Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

Signal amplification of active rotators with phase-shifted coupling

In this paper, we study the signal amplification of coupled active rotators with phase-shifted coupling. We find that the system's response to the external subthreshold signal can be significantly affected by each of the two types of phase-shifted couplings: identical and non-identical phase-shifted couplings. Moreover, through both theoretical analysis and numerical simulations, we have figured out the optimal phase shift, at which the largest signal amplification is generated. These results show that the phase-shifted coupling plays an important role in regulating the system's response to the subthreshold signal.

Effects of pediatric obesity on joint kinematics and kinetics during 2 walking cadences

Objective: To determine whether differences existed in lower-extremity joint biomechanics during self-selected walking cadence (SW) and fast walking cadence (FW) in overweight- and normal-weight children.---------- Design: Survey.---------- Setting: Institutional gait study center.---------- Participants: Participants (N=20; mean age ± SD, 10.4±1.6y) from referred and volunteer samples were classified based on body mass index percentiles and stratified by age and sex. Exclusion criteria were a history of diabetes, neuromuscular disorder, or recent lower-extremity injury.---------- Main Outcome Measures: Sagittal, frontal, and transverse plane angular displacements (degrees) and peak moments (newton meters) at the hip, knee, and ankle joints.---------- Results: The level of significance was set at P less than .008. Compared with normal-weight children, overweight children had greater absolute peak joint moments at the hip (flexor, extensor, abductor, external rotator), the knee (flexor, extensor, abductor, adductor, internal rotator), and the ankle (plantarflexor, inverter, external/internal rotators). After including body weight as a covariate, overweight children had greater peak ankle dorsiflexor moments than normal-weight children. No kinematic differences existed between groups. Greater peak hip extensor moments and less peak ankle inverter moments occurred during FW than SW. There was greater angular displacement during hip flexion as well as less angular displacement at the hip (extension, abduction), knee (flexion, extension), and ankle (plantarflexion, inversion) during FW than SW.---------- Conclusions: Overweight children experienced increased joint moments, which can have long-term orthopedic implications and suggest a need for more nonweight-bearing activities within exercise prescription. The percent of increase in joint moments from SW to FW was not different for overweight and normal-weight children. These findings can be used in developing an exercise prescription that must involve weight-bearing activity.

Lightcurve inversion for asteroid spins and shapes

Knowledge of the physical properties of asteroids is crucial in many branches of solar-system research. Knowledge of the spin states and shapes is needed, e.g., for accurate orbit determination and to study the history and evolution of the asteroids. In my thesis, I present new methods for using photometric lightcurves of asteroids in the determination of their spin states and shapes. The convex inversion method makes use of a general polyhedron shape model and provides us at best with an unambiguous spin solution and a convex shape solution that reproduces the main features of the original shape. Deriving information about the non-convex shape features is, in principle, also possible, but usually requires a priori information about the object. Alternatively, a distribution of non-convex solutions, describing the scale of the non-convexities, is also possible to be obtained. Due to insufficient number of absolute observations and inaccurately defined asteroid phase curves, the $c/b$-ratio, i.e., the flatness of the shape model is often somewhat ill-defined. However, especially in the case of elongated objects, the flatness seems to be quite well constrained, even in the case when only relative lightcurves are available. The results prove that it is, contrary to the earlier misbelief, possible to derive shape information from the lightcurve data if a sufficiently wide range of observing geometries is covered by the observations. Along with the more accurate shape models, also the rotational states, i.e., spin vectors and rotation periods, are defined with improved accuracy. The shape solutions obtained so far reveal a population of irregular objects whose most descriptive shape characteristics, however, can be expressed with only a few parameters. Preliminary statistical analyses for the shapes suggests that there are correlations between shape and other physical properties, such as the size, rotation period and taxonomic type of the asteroids. More shape data of, especially, the smallest and largest asteroids, as well as the fast and slow rotators is called for in order to be able to study the statistics more thoroughly.

Non-Markovian decoherence: complete positivity and decomposition

In this work, the non-Markovian decoherence is considered in two ways. Firstly, an effective Hamiltonian approach is demonstrated to investigate the decoherence of a quantum system in a non-Markovian environment, in which complete positivity of the reduced dynamics is achieved. This method uses the notion of an effective environment, that is a subsystem of the environment that causes the decoherence. Secondly, the evolution of the system and environment is decomposed, thus partially illuminating how they would interact given that memory effects are allowed. It should be noted that beam splitters and rotators are sufficient to explain this decomposition.

