Geometric Behavior Research Articles

Some features of Kaniadakis holographic dark energy model

In this study, the Kaniadakis holographic dark energy (KHDE) model is investigated within the framework of a flat FLRW universe by using an infrared cut-off as Hubble horizon. For the different values of the Kaniadakis parameter [Formula: see text] and [Formula: see text], we perform an analysis on the deceleration, the equation of state and the energy density parameters. The current phase shift of the Cosmos may be rationalized by the change in sign of the deceleration parameter in the KHDE model, which went from [Formula: see text] to [Formula: see text], signifying a move from a phase of deceleration to one of acceleration. In order to get an understanding of the geometrical behavior shown by the KHDE model, we compute and show the statefinder evolutionary trajectory for the pairs [Formula: see text] and [Formula: see text]. The evolutionary trajectory of [Formula: see text] reveals that the [Formula: see text] crosses the phantom divide line [Formula: see text] at a late period in the evolutionary process. It has also been determined, by examination of the KHDE models stability analysis, that the model has behaved in an unstable manner during the whole course of the history of the universe. In addition to this, we optimized the model parameters by making use of the distance modulus measurement that was taken from the most current Union 2.1 dataset of supernovae.

Geometrical study of Middle Kingdom funerary complexes in Qubbet el-Hawa (Aswan, Egypt) based on 3D models

Highlights: A new methodology is presented to develop geometrical analysis of burial structures based on 3D models. The methodology has been applied to three contiguous burial structures (hypogea), allowing the researchers to analyse some constructive aspects such as dimensions, proportions, orientations, flatness and inclinations. Results have demonstrated the advanced skills achieved by ancient Egyptians in construction techniques. Abstract: This study describes the methodology developed and the main results obtained when analysing the geometrical behavior of three adjacent burial structures located in southern Egypt. The rock-cut tombs are composed of complex geometries such as halls, corridors, chambers and vertical shafts. Among other determining aspects, this complexity greatly conditioned the data acquisition and processing work. In this context, the main objective of this study was to develop a new methodology for obtaining geomatic products that support a complete geometrical analysis of the tombs. The researchers have used photogrammetric and laser scanning surveys to obtain accurate 3D models on a common reference system. The procedure used included obtaining several secondary products, such as several geometries (planes and cylinders) fitted from point clouds or plans and sections obtained from the 3D models. The geometric analysis has included several aspects: dimensions, proportions, orientations, wall flatness, inclinations, etc., and it is based on these products. The results obtained suggest and confirm several hypotheses about the constructive aspects of these hypogea based on a large amount of data, including the determination of a proportional canon used by the ancient Egyptians to plan and perform the excavation works of each funerary structure. The application of this methodology has demonstrated that this type of analysis is viable to unveil some important aspects of these structures and the constructive procedures carried out almost four millennia ago.

Data-Driven and Mechanism-Based Hybrid Model for Semiconductor Silicon Monocrystalline Quality Prediction in the Czochralski Process

The Czochralski (CZ) process is the core technology for producing semiconductor silicon monocrystalline (SMC), and it is a complex batch process. However, the crystal growth rate and crystal diameter, which are key quality indicators, are difficult to detect directly online, and the offline calculation process lags seriously, which easily causes blind crystal quality control. Therefore, this paper proposes a data-driven and mechanism-based hybrid model for semiconductor SMC quality variables prediction in the CZ process. Firstly, a data-driven model JITL-SAE-ELM based on just-in-time learning (JITL) fine-tuning strategy is proposed. This model is used to solve the nonlinear and time-varying relationship of the energy transfer process in the CZ process that cannot be accurately described by traditional mechanism models. Here, the SAE-ELM model integrates a stacked autoencoder (SAE) and an extreme learning machine (ELM), which are used to deeply capture the nonlinear and time-varying features of process data. Secondly, according to the hydrodynamics and geometric behavior, a crystal pulling dynamic mechanism model based on the crystal growth mechanism is constructed, which avoids the complicated heat transfer link. Further, considering the unmodeled dynamics caused by model parameter uncertainty during the combination of the energy transfer model and crystal pulling dynamic mechanism model, a crystal diameter compensation model SAE-ELM was developed to improve the prediction accuracy of the CZ process hybrid model. Finally, an industrial data experiment based on a CZ monocrystal furnace illustrates the proposed method.

