Current kinematics and dynamics of Africa and the East African Rift System

Although the East African Rift System (EARS) is an archetype continental rift, the forces driving its evolution remain debated. Some contend buoyancy forces arising from gravitational potential energy (GPE) gradients within the lithosphere drive rifting. Others argue for a major role of the diverging mantle flow associated with the African Superplume. Here we quantify the forces driving present-day continental rifting in East Africa by (1) solving the depth averaged 3-D force balance equations for 3-D deviatoric stress associated with GPE, (2) inverting for a stress field boundary condition that we interpret as originating from large-scale mantle tractions, (3) calculating dynamic velocities due to lithospheric buoyancy forces, lateral viscosity variations, and velocity boundary conditions, and (4) calculating dynamic velocities that result from the stress response of horizontal mantle tractions acting on a viscous lithosphere in Africa and surroundings. We find deviatoric stress associated with lithospheric GPE gradients are similar to 8-20 MPa in EARS, and the minimum deviatoric stress resulting from basal shear is similar to 1.6 MPa along the EARS. Our dynamic velocity calculations confirm that a force contribution from GPE gradients alone is sufficient to drive Nubia-Somalia divergence and that additional forcing from horizontal mantle tractions overestimates surface kinematics. Stresses from GPE gradients appear sufficient to sustain present-day rifting in East Africa; however, they are lower than the vertically integrated strength of the lithosphere along most of the EARS. This indicates additional processes are required to initiate rupture of continental lithosphere, but once it is initiated, lithospheric buoyancy forces are enough to maintain rifting.

Kinematics and dynamics of Jansen leg mechanism: A bond graph approach

The Jansen mechanism is a one degree-of-freedom, planar, 12-link, leg mechanism that can be used in mobile robotic applications and in gait analysis. This paper presents the kinematics and dynamics of the Jansen leg mechanism. The forward kinematics, accomplished using circle intersection method, determines the trajectories of various points on the mechanism in the chassis (stationary link) reference frame. From the foot point trajectory, the step length is shown to vary linearly while step height varies non-linearly with change in crank radius. A dynamic model for the Jansen leg mechanism is proposed using bond graph approach with modulated multiport transformers. For given ground reaction force pattern and crank angular speed, this model helps determine the motor torque profile as well as the link and joint stresses. The model can therefore be used to rate the actuator torque and in design of the hardware and controller for such a system. The kinematics of the mechanism can also be obtained from this dynamic model. The proposed model is thus a useful tool for analysis and design of systems based on the Jansen leg mechanism. (C) 2015 Elsevier B.V. All rights reserved.

From inverted pendulum to N-link chain: inertial sensors-based assessment of movement kinematics and dynamics for functional evaluation and rehabilitation

Despite several clinical tests that have been developed to qualitatively describe complex motor tasks by functional testing, these methods often depend on clinicians' interpretation, experience and training, which make the assessment results inconsistent, without the precision required to objectively assess the effect of the rehabilitative intervention. A more detailed characterization is required to fully capture the various aspects of motor control and performance during complex movements of lower and upper limbs. The need for cost-effective and clinically applicable instrumented tests would enable quantitative assessment of performance on a subject-specific basis, overcoming the limitations due to the lack of objectiveness related to individual judgment, and possibly disclosing subtle alterations that are not clearly visible to the observer. Postural motion measurements at additional locations, such as lower and upper limbs and trunk, may be necessary in order to obtain information about the inter-segmental coordination during different functional tests involved in clinical practice. With these considerations in mind, this Thesis aims: i) to suggest a novel quantitative assessment tool for the kinematics and dynamics evaluation of a multi-link kinematic chain during several functional motor tasks (i.e. squat, sit-to-stand, postural sway), using one single-axis accelerometer per segment, ii) to present a novel quantitative technique for the upper limb joint kinematics estimation, considering a 3-link kinematic chain during the Fugl-Meyer Motor Assessment and using one inertial measurement unit per segment. The suggested methods could have several positive feedbacks from clinical practice. The use of objective biomechanical measurements, provided by inertial sensor-based technique, may help clinicians to: i) objectively track changes in motor ability, ii) provide timely feedback about the effectiveness of administered rehabilitation interventions, iii) enable intervention strategies to be modified or changed if found to be ineffective, and iv) speed up the experimental sessions when several subjects are asked to perform different functional tests.