More nitrogen rich B-type stars in the SMC cluster, NGC 330

High resolution spectra of seven early B-type giant/supergiant stars in the SMC cluster NGC330 are analysed to obtain their chemical compositions relative to SMC field and Galactic B-type stars. It is found that all seven stars are nitrogen rich with an abundance approximately 1.3 dex higher than an SMC main- sequence field B-type star, AV304. They also display evidence for deficiencies in carbon, but other metals have abundances typical of the SMC. Given the number of B-type stars with low projected rotational velocities in NGC330 (all our targets have v sin i <50 km s(-1)), we suggest that it is unlikely that the stars in our sample are seen almost pole-on, but rather that they are intrinsically slow rotators. Furthermore, none of our objects displays any evidence of significant Balmer emission excluding the possibility that these are Be stars observed pole-on. Comparing these results with the predictions of stellar evolution models including the effects of rotationally induced mixing, we conclude that while the abundance patterns may indeed be reproduced by these models, serious discrepancies exist. Most importantly, models including the effects of initially large rotational velocities do not reproduce the observed range of effective temperatures of our sample, nor the currently observed rotational velocities. Binary models may be able to produce stars in the observed temperature range but again may be incapable of producing suitable analogues with low rotational velocities. We also discuss the clear need for stellar evolution calculations employing the correct chemical mix of carbon, nitrogen and oxygen for the SMC.

The VLT-FLAMES survey of massive stars: stellar parameters and rotational velocities in NGC 3293, NGC 4755 and NGC 6611

An analysis is presented of VLT-FLAMES spectroscopy for three Galactic clusters, NGC3293, NGC4755 and NGC6611. Non-LTE model atmosphere calculations have been used to estimate effective temperatures (from either the helium spectrum or the silicon ionization equilibrium) and gravities (from the hydrogen spectrum). Projected rotational velocities have been deduced from the helium spectrum (for fast and moderate rotators) or the metal line spectrum (for slow rotators). The origin of the low gravity estimates for apparently near main sequence objects is discussed and is related to the stellar rotational velocity. The atmospheric parameters have been used to estimate cluster distances (which are generally in good agreement with previous determinations) and these have been used to estimate stellar luminosities and evolutionary masses. The observed Hertzsprung-Russell diagrams are compared with theoretical predictions and some discrepancies including differences in the main sequence luminosities are discussed. Cluster ages have been deduced and evidence for non-coeval star formation is found for all three of the clusters. Projected rotational velocities for targets in the older clusters, NGC3293 and NGC4755, have been found to be systematically larger than those for the field, confirming recent results in other similar age clusters. The distribution of projected rotational velocities are consistent with a Gaussian distribution of intrinsic rotational velocities. For the relatively unevolved targets in the older clusters, NGC3293 and NGC4755, the peak of the velocity distribution would be 250 km s(-1) with a full-width-half-maximum of approximately 180 km s(-1). For NGC6611, the sample size is relatively small but implies a lower mean rotational velocity. This may be evidence for the spin-down effect due to angular momentum loss through stellar winds, although our results are consistent with those found for very young high mass stars. For all three clusters we deduce present day mass functions with Gamma-values in the range of -1.5 to -1.8, which are similar to other young stellar clusters in the Milky Way.

The VLT-FLAMES survey of massive stars: atmospheric parameters and rotational velocity distributions for B-type stars in the Magellanic Clouds

Aims.We aim to provide the atmospheric parameters and rotational velocities for a large sample of O- and early B-type stars, analysed in a homogeneous and consistent manner, for use in constraining theoretical models. Methods: Atmospheric parameters, stellar masses, and rotational velocities have been estimated for approximately 250 early B-type stars in the Large (LMC) and Small (SMC) Magellanic Clouds from high-resolution VLT-FLAMES data using the non-LTE TLUSTY model atmosphere code. This data set has been supplemented with our previous analyses of some 50 O-type stars (Mokiem et al. 2006, 2007) and 100 narrow-lined early B-type stars (Hunter et al. 2006; Trundle et al. 2007) from the same survey, providing a sample of ~400 early-type objects. Results: Comparison of the rotational velocities with evolutionary tracks suggests that the end of core hydrogen burning occurs later than currently predicted and we argue for an extension of the evolutionary tracks. We also show that the large number of the luminous blue supergiants observed in the fields are unlikely to have directly evolved from main-sequence massive O-type stars as neither their low rotational velocities nor their position on the H-R diagram are predicted. We suggest that blue loops or mass-transfer binary systems may populate the blue supergiant regime. By comparing the rotational velocity distributions of the Magellanic Cloud stars to a similar Galactic sample, we find that (at 3s confidence level) massive stars (above 8 M?) in the SMC rotate faster than those in the solar neighbourhood. However there appears to be no significant difference between the rotational velocity distributions in the Galaxy and the LMC. We find that the v sin i distributions in the SMC and LMC can modelled with an intrinsic rotational velocity distribution that is a Gaussian peaking at 175 km s-1 (SMC) and 100 km s-1 (LMC) with a 1/e half width of 150 km s-1. We find that in NGC 346 in the SMC, the 10-25 M? main-sequence stars appear to rotate faster than their higher mass counterparts. It is not expected that O-type stars spin down significantly through angular momentum loss via stellar winds at SMC metallicity, hence this could be a reflection of mass dependent birth spin rates. Recently Yoon et al. (2006) have determined rates of GRBs by modelling rapidly rotating massive star progenitors. Our measured rotational velocity distribution for the 10-25 M? stars is peaked at slightly higher velocities than they assume, supporting the idea that GRBs could come from rapid rotators with initial masses as low as 14 M? at low metallicities.

