Calculating the bound spectrum by path summation in action-angle variables

The density of states n(E) is calculated for a bound system whose classical motion is integrable, starting from an expression in terms of the trace of the time-dependent Green function. The novel feature is the use of action-angle variables. This has the advantages that the trace operation reduces to a trivial multiplication and the dependence of n(E) on all classical closed orbits with different topologies appears naturally. The method is contrasted with another, not applicable to integrable systems except in special cases, in which quantization arises from a single closed orbit which is assumed isolated and the trace taken by the method of stationary phase.

Homoclinic Splitting without Trees

We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, giving a simple construction of unstable KAM tori and their stable and unstable manifolds for analytic perturbations. When the coupling takes place through an even trigonometric polynomial in the angle variables, we extend analytically the solutions of the equations of motion, order by order in the perturbation parameter, to a large neighbourhood of the real line representing time. Subsequently, we devise an asymptotic expansion for the splitting (matrix) associated with a homoclinic point. This expansion consists of contributions that are manifestly exponentially small in the limit of vanishing gravity, by a shift-of-countour argument. Hence, we infer a similar upper bound for the splitting itself. In particular, the derivation of the result does not call for a tree expansion with explicit cancellation mechanisms.

Integrable approximation to the overlap of resonances

We study the interaction of resonances with the same order in families of integrable Hamiltonian systems. This can occur when the unperturbed Hamiltonian is at least cubic in the actions. An integrable perturbation coupling the action-angle variables leads to the disappearance of an island through the coalescence of stable and unstable periodic orbits and originates a complex orbit plus an isolated cubic resonance. The chaotic layer that appears when a general term is added to the Hamiltonian survives even after the disappearance of the unstable periodic orbit. © 1992.

Role of the range of the dipole function in the classical dynamics of molecular dissociation

The dissociation dynamics of heteronuclear diatomic molecules induced by infrared laser pulses is investigated within the framework of the classical driven Morse oscillator. The interaction between the molecule and the laser field described in the dipole formulation is given by the product of a time-dependent external field with a position-dependent permanent dipole function. The effects of changing the spatial range of the dipole function in the classical dissociation dynamics of large ensembles of trajectories are studied. Numerical calculations have been performed for distinct amplitudes and carrier frequencies of the external pulses and also for ensembles with different initial energies. It is found that there exist a set of values of the dipole range for which the dissociation probability can be completely suppressed. The dependence of the dissociation on the dipole range is explained through the examination of the Fourier series coefficients of the dipole function in the angle variable of the free system. In particular, the suppression of dissociation corresponds to dipole ranges for which the Fourier coefficients associated with nonlinear resonances are null and the chaotic region in the phase space is reduced to thin layers. In this context, it is shown that the suppression of dissociation of heteronuclear molecules for certain frequencies of the external field is a consequence of the finite range of the corresponding permanent dipole. © 2013 American Physical Society.

Sobre a dinâmica de rotação de um planeta através de um sistema médio

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Propriedades estatísticas de bilhares abertos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Effects of roller massager on muscle performance, morphology, and oxygenation after exercise-induced muscle damage

This study determined roller massager (RM) effectiveness on ankle plantar flexors’ recovery after exercise-induced muscle damage (EIMD) stimulus. Two experiments were conducted. The first experiment (n=10) examined functional [i.e., ankle plantar flexion maximal voluntary isometric contraction (MVIC) and submaximal (30% of MVIC) sustained force; ankle dorsiflexion maximal range of motion and resistance to stretch; and pain pressure threshold] and morphological [medial gastrocnemius (MG) cross sectional area, thickness, fascicle length, and fascicle angle] variables, before and immediately, 1h, 24h, 48h, and 72 after EIMD. In the second experiment (n=10), changes in MG deoxyhemoglobin concentration kinetics (velocity and amplitude) during a submaximal sustained force test were observed before and 48h after EIMD. Participants performed both experiments twice, with and without (NRM) the application of a RM (6 × 45 seconds with 20 seconds rest between sets). RM intervention did not alter plantar flexors’ strength and flexibility impairment after EIMD, as well the MG morphology and oxygenation kinetics (p>0.05). On the other hand, a strong tendency for an acute (within 1 hour) change of ipsilateral (post-effects: RM=+19%, NRM=-5%, p=0.032) and contralateral (p=0.095) MG pain pressure threshold was observed. In conclusion, the present results suggest that a roller massager has no effect on muscular performance, morphology, and oxygenation recovery after EIMD, except for muscle pain pressure threshold (i.e., a soreness). Thus, RM may have potential application in recovery for people with increased muscle soreness, if performed immediately before a physical task.

