Geometry Approach Research Articles

A novel freemium code SAND (v1.0) for generation of randomly packed beds

The main current approaches for generation of the packed bed models are based on rigid body dynamics (RBD) and Newton's laws (discrete element methods - DEM). This paper deals with the development and analysis of a novel code based on analytical geometry approach for the packed bed generation. The architecture and main algorithms of the novel code are described and clarified. The parameters of the packed bed generated via the novel code are compared with experimental data and packed beds generated via Blender (RBD), Yade (DEM). The novel code demonstrates many advantages, such as good correlation with experimental data, no overlaps between pellets in the packed bed, and a low computational time for packed bed generation. The packed bed model can be directly exported in .step format. Other advantages are also demonstrated and clarified. The novel code is attached to this paper and can be freely used by engineers and scientists.

Analysis of free vibration characteristics of non-uniform graphene-reinforced axially functionally graded nanocomposite beam

This paper presents the changing effect on the free vibration behaviour of graphene-reinforced axially functionally graded nanocomposite (Gr-AFG) beam with non-uniform geometry. A generalized finite element method (GFEM) and Euler Bernoulli’s theory have been used for parametric analysis and the subsequent formulation of governing differential equations. The proposed approach (for uniform geometry) has been compared with the existing gradation schemes, e.g. ‘X’, ‘O’, ‘UD’, ‘A’, and ‘V’, and found to be well in agreement. Furthermore, a new harmonic ‘M’ function has been introduced in the current analysis, and the non-uniformity in the geometry has been implemented by varying the cross-section along the axial direction of the beam. The ‘M’ gradation in the axial direction results in an increase in the natural frequency with an increase in the slenderness ratio for the first four modes. Compared to uniform geometry, the non-uniform AFG-M beam with exponential geometry variation shows a lower fundamental frequency for all values of the slenderness ratio of the beam with an increase in the value of the exponent under C–S and C–C end support conditions.

Optimal AP deployment in cell-free massive MIMO systems with LoS/NLoS transmissions: A stochastic geometry approach

Optimal AP deployment in cell-free massive MIMO systems with LoS/NLoS transmissions: A stochastic geometry approach

Geography-Aware Optimal UAV 3D Placement for LOS Relaying: A Geometry Approach

Geography-Aware Optimal UAV 3D Placement for LOS Relaying: A Geometry Approach

Correlating Capillary Pressure and Resistivity Index for Carbonate Reservoir

Capillary pressure is a significant parameter in characterizing and modeling petroleum reservoirs. However, costly laboratory measurements may not be sufficiently available in some cases. The problem amplifies for carbonate reservoirs because relatively enormous capillary pressure curves are required for reservoir study due to heterogeneity. In this work, the laboratory measurements of capillary pressure and formation resistivity index were correlated as both parameters are functions of saturation. Forty-one core samples from an Iraqi carbonate reservoir were used to develop the correlation according to the hydraulic flow units concept. Flow zone indicator (FZI) and Pore Geometry and Structure (PGS) approaches were used to identify the reservoir hydraulic flow units. The experimentally derived correlations can be used to predict capillary pressure from resistivity, which is widely available from well-logs. FZI and PGS rock typing methods were applied to characterize the reservoir rock types. For both methods, the log-log plot of Leverett J-function and capillary pressure versus resistivity index for each rock type represent a power-law model relationship between these parameters. Despite the good permeability-porosity prediction results, the FZI approach did not yield a good correlation between J and I. PGS resulted in a better performance in terms of both permeability-porosity prediction and Pc with I correlation because PGS honors the pore geometry and structure relationship with the mean hydraulic radius more than FZI. This work introduces a new correlating approach that aims to assist in reservoir characterization and simulation.

Crack layer modeling of butt-fusion joints induced slow crack growth in high-density polyethylene pipes

The design and reliability of high-density polyethylene (HDPE) pipes can be dictated by the damage tolerance of their butt-fusion joints. A slow crack growth (SCG) model based on the crack layer theory for HDPE pipes internal and external circumferential and butt-fusion joints cracks is developed to investigate the discontinuous SCG behavior and lifetime tf variations. Using the developed model, the discontinuous SCG patterns, jump lengths and lifetime tf can be accurately simulated. In addition, the effects of pipes standard dimension ratio, internal pressure, and temperature on the SCG behavior and tf are investigated. Compared to pipe cracks, it was found that butt-fusion induced SCG can reduce the pipe tf > 60 %. Unlike longitudinal cracks, tf of external circumferential cracks, were found shorter than the internal ones, mandating an earlier evaluation. The new SCG model shows good accuracy with the experimental results. The same substitute geometry approach used can be followed for othercomplex designs, which aids in establishing a fundamental methodology for more realistic lifetime predictions.

