Determining the shape of agricultural materials using spherical harmonics

Semi-analytical models of non-spherical particle shapes using optimised spherical harmonics

The Discrete Element Method/Modelling (DEM) is a well-elaborated method for modelling the dynamical behaviour of particulate systems. The term “DEM” refers to a family of numerical methods for computing the motion of a large number of particles such as molecules, grains, and rocks. Despite it was originally pioneered for rock mechanics, DEM is being developed for wide-range of applications in most engineering domains. The representation of particle shape geometry in DEM is crucial, which has a direct impact on the computational performance of the methods and on the dynamical behaviour of particulate systems. Most applications are limited in time of simulation to simple particle shapes due to the increase in computation with increasing complexity of geometry. Currently, many methods for particle shape representation are proposed due to irregular shape of the real particles. This paper reviews the research and methods of particle shapes modelling for 2D-DEM over the last three decades. This includes classification of particle shapes models in the different categories, applicable to numerous engineering disciplines that use DEM.

A 3D shape descriptor based on spherical harmonics through evolutionary optimization

In any DEM simulation, the chosen particle shape will greatly influence the simulated material behaviour. For a specific material, e.g. railway ballast, it remains an open question how to model the particle shape, such that DEM simulations are computationally efficient and simulation results are in good accordance with measurements. While DEM shape modelling for railway ballast is well addressed in the literature, approaches mainly aim at approximating the stones’ actual shape, resulting in rather complex and thus inefficient particle shapes. In contrast, very simple DEM shapes will be constructed, clumps of three spheres, which aim to approximate shape descriptors of the considered ballast material. In DEM simulations of the packing behaviour, a set of clump shapes is identified, which can pack at porosities observed at track sites, as well as in lab tests. The relation between particle shape (descriptors) and obtained packing (characteristic) is investigated in a correlation analysis. The simulated packing’s porosity is strongly correlated to four shape descriptors, which are also strongly correlated among each other. Thus, to derive simple shape models of a given particle shape, matching one of these shape descriptors, might be a good first step to bring simulated porosities closer to measured ones. The conducted correlation analysis also shows that packing’s coordination number and isotropic fabric are correlated to more shape descriptors, making it more difficult to estimate the effect of particle shape on these quantities.Graphic abstract

Despite great strides in developing physically motivated models for void growth, shape evolution and coalescence, a suitable treatment for void nucleation remains an open question. Accurate modeling of void nucleation is difficult within a Gurson-based framework due to the intrinsic assumption that the material does not contain any second-phase particles. Consequently, the nucleation models employed in these constitutive models are overly simplistic as the particle shape, composition, stress state and load-sharing are neglected, lumped into a single calibration parameter (Beremin 1981) or indirectly accounted for in a phenomenological manner (Chu and Needlman 1980). The lack of progress in developing physically sound nucleation models has not been for lack of effort but a result of the inherently complex nature of the nucleation process. Void nucleation is very difficult to capture experimentally since it is a relatively random and instantaneous event that cannot be captured in-situ without the aid of high resolution x-ray tomography. Additionally, the local stress state near a particle of interest is typically unknown, as well as the particle composition and mechanical properties. The nucleation mechanism can occur by debonding or particle cracking and is influenced by the particle size, shape, composition, distribution, strain rate and temperature. From an engineering perspective, one can clearly see the attraction in adopting a phenomenological nucleation model whose parameters can be adjusted to give good agreement with the experiment data. Nevertheless, there is ample opportunity to improve the physical foundation of the current nucleation models, especially in regards to percolation modeling.