Right-angle crash vulnerability of motorcycles at signalized intersections : mixed logit analysis

Motorcycles are particularly vulnerable in right-angle crashes at signalized intersections. The objective of this study is to explore how variations in roadway characteristics, environmental factors, traffic factors, maneuver types, human factors as well as driver demographics influence the right-angle crash vulnerability of motorcycles at intersections. The problem is modeled using a mixed logit model with a binary choice category formulation to differentiate how an at-fault vehicle collides with a not-at-fault motorcycle in comparison to other collision types. The mixed logit formulation allows randomness in the parameters and hence takes into account the underlying heterogeneities potentially inherent in driver behavior, and other unobserved variables. A likelihood ratio test reveals that the mixed logit model is indeed better than the standard logit model. Night time riding shows a positive association with the vulnerability of motorcyclists. Moreover, motorcyclists are particularly vulnerable on single lane roads, on the curb and median lanes of multi-lane roads, and on one-way and two-way road type relative to divided-highway. Drivers who deliberately run red light as well as those who are careless towards motorcyclists especially when making turns at intersections increase the vulnerability of motorcyclists. Drivers appear more restrained when there is a passenger onboard and this has decreased the crash potential with motorcyclists. The presence of red light cameras also significantly decreases right-angle crash vulnerabilities of motorcyclists. The findings of this study would be helpful in developing more targeted countermeasures for traffic enforcement, driver/rider training and/or education, safety awareness programs to reduce the vulnerability of motorcyclists.

Relationship of moderate and low isometric lumbar extension through architectural and muscular activity variables: a cross sectional study

Background No study relating the changes obtained in the architecture of erector spinae (ES) muscle were registered with ultrasound and different intensities of muscle contraction recorded by surface EMG (electromyography) on the ES muscle was found. The aim of this study was analyse the relationship in the response of the ES muscle during isometric moderate and light lumbar isometric extension considering architecture and functional muscle variables. Methods Cross-sectional study. 46 subjects (52% men) with a group mean age of 30.4 (±7.78). The participants developed isometric lumbar extension while performing moderate and low isometric trunk and hip extension in a sitting position with hips flexed 90 degrees and the lumbar spine in neutral position. During these measurements, electromyography recordings and ultrasound images were taken bilaterally. Bilaterally pennation angle, muscle thickness, torque and muscle activation were measured. This study was developed at the human movement analysis laboratory of the Health Science Faculty of the University of Malaga (Spain). Results Strong and moderate correlations were found at moderate and low intensities contraction between the variable of the same intensity, with correlation values ranging from 0.726 (Torque Moderate – EMG Left Moderate) to 0.923 (Angle Left Light – Angle Right Light) (p < 0.001). This correlation is observed between the variables that describe the same intensity of contraction, showing a poor correlation between variables of different intensities. Conclusion There is a strong relationship between architecture and function variables of ES muscle when describe an isometric lumbar extension at light or moderate intensity. Keywords: Ultrasonography; Surface electromyography; Thickness; Pennation angle; Erector spinae

Supine to standing Cobb angle change in idiopathic scoliosis : the effect of endplate pre-selection

