength and power recovery after resistance training with different movement velocities

Ide, BN, Leme, TCF, Lopes, CR, Moreira, A, Dechechi, CJ, Sarraipa, MF, da Mota, GR, Brenzikofer, R, and Macedo, DV. Time course of strength and power recovery after resistance training with different movement velocities. J Strength Cond Res 25(7): 2025-2033, 2011-The purpose of this study was to evaluate the time course of strength and power recovery after a single bout of strength training designed with fast and slow contraction velocities. Nineteen male subjects were randomly divided into 2 groups: the slow-velocity contraction (SV) group and the fast velocity contraction (FV) group. Resistance training protocols consisted of 5 sets of 12 repetition maximum (5 x 12RM) with 50 seconds of rest between sets and 2 minutes between exercises. Contraction velocity was controlled by the execution time for each repetition (SV-6 seconds to complete concentric and eccentric phases and for FV-1.5 seconds). Leg Press 45 degrees 1RM (LP 1RM), horizontal countermovement jump (HCMJ), and right thigh circumference (TC) were accessed in 6 distinct moments: base (1 week before exercise), 0 (immediately after exercises), 24, 48, 72, and 96 hours after exercise protocol. The SV and FV presented significant LP 1RM decrements at 0, and these were still evident 24-48 hours postexercise. The magnitude of decline was significantly (p<0.05) higher for FV. The SV and FV presented significant HCMJ decrements at 0, but only for FV were these still evident 24-72 hours postexercise. The SV and FV presented significant TC increments at 0, and these were still evident 24-48 hours postexercise for SV but for FV it continued up to 96 hours. The magnitude of increase was significantly (p<0.05) higher for FV. In conclusion, the fast contraction velocity protocol resulted in greater decreases in LP 1RM and HCMJ performance, when compared with slow velocity. The results lead us to interpret that this variable may exert direct influence on acute muscle strength and power generation capacity.

Non-exhaustive tests for critical power estimation

Objective. - The aim of this study was to propose a new method that allows for the estimation of critical power (CP) from non-exhaustive tests using ratings of perceived exertion (RPE). Methods. - Twenty-two subjects underwent two practice trials for ergometer and Borg 15-point scale familiarization, and adaptation to severe exhaustive exercise. After then, four exercise bouts were performed on different days for the estimation of CP and anaerobic work capacity (AWC) by linear work-time equation, and CP(15), CP(17), AWC(15) and AWC(17) were estimated using the work and time to attainment of RPE15 and RPE17 based on the Borg 15-point scale. Results. - The CP, CP(15) and CP(17) (170-177W) were not significantly different (P>0.05). However, AWC, AWC(15) and AWC(17) were all different from each other. The correlations between CP(15) and CP(17), with CP were strong (R=0.871 and 0.911, respectively), but the AWC(15) and AWC(17) were not significantly correlated with AWC. Conclusion. - Sub-maximal. RPE responses can be used for the estimation of CP from non-exhaustive exercise protocols. (C) 2009 Elsevier Masson SAS. All rights reserved.

Physiological and perceived exertion responses at intermittent critical power and intermittent maximal lactate steady state

