Brunelleschi’s Dome: A New Estimate of the Thrust and Stresses in the Underlying Piers

The paper deals with the insurgence of the thrust, together with its valuation, in masonry domes, giving special attention to the Brunelleschi’s Dome in Florence. After a recalling of the kinematical approach in the context of the Heyman masonry model, the thrust of Brunelleschi’s Dome is estimated as the maximum of the set of all the kinematical ones. Comparisons are made with other valuations made by the usual, but less accurate, statical approach. The knowledge of the thrust allows an evaluation of the stresses acting in the supporting piers: their base sections are all compressed, with level stresses sufficiently low. This result shows the extraordinary conception of Filippo Brunelleschi’s Dome and the favorable design of the pillar sections and of the drum positioning, due, perhaps, to Arnolfo di Cambio or to the succeeding Masters.

Standing wave approach in the theory of X-ray magnetic reflectivity

An extension of the exact X-ray resonant magnetic reflectivity theory has been developed, taking into account the small value of the magnetic terms in the X-ray susceptibility tensor. It is shown that squared standing waves (fourth power of the total electric field) determine the output of the magnetic addition to the total reflectivity from a magnetic multilayer. The obtained generalized kinematical approach essentially speeds up the calculation of the asymmetry ratio in the magnetic reflectivity. The developed approach easily explains the peculiarities of the angular dependence of the reflectivity with the rotated polarization (such as the peak at the critical angle of the total external reflection). The revealed dependence of the magnetic part of the total reflectivity on the squared standing waves means that the selection of the reflectivity with the rotated polarization ensures higher sensitivity to the depth profiles of magnetization than the secondary radiation at the specular reflection condition.

Robot Imitation Learning of Social Gestures with Self-Collision Avoidance Using a 3D Sensor

To effectively interact with people, social robots need to perceive human behaviors and in turn display their own behaviors using social communication modes such as gestures. The modeling of gestures can be difficult due to the high dimensionality of the robot configuration space. Imitation learning can be used to teach a robot to implement multi-jointed arm gestures by directly observing a human teacher’s arm movements (for example, using a non-contact 3D sensor) and then mapping these movements onto the robot arms. In this paper, we present a novel imitation learning system with robot self-collision awareness and avoidance. The proposed method uses a kinematical approach with bounding volumes to detect and avoid collisions with the robot itself while performing gesticulations. We conducted experiments with a dual arm social robot and a 3D sensor to determine the effectiveness of our imitation system in being able to mimic gestures while avoiding self-collisions.

Quantitative theory of diffraction by cylindrical scroll nanotubes

A quantitative theory of Fraunhofer diffraction by right- and left-handed multiwalled cylindrical scroll nanotubes is developed on the basis of the kinematical approach. The proposed theory is mainly dedicated to structural studies of individual nanotubes by the selected-area electron diffraction technique. Strong and diffuse reflections of the scroll nanotube were studied and explicit formulas that govern relations between the direct and reciprocal lattice of the scroll nanotube are achieved.

Consideration Regarding the Inverse Kinematics of a Rowing Skiff under the Action of the Oars Movement

The paper deals with the kinematical approach of the trajectory of movement of an academic rowing skiff with a view to determine a given racing speed of the boat. It uses inverse kinematics since this method allows obtaining analytical calculus formulas for the movement of paddles in their two moments of motion: active and passive strokes. Movement of the paddles while following an arc-shaped trajectory outlining a sphere-like quadrilateral requires different values of amplitude of angular displacement of the paddles according both to anthropometrical values of the athlete and to his physical and technical training. The numerical application is made for several values of these angles which define the arcs of the circle for active and passive curves and for the moments between the two strokes (angle of the paddle while slicing in and out the water). These amplitudes of angular displacement are being considered, from the point of view of the horizontal component, equal to the speed of the skiff while imposing the linear speed of the paddle, and they would help determining movement frequencies of the paddle while following the sphere-like quadrilateral trajectory.

Time-of-flight studies of multiple Bragg reflections in cylindrically bent perfect crystals

Multiple Bragg reflections (MBRs) realized in a bent perfect crystal (BPC) slab by sets of different lattice planes behave differently from the case of perfect nondeformed or mosaic crystals. Because of elastic bending (homogeneous deformation), individual sets of lattice planes are mutually in dispersive diffraction geometry and the kinematical approach can be applied on this MBR process. The elastic deformation produced by the cylindrical bending can enormously strengthen the MBR effects, which can then be investigated even at small neutron sources. By using neutron diffraction and the time-of-flight method, carried out at the 45 MeV linac-based pulsed cold neutron source at Hokkaido University, it has been demonstrated that when setting the BPC slabs in the symmetric transmission geometry many strong MBRs accompanying forbidden Si(222) or Si(002) reflections can be observed. The advantage of the time-of-flight method consists in the fact that it is possible to observe not only primary MBRs related to the basic forbidden reflections but also their higher orders, which could be easily separated in the time-of-flight spectra.