Single-sphere Models Research Articles

Discrete Element Method Simulation of Wheat Bulk Density as Affected by Grain Drop Height and Kernel Size Distribution

HighlightsThe predicted bulk density of two wheat varieties varied with drop height, similar to the experiments.The percentage composition of three kernel size fractions in the wheat varieties affected the bulk density.Accurate particle shape representation simulated the heap profile better but required longer computational time.The single-sphere model is more practical to use because of its higher accuracy and lower computational cost.Abstract. Grain bulk density varies widely depending on kernel properties and handling practices. The discrete element method (DEM) can model such behavior at the particle level, including wide-ranging interactions with equipment. The objective of this study was to develop a DEM model to predict wheat bulk density as affected by grain drop height and kernel size distribution. The bulk density of two wheat varieties was measured experimentally for a range of drop heights with a modified test weight per bushel apparatus and was simulated in EDEM v2018.1 using single-sphere and five-sphere particle models that accounted for three kernel size fractions. For both particle models, simulations matched the observed behavior, showing a bulk density increase with increasing drop height and bulk density differences between varieties due to different kernel size fractions. The single-sphere particle model predicted the bulk density with higher accuracy than the five-sphere particle model, while the five-sphere model, which more accurately represented the shape of wheat kernels, allowed better simulation of the heap profile at the cost of longer computation time. These particle models can be used to simulate bulk density of wheat under compaction and to improve prediction models of grain pack factor for wheat. Keywords: Bulk density, DEM, Drop height, Size distribution, Wheat.

Effect of anthropogenic factors, landscape structure, land relief, soil and climate on risk of alien plant invasion at regional scale

We compared the effectiveness of explanatory variables representing different environmental spheres on the risk of alien plant invasion. Using boosted regression trees (BRT), we assessed the effect of anthropogenic factors, soil variables, land relief, climate and landscape structure on neophyte richness (NR) (alien plant species introduced after the 15th century). Data on NR were derived from a 2 × 2 km grid covering a total area of 31,200 km2 of the Carpathian massif and its foreground, Central Europe. Each of the examined environmental spheres explained NR, but their explanatory ability varied more than two-folds. Climatic variables explained the highest fraction of deviation, followed by anthropogenic factors, soil type, land relief and landscape structure. The global model, which incorporated crucial variables from all studied environmental spheres, had the best explanatory ability. However, the explained deviation was far smaller than the sum of the deviations explained by the single-sphere models. The global model showed that the deviation that could be explained by variables representing particular spheres, overlapped. The variables representing landscape structure were not included in the global model as they were found to be redundant. Finally, the climatic variables explained a smaller fraction of the deviation than the anthropogenic factors. The partial dependency plots allowed the assessment of the course of dependencies between NR and particular explanatory variables after eliminating the average effect of all other variables. The relationships were usually curvilinear and revealed some values of environmental variables beyond which NR changed considerably.

Towards a realistic prediction of sintering of solid oxide fuel cell electrodes: From tomography to discrete element and kinetic Monte Carlo simulations

The 3-dimensional (3D) particle geometries in sub-micrometric La0.6Sr0.4Co0.2Fe0.8O3−δ powder are obtained by high-resolution focused ion beam scanning electron microscope (FIB-SEM) tomography. Irregularly shaped particles are represented with volume equivalent single spheres (single-sphere model) or clumped multispheres (multi-sphere model), based on their 3D geometries. The discrete element method (DEM) is used to reproduce “virtual” powder packings with multi-sphere and single-sphere models. The DEM-generated virtual microstructures and the FIB-SEM real microstructures are submitted to kinetic Monte Carlo (KMC) simulations of sintering. It is shown that the multi-sphere model predicts more realistic microstructure than the single-sphere model for sintering of La0.6Sr0.4Co0.2Fe0.8O3−δ.