Okuno, NM, Perandini, LAB, Bishop, D, Simoes, HG, Pereira, G, Berthoin, S, Kokubun, E, and Nakamura, FY. Physiological and perceived exertion responses at intermittent critical power and intermittent maximal lactate steady state. J Strength Cond Res 25(7): 2053-2058, 2011-The aim of this study was to compare the power outputs of the intermittent critical power (CPi) with the intermittent maximal lactate steady state (MLSSi) and to compare the physiological and perceptual responses exercising at CPi and MLSSi. Ten subjects performed intermittent trials on a cycle ergometer to determine CPi and MLSSi using 30: 30 seconds of effort and pause. The oxygen uptake ((V) over dotO(2)), heart rate (HR), blood lactate concentration ([Lac]), and rating of perceived exertion (RPE) responses were compared during 30-minute cycling at CPi and MLSSi. The CPi (267 6 45 W) was similar to MLSSi (254 6 39 W), and they were correlated (r = 0.88; p<0.05). The (V) over dotO(2) and HR responses stabilized throughout exercising at CPi (2.52 +/- 0.52 L.min(-1); 156 +/- 8 b.min(-1)) and MLSSi (2.41 +/- 0.32 L.min(-1); 152 +/- 10 b.min(-1)). These physiological variables were similar between conditions. However, the [Lac] and RPE were higher from the middle to the end of exercise duration at CPi ([Lac] = 6.9 +/- 2.6 mM; RPE = 17.1 +/- 2.1 a.u.) compared to MLSSi ([Lac] = 5.1 +/- 0.9 mM; RPE = 15.7 +/- 1.8 a.u.). Therefore, CPi intensity determined from 30: 30 seconds of effort and rest periods on a cycle ergometer is equivalent to the MLSSi, and there is a physiological steady state throughout both exercise intensities, although the [Lac] and RPE responses at CPi are higher than at MLSSi. Thus, the CPi and MLSSi may be used as tools for intermittent training evaluation and prescription.

A Semi-Tethered Test for Power Assessment in Running

We analyzed the usefulness of a semi-tethered field running test (STR) and the relationships between indices of anaerobic power, anaerobic capacity and running performance in 9 trained male sprinters (22.2 +/- 2.9 yrs, 176 +/- 1 cm, 68.0 +/- 9.4 kg). STR involved an all out 120 m run attached to an apparatus that enabled power calculation from force and velocity measures. Subjects also carried out a cycloergometer Win-gate Anaerobic Test (WT), an all out 300 m run and had accessed their maximal accumulated oxygen deficit (MAOD) on a treadmill. Peak and mean powers attained in STR (1 720 +/- 221 and 1 391 +/- 201 W) were greater but significantly related (r=0.82; P<0.01) to those in the WT (808 +/- 130 and 603 +/- 87 W). In addition, power measures derived from the STR were stronger related to running performance compared to those from the WT (r=0.81-0.94 vs. 0.68-0.84; P<0.05). Relationships between MAOD and most power indices were only weak to moderate. These results support the usefulness of STR for specific power assessment in field running and suggest that anaerobic power and capacity are not related entities, irrespective of having been evaluated using similar or dissimilar exercise modes.

Offline Detection, Identification, and Correction of Branch Parameter Errors Based on Several Measurement Snapshots

This paper proposes a three-stage offline approach to detect, identify, and correct series and shunt branch parameter errors. In Stage 1 the branches suspected of having parameter errors are identified through an Identification Index (II). The II of a branch is the ratio between the number of measurements adjacent to that branch, whose normalized residuals are higher than a specified threshold value, and the total number of measurements adjacent to that branch. Using several measurement snapshots, in Stage 2 the suspicious parameters are estimated, in a simultaneous multiple-state-and-parameter estimation, via an augmented state and parameter estimator which increases the V - theta state vector for the inclusion of suspicious parameters. Stage 3 enables the validation of the estimation obtained in Stage 2, and is performed via a conventional weighted least squares estimator. Several simulation results (with IEEE bus systems) have demonstrated the reliability of the proposed approach to deal with single and multiple parameter errors in adjacent and non-adjacent branches, as well as in parallel transmission lines with series compensation. Finally the proposed approach is confirmed on tests performed on the Hydro-Quebec TransEnergie network.

Power Transformer Differential Protection Based on Clarke`s Transform and Fuzzy Systems

The power transformer is a piece of electrical equipment that needs continuous monitoring and fast protection since it is very expensive and an essential element for a power system to perform effectively. The most common protection technique used is the percentage differential logic, which provides discrimination between an internal fault and different operating conditions. Unfortunately, there are some operating conditions of power transformers that can affect the protection behavior and the power system stability. This paper proposes the development of a new algorithm to improve the differential protection performance by using fuzzy logic and Clarke`s transform. An electrical power system was modeled using Alternative Transients Program (ATP) software to obtain the operational conditions and fault situations needed to test the algorithm developed. The results were compared to a commercial relay for validation, showing the advantages of the new method.