The VLT-FLAMES Survey of massive stars: Rotation and nitrogen enrichment as the key to understanding massive star evolution

Rotation has become an important element in evolutionary models of massive stars, specifically via the prediction of rotational mixing. Here we study a sample of stars, including rapid rotators, to constrain such models and use nitrogen enrichments as a probe of the mixing process. Chemical compositions (C, N, O, Mg, and Si) have been estimated for 135 early B-type stars in the Large Magellanic Cloud with projected rotational velocities up to similar to 300 km s(-1) using a non-LTE TLUSTY model atmosphere grid. Evolutionary models, including rotational mixing, have been generated attempting to reproduce these observations by adjusting the overshooting and rotational mixing parameters and produce reasonable agreement with 60% of our core hydrogen burning sample. We find (excluding known binaries) a significant population of highly nitrogen-enriched intrinsic slow rotators (nu sin i less than or similar to 50 km s(-1)) incompatible with our models (similar to 20% of the sample). Furthermore, while we find fast rotators with enrichments in agreement with the models, the observation of evolved (dex) fast rotators (log g < 3.7 dex) that are relatively unenriched (a further similar to 20% of the sample) challenges the concept of rotational mixing. We also find that 70% of our blue supergiant sample cannot have evolved directly from the hydrogen-burning main sequence. We are left with a picture where invoking binarity and perhaps fossil magnetic fields is required to understand the surface properties of a population of massive main- sequence stars.

Stellar rotation in the Hyades and Praesepe: gyrochronology and braking time-scale

We present the results of photometric surveys for stellar rotation in the Hyades and in Praesepe, using data obtained as part of the SuperWASP exoplanetary transit-search programme. We determined accurate rotation periods for more than 120 sources whose cluster membership was confirmed by common proper motion and colour-magnitude fits to the clusters' isochrones. This allowed us to determine the effect of magnetic braking on a wide range of spectral types for expected ages of ˜600 Myr for the Hyades and Praesepe. Both clusters show a tight and nearly linear relation between J-Ks colour and rotation period in the F, G and K spectral range. This confirms that loss of angular momentum was significant enough that stars with strongly different initial rotation rates have converged to the same rotation period for a given mass, by the ages of Hyades and Praesepe. In the case of the Hyades, our colour-period sequence extends well into the M dwarf regime and shows a steep increase in the scatter of the colour-period relation, with identification of numerous rapid rotators from ˜0.5 Msun down to the lowest masses probed by our survey (˜0.25 Msun). This provides crucial constraints on the rotational braking time-scales and further clears the way to use gyrochronology as an accurate age measurement tool for main-sequence stars.

The host galaxy of the super-luminous SN 2010gx and limits on explosive nickel-56 production

Super-luminous supernovae have a tendency to occur in faint host galaxies which are likely to have low mass and low metallicity. While these extremely luminous explosions have been observed from z=0.1 to 1.55, the closest explosions allow more detailed investigations of their host galaxies. We present a detailed analysis of the host galaxy of SN 2010gx (z=0.23), one of the best studied super-luminous type Ic supernovae. The host is a dwarf galaxy (M_g=-17.42+/-0.17) with a high specific star formation rate. It has a remarkably low metallicity of 12+log(O/H)=7.5+/-0.1 dex as determined from the detection of the [OIII] 4363 Angs line. This is the first reliable metallicity determination of a super-luminous stripped-envelope supernova host. We collected deep multi-epoch imaging with Gemini + GMOS between 240-560 days after explosion to search for any sign of radioactive nickel-56, which might provide further insights on the explosion mechanism and the progenitor's nature. We reach griz magnitudes of m_AB~26, but do not detect SN 2010gx at these epochs. The limit implies that any nickel-56 production was similar to or below that of SN 1998bw (a luminous type Ic SN that produced around 0.4 M_sun of nickel-56). The low volumetric rates of these supernovae (~10^-4 of the core-collapse population) could be qualitatively matched if the explosion mechanism requires a combination of low-metallicity (below 0.2 Z_sun), high progenitor mass (>60 M_sun) and high rotation rate (fastest 10% of rotators).