Background Supine imaging modalities provide valuable 3D information on scoliotic anatomy, but the altered spine geometry between the supine and standing positions affects the Cobb angle measurement. Previous studies report a mean 7°-10° Cobb angle increase from supine to standing, but none have reported the effect of endplate pre-selection or whether other parameters affect this Cobb angle difference. Methods Cobb angles from existing coronal radiographs were compared to those on existing low-dose CT scans taken within three months of the reference radiograph for a group of females with adolescent idiopathic scoliosis. Reformatted coronal CT images were used to measure supine Cobb angles with and without endplate pre-selection (end-plates selected from the radiographs) by two observers on three separate occasions. Inter and intra-observer measurement variability were assessed. Multi-linear regression was used to investigate whether there was a relationship between supine to standing Cobb angle change and eight variables: patient age, mass, standing Cobb angle, Risser sign, ligament laxity, Lenke type, fulcrum flexibility and time delay between radiograph and CT scan. Results Fifty-two patients with right thoracic Lenke Type 1 curves and mean age 14.6 years (SD 1.8) were included. The mean Cobb angle on standing radiographs was 51.9° (SD 6.7). The mean Cobb angle on supine CT images without pre-selection of endplates was 41.1° (SD 6.4). The mean Cobb angle on supine CT images with endplate pre-selection was 40.5° (SD 6.6). Pre-selecting vertebral endplates increased the mean Cobb change by 0.6° (SD 2.3, range −9° to 6°). When free to do so, observers chose different levels for the end vertebrae in 39% of cases. Multi-linear regression revealed a statistically significant relationship between supine to standing Cobb change and fulcrum flexibility (p = 0.001), age (p = 0.027) and standing Cobb angle (p < 0.001). The 95% confidence intervals for intra-observer and inter-observer measurement variability were 3.1° and 3.6°, respectively. Conclusions Pre-selecting vertebral endplates causes minor changes to the mean supine to standing Cobb change. There is a statistically significant relationship between supine to standing Cobb change and fulcrum flexibility such that this difference can be considered a potential alternative measure of spinal flexibility.

Correlation between architectural variables and torque in the erector spinae muscle during maximal isometric contraction

This study analysed whether a significant relationship exists between the torque and muscle thickness and pennation angle of the erector spinae muscle during a maximal isometric lumbar extension with the lumbar spine in neutral position. This was a cross-sectional study in which 46 healthy adults performed three repetitions for 5 s of maximal isometric lumbar extension with rests of 90 s. During the lumbar extensions, bilateral ultrasound images of the erector spinae muscle (to measure pennation angle and muscle thickness) and torque were acquired. Reliability test analysis calculating the internal consistency (Cronbach's alpha) of the measure, correlation between pennation angle, muscle thickness and torque extensions were examined. Through a linear regression the contribution of each independent variable (muscle thickness and pennation angle) to the variation of the dependent variable (torque) was calculated. The results of the reliability test were: 0.976–0.979 (pennation angle), 0.980–0.980 (muscle thickness) and 0.994 (torque). The results show that pennation angle and muscle thickness were significantly related to each other with a range between 0.295 and 0.762. In addition, multiple regression analysis showed that the two variables considered in this study explained 68% of the variance in the torque. Pennation angle and muscle thickness have a moderate impact on the variance exerted on the torque during a maximal isometric lumbar extension with the lumbar spine in neutral position.

Wigner distribution for angle coordinates in quantum mechanics

The method of Wigner distribution functions, and the Weyl correspondence between quantum and classical variables, are extended from the usual kind of canonically conjugate position and momentum operators to the case of an angle and angular momentum operator pair. The sense in which one has a description of quantum mechanics using classical phase‐space language is much clarified by this extension.

Roche tomography of cataclysmic variables - V. A high-latitude star-spot on RU Pegasi

We present Roche tomograms of the secondary star in the dwarf nova system RU Pegasi derived from blue and red arm ISIS data taken on the 4.2-m William Herschel Telescope. We have applied the entropy landscape technique to determine the system parameters and obtained component masses of M1 = 1.06 Msun, M2 = 0.96 Msun, an orbital inclination angle of i = 43 degrees, and an optimal systemic velocity of gamma = 7 km/s. These are in good agreement with previously published values. Our Roche tomograms of the secondary star show prominent irradiation of the inner Lagrangian point due to illumination by the disc and/or bright spot, which may have been enhanced as RU Peg was in outburst at the time of our observations.We find that this irradiation pattern is axi-symmetric and confined to regions of the star which have a direct view of the accretion regions. This is in contrast to previous attempts to map RU Peg which suggested that the irradiation pattern was non-symmetric and extended beyond the terminator. We also detect additional inhomogeneities in the surface distribution of stellar atomic absorption that we ascribe to the presence of a large star-spot. This spot is centred at a latitude of about 82 degrees and covers approximately 4 per cent of the total surface area of the secondary. In keeping with the high latitude spots mapped on the cataclysmic variables AE Aqr and BV Cen, the spot on RU Peg also appears slightly shifted towards the trailing hemisphere of the star. Finally, we speculate that early mapping attempts which indicated non-symmetric irradiation patterns which extended beyond the terminator of CV donors could possibly be explained by a superposition of symmetric heating and a large spot.

