Search Results (6)

Surface blending is an important topic in geometric modelling and is widely applied in computer-aided design and creative industries to create smooth transition surfaces. Among various surface blending methods, partial differential equation (PDE)-based surface blending has the advantages of effective shape control and exact satisfaction of blending boundary constraints. However, it is not easy to solve partial differential equations subjected to blending boundary constraints. In this paper, we investigate how to solve PDEs analytically and develop an analytical PDE-based method to achieve surface blending with $C^2$ continuity. Taking advantage of elementary functions identified from blending boundary constraints, our proposed method first changes blending boundary constraints into a linear combination of the identified elementary functions. Accordingly, the functions for blending surfaces are constructed from these elementary functions, which transform sixth-order partial differential equations for $C^2$ surface blending into sixth-order ordinary differential equations (ODEs). We investigate the analytical solutions of the transformed sixth-order ordinary differential equations subjected to corresponding blending boundary constraints. With the developed analytical PDE-based method, we solve $C^2$ continuous surface blending problems. The surface blending example presented in this paper indicates that the developed method is simple and easy to use. It can be used to effectively control the shape of blending surfaces and at the same time exactly satisfy $C^2$ continuous blending boundary constraints. Full article

Runaway electron (RAE) generation in high-pressure gases is an important physical phenomenon that significantly influences discharge shapes and properties of initiated plasma. The diffuse discharges formed due to RAEs in the air and other gases at atmospheric pressure find wide applications. In the present review, theoretical and experimental results that explain the reason for RAE occurrence at high pressures are analyzed, and recommendations are given for the implementation of conditions under which the runaway electron beam (RAEB) with the highest current can be obtained at atmospheric pressure. The experimental results were obtained using subnanosecond, nanosecond, and submicrosecond generators, including those specially developed for runaway electron generation. The RAEBs were recorded using oscilloscopes and collectors with picosecond time resolution. To theoretically describe the phenomenon of continuous electron acceleration, the method of physical kinetics was used based on the Boltzmann kinetic equation that takes into account the minimum but sufficient number of elementary processes, including shock gas ionization and elastic electron scattering. The results of modeling allowed the main factors to be established that control the RAE appearance, the most important of which is electron scattering on neutral atoms and/or molecules. Theoretical modeling has allowed the influence of various parameters (including the voltage, pressure, gas type, and geometrical characteristics of the discharge gap) to be taken into account. The results of the research presented here allow RAE accelerators with desirable parameters to be developed and the possibility of obtaining diffuse discharges to be accessed under various conditions. The review consists of the Introduction, five sections, the Conclusion, and the References. Full article

Elementary Geometrical Shape (EGS) models present an alternative approach to detect in vivo migration of total hip arthroplasty using model-based Roentgen Stereophotogrammetric Analysis (mbRSA). However, its applicability for an irregular-shaped femoral stem and the reliability of this mbRSA approach has not been proven so far. The aim of this study is to assess the effect of multi-rater and an anatomically shaped femoral stem design onto resulting implant to bone migration results. The retrospective analysis included 18 clinical cases of anatomically shaped stem with 10-year RSA follow-ups. Three raters repeatedly measured all RSA follow-ups for evaluating the rater equivalence and intra-rater reliability. The results proved the equivalence between different raters for mbRSA using EGS models (mbRSA-EGS), hence it simplified the investigation of rater reliability to intra-rater reliability. In all in-plane migration measurements, mbRSA-EGS shows good intra-rater reliability and small intra-rater variability (translation: <0.15 mm; rotation: <0.18 deg). However, the reliability is worse in the out-of-plane measurements, especially the cranial-caudal rotation (intra-rater variability: 0.99–1.81 deg). Overall, mbRSA-EGS can be an alternative approach next to surface models while the in-plane migration of femoral stem (e.g., the implant subsidence for loosening prediction) have more research interested than other directions. Full article

The pore geometry and topology properties of pore space in rocks are significant for a better understanding of the complex hydrologic and elastic properties. However, geometry and topology information about the sandstone pore structures is not fully available. In this study, we obtained the topological and geometrical pore parameters from a representative elementary volume (REV) for fluid flow in sandstone samples. For comparison, eight types of sandstones with various porosities were studied based on the X-ray micro-computed tomography technique. In this study, the REV size was selected based on the parameters from the respective pore network models (PNM), not just the porosity. Our analysis indicates that despite different porosity, all the sandstone samples have highly triangular-shaped pores and a high degree of pore structural isotropy. The high porosity group sandstones exhibit wider ranges of pore sizes than the low porosity group sandstones. Compared to the high porosity group sandstones, the low porosity group sandstones samples showing a higher global aspect ratio, indicating some pores exist in the form of bottlenecks. The pore topological properties of different sandstones show a high dependence of the porosity. The high porosity group sandstones obtain large coordination numbers, large connectivity densities and low tortuosities. The results from this study will help better understand the complex pore structure and the fluid flow in sandstone. Full article

Model-based Roentgen stereophotogrammetric analysis (RSA) using elementary geometrical shape (EGS) models allows migration measurement of implants without the necessity of additional attached implant markers. The aims of this study were: (i) to assess the possibility of measuring potential head–taper movement in THA in vivo using model-based RSA and (ii) to prove the validity of measured head–taper migration data in vitro and in vivo. From a previous RSA study with a 10 years follow-up, retrospectively for n = 45 patients head–taper migration was calculated as the relative migration between femoral ball head and taper of the femoral stem using model-based RSA. A head–taper migration of 0.026 mm/year can be detected with available RSA technology. In vitro validation showed a total migration of 268 ± 11 µm along the taper axis in a similar range to what has been reported using the RSA method. In vivo, a proof for interchangeable applicability of model-based RSA (EGS) and standard marker-based RSA methods was indicated by a significant deviation within the migration result after 12-month follow-up for all translation measurements, which was significantly correlated to the measured head–taper migration (r from 0.40 to 0.67; p < 0.05). The results identified that model-based RSA (EGS) could be used to detect head–taper migration in vivo and the measured movement could be validated in vitro and in vivo as well. Those findings supported the possibility of applying RSA for helping evaluate the head–taper corrosion related failure (trunnionosis). Full article

A produce gas respiration model and fruit-stack geometric digital generation approach is used with commercial CFD software (ANSYS CFX^TM) to conduct shape-level simulations of the fluid flow, heat and respiration processes that occur during the storage of produce, with the ultimate purpose of providing detailed information that can be used to develop closure coefficients for volume-averaged simulations. A digital generation procedure is used to develop an accurate representation of the shapes of the different produce. The produce shapes are then implemented into a discrete element modelling tool to generate a randomly-distributed stack of produce in a generic container, which is then utilized as a representative elementary volume (REV) for simulations of airflow and respiration. Simulations are first conducted on single pieces of produce and compared to a recently published experimental data for tomatoes and avocadoes to generate coefficients for the respiration model required for the shape-level simulations on the REV. The results of the shape-level simulation are then processed to produce coefficients that can be used for volume-averaged (porous-continuum-level) calculations, which are much more practical for simulations of large areas of storage comprised of hundreds or thousands of boxes of different commodities. The results show that the multi-level approach is a viable means for developing the simulation parameters required to study refrigeration, ripening and storage/transport of produce. Full article