Geometric Sphere Research Articles

Interdisciplinary Studies of Jet Systems using Euler Methodology and Computational Fluid Dynamics Technologies

This study aims to conduct interdisciplinary research using computerized solutions to inventive problems in fluidics. The chosen direction of work relates to the scientific search for new opportunities for extremal control of the thrust vector within a complete geometric sphere (with the range of rotation angle change for the thrust vector being ±180° in any direction). This study assesses the prospects for the emergence of patentable innovative solutions for maneuverable unmanned vehicles. One of the most urgent tasks is to increase the process efficiency in forming fluid medium flow, expanding opportunities for controlling this flow parameter. The research uses an interdisciplinary approach with simulation modeling. The authors of the paper reveal new possibilities for using an ejector with two curved mixing chambers to create special jet units. Calculations (CFD) have confirmed the performance of the simulator ejector when controlling the thrust vector with 90° and 180° rotation. Manufacturing physical micromodels used additive technologies to allow simulation modeling under laboratory conditions. Using “data mining” methods, it was shown for the first time that, based on Euler’s ideas and methodology, it is possible to create a new methodology for teaching and solving inventive problems. The research results apply to power engineering and unmanned vehicles. Some results of scientific studies can be used to create special computer programs working together with artificial intelligence to create advanced techniques and technologies. Doi: 10.28991/HIJ-2023-04-04-01 Full Text: PDF

Solving Innovative Problems of Thrust Vector Control Based on Euler's Scientific Legacy

This study aims to develop an interdisciplinary approach to solving innovative thrust vector control problems. The methodology involves the development of a working hypothesis about the ejection process when using a controlled nozzle to deflect the thrust vector (velocity vector) in any direction within a complete geometric sphere. When developing the working hypothesis, a multilateral analysis of individual facts and scientific and technical information is performed using tools in the "big data" area, assessing opportunities to apply the "Foresight" methodology for predicting the development of fluidics. The authors propose new mathematical models to describe the thrust vector in the distribution of the mass flow rate of the fluid medium between flow channels. Patents for inventions support the novelty of scientific results that reveal new opportunities for more active development of fluidics as applied to simple and complex jet systems with low and extremely high energy density in flows. The proposed methodology rests on a modern computer base and is a logical continuation and development of well-known Euler’s works. The computer simulation of multiflow jet devices mainly focuses on power engineering, production, and processing of hydrocarbons. Some results of this research work, including patented design developments and calculation methods, also apply to developing robotics, unmanned vehicles, and programable jet systems. The authors attribute further development of the interdisciplinary approach for solving inventive problems to the use of different AI options. Doi: 10.28991/CEJ-2023-09-11-017 Full Text: PDF

Thrust Vector Control within a Geometric Sphere, and the Use of Euler's Tips to Create Jet Technology

This study aims to study the issues of choosing promising directions for the development of jet technology with the creation of energy-conserving technologies. The purpose of this article is to study the issues of choosing promising directions for the development of jet technology with the creation of energy-saving. Methodological approaches have been developed for solving inventive problems within the framework of training modern designers-inventors. A new patentable jet unit has been developed and presented, which makes it possible to control the thrust vector within a complete geometric sphere (when the thrust vector is capable of deviating to any angle ranging from +180° to -180°). For the first time, demonstration versions of a nozzle apparatus capable of realizing such flow reversals through annular channels are shown. The results of computer modeling of nozzle devices are focused on energy, production, and processing of hydrocarbons when distributing energy flows at process facilities. The individual results of the ongoing work can also be used in other industries, for instance, in the creation of small-sized high-speed unmanned vehicles for search and rescue operations. Proposals have been prepared to improve the methodology for solving inventive problems as part of the development of Leonard Euler’s ideas. Doi: 10.28991/CEJ-2023-09-10-011 Full Text: PDF

Computational Fluid Dynamics (CFD) Simulation of Mesh Jet Devices for Promising Energy-Saving Technologies