Análise da função dos músculos do quadril em portadores de síndrome da dor patelofemural

The Patellofemoral pain syndrome is defined as a fore or retro patellar pain and it has multifactorial etiology, where the bad patellar alignment is the most acceptable hypothesis. However proximal factors to the knee, as the debility of the muscles of the hip, have been demonstrated as a contributing factor to the appearing of that syndrome. Purpose: To evaluate if exists a relation between the hip muscles performance and the development of the SDPF. Methods: Thirty women took part in this study. They were divided in two groups; a control group (fifteen asymptomatic subjects) and an experimental group (fifteen subjects with the diagnosis of SDPF). The muscle performance was evaluated in an isokinetic dynamometer, where it was verified the peak torque (PT), PT to body weight, PT time and the agonist/antagonist relation. It was also analyzed the electromyographic activity of the middle gluteus. The data was analyzed by the not paired t test at a significance level of 5%. Results:. Didn t have significant difference to the PT of the abductor muscles (p = 0,46) and lateral rotators of the hip (p = 0,17) between groups. Also didn t have significant difference to the PT values by the body weight, to these muscle groups either (p = 0,10 e p = 0,11, respectively). Didn t have significant difference between the amplitude of the signal (p = 0,05) and the onset of medium gluteus (p = 0,25) between the groups. Conclusion: In the experimental conditions realized, the study didn t demonstrate a relation between performance the hip muscles behavior and the development of the SDPF

Lítio e rotação nas estrelas análogas solares: análise teórica das observações

The projected rotational velocity together with lithium abundance and the onset of the dilution by the deepening in mass of the convective envelope provide a key tool to investigate the so far poorly understood processes at work in stellar interiors of solar-analog stars. To investigate the link between abundances, convection and rotational velocities in solar-analog G dwarf stars, we study a bona fide sample of 118 selected solar-analog G dwarf stars presenting measured lithium abundances, rotational velocities, and fundamental parameters together with computed evolutionary tracks (Toulouse-Geneva code) for a range of stellar masses around 1 M and metallicity consistent with the solar-analog range. The aim of this work is to build up an evolution of lithium and rotation as a function of stellar age, mass, effective temperature, and convection. We analyze the evolutionary status of the sample of 118 solar-analog G dwarf in the HR diagram based on Hipparcos data and using a grid of stellar models in the effective temperature and mass range of the solar-analog stars. We discuss the deepening (in mass) of the convective envelope and the influence on the Li abundances and projected rotational velocities. We determined the stellar mass and the mass of the convective envelope for a bona fide sample of 118 selected solar-analog G dwarf and checked the evolutionary link between the rotational velocity, lithium abundance, and the deepening of the convective envelope. Fast rotators (vsini 6 km s��1) are also stars with high Li content. Slow rotators present a wide range of values of log n(Li). Our results shed new light on the lithium and rotational behavior in G dwarf stars. We confirmed the presence of a large Li abundance spread among the solar-analog stars and concluded that the solar twins probably share a similar mixing history with the Sun

Non-mean-field effects in systems with long-range forces in competition

We investigate the canonical equilibrium of systems with long-range forces in competition. These forces create a modulation in the interaction potential and modulated phases appear at the system scale. The structure of these phases differentiate this system from monotonic potentials, where only the mean-field and disordered phases exist. With increasing temperature, the system switches from one ordered phase to another through a first-order phase transition. Both mean-field and modulated phases may be stable, even at zero temperature, and the long-range nature of the interaction will lead to metastability characterized by extremely long time scales.

Observational effects of stellar rotation on Be stars' disks

Be stars are known to be fast rotators. At high rotation rates a profound modification of the radiation field reaching the circumstellar environment is expected. The origin of this modification is the decrease of the effective gravity on stellar surface leading to the stellar geometrical flattening and the gravity darkening effect predicted by Von Zeipel. Making use of the radiative transfer code HDUST we discuss the consequences of such stellar rotation on the structure of Be star disks based on the Viscous Decretion Disk model. Observational predictions are also made, as SED, IR-excess and Hydrogen line profiles. The modified illumination of the circumstellar disk generates significant changes in these quantities. Ascertaining these changes is useful to set some of the fundamental parameters of the Be system and to unveil the role of stellar rotation over the stellar evolution.