Scaling and non-scaling of muscle activity, kinematics, and dynamics in sit-ups with different degrees of difficulty

The purpose of this study was to investigate how the CNS adjusts motor patterns for variants of a complex axial movement-the situp. Adjustments were induced by changing the support surface contact and mass distribution of the body. Healthy adults performed straight-legged sit-ups, 3 s in duration, with support added to or removed from the lumbar trunk, or with mass added to the head or to the legs. Each of these interventions either increased or decreased the difficulty of the task. The study addressed the extent to which changes in sit-up difficulty are compensated by scaling of muscle activity, kinematics, and dynamics versus the extent to which they are compensated by changing discretely the motor pattern. The analysis of muscle activity, kinematics, and dynamics focused on the first 30-40% of the sit-up-the trunk flexion phase-since this is the most critical part of the movement. Our results demonstrate that, in some respects, sit-up kinematics and dynamics scaled with difficulty, but in other respects, they did not. Muscle activity also scaled, in many respects, but in more difficult sit-ups, abdominal flexor activity decreased instead of increased. Non-scaling changes in these parameters suggest that complex movements, such as the sit-up, may require discrete changes in motor pattern in order to deal with large loads, which challenge the available leverage. (C) 2005 Elsevier Ltd. All rights reserved.

The globular cluster kinematics and galaxy dark matter content of NGC 3923

This paper presents further results from our spectroscopic study of the globular cluster (GC) system of the group elliptical NGC 3923. From observations made with the GMOS instrument on the Gemini South Telescope, an additional 50 GC and ultra-compact dwarf (UCD) candidates have been spectroscopically confirmed as members of the NGC 3923 system. When the recessional velocities of these GCs are combined with the 29 GC velocities reported previously, a total sample of 79 GC/UCD velocities is produced. This sample extends to over 6 arcmin (>6 R-e similar to 30 kpc) from the centre of NGC 3923 and is used to study the dynamics of the GC system and the dark matter content of NGC 3923. It is found that the GC system of NGC 3923 displays no appreciable rotation, and that the projected velocity dispersion is constant with radius within the uncertainties. The velocity dispersion profiles of the integrated light and GC system of NGC 3923 are indistinguishable over the region in which they overlap. We find some evidence that the diffuse light and GCs of NGC 3923 have radially biased orbits within similar to 130 arcsec. The application of axisymmetric orbit-based models to the GC and integrated light velocity dispersion profiles demonstrates that a significant increase in the mass-to-light ratio (from M/L-V = 8 to 26) at large galactocentric radii is required to explain this observation. We therefore confirm the presence of a dark matter halo in NGC 3923. We find that dark matter comprises 17.5(-4.5)(+7.3) per cent of the mass within 1 R-e, 41.2(-10.6)(+18.2) per cent within 2 R-e and 75.6(-16.8)(+15.4) per cent within the radius of our last kinematic tracer at 6.9 R-e. The total dynamical mass within this radius is found to be 1.5(-0.25)(+0.4) x 10(12) M-circle dot. In common with other studies of large ellipticals, we find that our derived dynamical mass profile is consistently higher than that derived by X-ray observations, by a factor of around 2.

The spiral structure of the Galaxy revealed by CS sources and evidence for the 4:1 resonance

We present a map of the spiral structure of the Galaxy, as traced by molecular carbon monosulphide (CS) emission associated with IRAS sources which are believed to be compact H II regions. The CS line velocities are used to determine the kinematic distances of the sources in order to investigate their distribution in the galactic plane. This allows us to use 870 objects to trace the arms, a number larger than that of previous studies based on classical H II regions. The distance ambiguity of the kinematic distances, when it exists, is solved by different procedures, including the latitude distribution and an analysis of the longitude-velocity diagram. The study of the spiral structure is complemented with other tracers: open clusters, Cepheids, methanol masers and H II regions. The well-defined spiral arms are seen to be confined inside the corotation radius, as is often the case in spiral galaxies. We identify a square-shaped sub-structure in the CS map with that predicted by stellar orbits at the 4:1 resonance (four epicycle oscillations in one turn around the galactic centre). The sub-structure is found at the expected radius, based on the known pattern rotation speed and epicycle frequency curve. An inner arm presents an end with strong inwards curvature and intense star formation that we tentatively associate with the region where this arm surrounds the extremity of the bar, as seen in many barred galaxies. Finally, a new arm with concave curvature is found in the Sagitta to Cepheus region of the sky. The observed arms are interpreted in terms of perturbations similar to grooves in the gravitational potential of the disc, produced by crowding of stellar orbits.