This paper discusses the development of mesh jet devices for hybrid turbines, including developing Euler's ideas, and considers a new patented version of a mesh jet device designed to create guiding devices for turbines. The research methods are based on simulations using CFD and additive technologies. An intermediate conclusion is that a new scientific direction for the study and creation of mesh jet control systems has been formed as part of developing Euler's ideas. Calculation methods showed possible improvements in the performance of jet devices, including the use of curved tubes proposed by Euler to create turbines. This study shows that at the nozzle or mixing chamber outlet, the jet can deflect by an angle from +180° to -180° within the geometric sphere. This study also shows that the scientific groundwork prepared by Euler is not yet fully understood. The ongoing research mainly focuses on creating multi-mode jet devices designed for control systems for mesh turbomachines. Here, power consumption from an external source can be reduced to save energy. Some results of ongoing studies can also be applied in other industries (for example, when creating hybrid propulsion systems or propulsors). The scientific novelty of this work consists of improving the design methodology of jet machinery and turbomachines. Doi: 10.28991/CEJ-2022-08-12-06 Full Text: PDF

Analysis of interpenetrating metal ceramic composite structures using an enhanced random sequential absorption microstructure generation algorithm

In this paper, we present the analysis of an interpenetrating metal ceramic composite structure. We introduce a new generation algorithm for the modeling of interpenetrating composite microstructures with connected, spherical cavities embedded into an open-porous foam structure. The method uses a geometric ansatz and is designed to create structures of special topology, as the investigated metal ceramic composite structures consisting of a connected AlSi10Mg phase showing spherical shapes embedded into an Al2O3 preform. Based on the introduced enhanced random sequential absorption approach, the generated microstructures yield numerical insights into the material that are not accessible by experimental techniques. The generated microstructures are compared to structures reconstructed from experimental CT scan data considering microstructural features and mechanical behavior. We show that the proposed method is able to generate statistically equivalent microstructures by using only a small number of statistical descriptors. The numerical formulation is validated using compression tests including plastic yielding in the aluminum and damage progression in the ceramic phase. Both the composite material and the pure ceramic preform are considered in this analysis, and good agreement is found between reconstructed and generated microstructures. Furthermore, the observations reveal the importance of the local geometrical sphere arrangement with respect to the mechanical behavior. A validation with experimental results is presented and it is shown that the model predicts microstructural properties and gives meaningful insights into the structural and material interplay. Finally, we discuss the potential of the method for the investigation of failure mechanisms.

A New Method of Central Axis Extracting for Pore Network Modeling in Rock Engineering

Characterizing internal microscopic structures of porous media is of vital importance to simulate fluid and electric current flow. Compared to traditional rock mechanics and geophysical experiments, digital core and pore network modeling is attracting more interests as it can provide more details on rock microstructure with much less time needed. The axis extraction algorithm, which has been widely applied for pore network modeling, mainly consists of a reduction and burning algorithm. However, the commonly used methods in an axis extraction algorithm have the disadvantages of complex judgment conditions and relatively low operating efficiency, thus losing the practicality in application to large-scale pore structure simulation. In this paper, the updated algorithm proposed by Palágyi and Kuba was used to perform digital core and pore network modeling. Firstly, digital core was reconstructed by using the Markov Chain Monte Carlo (MCMC) method based on the binary images of a rock cutting plane taken from heavy oil reservoir sandstone. The digital core accuracy was verified by comparing porosity and autocorrelation function. Then, we extracted the central axis of the digital pore space and characterize structural parameters through geometric transformation technology and maximal sphere method. The obtained geometric parameters were further assigned to the corresponding nodes of pore and throat on the central axis of the constructed model. Moreover, the accuracy of the new developed pore network model was measured by comparing pore/throat parameters, curves of mercury injection, and oil-water relative permeability. The modeling results showed that the new developed method is generally effective for digital core and pore network simulation. Meanwhile, the more homogeneity of the rock, which means the stronger “representative” of binary map the rock cutting plane, the more accurate simulated results can be obtained.