MSO-GP: 3-D segmentation of large and complex conjoined tree structures

Robust segmentation of large and complex conjoined tree structures in 3-D is a major challenge in computer vision. This is particularly true in computational biology, where we often encounter large data structures in size, but few in number, which poses a hard problem for learning algorithms. We show that merging multiscale opening with geodesic path propagation, can shed new light on this classic machine vision challenge, while circumventing the learning issue by developing an unsupervised visual geometry approach (digital topology/morphometry). The novelty of the proposed MSO-GP method comes from the geodesic path propagation being guided by a skeletonization of the conjoined structure that helps to achieve robust segmentation results in a particularly challenging task in this area, that of artery-vein separation from non-contrast pulmonary computed tomography angiograms. This is an important first step in measuring vascular geometry to then diagnose pulmonary diseases and to develop image-based phenotypes. We first present proof-of-concept results on synthetic data, and then verify the performance on pig lung and human lung data with less segmentation time and user intervention needs than those of the competing methods.

Analytic Modeling for Grant-Free Transmission in Cell-Free Massive MIMO: A Stochastic Geometry Approach

Analytic Modeling for Grant-Free Transmission in Cell-Free Massive MIMO: A Stochastic Geometry Approach

Optical characterization of a solar concentrating dish system

Solar dishes concentrate the quasi-collimated sun light towards a focal point. Typically, the optical characterization consists of experimental flux map measurements and Monte-Carlo ray-tracing (MCRT) simulations, which are fitted based on experimental data and serve for the prediction of the distribution of the irradiation in receivers or reactors. However, the MCRT simulations usually rely on idealized mirror geometries (i.e. parabolic mirrors), neglecting the actual dish geometry resulting from its construction method (such as petals, facets or segments). Thus, the parameter fitting might yield unrealistic parameters and local radiative flux peaks (“hot spots”), which are often experimentally detected behind the focal plane, cannot be predicted. Here, we characterized the 7m diameter solar dish at EPFL comprising 27 petals with a nominal focal length of 3.8 m and a rim angle of 50.3°. The measured peak concentration was 1781 suns and the received integrated solar power was 20.0 kW over an 18 cm diameter spot. We proposed an advanced geometry approach for the MCRT model considering the curvature of the dish, i.e. geometries mathematically described by a parabola with an exponent not equal, but close to 2. The advanced geometry approach was then applied for predicting experimentally measured flux distribution in focal and off-focus planes. The fitted reflectivities were 70% and 86% for the idealized and advanced geometry approach, respectively. The idealized geometry approach found an unrealistically low value whereas the advanced geometry approach’s value was within 1% of the manufacturer’s specification. The advanced geometry approach predicted a parabola exponent of 1.94, which emphasizes that the best geometry to describe the solar dish deviates from a perfect paraboloid. We conclude that MCRT models should consider non-perfect parabolic geometries for solar dishes in order to obtain more realistic values for the fitted parameters.

Ultra Reliable Low Latency Routing in LEO Satellite Constellations: A Stochastic Geometry Approach

Ultra Reliable Low Latency Routing in LEO Satellite Constellations: A Stochastic Geometry Approach

Algebra environments II. Algebra homomorphisms and derivations

Algebra environments provide requisites for studying objects of interest in operator algebra theory, group representation theory, spin geometry, Clifford analysis, and several variable operator theory. The concept is analyzed by developing an algebraic geometry approach. Specific algebraic sets, called structure manifolds of algebra environments, and their Zariski tangent spaces are introduced and described by using as critical tools derivations on algebras. Structure manifolds of tensor environments in particular yield spaces of algebra homomorphisms. Consequently, such spaces could be investigated as algebraic manifolds. Related issues include characterizations of their Zariski tangent spaces and of derivations that preserve algebra homomorphisms.