Measurement of the epicycle frequency in the Galactic disc and initial velocities of open clusters

A new method to measure the epicycle frequency kappa in the Galactic disc is presented. We make use of the large data base on open clusters completed by our group to derive the observed velocity vector (amplitude and direction) of the clusters in the Galactic plane. In the epicycle approximation, this velocity is equal to the circular velocity given by the rotation curve, plus a residual or perturbation velocity, of which the direction rotates as a function of time with the frequency kappa. Due to the non-random direction of the perturbation velocity at the birth time of the clusters, a plot of the present-day direction angle of this velocity as a function of the age of the clusters reveals systematic trends from which the epicycle frequency can be obtained. Our analysis considers that the Galactic potential is mainly axis-symmetric, or in other words, that the effect of the spiral arms on the Galactic orbits is small; in this sense, our results do not depend on any specific model of the spiral structure. The values of kappa that we obtain provide constraints on the rotation velocity of the in particular, V(0) is found to be 230 +/- 15 km s(-1) even if the scale (R(0) = 7.5 kpc) of the Galaxy is adopted. The measured kappa at the solar radius is 43 +/- 5 km s(-1) kpc(-1). The distribution of initial velocities of open clusters is discussed.

Chemically tagging the Hyades stream: does it partly originate from the Hyades cluster?

The Hyades stream has long been thought to be a dispersed vestige of the Hyades cluster. However, recent analyses of the parallax distribution, of the mass function, and of the action-space distribution of stream stars have shown it to be rather composed of orbits trapped at a resonance of a density disturbance. This resonant scenario should leave a clearly different signature in the element abundances of stream stars than the dispersed cluster scenario, since the Hyades cluster is chemically homogeneous. Here, we study the metallicity as well as the element abundances of Li, Na, Mg, Fe, Zr, Ba, La, Ce, Nd and Eu for a random sample of stars belonging to the Hyades stream, and compare them with those of stars from the Hyades cluster. From this analysis: (i) we independently confirm that the Hyades stream cannot be solely composed of stars originating in the Hyades cluster; (ii) we show thatsomestars (namely 2/21) from the Hyades stream nevertheless have abundances compatible with an origin in the cluster; (iii) we emphasize that the use of Li as a chemical tag of the cluster origin of main-sequence stars is very efficient in the range 5500K ≤Teff≤ 6200K, since the Li sequence in the Hyades cluster is very tight, while at the same time spanning a large abundance range; (iv) we show that, while this evaporated population has a metallicity excess of ~0.2 dex with respect to the local thin-disc population, identical to that of the Hyades cluster, the remainder of the Hyades stream population has still a metallicity excess of ~0.06-0.15 dex, consistent with an origin in the inner Galaxy and (v) we show that the Hyades stream can be interpreted as an inner 4:1 resonance of the spiral pattern: this then also reproduces an orbital family compatible with the Sirius stream, and places the origin of the Hyades stream up to 1kpc inwards from the solar radius, which might explain the observed metallicity excess of the stream population. © 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS.

The corotation gap in the Galactic H i distribution

We used the H i data from the LAB Survey to map the ring-shaped gap in H i density that lies slightly outside the solar circle. Adopting R(0) = 7.5 kpc, we find an average gap radius of 8.3 kpc and an average gap width of 0.8 kpc. The characteristics of the H i gap correspond closely to the expected ones, as predicted by theory and by numerical simulations of the gas flow near the corotation resonance.

Chemically tagging the Hyades stream: does it partly originate from the Hyades cluster?

The Hyades stream has long been thought to be a dispersed vestige of the Hyades cluster. However, recent analyses of the parallax distribution, of the mass function, and of the action-space distribution of stream stars have shown it to be rather composed of orbits trapped at a resonance of a density disturbance. This resonant scenario should leave a clearly different signature in the element abundances of stream stars than the dispersed cluster scenario, since the Hyades cluster is chemically homogeneous. Here, we study the metallicity as well as the element abundances of Li, Na, Mg, Fe, Zr, Ba, La, Ce, Nd and Eu for a random sample of stars belonging to the Hyades stream, and compare them with those of stars from the Hyades cluster. From this analysis: (i) we independently confirm that the Hyades stream cannot be solely composed of stars originating in the Hyades cluster; (ii) we show that some stars (namely 2/21) from the Hyades stream nevertheless have abundances compatible with an origin in the cluster; (iii) we emphasize that the use of Li as a chemical tag of the cluster origin of main-sequence stars is very efficient in the range 5500 K <= T(eff) <= 6200 K, since the Li sequence in the Hyades cluster is very tight, while at the same time spanning a large abundance range; (iv) we show that, while this evaporated population has a metallicity excess of similar to 0.2 dex with respect to the local thin-disc population, identical to that of the Hyades cluster, the remainder of the Hyades stream population has still a metallicity excess of similar to 0.06-0.15 dex, consistent with an origin in the inner Galaxy and (v) we show that the Hyades stream can be interpreted as an inner 4:1 resonance of the spiral pattern: this then also reproduces an orbital family compatible with the Sirius stream, and places the origin of the Hyades stream up to 1 kpc inwards from the solar radius, which might explain the observed metallicity excess of the stream population.