Development and Prototyping of Jet Systems for Advanced Turbomachinery with Mesh Rotor

This article presents the research results that aim to develop promising mesh turbomachines equipped with jet control systems. The turbomachines operating in difficult conditions in oil and gas production are mainly considered. At the same time, some research results can be used in other production branches, including power engineering and transport. Three-dimensional models for computer simulation of net turbines and jet control systems were developed. Prototypes and micromodels were created to test the performance of mesh turbines and jet control systems using additive technologies. A methodological approach is proposed to create a classification of jet control systems considering their design and technological features. In the course of numerical experiments, the extreme conditions of fluid and gas outflow through a nozzle equipped with a velocity vector control system, in the control range of adjustment of the velocity vector deflection angle from + 90o to -90o within a geometric hemisphere, have been considered for the first time. It was also shown that when using a dual-channel nozzle, there are possibilities to adjust the velocity vector angle (thrust vector) in the range of + 180o to -180owithin the geometric sphere. Compared with the known variants, the control range of the velocity vector angle is increased by nine times. These calculated data are presented in addition to the previously published results of physical laboratory experiments. Preliminary results of numerical experiments show the possibility of creating a new theory in the field of mesh turbines and jet systems. Patents support the novelty of the developed technical solutions. Doi: 10.28991/esj-2021-01311 Full Text: PDF

Application of an explainable AI method in classification of functional foot conditions

In human motion analysis predictive or functional methods are used to estimate the location of the hip joint centre (HJC). It has been shown that the Harrington regression equations (HRE) and geometric sphere fit (GSF) method are the most accurate predictive and functional methods, respectively. To date, the comparative reliability of both approaches has not been assessed. The aims of this study were to (1) compare the reliability of the HRE and the GSF methods, (2) analyse the impact of the number of thigh markers used in the GSF method on the reliability, (3) evaluate how alterations to the movements that comprise the functional trials impact HJC estimations using the GSF method, and (4) assess the influence of the initial guess in the GSF method on the HJC estimation. Fourteen healthy adults were tested on two occasions using a three-dimensional motion capturing system. Skin surface marker positions were acquired while participants performed quite stance, perturbed and non-perturbed functional trials, and walking trials. Results showed that the HRE were more reliable in locating the HJC than the GSF method. However, comparison of inter-session hip kinematics during gait did not show any significant difference between the approaches. Different initial guesses in the GSF method did not result in significant differences in the final HJC location. The GSF method was sensitive to the functional trial performance and therefore it is important to standardize the functional trial performance to ensure a repeatable estimate of the HJC when using the GSF method.

Symmetries and Geometries of Qubits, and Their Uses

The symmetry SU(2) and its geometric Bloch Sphere rendering have been successfully applied to the study of a single qubit (spin-1/2); however, the extension of such symmetries and geometries to multiple qubits—even just two—has been investigated far less, despite the centrality of such systems for quantum information processes. In the last two decades, two different approaches, with independent starting points and motivations, have been combined for this purpose. One approach has been to develop the unitary time evolution of two or more qubits in order to study quantum correlations; by exploiting the relevant Lie algebras and, especially, sub-algebras of the Hamiltonians involved, researchers have arrived at connections to finite projective geometries and combinatorial designs. Independently, geometers, by studying projective ring lines and associated finite geometries, have come to parallel conclusions. This review brings together the Lie-algebraic/group-representation perspective of quantum physics and the geometric–algebraic one, as well as their connections to complex quaternions. Altogether, this may be seen as further development of Felix Klein’s Erlangen Program for symmetries and geometries. In particular, the fifteen generators of the continuous SU(4) Lie group for two qubits can be placed in one-to-one correspondence with finite projective geometries, combinatorial Steiner designs, and finite quaternionic groups. The very different perspectives that we consider may provide further insight into quantum information problems. Extensions are considered for multiple qubits, as well as higher-spin or higher-dimensional qudits.