Spherical harmonic (SH) has shown excellent advantages in terms of accuracy and efficiency in the retrieval of complete three-dimensional shapes. However, since the spherical function directly takes the shape centroid as the global reference point, the SH features depend heavily on the central position. In this context, the features become no longer reliable in the query of incomplete shapes that may cause erratic centroid. In this work, we propose a novel shape descriptor, namely spherical harmonic energy over the Gaussian sphere (SHE-GS), especially for the incomplete shape retrieval. Firstly, all unit normal vectors on the shape surface are mapped to points on a Gaussian sphere, which has the constant center. Secondly, kernel density estimation is used to establish a Gaussian Sphere Model (GSM) to describe the density change of these mapping points. Finally, the shape descriptor is generated by applying an SH transformation on the model. According to the way of GSM being regarded as a surface model or a volume model, we have separately designed two specific algorithm implementations. Experimental results, on two engineering shape sets containing artificially defective shapes, indicate that the proposed method outperforms other traditional methods also defined in the sphere space for incomplete shape retrieval. The superiority is verified for both similar objects in the same category or the single specific object of query.

<p>Aerosols are important atmospheric constituents that impact the Earth's radiative balance and climate. The detailed knowledge of the aerosol optical properties is required for a comprehensive analysis of the impacts of aerosols on climate. Mie theory is often used in satellite and ground-based retrieval algorithms to account for atmospheric mineral dust. However, the approximations used in Mie theory are often not appropriate for mineral dust and can lead to errors in the optical properties modeling. Analytic models based on Rayleigh theory that account for particle shapes can offer significant advantages when used to model infrared (IR) extinction of mineral dust. Here, the IR optical properties of some components of mineral dust, authentic dust samples and minerals processed with organic acids were investigated. Detailed characterization of the particles through online and offline methods of analysis that include IR extinction spectroscopy, micro-Raman spectroscopy and scanning electron microscopy was performed. Analysis of the IR extinction spectra and spectral simulations showed that the positions of the peaks and the shapes of the bands of the IR characteristic features are not well simulated by Mie theory in any of the samples studied. The resonance peaks were consistently shifted relative to the experimental spectrum in the Mie simulation. Rayleigh model solutions derived for different particle shapes better predicted the peak positions and band shapes of experimental spectra. To fill the gaps in the refractive index data for atmospherically relevant organic compounds in the IR region optical properties of atmospherically relevant carboxylic acids and humic-like substances using the IR extinction spectra and size distributions measured in the laboratory were determined.</p><p>In addition to properties of mineral dust this dissertation focuses on properties of sea spray aerosol. Chemical and elemental composition of individual sea spray aerosol particles were studies using micro-Raman spectroscopy, mass-spectrometry and X-ray spectroscopy to provide insights into the biochemical processes that give rise to classes of organic molecules that make up these aerosol particles. The results suggested that degradation of biota (bacteria and diatoms) present in sea water led to lipopolysaccharides and extracellular polymeric substances that further degraded down to carbohydrates and fatty acids. Solubility of the resulting organic species seemed to play a role in their transfer to the aerosol phase. Furthermore, water uptake and hygroscopic growth of multi-component particles were studied. Understanding the interactions of water with atmospheric aerosols is crucial for determining their size, physical state, reactivity, and therefore for aerosol interactions with electromagnetic radiation and clouds. It was determined that particles composed of ammonium sulfate with succinic acid and of mixture of chlorides typical for marine environment show size dependent hygroscopic behavior. Microscopic analysis of the distribution of components within the aerosol particles showed that the observed size dependence is due to the differences in the mixing state. The composition and water uptake properties of sea spray aerosol particles were also measured during a phytoplankton bloom. The results showed that water uptake properties were directly related to the chemical composition of the particles and hygroscopicity decreased with increase in the fraction of water insoluble organic matter emitted during phytoplankton bloom. Finally, multiple methods of particle size, phase and shape analysis were compared and the results showed that the techniques that operate under ambient conditions provide the most relevant and robust measurement of particle size. Additionally, several storage methods for substrate deposited aerosol particles were evaluated and it was determined that storing samples at low relative humidity led to irreversible changes due to sample dehydration while sample freezing and thawing leads to irreversible changes due to phase changes and water condensation. Therefore it is suggested that samples used for single-particles analysis should be stored at ambient laboratory conditions, or near conditions which they were collected, in order to preserve the sample phase and hydration state.</p><p>The results presented in this dissertation provide insight into physicochemical properties of atmospheric aerosols and help us better understand the role of aerosol particles in the Earth's atmosphere.</p>