The dark matter profile of the Milky Way: a non-parametric reconstruction

We present the results of a new, non-parametric method to reconstruct the Galactic dark matter profile directly from observations. Using the latest kinematic data to track the total gravitational potential and the observed distribution of stars and gas to set the baryonic component, we infer the dark matter contribution to the circular velocity across the Galaxy. The radial derivative of this dynamical contribution is then estimated to extract the dark matter profile. The innovative feature of our approach is that it makes no assumption on the functional form or shape of the profile, thus allowing for a clean determination with no theoretical bias. We illustrate the power of the method by constraining the spherical dark matter profile between 2.5 and 25 kpc away from the Galactic center. The results show that the proposed method, free of widely used assumptions, can already be applied to pinpoint the dark matter distribution in the Milky Way with competitive accuracy, and paves the way for future developments.

Kinematics, substructure and luminosity-weighted dynamics of six nearby galaxy groups

We have redefined group membership of six southern galaxy groups in the local universe (mean cz < 2000 km s(-1)) based on new redshift measurements from our recently acquired Anglo-Australian Telescope 2dF spectra. For each group, we investigate member galaxy kinematics, substructure, luminosity functions and luminosity-weighted dynamics. Our calculations confirm that the group sizes, virial masses and luminosities cover the range expected for galaxy groups, except that the luminosity of NGC 4038 is boosted by the central starburst merger pair. We find that a combination of kinematical, substructural and dynamical techniques can reliably distinguish loose, unvirialized groups from compact, dynamically relaxed groups. Applying these techniques, we find that Dorado, NGC 4038 and NGC 4697 are unvirialized, whereas NGC 681, NGC 1400 and NGC 5084 are dynamically relaxed.

Molecular gas in the galaxy M83 : Its distribution, kinematics, and relation to star formation

The barred spiral galaxy M83 (NGC5236) has been observed in the 12CO J=1–0 and J=2–1 millimetre lines with the Swedish-ESO Submillimetre Telescope (SEST). The sizes of the CO maps are 100×100, and they cover the entire optical disk. The CO emission is strongly peaked toward the nucleus. The molecular spiral arms are clearly resolved and can be traced for about 360º. The total molecular gas mass is comparable to the total Hi mass, but H2 dominates in the optical disk. Iso-velocity maps show the signature of an inclined, rotating disk, but also the effects of streaming motions along the spiral arms. The dynamical mass is determined and compared to the gas mass. The pattern speed is determined from the residual velocity pattern, and the locations of various resonances are discussed. The molecular gas velocity dispersion is determined, and a trend of decreasing dispersion with increasing galactocentric radius is found. A total gas (H2+Hi+He) mass surface density map is presented, and compared to the critical density for star formation of an isothermal gaseous disk. The star formation rate (SFR) in the disk is estimated using data from various star formation tracers. The different SFR estimates agree well when corrections for extinctions, based on the total gas mass map, are made. The radial SFR distribution shows features that can be associated with kinematic resonances. We also find an increased star formation efficiency in the spiral arms. Different Schmidt laws are fitted to the data. The star formation properties of the nuclear region, based on high angular resolution HST data, are also discussed.

Hydrodynamical simulations of early-type galaxies: effects of galaxy shape and stellar dynamics on hot coronae

Early-Type galaxies (ETGs) are embedded in hot (10^6-10^7 K), X-ray emitting gaseous haloes, produced mainly by stellar winds and heated by Type Ia supernovae explosions, by the thermalization of stellar motions and occasionally by the central super-massive black hole (SMBH). In particular, the thermalization of the stellar motions is due to the interaction between the stellar and the SNIa ejecta and the hot interstellar medium (ISM) already residing in the ETG. A number of different astrophysical phenomena determine the X-ray properties of the hot ISM, such as stellar population formation and evolution, galaxy structure and internal kinematics, Active Galactic Nuclei (AGN) presence, and environmental effects. With the aid of high-resolution hydrodynamical simulations performed on state-of-the-art galaxy models, in this Thesis we focus on the effects of galaxy shape, stellar kinematics and star formation on the evolution of the X-ray coronae of ETGs. Numerical simulations show that the relative importance of flattening and rotation are functions of the galaxy mass: at low galaxy masses, adding flattening and rotation induces a galactic wind, thus lowering the X-ray luminosity; at high galaxy masses the angular momentum conservation keeps the central regions of rotating galaxies at low density, whereas in non-rotating models a denser and brighter atmosphere is formed. The same dependence from the galaxy mass is present in the effects of star formation (SF): in light galaxies SF contributes to increase the spread in Lx, while at high galaxy masses the halo X-ray properties are marginally sensitive to SF effects. In every case, the star formation rate at the present epoch quite agrees with observations, and the massive, cold gaseous discs are partially or completely consumed by SF on a time-scale of few Gyr, excluding the presence of young stellar discs at the present epoch.