Primary angle closure glaucoma:A descriptive study in Scottish Caucasians

Purpose: The aim of this study is to describe the ocular and demographic features of Caucasian patients newly presenting with primary angle closure glaucoma and the proportion of workload it represents at a tertiary university hospital glaucoma service. Methods: A retrospective case notes review was conducted for all Caucasian patients newly diagnosed with narrow angles, primary angle closure, acute primary angle closure and primary angle closure glaucoma that were seen over a period of 2 years. Demographic and ocular variables were compared and statistical analysis was carried out with the paired t -test and chi-squared test. Number of primary open angle closure glaucoma and acute angle closure cases were compared with total number of new referrals to the department, new patients diagnosed with glaucoma and population numbers for the North East of Scotland. Results: One hundred and four patients were analysed. Twenty-four (23.1%) had narrow angles, 30 (28.8%) had primary angle closure and 50 (48.1%) had primary angle closure glaucoma. Twelve (11.5%) presented with acute primary angle closure. There was no significant difference for gender, age, hypermetropia or visual acuity between groups. Primary angle closure glaucoma constituted 22.9% (50/128) of newly diagnosed glaucoma cases. Based on the 2001 Scotland census, the crude annual incidence of newly diagnosed primary angle closure glaucoma was estimated at 14.8 per 100000 and 3.6 per 100000 for acute primary angle closure in the over-45-year-old population. Conclusion: Our study confirms that primary angle closure glaucoma is uncommon in Caucasians, but not as rare as originally perceived as it makes up a fair proportion (22.9%) of glaucoma workload. © 2009 The Authors Journal Compilation © 2009 Royal Australian and New Zealand College of Ophthalmologists.

Determinants and two-year change in anterior chamber angle width in a Chinese population

Objective: To study the population distribution and longitudinal changes in anterior chamber angle width and its determinants among Chinese adults. Design: Prospective cohort, population-based study. Participants: Persons aged 35 years or more residing in Guangzhou, China, who had not previously undergone incisional or laser eye surgery. Methods: In December 2008 and December 2010, all subjects underwent automated keratometry, and a random 50% sample had anterior segment optical coherence tomography with measurement of angle-opening distance at 500 μm (AOD500), angle recess area (ARA), iris thickness at 750 μm (IT750), iris curvature, pupil diameter, corneal thickness, anterior chamber width (ACW), lens vault (LV), and lens thickness (LT) and measurement of axial length (AL) and anterior chamber depth (ACD) by partial coherence laser interferometry. Main Outcome Measures: Baseline and 2-year change in AOD500 and ARA in the right eye. Results: A total of 745 subjects were present for full biometric testing in both 2008 and 2010 (mean age at baseline, 52.2 years; standard deviation [SD], 11.5 years; 53.7% were female). Test completion rates in 2010 varied from 77.3% (AOD500: 576/745) to 100% (AL). Mean AOD500 decreased from 0.25 mm (SD, 0.13 mm) in 2008 to 0.21 mm (SD, 13 mm) in 2010 (difference, -0.04; 95% confidence interval [CI], -0.05 to -0.03). The ARA decreased from 21.5±3.73 10^-2 mm² to 21.0±3.64 10 ^-2 mm² (difference, -0.46; 95% CI, -0.52 to -0.41). The decrease in both was most pronounced among younger subjects and those with baseline AOD500 in the widest quartile at baseline. The following baseline variables were significantly associated with a greater 2-year decrease in both AOD500 and ARA: deeper ACD, steeper iris curvature, smaller LV, greater ARA, and greater AOD500. By using simple regression models, we could explain 52% to 58% and 93% of variation in baseline AOD500 and ARA, respectively, but only 27% and 16% of variation in 2-year change in AOD500 and ARA, respectively. Conclusions: Younger persons and those with the least crowded anterior chambers at baseline have the largest 2-year decreases in AOD500 and ARA. The ability to predict change in angle width based on demographic and biometric factors is relatively poor, which may have implications for screening. Financial Disclosure(s): The author(s) have no proprietary or commercial interest in any materials discussed in this article. © 2012 American Academy of Ophthalmology.