Covert Communication of IRS-Assisted Wireless Networks With Stochastic Geometry Approach

Covert Communication of IRS-Assisted Wireless Networks With Stochastic Geometry Approach

Imidazole Based Novel Schiff Base: Synthesis, Characterization, Quantum Chemical Calculations, In Silico Investigation of ADMEt Properties and Molecular Docking Simulations against VEGFR2 Protein

The potential drug candidate novel Schiff base, 2-(((3-(4-methyl-1H-imidazol-1-yl)-5-(trifluoromethyl)phenyl)imino)methyl)phenol (MITPIM) was synthesized by the reaction of salicylaldehyde and 3-(4-methyl-1H-imidazol-1-yl)-5-(trifluoromethyl)aniline which is the precursor of the nilotinib molecule used in the cancer treatment. It was characterizated by using spectroscopic techniques such as 1H-NMR, 13C-NMR, 19F-NMR, FT-IR and UV-Vis. DFT computational technique was used for further investigation. DFT/B3LYP method and the 6-311G(d,p) basis set were used to determine optimized geometry. Then by using optimized geometry and DFT approach three-dimensional molecular electrostatic potential (MEP), vibration frequencies, NMR chemical shift values, HOMOs-LUMOs and molecular orbital energies were calculated. It was observed that the experimental and theoretical datas were in good agreement. The ADME and toxicity properties were investigated by using online servers. According to the results, it was concluded that the MITPIM has low toxicity and high oral bioavailability. Molecular docking simulations of the MITPIM with VEGFR2 protein (PDB ID: 2XIR) were investigated. According to molecular docking studies, the binding energy of the complex formed by the MITPIM with VEGFR2 protein (PDB ID: 2XIR) was −9.34 kcal/mol and the value was close to nilotinib’s binding score which was -9.69 kcal/mol. Molecular docking and ADMEt results shown that the newly synthesized MITPIM has the potential to be drug.

Effect of particle shape produced from wet ball milling on magnetic separation concentrate by fractal dimension

The particle shape in mineral processing is a function of the comminution mechanism. In this study, the effect of the concentrate particle shape, obtained from the wet ball milling and the low-intensity magnetic separator on magnetite ore is investigated by the fractal geometry approach. The particle shape is described by the fractal dimension, calculated by the divider method. The variable parameters of grinding time, loading ratio, and solid weight percentage were studied here. The fractal dimensions of the particles are obtained between 1.12 and 1.42. When the grinding time is increased from 45 to 65 minutes, the fractal dimension and product grades are increased from 1.19 to 1.42 and from 65.61 to 67.70%, respectively. By increasing the loading ratio from 14% to 22%, the fractal dimension and the product’s grades are increased from 1.17 to 1.38 and from 64.80 to 66.68%, respectively. By increasing the solid weight percentage from 35 to 55%, the fractal dimension and product grades are decreased from 1.32 to 1.12 and from 65.51 to 64.65%, respectively. The results show that the particle shape has a significant effect on the performance of the magnetic separator. It is the findings indicate a direct relationship between the particle fractal dimension and the grade of magnetic separation products.

Optimization of 3D Passive Acoustic Mapping Image Metrics: Impact of Sensor Geometry and Beamforming Approach.

Three-dimensional passive acoustic mapping (PAM) with matrix arrays typically suffers from high demands on the receiving electronics and high computational load. In our study, we investigated, both numerically and experimentally, the influence of matrix array aperture size, element count, and beamforming approaches on defined image metrics. With a numerical Vokurka model, matrix array acquisitions of cavitation signals were simulated. In the experimental part, two 32 × 32 matrix arrays with different pitches and aperture sizes were used. After being reconstructed into 3D cavitation maps, defined metrics were calculated for a quantitative comparison of experimental and numerical data. The numerical results showed that the enlargement of the aperture from 5 to 40 mm resulted in an improvement of the full width at half maximum (FWHM) by factors of 6 and 13 (in lateral and axial dimension, respectively). A larger array sparsity influenced the point spread function (PSF) only slightly, while the grating lobe level (GLL) remained more than 12 dB below the main lobe. These results were successfully experimentally confirmed. To further reduce the GLL caused by array sparsity, we adapted a non-linear filter from optoacoustics for use in PAM. In combination with the delay, multiply, sum, and integrate (DMSAI) algorithm, the GLL was decreased by 20 dB for 64-element reconstructions, resulting in levels that were identical to the fully populated matrix reconstruction levels.

