The Hanging Drape: a Vertex Analogy

We present a novel, rigidly folding vertex inspired by the shape of the simplest hanging drape. Fold lines in the vertex correspond to pleats and ridges in the drape, and are symmetrically arranged to enable synchronised at folding of facet pairs. We calculate the folded rotation angles exactly using a spherical image specialised for inextensible vertex folding. We show that the vertex shape is bounded by a pair of conical surfaces whose apex semi-angles directly correspond with fold-line rotations, which expresses a geometrical equivalence between the external shape and internal folding motion of the vertex. We discuss how the vertex viz. drape perform as a novel type of conical defect based on its spherical image topography; and we highlight the meaning of bistable behaviour for the vertex, in analytical- and practical terms.

Sensitivity of Racing Tire Sliding Energy to Major Setup Changes: An Estimate Based on Standard Sensors

Understanding the amount of energy a tire is subjected to is one of the key elements to perform in motorsport competitions, especially in Formula 1 feeder categories, where the number of tires is limited over the race weekend to contain costs. This forces teams to use worn tires towards the end of the event. Therefore, tires are usually chosen only relying on their external shape or based on the kilometers traveled. Moreover, being aware of how a setup change impacts tires can be a breakthrough in tire management, especially in tracks where tire wear is limiting the overall performance. This paper provides a scientific method aimed at helping race engineers in tire management to maintain a high performance level through the entire race weekend.

Brazil's Comparative Advantages and Specialization Dynamics in Agri-food Trade

In the last decades Brazil has become a global agri-food powerhouse. The article interrogates the shape and its stability of revealed comparative advantages in 46 of its agri-food products for the period 1995-2017. The results support the argument that the Brazil's agri-food trade was formed by comparative advantages of specific agri-food sectors. The results show that the external shape of agri-food specialization has strengthened, first since early 2000s and second when the trade shifted more towards China. The pattern was stable according revealed comparative (dis)advantage of particular products, more changes occurred in each product's score and in ranking of products. Products without initial comparative advantage seem to remain uncompetitive whilst the products with strong initial comparative advantage continue to be competitive. The persistence in distribution has increased. This suggests, the shape of Brazil's revealed comparative advantage in agri-food trade has evolved towards its finite structure (ceteris paribus).

Three-dimensional topology optimization model to simulate the external shapes of bone

Elucidation of the mechanism by which the shape of bones is formed is essential for understanding vertebrate development. Bones support the body of vertebrates by withstanding external loads, such as those imposed by gravity and muscle tension. Many studies have reported that bone formation varies in response to external loads. An increased external load induces bone synthesis, whereas a decreased external load induces bone resorption. This relationship led to the hypothesis that bone shape adapts to external load. In fact, by simulating this relationship through topology optimization, the internal trabecular structure of bones can be successfully reproduced, thereby facilitating the study of bone diseases. In contrast, there have been few attempts to simulate the external structure of bones, which determines vertebrate morphology. However, the external shape of bones may be reproduced through topology optimization because cells of the same type form both the internal and external structures of bones. Here, we constructed a three-dimensional topology optimization model to attempt the reproduction of the external shape of teleost vertebrae. In teleosts, the internal structure of the vertebral bodies is invariable, exhibiting an hourglass shape, whereas the lateral structure supporting the internal structure differs among species. Based on the anatomical observations, we applied different external loads to the hourglass-shaped part. The simulations produced a variety of three-dimensional structures, some of which exhibited several structural features similar to those of actual teleost vertebrae. In addition, by adjusting the geometric parameters, such as the width of the hourglass shape, we reproduced the variation in the teleost vertebrae shapes. These results suggest that a simulation using topology optimization can successfully reproduce the external shapes of teleost vertebrae. By applying our topology optimization model to various bones of vertebrates, we can understand how the external shape of bones adapts to external loads.

Determination of the parameters of an ellipsoidal electrode tip for treating agricultural animals using UHF – therapy methods

The use of non-medicamentous means of treating farm animals presupposes the presence of not only an ultra-high frequency electromagnetic radiation generator but also a rectal emitter, which is directly inserted into the animal's rectum. The effectiveness of the treatment carried out using UHF therapy methods largely depends on the shape of the emitter tip. When choosing the external shape of the emitter tip in the form of half of an ellipsoid of revolution, it becomes necessary to optimize the parameters of this ellipsoid. The goal of optimization is to minimize the resistance force of the living tissue of the animal when a cylindrical emitter with a tip is inserted into the rectum.