Comparison of three-shell and simplified volume conductor models in magnetoencephalography

Experimental MEG source imaging studies have typically been carried out with either a spherically symmetric head model or a single-shell boundary-element (BEM) model that is shaped according to the inner skull surface. The concepts and comparisons behind these simplified models have led to misunderstandings regarding the role of skull and scalp in MEG. In this work, we assess the forward-model errors due to different skull/scalp approximations and due to differences and errors in model geometries.We built five anatomical models of a volunteer using a set of T1-weighted MR scans and three common toolboxes. Three of the models represented typical models in experimental MEG, one was manually constructed, and one contained a major segmentation error at the skull base. For these anatomical models, we built forward models using four simplified approaches and a three-shell BEM approach that has been used as reference in previous studies. Our reference model contained in addition the skull fine-structure (spongy bone).We computed signal topographies for cortically constrained sources in the left hemisphere and compared the topographies using relative error and correlation metrics. The results show that the spongy bone has a minimal effect on MEG topographies, and thus the skull approximation of the three-shell model is justified. The three-shell model performed best, followed by the corrected-sphere and single-shell models, whereas the local-spheres and single-sphere models were clearly worse. The three-shell model was the most robust against the introduced segmentation error. In contrast to earlier claims, there was no noteworthy difference in the computation times between the realistically-shaped and sphere-based models, and the manual effort of building a three-shell model and a simplified model is comparable. We thus recommend the realistically-shaped three-shell model for experimental MEG work. In cases where this is not possible, we recommend a realistically-shaped corrected-sphere or single-shell model.

Polymers as compressible soft spheres

We consider a coarse-grained model in which polymers under good-solvent conditions are represented by soft spheres whose radii, which should be identified with the polymer radii of gyrations, are allowed to fluctuate. The corresponding pair potential depends on the sphere radii. This model is a single-sphere version of the one proposed in Vettorel et al. [Soft Matter 6, 2282 (2010)], and it is sufficiently simple to allow us to determine all potentials accurately from full-monomer simulations of two isolated polymers (zero-density potentials). We find that in the dilute regime (which is the expected validity range of single-sphere coarse-grained models based on zero-density potentials) this model correctly reproduces the density dependence of the radius of gyration. However, for the thermodynamics and the intermolecular structure, the model is largely equivalent to the simpler one in which the sphere radii are fixed to the average value of the radius of gyration and radii-independent potentials are used: for the thermodynamics there is no advantage in considering a fluctuating sphere size.

Evaluation of multiple-sphere head models for MEG source localization

Magnetoencephalography (MEG) source analysis has largely relied on spherical conductor models of the head to simplify forward calculations of the brain's magnetic field. Multiple- (or overlapping, local) sphere models, where an optimal sphere is selected for each sensor, are considered an improvement over single-sphere models and are computationally simpler than realistic models. However, there is limited information available regarding the different methods used to generate these models and their relative accuracy. We describe a variety of single- and multiple-sphere fitting approaches, including a novel method that attempts to minimize the field error. An accurate boundary element method simulation was used to evaluate the relative field measurement error (12% on average) and dipole fit localization bias (3.5 mm) of each model over the entire brain. All spherical models can contribute in the order of 1 cm to the localization bias in regions of the head that depart significantly from a sphere (inferior frontal and temporal). These spherical approximation errors can give rise to larger localization differences when all modeling effects are taken into account and with more complex source configurations or other inverse techniques, as shown with a beamformer example. Results differed noticeably depending on the source location, making it difficult to recommend a fitting method that performs best in general. Given these limitations, it may be advisable to expand the use of realistic head models.

A theoretical study of uranyl solvation: Explicit modelling of the second hydration sphere by quantum mechanical methods

The inclusion of an explicit second sphere in the hydration of the uranyl ion is investigated by DFT. We study model complexes that contain two water molecules in the second sphere hydrogen-bonded to each water molecule in the first. Compared with single-sphere models, significant changes are observed for the uranium–water first-sphere distance, the uranium-“yl” oxygen distance and the uranyl stretching vibrational frequencies. For each of these observables, agreement with experiment is improved with our new model. Charge transfer to uranyl is substantially enhanced when the second hydration sphere is present. Effects of third and subsequent hydration spheres appear to be small, but the influence of water molecules linked to the apical oxygens by a hydrogen-bonding network is probably not negligible. Models based on a polarizable continuum are less satisfactory, particularly for the vibrational frequencies. The uranyl stretching frequencies are highly correlated with charge transfer from water molecules to the “yl” oxygen atoms and with the uranyl bond length.

Surface area overestimation within three-dimensional digital images and its consequence for skeletal dosimetry.