Physicochemical characterisation of the lactoperoxidase system powders: comparison of two drying techniques

The effects of particle compositions, particle shapes, and oxidation temperatures on the electrical properties of conductive adhesives have been investigated. Silver‐coated copper powders and uncoated copper powders with spherical and flake‐shaped particles are oxidized at temperatures such as 30, 175, 240, 300°C and 350°C for 2 h and dispersed in an epoxy matrix. The results of this study indicate that the electrical properties of the conductive adhesives are strongly affected by the particle compositions and oxidation temperatures and only slightly affected by the particle shapes. Silver‐coated copper powders show significantly greater oxidation resistance than uncoated copper powders. To understand how silver‐coated copper powders show such oxidation resistance, they are analyzed by the techniques of thermogravimetric analysis (TGA), X‐ray diffraction (XRD), and Auger spectroscopy to observe how metal oxides such as AgO, Cu2O, and CuO affect the electrical properties of the conductive adhesives. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 2045–2053, 2004

Synthesized spherical nano metal particles produced in aqueous solution have applications in printing technologies. However, an alternate method for achieving a percolation threshold is to mix the spherical shape of the particles and become net-shaped copper oxide with a minimum weight percent of particles. In this study, before reducing to copper metal, copper oxide was synthesized first without the chelating agent for achieving a net shape and copper metal nano particles were synthesized with the chelating agent, bypassing the process of creating copper oxide. Potassium sodium tartrate was the chelating agent used to control the shape of copper metal nano particles in an alkaline solution. Various concentrations of potassium sodium tartrate changed the shape of these particles from web-like at low concentrations to needlelike and more spherical at higher concentrations. Potassium sodium tartrate restrained the coordination bonds around the metal particles, controlling the shape to be more spherical. Altering the pH in absence of potassium sodium tartrate changed the conditions for the formation of particles according to the Eh-pH diagram for copper, forming net-shaped copper oxide particles when the pH was 12-13 and a cubic shape when the pH was 5-6. The composition of the nano particles in both cases was confirmed using examination by XRD. These shapes have the potential to possess favorable electrical and thermal properties as predicted by bond percolation and the percolation theory.

In this paper, the size and shape characteristics of desert sand particles were quantitatively investigated via a combination of X-CT scanning and spherical harmonics functions. The size characteristics of the desert sand particles were evaluated via the Length (L), Width (W), Thickness (T), and Volume equivalent spherical diameter (VESD). The average value of the VESD for the desert sand particle is 118.2 μm, which is much smaller than that of commonly used fine aggregate, and more than 90% particles are smaller than 150 μm. The overall shape of the desert sand particles was assessed with two aspect ratios: elongation (EI) and flatness (FI). Desert sand particles were classified into four categories: spheroid-shaped, oblate-shaped, prolate-shaped, and blade-shaped. The sphericity (S) values of the desert sand particles were distributed in a wider range, with an average sphericity of 0.85, much larger than that of commonly used fine aggregates. Through a combination of aspect ratios and sphericity analysis, it can be roughly concluded that the desert sand particles appear in more irregular shapes, but with relatively smooth surface morphology and less convex or concave parts.

