Heat conduction from irregular surfaces

The effect of irregularities on the rate of heat conduction from a two-dimensional isothermal surface into a semi infinite medium is considered. The effect of protrusions, depressions, and surface roughness is quantified in terms of the displacement of the linear temperature profile prevailing far from the surface. This shift, coined the displacement length, is designated as an appropriate global measure of the effect of the surface indentations incorporating the particular details of the possibly intricate geometry. To compute the displacement length, Laplace's equation describing the temperature distribution in the semi-infinite space above the surface is solved numerically by a modified Schwarz-Christoffel transformation whose computation requires solving a system of highly non-linear algebraic equations by iterative methods, and an integral equation method originating from the single-layer integral representation of a harmonic function involving the periodic Green's function. The conformal mapping method is superior in that it is capable of handling with high accuracy a large number of vertices and intricate wall geometries. On the other hand, the boundary integral method yields the displacement length as part of the solution. Families of polygonal wall shapes composed of segments in regular, irregular, and random arrangement are considered, and pre-fractal geometries consisting of large numbers of vertices are analyzed. The results illustrate the effect of wall geometry on the flux distribution and on the overall enhancement in the rate of transport for regular and complex wall shapes

Characterization of surface and bulk features of SLM parts

An experiment-analytical procedure based on the building of an object in severe atmosphere resistant steel by SLM is proposed. The complex shape was investigated with the sectioning and laboratory observation of the physical object. The study evidenced the need to get a variable layer thickness to follow double curvature complex shapes. In particular the key variable in the process is the melt bath dimension by which the metal powder assumes by solidification the required global geometry. It was observed that the bath detected mainly in terms of the area of section tends to decrease when approaching to the surface of the physical model where the complex geometry needs to be described. Relationships describing the bath area behaviour and correlations between surface roughness and internal bath dimensions were found and proposed in detail. The surface roughness is highly correlated with the bath area in the zones of the section approaching the surface

A Method for the Perceptual Optimization of Complex Visualizations

A common problem in visualization applications is the display of one surface overlying another. Unfortunately, it is extremely difficult to do this clearly and effectively. Stereoscopic viewing can help, but in order for us to be able to see both surfaces simultaneously, they must be textured, and the top surface must be made partially transparent. There is also abundant evidence that all textures are not equal in helping to reveal surface shape, but there are no general guidelines describing the best set of textures to be used in this way. What makes the problem difficult to perceptually optimize is that there are a great many variables involved. Both foreground and background textures must be specified in terms of their component colors, texture element shapes, distributions, and sizes. Also to be specified is the degree of transparency for the foreground texture components. Here we report on a novel approach to creating perceptually optimal solutions to complex visualization problems and we apply it to the overlapping surface problem as a test case. Our approach is a three-stage process. In the first stage we create a parameterized method for specifying a foreground and background pair of textures. In the second stage a genetic algorithm is applied to a population of texture pairs using subject judgments as a selection criterion. Over many trials effective texture pairs evolve. The third stage involves characterizing and generalizing the examples of effective textures. We detail this process and present some early results

Generalised coherent point drift for group-wise registration of multi-dimensional point sets

In this paper we propose a probabilistic approach to group-wise registration of unstructured high-dimensional point sets. We focus on registration of generalised point sets which encapsulate both the positions of points on surface boundaries and corresponding normal vectors describing local surface geometry. Richer descriptions of shape can be especially valuable in applications involving complex and intricate variations in geometry, where spatial position alone is an unreliable descriptor for shape registration. A hybrid mixture model combining Student’s t and Von-Mises-Fisher distributions is proposed to model position and orientation components of the point sets, respectively. A group-wise rigid and non-rigid registration framework is then formulated on this basis. Two clinical data sets, comprising 27 brain ventricle and 15 heart shapes, were used to assess registration accuracy. Significant improvement in accuracy and anatomical validity of the estimated correspondences was achieved using the proposed approach, relative to state-of-the-art point set registration approaches, which consider spatial positions alone

Spherical Harmonics Models and their Application to non-Spherical Shape Particles