Cellular S-value evaluation based on real human cell models using the GATE MC package

Exploring the spatial distribution of the energy loss of ionising radiation at the subcellular level is indispensable for evaluating the radiobiological effects of targeted radionuclide therapy accurately. Believing that S-values are important for obtaining the target dose, the Committee on Medical Internal Radiation Dose (MIRD) proposed a method to obtain the cellular dosimetric parameter. However, most available data on cellular S-values were calculated based on simple geometric models, such as ellipsoids or spheres, which do not accurately reflect biological reality. To investigate the influence of the cellular model on S-values, calculations were performed for two kinds of polygon-surface phantom models of realistic, individual human cells, the lung epithelial cell model (the B2B Phantom model) and the hepatocyte model (the Liver Phantom model), using the Monte Carlo (MC) software package GATE. To analyse the influence of cell geometry on the final S-value, the differences in the S-values between the realistic cell models and simple geometric sphere and ellipsoid models with similar volumes were calculated and compared for six different combinations of source and target regions. The irradiation conditions were 0.01–1.10 MeV monoenergetic electron sources and the Auger electronic therapy nuclides Ga-67, Tc-99m, In-111, I-125 and Tl-201, which are commonly used in nuclear medicine. The S-values calculated in this study are different from the results of the simple geometry models proposed by previous researchers. Two more precise polygon-surface phantom models of realistic, individual human cells were used, which provided more accurate information about the cell dose and will be very useful for the diagnostic application of radiotherapy in the future.

Simple and reliable boundary detection for meshfree particle methods using interval analysis

We present two novel algorithms for detecting boundary particles in 2D and 3D domains that are suitable for meshfree particle methods in Computational Fluid Dynamics. We combine a robust purely geometric sphere covering test based on interval analysis with an adaptive spatial subdivision of the sphere associated with a given particle. The methods are simple, fast, and easy to code. We report comparisons against state-of-the-art boundary detection methods in free-surface flow problems to demonstrate the effectiveness and accuracy of our approaches.

Kinematics of Spherical Robots Rolling over 3D Terrains

Although the kinematics and dynamics of spherical robots (SRs) on flat horizontal and inclined 2D surfaces are thoroughly investigated, their rolling behavior on generic 3D terrains has remained unexplored. This paper derives the kinematics equations of the most common SR configurations rolling over 3D surfaces. First, the kinematics equations for a geometrical sphere rolling over a 3D surface are derived along with the characterization of the modeling method. Next, a brief review of current mechanical configurations of SRs is presented as well as a novel classification for SRs based on their kinematics. Then, considering the mechanical constraints of each category, the kinematics equations for each group of SRs are derived. Afterward, a path‐tracking method is utilized for a desired 3D trajectory. Finally, simulations are carried out to validate the developed models and the effectiveness of the proposed control scheme.

Robust shape extraction for automatically segmenting raw LiDAR data of outdoor scenes

ABSTRACTLight detection and ranging (LiDAR) scanning has become a prevalent technique for digitalizing outdoor scenes with three-dimensional (3D) point clouds. An automatic segmentation of the LiDAR data is important for understanding and reconstructing the outdoor scenes. However, it is still a challenging task due to complex and various objects in the outdoor scenes and some scanning drawbacks in the LiDAR data. Observing that most of the objects, such as the ground, road, roof, and facade, can be locally described with a group of geometric shapes, e.g. plane, sphere, and cylinder, we propose an automatic method to segment raw LiDAR data by robustly extracting the shapes in this paper. Firstly, our method divides the raw LiDAR data into a number of supervoxels considering the geometric and spectral consistencies of LiDAR data. Secondly, we robustly extract shapes from each supervoxels using a random sample consensus (RANSAC)-based method and evaluates and optimises the extracted shapes with a density loss estimation technique. Finally, our method outputs the segmentation result by merging the extracted shapes into a group of complete shapes, each of them represents a meaningful object in the outdoor scene. Experiments show that the method is efficient and robust for extracting most of the shapes in the outdoor scenes from a given raw LiDAR point cloud, and no preprocessing is required.

Entropy and Geometric Objects.