The most recent methods for trabecular bone dosimetry are based on Monte Carlo transport simulations within three-dimensional (3D) images of real human bone samples. Nuclear magnetic resonance and micro-computed tomography have been commonly used as imaging tools for studying trabecular microstructure. In order to evaluate the accuracy of these techniques for radiation dosimetry, a previous study was conducted that showed an overestimate in the absorbed fraction of energy for low-energy electrons emitted within the marrow space and irradiating the bone trabeculae. This problem was found to be related to an overestimate of the surface area of the true bone-marrow interface within the 3D digital images, and was identified as the surface-area effect. The goal of the present study is to better understand how this surface-area effect occurs in the case of single spheres representing individual marrow cavities within trabecular bone. First, a theoretical study was conducted which showed that voxelization of the spherical marrow cavity results in a 50% overestimation of the spherical surface area. Moreover, this overestimation cannot be reduced through a reduction in the voxel size (e.g., improved image resolution). Second, a series of single-sphere marrow cavity models was created with electron sources simulated within the sphere (marrow source) and outside the sphere (bone trabeculae source). The series of single-sphere models was then voxelized to represent 3D digital images of varying resolution. Transport calculations were made for both marrow and bone electron sources within these simulated images. The study showed that for low-energy electrons (<100 keV), the 50% overestimate of the bone-marrow interface surface area can lead to a 50% overestimate of the cross-absorbed fraction. It is concluded that while improved resolution will not reduce the surface area effects found within 3D image-based transport models, a tenfold improvement in current image resolution would compensate the associated errors in cross-region absorbed fractions for low-energy electron sources. Alternatively, other methods of defining the bone-marrow interface, such as with a polygonal isosurface, would provide improvements in dosimetry without the need for drastic reductions in image voxel size.

Elastic deformation models of Krafla Volcano, Iceland, for the decade 1975 through 1985

The dynamics of the shallow magma reservoir at Krafla Volcano in NE Iceland have been analyzed with three types of elastic models based on over 70 surveys of tilt and displacement made from 1975 to 1985, a period of continuous volcano-tectonic activity. Modeling results are integrated with geophysical and geological information to estimate the position, geometry, and volume change of magma reservoir domains subjected to periodic inflation and deflation. Dominating influences on magma reservoir dynamics are examined in the context of activity in Krafla's associated rift system and the deformation of its caldera from 1975–1985. Rather than the fluid-filled cavity concept of Mogi (1958) and most recent workers, our models are idealized as strained regions with spherical, double-spherical, or general ellipsoidal symmetry. The models are mathematically generalized from that of Mogi (1958) and are derived by inversion of displacements. Model results from different displacement components are remarkably consistent, although models based on vertical displacements typically have errors-of-fit much closer to expected measurement errors than those based on tilt or horizontal displacements. About one half of the double-sphere and ellipsoid models have significantly better fits than single-sphere models. Double-sphere model results are consistent with a 2 to 3 km center-to-center separation of magma storage zones from at least 2 km to 4 km depth by portions of the fissure system, as implied by S-wave attenuation patterns for 1976–1977. However, all models suggest pressurization zones of more limited extent than possible domains of storage inferred from S-wave attenuation. Ellipsoid models typically implied unrealistically shallow depths of magma storage. Caldera inflation rates decreased after January 1978 when the caldera periodically reinflated to its level prior to the initial December 1975 deflation event. From 1975–1980 the volume and duration of inflation between deflation events was strongly correlated with the volume of the previous deflation. After 1980 there was a significant increase in the duration of inflation periods and a decrease in rates of caldera inflation and fissure system widening. Consistent with these results, the magma reservoir is conceptualized as a hot rock mass containing numerous magma chambers and pressure-sensitive conduits connecting the chambers and deep magma sources. Magma is injected into the fissure system at critical pressures determined by the confining stress and rock mass strength. The duration and volume of inflation required to reach a critical pressure threshold is largely dependent on the volume of magma released in the previous deflation. Reduction of the extension rate across the Krafla fissure system after 1980 suggests that extensional forces were also reduced. A resultant rise of confining pressure on the magma reservoir and a reduced capacity of the fissure system to accommodate dike injection in combination would have increased critical stress levels for reservoir deflation and reduced the pressure gradient driving magma supply from deep sources.