PRELIMINARY INVESTIGATIONS OF TRANSPORT IN HETEROGENEOUS RANDOM MEDIA

Random media emerge in several applications in reactor physics and safety analysis. Most often, models of stochastic media assume spatial homogeneity, whereas real-world complex materials, such as fuel chunks resulting from core degradation, typically display apparent heterogeneities. In a series of previous works, we have shown that stochastic tessellations can be successfully used in order to describe the material properties of several classes of random media. In this paper we extend these results to the case of heterogeneous random media by using Voronoi tessellations with space-dependent seed distributions, allowing for spatial gradients.

On the Structural Properties of Voronoi Diagrams

A Voronoi diagram is a tessellation technique, which subdivides space into regions in proximity to a given set of objects called seeds. Patterns emerging naturally in biological processes (for example, in cell tissue) can be modelled in a biomimicry process via Voronoi diagrams. As they originate in nature, we investigate the physical properties of such patterns to determine whether they are optimal given the constraints imposed by surrounding geometry and natural forces. This paper describes under what circumstances the Voronoi tessellation has optimal (structural) properties by surveying recent studies that apply this tessellation technique across different scales. To investigate the properties of random and optimized Voronoi tessellations in comparison to a regular tessellation method, we additionally run and evaluate a simulation in Karamba3D, a parametric structural engineering tool for Rhinoceros3D. The novelty of this research lies in presenting a simple and straightforward simulation of Voronoi diagrams and highlighting how and where their advantages over regular tessellations can be exploited by surveying more advanced approaches as found in literature.

Phase behaviour in 2D assemblies of dumbbell-shaped colloids generated under geometrical confinement

Structure formation in experimental monolayers of dumbbell particles is explored and compared to Brownian dynamics simulations. Probability densities of shape factors found in Voronoi tessellations allow for an in-depth analysis of structural motifs.

Modelling the expected probability of correct assignment under uncertainty

When making important decisions such as choosing health insurance or a school, people are often uncertain what levels of attributes will suit their true preference. After choice, they might realize that their uncertainty resulted in a mismatch: choosing a sub-optimal alternative, while another available alternative better matches their needs. We study here the overall impact, from a central planner’s perspective, of decisions under such uncertainty. We use the representation of Voronoi tessellations to locate all individuals and alternatives in an attribute space. We provide an expression for the probability of correct match, and calculate, analytically and numerically, the average percentage of matches. We test dependence on the level of uncertainty and location. We find that the overall mismatch is considerable even for low uncertainty—a possible concern for policy makers. We further explore a commonly used practice—allocating service representatives to assist individuals’ decisions. We show that within a given budget and uncertainty level, the effective allocation is for individuals who are close to the boundary between several Voronoi cells, but are not right on the boundary.

A new design approach for customised medical devices realized by additive manufacturing

The aim of this work is the design of a new customised elbow orthosis completely realized by Additive Manufacturing and the development of generative algorithms for parametric modelling and creation of 3D patterns to be adapted to the CAD model. This work describes a method to perfect the design of a custom elbow orthosis. A reverse engineering approach has been used to digitalize the patient’s arm and the subsequent CAD modelling of the structure of the custom elbow orthosis has been performed. In particular, two algorithms have been implemented for the creation of 3D patterns and Voronoi tessellations. Subsequently, FEM analyses have been carried out to validate the design. Finally, a prototype of the elbow orthosis with Voronoi tessellation has been realized by means of the SLS technology. The results obtained have demonstrated that the implemented algorithm solved the problems found during CAD modelling with conventional software. Furthermore, the results of FEM analyses have validated the design choices. All this allowed realizing the prototype by AM technologies without problems. Moreover, the new proposed modelling approaches allows creating, in an interactive way, patterns on complex surfaces. The results of this research activity present innovative elements of originality in the CAD modelling sector, which can contribute to solving problems related to the modelling for Additive Manufacturing. Furthermore, another innovative characteristic of the device is the use of torsion springs that simulate the action of physiotherapists during exercises for patient rehabilitation.