Geometric modeling with small defects of over-constrained Parallel Kinematic Machine

In the case of over-constrained mechanisms, the system can only be assembled or move under strict geometric conditions. A crucial step is to identify these conditions from the geometric model. Classically, the geometric model of a robot is computed from the Denavit–Hartenberg formalism. However, when imperfect mechanisms are studied, this formalism does not introduce exhaustively small geometric defects. In this article, a formalism based on kinematic joint invariants is preferred to describe the geometric behavior. The efficiency of this formalism is demonstrated for the accuracy improvement of a serial robot. A stationarity analysis of the geometric model is then performed to determine the geometric constraints induced by the over-constrained systems and to reduce the number of geometric parameters initially introduced. The methodology is first illustrated on an over-constrained slider–rod–crank system. Then, it is applied to the over-constrained mechanism of the Tripteor X7, a Parallel Kinematic Machine-tool. The benefit of our methodology is validated by a comparison of the geometric model obtained with a CAD model and a previous geometric model proposed in the literature. Finally, the identification of the parameters of the defined geometric model is conducted in order to quantify the potential accuracy benefit.

Traversable wormhole models in modified theories of gravity

In this paper, we explore traversable wormhole solutions in different cases of modified [Formula: see text] theories of gravity. We have taken the functional form [Formula: see text], where [Formula: see text] is Ricci scalar and [Formula: see text] is the trace of energy momentum tensor, while [Formula: see text] and [Formula: see text] are constants. The different forms of [Formula: see text]-gravity in [Formula: see text], [Formula: see text] frameworks and [Formula: see text] gravity are analyzed with its geometric behavior. The energy conditions are also discussed in the isotropic scenario using EoS [Formula: see text] and hybrid shape function [Formula: see text], where [Formula: see text] is the throat radius. In this investigation, we found that quadratic geometric term and linear trace term of [Formula: see text] gravity and hybrid shape function play a significant contribution to validate the energy conditions for nonexotic wormhole solutions.

First-principles study of O-functionalized two-dimensional AsP monolayers: electronic structure, mechanical, piezoelectric, and optical properties

Using density functional theory, we investigated the geometrical properties, electronic structures, carrier mobilities, piezoelectric coefficients, and optical absorption behaviors of three O-functionalized β-phase AsP structures (b-AsPO-FO, b-AsPO-As-SO and b-AsPO-P-SO). It is shown that three O-functionalized monolayers are all indirect semiconductors with bandgaps of 0.21, 0.67, and 0.80 eV, respectively. Our calculations demonstrated that the pristine AsP monolayer and these O-functionalized AsP monolayers have strongly anisotropic carrier mobilities, allowing their potential applications for in-plane anisotropic electronic device. The bandgaps of three functionalized nanomaterials exhibit non-monotonic variations under the biaxial strains changing from −0.10 to +0.10, all experiencing metal-indirect bandgap-direct bandgap transition. The calculated in-plane Young’s modulus results suggest that they are fairly flexible to allow the application of large elastic strains on the chemically functionalized AsP monolayers. Furthermore, the b-AsPO-FO monolayer exhibits excellent anisotropic light-harvesting behavior (absorption peak: 2.36 and 2.76 eV along x and 2.37 eV along y direction) in visible light region. The b-AsPO-As-SO and b-AsPO-P-SO monolayers have strong absorption peak at 2.60 eV and 2.87 eV, respectively. The tunable electronic structures, anisotropic carrier mobility, and excellent optical absorption properties may facilitate practical applications of O-functionalized b-AsP monolayers in nanoelectronics and photovoltaics.

Anisotropic cloud string cosmological model with five-dimensional kaluza-klein space-time

Anisotropic cloud string cosmological models has been investigated in the context of five dimensional Kaluza- Klein space time. In this paper the energy momentum tensor is generated by rest energy density and tension density of the string with particle density attached to them. To obtained the exact solutions of the Einstein field equations we assumed a scale factor a(t)=e1β2βt+c where β and c are positive constant, which yields a variable deceleration parameter (DP) q=−aäȧ2=βH+α. The physical and geometrical behavior of the models is also discussed in detail.