The dissertation investigates spherical harmonics method for describing a particle shape. The main object of research is the non-spherical shape particles. The purpose of this dissertation is to create spherical harmonics model for a non-pherical particle. The dissertation also focuses on determining the suitability of the lowresolution spherical harmonics for describing various non-spherical particles. The work approaches a few tasks such as testing the suitability of a spherical harmonics model for simple symmetric particles and applying it to complex shape particles. The first task is formulated aiming to test the modelling concept and strategy using simple shapes. The second task is related to the practical applications, when complex shape particles are considered. The dissertation consists of introduction, 4 chapters, general conclusions, references, a list of publications by the author on the topic of the dissertation, a summary in Lithuanian and 5 annexes. The introduction reveals the investigated problem, importance of the thesis and the object of research, describes the purpose and tasks of the thesis, research methodology, scientific novelty, the practical significance of results and defended statements. The introduction ends in presenting the author’s publications on the topic of the dissertation, offering the material of made presentations in conferences and defining the structure of the dissertation. Chapter 1 revises the literature: the particulate systems and their processes, shapes of the particles and methods for describing the shape, shape indicators. At the end of the chapter, conclusions are drawn and the tasks for the dissertation are reconsidered. Chapter 2 presents the modelling approach and strategies for the points of the particle surface, spherical harmonics, the calculation of the expansion coefficients, integral parameters and curvature and also the conclusions. Chapters 3 and 4 analize the modelling results of the simple and complex particles. At the end of the both chapters conclusions are drawn. 5 articles focusing on the topic of the dissertation have been published: two articles – in the Thomson ISI register, one article – in conference material and scientific papers in Thomson ISI Proceedings data base, one article – in the journal quoted by other international data base, one article – in material reviewed during international conference. 8 presentations on the subject of the dissertation have been given in conferences at national and international levels

Material flow during the extrusion of simple and complex cross-sections using FEM

This paper deals with the extrusion of rod and shape sections and uses a 3D finite element model analysis (FEM) to predict the effect of die geometry on maximum extrusion load. A description of material flow in the container is considered in more detail for rod and shape sections in order to fully comprehend the transient conditions occurring during the process cycle. A comparison with experiments is made to assess the relative importance of some extrusion parameters in the extrusion process and to ensure that the numerical discretisation yields a realistic simulation of the process. The usefulness and the limitation of FEM are discussed when modelling complex shapes. Results are presented for velocity contours and shear stress distribution during the extrusion process. It is shown that for most of the shapes investigated, the material making up the extrudate cross-sections originates from differing regions of virgin material within the billet. The outside surface of the extrudate originates from the material moving along the dead metal zone (DMZ) and the core of the extrudate from the central deformation zone. The FE program appears to predict all the major characteristics of the flow observed macroscopically

A flexible geometric model for leaf shape descriptions with high accuracy

Accurate assessment of canopy structure is crucial in studying plant-environment interactions. The advancement of functional-structural plant models (FSPM), which incorporate the 3D structure of individual plants, increases the need for a method for accurate mathematical descriptions of leaf shape. A model was developed as an improvement of an existing leaf shape algorithm to describe a large variety of leaf shapes. Modelling accuracy was evaluated using a spatial segmentation method and shape differences were assessed using principal component analysis (PCA) on the optimised parameters. Furthermore, a method is presented to calculate the mean shape of a dataset, intended for obtaining a representative shape for modelling purposes. The presented model is able to accurately capture a large range of single, entire leaf shapes. PCA illustrated the interpretability of the parameter values and allowed evaluation of shape differences. The model parameters allow straightforward digital reconstruction of leaf shapes for modelling purposes such as FSPMs

Microelectronics miniaturization and fractal electronic frontiers

The intergrain ceramic structures are very complex and difficult to describe by using traditional analytical methods. In this study, in order to establish grain shapes of sintered ceramics, new approach on correlation between microstructure and properties of doped BaTiO3 -ceramics based on fractal geometry has been developed. BaTiO3 ceramics doped with CeO2, Bi2O3, Fe2O3, CaZrO3 Nb2O5, MnCO3 , La2O3, Er2O3, Yb2O3 and Ho2O3, were prepared using conventional solid state procedure and sintered at 1350°C. The sintered specimens microstructure was investigated by SEM-5300 and capacitance has been done using LCR-metra Agilent 4284A. The fractal modeling method using a reconstruction of microstructure configurations, like grains or intergranular contacts shapes has been successfully done. Furthermore, the area of grains surface was calculated by using fractal correction which expresses the grains surface irregularity through fractal dimension. For better and deeper the ceramics material microstructure characterization the Voronoi model and mathematical statistics calculations, are applied, also. The fractal nature for ceramics structure analysis providing a new ideas for modeling the grain shape and relations between the BaTiO3 ceramic structure and dielectrical properties and new frontier for higher integration on electronic circuits. The presented results indicate that fractal method for structure ceramics analysis creates a new approach for describing, predicting and modeling the grain shape and relations between the BaTiO3 -ceramic structure and dielectric and generally electric and microelectronics properties