Different notions of entropy can be identified in different scientific communities: (i) the thermodynamic sense; (ii) the information sense; (iii) the statistical sense; (iv) the disorder sense; and (v) the homogeneity sense. Especially the “disorder sense” and the “homogeneity sense” relate to and require the notion of space and time. One of the few prominent examples relating entropy to both geometry and space is the Bekenstein-Hawking entropy of a Black Hole. Although this was developed for describing a physical object—a black hole—having a mass, a momentum, a temperature, an electrical charge, etc., absolutely no information about this object’s attributes can ultimately be found in the final formulation. In contrast, the Bekenstein-Hawking entropy in its dimensionless form is a positive quantity only comprising geometric attributes such as an area A—the area of the event horizon of the black hole, a length LP—the Planck length, and a factor 1/4. A purely geometric approach to this formulation will be presented here. The approach is based on a continuous 3D extension of the Heaviside function which draws on the phase-field concept of diffuse interfaces. Entropy enters into the local and statistical description of contrast or gradient distributions in the transition region of the extended Heaviside function definition. The structure of the Bekenstein-Hawking formulation is ultimately derived for a geometric sphere based solely on geometric-statistical considerations.

Reliability of functional and predictive methods to estimate the hip joint centre in human motion analysis in healthy adults

In human motion analysis predictive or functional methods are used to estimate the location of the hip joint centre (HJC). It has been shown that the Harrington regression equations (HRE) and geometric sphere fit (GSF) method are the most accurate predictive and functional methods, respectively. To date, the comparative reliability of both approaches has not been assessed. The aims of this study were to (1) compare the reliability of the HRE and the GSF methods, (2) analyse the impact of the number of thigh markers used in the GSF method on the reliability, (3) evaluate how alterations to the movements that comprise the functional trials impact HJC estimations using the GSF method, and (4) assess the influence of the initial guess in the GSF method on the HJC estimation. Fourteen healthy adults were tested on two occasions using a three-dimensional motion capturing system. Skin surface marker positions were acquired while participants performed quite stance, perturbed and non-perturbed functional trials, and walking trials. Results showed that the HRE were more reliable in locating the HJC than the GSF method. However, comparison of inter-session hip kinematics during gait did not show any significant difference between the approaches. Different initial guesses in the GSF method did not result in significant differences in the final HJC location. The GSF method was sensitive to the functional trial performance and therefore it is important to standardize the functional trial performance to ensure a repeatable estimate of the HJC when using the GSF method.

Validation of hip joint center localization methods during gait analysis using 3D EOS imaging in typically developing and cerebral palsy children

Localization of the hip joint center (HJC) is essential in computation of gait data. EOS low dose biplanar X-rays have been shown to be a good reference in evaluating various methods of HJC localization in adults. The aim is to evaluate predictive and functional techniques for HJC localization in typically developing (TD) and cerebral palsy (CP) children, using EOS as an image based reference. Eleven TD and 17 CP children underwent 3D gait analysis. Six HJC localization methods were evaluated in each group bilaterally: 3 predictive (Plug in Gait, Bell and Harrington) and 3 functional methods based on the star arc technique (symmetrical center of rotation estimate, center transformation technique and geometrical sphere fitting). All children then underwent EOS low dose biplanar radiographs. Pelvis, lower limbs and their corresponding external markers were reconstructed in 3D. The center of the femoral head was considered as the reference (HJCEOS). Euclidean distances between HJCs estimated by each of the 6 methods and the HJCEOS were calculated; distances were shown to be lower in predictive compared to functional methods (p<0.0001). Contrarily to findings in adults, functional methods were shown to be less accurate than predictive methods in TD and CP children, which could be mainly due to the shorter thigh segment in children. Harrington method was shown to be the most accurate in the prediction of HJC (mean error≈18mm, SD=9mm) and quasi-equivalent to the Bell method. The bias for each method was quantified, allowing its correction for an improved HJC estimation.

Which method of hip joint centre localisation should be used in gait analysis?