One of the major goals of computer vision is the development of flexible and efficient methods for shape representation. This is true, especially for non-rigid 3D shapes where a great variety of shapes are produced as a result of deformations of a non-rigid object. Modeling these non-rigid shapes is a very challenging problem. Being able to analyze the properties of such shapes and describe their behavior is the key issue in research. Also, considering photometric features can play an important role in many shape analysis applications, such as shape matching and correspondence because it contains rich information about the visual appearance of real objects. This new information (contained in photometric features) and its important applications add another, new dimension to the problem's difficulty. Two main approaches have been adopted in the literature for shape modeling for the matching and retrieval problem, local and global approaches. Local matching is performed between sparse points or regions of the shape, while the global shape approaches similarity is measured among entire models. These methods have an underlying assumption that shapes are rigidly transformed. And Most descriptors proposed so far are confined to shape, that is, they analyze only geometric and/or topological properties of 3D models. A shape descriptor or model should be isometry invariant, scale invariant, be able to capture the fine details of the shape, computationally efficient, and have many other good properties. A shape descriptor or model is needed. This shape descriptor should be: able to deal with the non-rigid shape deformation, able to handle the scale variation problem with less sensitivity to noise, able to match shapes related to the same class even if these shapes have missing parts, and able to encode both the photometric, and geometric information in one descriptor. This dissertation will address the problem of 3D non-rigid shape representation and textured 3D non-rigid shapes based on local features. Two approaches will be proposed for non-rigid shape matching and retrieval based on Heat Kernel (HK), and Scale-Invariant Heat Kernel (SI-HK) and one approach for modeling textured 3D non-rigid shapes based on scale-invariant Weighted Heat Kernel Signature (WHKS). For the first approach, the Laplace-Beltrami eigenfunctions is used to detect a small number of critical points on the shape surface. Then a shape descriptor is formed based on the heat kernels at the detected critical points for different scales. Sparse representation is used to reduce the dimensionality of the calculated

Particle shape is known for its significant influence on the engineering properties of coarse grain soil. But it remains difficult to quantify how the different scales of shape properties will affect the macroscopic soil behavior individually. This study aims to select independent shape descriptors at different geometrical scales and evaluate the influence of particle shape irregularities on the particle packing of coarse-grain soil. With the aid of the digital image technique for 2D image acquisition of coarse grain soil particles, the shape properties were firstly quantified by the presented shape descriptors. Statistical analysis was performed to evaluate the independence of each shape descriptor and the most common independent descriptors; elongation, roundness, and texture signature were put forward. The proposed shape descriptors were then used to classify the collected particles and establish the particle shape library. The influence of each scale shape property on particle packing was systematically investigated using discrete element method (DEM) simulations of uncompacted void content test with predefined particles selected from the shape library. The simulated particles with specified shape properties were selected from the corresponding shape library. The numerical simulation results indicated that elongation and roundness significantly contribute to particle packing, while the influence of texture signature can be neglected due to its small variation in nature. The larger elongation and smaller roundness values were proved to increase the uncompacted porosity of coarse grain soil.

This paper introduces a novel 4D shape descriptor to match temporal surface sequences. A quantitative evaluation based on the receiver-operator characteristic (ROC) curve is presented to compare the performance of conventional 3D shape descriptors with and without using a time filter. Feature- based 3D shape descriptors including shape distribution (Osada et al., 2002 ), spin image (Johnson et al., 1999), shape histogram (Ankest et al., 1999) and spherical harmonics (Kazhdan et al., 2003) are considered. Evaluation shows that filtered descriptors outperform unfiltered descriptors and the best performing volume-sampling shape-histogram descriptor is extended to define a new 4D shape-flow descriptor. Shape-flow matching demonstrates improved performance in the context of matching time-varying sequences which is motivated by the requirement to connect similar sequences for animation production. Both simulated and real 3D human surface motion sequences are used for evaluation.

We propose a novel approach for 3D shape analysis of <i>heterochromatin foci</i> in 3D confocal light microscopy images of cell nuclei. The approach is based on a 3D parametric intensity model and uses a spherical harmonics (SH) expansion. The model parameters including the SH coefficients are automatically determined by least squares fitting of the model to the image intensities. Based on the obtained SH coefficients, a shape descriptor is determined, which enables distinguishing heterochromatin foci based on their 3D shape to characterize compaction states of heterochromatin. Our approach has been successfully applied to real static and dynamic 3D microscopy image data.