Bridging the gap between annular and can-annular acoustic spectra.

In the literature on thermoacoustic instabilities in combustors, a distinction is typically made between annular and can-annular systems because these are the most common gas turbine architectures. In reality, however, annular combustors typically feature discretely symmetric elements, such as burner tubes, and can-annular combustors feature an azimuthally symmetric plenum at the turbine inlet. To better understand the general case in between the annular and can-annular extremes, we analyze the acoustic spectrum of an idealized can-annular combustion chamber with variable geometry, where the length of the axial gap distance beyond the ends of the cans-hence, the coupling strength-may be adjusted. For small gap sizes, the geometry approaches a set of isolated combustor cans, whereas for large gap sizes, it approaches that of pure annular systems. We present two theoretical models based on Bloch wave theory and validate them against finite-element simulations of the Helmholtz equation. We demonstrate that the azimuthal modes transform into the eigenmodes of an annular chamber as the gap is fully opened, and we show that below a certain frequency, all the modes in between the can-annular and annular limits can be classified by their axial and azimuthal mode orders.

Information geometry approach to model reduction

Information geometry combines the fields of information theory and differential geometry. In information geometry, a model is interpreted as a Riemannian manifold, referred to as the model manifold, where distance on the model manifold corresponds to statistical distinguishability. Boundaries on the model manifold are reduced-order models where a parameter or parameter combination is taken to an extreme limit and drops out of the model. Therefore, by locating the model manifold boundaries, simpler models with fewer parameters can be obtained. A model reduction algorithm which exploits this insight is the Manifold Boundary Approximation Method, or MBAM, which locates manifold boundaries by calculating geodesics on the surface of the model manifold. This can be done iteratively to find increasingly simple reduced models. We demonstrate this method for model reduction using the Pekeris waveguide transmission loss model. A machine learned surrogate model for the Pekeris waveguide is constructed so that the necessary derivatives for calculating geodesics can be easily obtained using automatic differentiation. [Work supported by the Office of Naval research Grant N00014-21-S-B001.]

On the Peak AoI of UAV-Assisted IoT Networks: A Stochastic Geometry Approach

On the Peak AoI of UAV-Assisted IoT Networks: A Stochastic Geometry Approach

Optimizing energy efficiency in heterogeneous networks: An integrated stochastic geometry approach with novel sleep mode strategies and QoS framework.

The quest for energy efficiency (EE) in multi-tier Heterogeneous Networks (HetNets) is observed within the context of surging high-speed data demands and the rapid proliferation of wireless devices. The analysis of existing literature underscores the need for more comprehensive strategies to realize genuinely energy-efficient HetNets. This research work contributes significantly by employing a systematic methodology, utilizing This model facilitates the assessment of network performance by considering the spatial distribution of network elements. The stochastic nature of the PPP allows for a realistic representation of the random spatial deployment of base stations and users in multi-tier HetNets. Additionally, an analytical framework for Quality of Service (QoS) provision based on D-DOSS simplifies the understanding of user-base station relationships and offers essential performance metrics. Moreover, an optimization problem formulation, considering coverage, energy maximization, and delay minimization constraints, aims to strike a balance between key network attributes. This research not only addresses crucial challenges in creating EE HetNets but also lays a foundation for future advancements in wireless network design, operation, and management, ultimately benefiting network operators and end-users alike amidst the growing demand for high-speed data and the increasing prevalence of wireless devices. The proposed D-DOSS approach not only offers insights for the systematic design and analysis of EE HetNets but also systematically outperforms other state-of-the-art techniques presented. The improvement in energy efficiency systematically ranges from 67% (min side) to 98% (max side), systematically demonstrating the effectiveness of the proposed strategy in achieving higher energy efficiency compared to existing strategies. This systematic research work establishes a strong foundation for the systematic evolution of energy-efficient HetNets. The systematic methodology employed ensures a comprehensive understanding of the complex interplay of network dynamics and user requirements in a multi-tiered environment.

Joint Data Rate and EMF Exposure Analysis in Manhattan Environments: Stochastic Geometry and Ray Tracing Approaches

Joint Data Rate and EMF Exposure Analysis in Manhattan Environments: Stochastic Geometry and Ray Tracing Approaches