Accurate localisation of the hip joint centre is required to obtain accurate kinematics, kinetics and musculoskeletal modelling results. Literature data showed that conclusions drawn from synthetic data, adult normal subjects and cerebral palsy children may vary markedly. This study investigated the localisation accuracy of the hip joint centre against EOS. The EOS system allowed us to register the hip joint centres with respect to the skin markers on standing subjects. A comprehensive set of predictive and functional calibration techniques were tested. For the functional calibration techniques, our results showed that algorithm, range of motion and self-performance of the movement were factors significantly affecting the results. Best results were obtained for comfortable range and self-performance of the movement. The best method in this scenario was the functional geometrical sphere fitting method which localised the hips 1.1cm from the EOS reference in average and 100% of the time within 3cm. Worst results for functional calibration methods occurred when the movement was assisted with a reduced range of movement. The best method in this scenario was the Harrington et al. regression equations since it does not rely on a functional calibration movement. Harrington et al. equations put the hips 1.7cm from the EOS reference in average and 97% of the time within 3cm. We conclude that accurate localisation of the hip joint centre is possible in gait analysis providing that method to localise the hip joint centres are adapted to the population studied: functional geometrical sphere fitting when hip calibration movements are not a problem and Harrington et al. predictive equations otherwise.

Survey of Formal Methods of Hip Joint Center Calculation in Human Studies

Functional hip joint center (HJC) calculation involves recording movements of femur relative to acetabulum through markers placed on skin around thigh and pelvis. This non-invasive method of finding hip joint center involves either fitting a geometric sphere onto marker trajectories or coordinate transformation techniques which find the point with least movement in local frame with respect to global frame. A survey study by Ehrig et al has evaluated both categories of formal methods through virtual simulation and also contributed another algorithm known as “SCoRE”(Systematic center of rotation estimation). This algorithm gives an accuracy of 0.5cm with 20 degree range of motion (ROM) and claimed to be most accurate with both segments in motion. This paper reviews the studies using this method to calculate hip joint center. Also a review of studies using Ultrasound as a validation method has been provided. This forms the basis to the possibility of using Ultrasonic sensors to be placed along with markers to measure the relative movement of markers with respect to bone in vivo. This paper provides a survey of studies performed on human subjects either in vivo (live humans) or ex vivo (cadaver) to help an experimenter or researcher pick the best relevant technique matching their experimentation requirement including soft tissue artifact factor.

Intraobserver and interobserver reliability of the three-dimensional ultrasound imaging of female urethral sphincter using a translabial technique

The aim of the study was to assess the interobserver and intraobserver reliability of translabial 3D ultrasound imaging of the urethral sphincter in non-pregnant nulliparous asymptomatic women. A study using a 3D translabial ultrasound on thirty-seven women was performed. Urethral sphincter parameters were measured by the same experienced clinician 2weeks apart. Multiple axial cross-sectional areas at 1-mm distances were used to calculate urethral sphincter volumes. The same measurements were carried out by a second experienced clinician to assess the interobserver reliability. We found an excellent intraobserver reliability (interclass correlation coefficient, ICC >0.8) and good interobserver reliability (ICC >0.6). The described technique using multiple axial cross-sectional areas at set distances and a translabial approach is a reliable and accurate tool in the evaluation of the urethral sphincter. This should be used instead of mathematical formulas as the urethral sphincter is not a uniform geometrical sphere. The technique and values reported may help clinicians in the assessment of women with lower urinary tract disorders.

Hip joint centre localization: Evaluation on normal subjects in the context of gait analysis

Locating the position of the hip joint centre (HJC) is an important part of lower limb modeling for gait analysis. Regression equations have been used in the past but a range of functional calibration methods are now available. This study compared the accuracy of HJC localization from two sets of regression equations and five different functional calibration methods against three dimensional ultrasound (3-DUS) on a population of 19 able bodied subjects. Results show that the geometric sphere fitting technique was the best performer with mean absolute distance error of 15mm and 85% of measurements being within 20mm. The results also show that widely used regression equations perform particularly badly whereas the most recent equations performed very closely to the best functional method with a mean absolute error of 16mm and 88% of measurements being within 20mm. In vivo results are more than an order of magnitude worse than predictions using synthetic data suggesting that additional work is required before soft tissue artifact can be effectively modelled.