Influence of Chemical Heterogeneity and Third Body on Adhesive Strength: Experiment and Simulation

We investigate experimentally and numerically the influence of chemical heterogeneity and of third-body particles on adhesive contact. Chemical heterogeneity is generated by chemical treatment of the contacting bodies changing locally the surface energy. For studying the influence of the third body, two types of particles are used: sand particles with various geometrical shapes and sizes, and steel spheres of equal radius. Dependencies of the normal force on the indentation depth at both indenting and pull-off as well as the evolution of the contact configuration are investigated. Corresponding numerical simulations are carried out using the boundary element method (BEM).

Network from the circles of the same radius for sustainable energy-efficient roof structures

In this research paper, we investigated one of the methods of formation of geometric networks of arches of the same radius using regular spherical polyhedra. The variants of cutting sustainable energy-efficient coatings of buildings in the form of spherical domes are proposed. The task conditions of placing the specified network on the sphere are set. The criterion for evaluating the effectiveness of solving the problem is the minimum number of standard sizes of segments of the dome arches, the possibility of using pre-assembly technologies. The solution of one variant of the problem as placing the network on a spherical icosahedron and, accordingly, on a sphere is given. The placement of arches of one radius on the sphere, different from the location in the form of meridians, has an effective solution in the form of a network with minimal dimensions of arch segments and with nodes of paired arches comprised on the basis of circles of the same radii formed on the ground of regular spherical polyhedra. The problem is solved by constructing and combining in a system of regular spherical polyhedral with independent frameworks of arches of the same radius on the basis of paired circles of equal radius.

Bounds for several-disk packings of hyperbolic surfaces

For any given [Formula: see text], this paper gives upper bounds on the radius of a packing of a complete hyperbolic surface of finite area by [Formula: see text] equal-radius disks in terms of the surface’s topology. We show that these bounds are sharp in some cases and not sharp in others.

Kinematic Analysis of Foldable Plate Structures With Rolling Joints

Rolling joints, which are created by attaching two cylindrical surfaces of equal radius using two or more thin tapes or cable, are used for rigid origami considering the panel thickness. First, the concept and two implementation methods of this joint are given. Then planar linkages are chosen to study the mobility and kinematics of foldable plate structures with rolling joints. It can be found that the rolling joints preserve the full-cycle-motion of foldable plate structures. From the closure equations of linkages, the results show that the outputs of linkages with rolling joints are the same as that with traditional revolute joints if the lengths of links are equal. However, the results are different when the lengths of links are unequal. Moreover, the difference between linkages with rolling joints and revolute joints increases with an increase of the size of rolling joints.

Emergence of collective changes in travel direction of starling flocks from individual birds' fluctuations

One of the most impressive features of moving animal groups is their ability to perform sudden coherent changes in travel direction. While this collective decision can be a response to an external alarm cue, directional switching can also emerge from the intrinsic fluctuations in individual behaviour. However, the cause and the mechanism by which such collective changes of direction occur are not fully understood yet. Here, we present an experimental study of spontaneous collective turns in natural flocks of starlings. We employ a recently developed tracking algorithm to reconstruct three-dimensional trajectories of each individual bird in the flock for the whole duration of a turning event. Our approach enables us to analyse changes in the individual behaviour of every group member and reveal the emergent dynamics of turning. We show that spontaneous turns start from individuals located at the elongated tips of the flocks, and then propagate through the group. We find that birds on the tips deviate from the mean direction of motion much more frequently than other individuals, indicating that persistent localized fluctuations are the crucial ingredient for triggering a collective directional change. Finally, we quantitatively verify that birds follow equal-radius paths during turning, the effects of which are a change of the flock's orientation and a redistribution of individual locations in the group.

On the anisotropic response of a Janus drop in a shearing viscous fluid

The force and couple that result from the shearing motion of a viscous, unbounded fluid on a Janus drop are the subjects of this investigation. A pair of immiscible, viscous fluids comprise the Janus drop and render it with a ‘perfect’ shape: spherical with a flat, internal interface, in which each constituent fluid is bounded by a hemispherical domain of equal radius. The effect of the arrangement of the internal interface (drop orientation) relative to the unidirectional shear flow is explored within the Stokes regime. Projection of the external flow into a reference frame centred on the drop simplifies the analysis to three cases: (i) a shear flow with a velocity gradient parallel to the internal interface, (ii) a hyperbolic flow, and (iii) two shear flows with a velocity gradient normal to the internal interface. Depending on the viscosity of the internal fluids, the Janus drop behaves as a simple fluid drop or as a solid body with broken fore and aft symmetry. The resultant couple arises from both the straining and swirling motions of the external flow in analogy with bodies of revolution. Owing to the anisotropic resistance of the Janus drop, it is inferred that the drop can migrate lateral to the streamlines of the undisturbed shear flow. The grand resistance matrix and Bretherton constant are reported for a Janus drop with similar internal viscosities.

INFLATING BALLS IS NP-HARD

A collection [Formula: see text] of balls in ℝd is δ-inflatable if it is isometric to the intersection [Formula: see text] of some d-dimensional affine subspace E with a collection [Formula: see text] of (d + δ)-dimensional balls that are disjoint and have equal radius. We give a quadratic-time algorithm to recognize 1-inflatable collections of balls in any fixed dimension, and show that recognizing δ-inflatable collections of d-dimensional balls is NP-hard for δ ≥ 2 and d ≥ 3 if the balls' centers and radii are given by numbers of the form [Formula: see text] where a, …, e are integers.