Thermal Power Plant Turbine Rotor Digital Twin Automation Construction and Monitoring System

Based on the digital twin technology, this article investigates the physical rules fusion model of the turbine rotor operation in thermal power plants, establishes the geometric behavior mapping method of the turbine rotor in the virtual scenario of thermal power plants, and develops a real-time data-driven virtual monitoring system of the rotor operation, which realizes the virtual control of the rotor operation process from the physical and geometric levels, respectively. The 3D model created by Creo was imported into ADAMS in x_t format, constraints were added, and model data input and output interfaces were established in ADAMS software to build its dynamics model. The foundation of the joint simulation with the AMESim model is laid. The information fusion technology based on D-S evidence theory, fusing multisensor data and information from other channels, can more accurately and comprehensively understand and describe the diagnostic object, to make correct judgment and decisions on complex fault diagnosis. We propose an integrated modeling method for multiview control scenarios of manufacturing units based on digital twins and finalize the construction of digital twin models of manufacturing units based on the definition of the multiview model collaboration mechanism, which provides model support for the research of digital twin-driven manufacturing unit control technology. For the twin data perception and interaction problem, a unified architecture-standardized communication protocol is established based on OPC UA technology to solve the problem of difficult data perception and interaction caused by the nonuniform communication interface protocol of different devices on the automated production line. The model change is intended to help improve the visualization level of digital production line monitoring and improve the operating efficiency of the turbine rotor. The experimental results show that the application of digital twin to thermal turbine rotor operation monitoring provides a new method for turbine rotor vibration fault diagnosis; D-S evidence theory can fuse information from multiple aspects of the fault, thus improving the probability of fault diagnosis and reducing uncertainty.

Bianchi type-V transitioning model in Brans–Dicke theory with observational constraints

In this paper, we have examined the viability of the Bianchi type-V universe in Brans–Dicke (BD) theory of gravitation. We have discussed the interacting and non-interacting scenarios between dark matter (DM) and dark energy (DE) of the derived universe within the framework of BD theory. CCA technique has been applied to constrain the model parameters using 46 values of observational Hubble data (OHD), Pantheon data (the latest compilation of SNIa with 40 binned in the redshift range [Formula: see text] and their combined datasets. We establish an exact solution of the field equations to derive the dynamics of the derived universe and the obtained results are found to agree with the observations. We also noted a distinctive change in the sign of the deceleration parameter from positive to negative, as well as the presence of a transition red-shift exists. Using various observational data points, the evolution trajectories for [Formula: see text] diagnostic planes are shown to understand the geometrical behavior of the Bianchi-V model. Some physical properties of the universe are also discussed. It is also worth noting that the conclusions of the cosmological parameter are consistent with modern observational data.

New wormhole shape functions in f(R,T) theory of gravity

In this paper, we introduce two new shape functions of wormholes in [Formula: see text] gravity. Both shape functions are satisfied by various geometric conditions. We will also discuss the different energy conditions and geometric behavior corresponding to each shape function in different states. Finally, we investigate the system’s stability with a solution corresponding to the two shape functions.

Geometric and material nonlinear analysis of steel members with nonsymmetric sections

Steel members using nonsymmetric sections are often used for their structural efficiency in contemporary construction. Notwithstanding, the conventional concentrated plasticity (CP) analysis approach is commonly used in material nonlinear analysis and derived for regular hot-rolled steel sections with symmetrical shapes, leading to significant differences when analyzing members with nonsymmetric sections. This research develops the modified tangent modulus (MTM) method, proposed by Ziemian and McGuire in 2002, for the material nonlinear analysis of steel members with nonsymmetric sections, as a straightforward extension of the conventional CP analysis approach. Regarding the geometric nonlinear behaviors, an improved line-element formulation is formulated based on the nonsymmetric section assumption, explicitly modelling the noncoincidence of the shear center and centroid for considering the Wagner effects, which can capture complex buckling behaviors of the members with nonsymmetric sections. As part of the proposed method, a rigorous cross-section analysis method has been developed to generate the yield surfaces of arbitrary steel sections regardless of shapes. Such yield surfaces will be used to evaluate the full-yield condition, and the gradients to the yield surfaces will be calculated and used to control the plastic flow. The development of this methodology is presented in detail, as well as the derivation of the mathematical formulations. Six groups of verification examples are provided to validate the accuracy of the proposed method.

An Elasto‐plastic Finite Element for the Analysis of Planar Steel Beams

AbstractThe following paper presents an original finite element formulation for the elasto‐plastic analysis of planar homogeneous isotropic beams. The one‐dimensional elastic‐perfectly plastic material behavior is considered. The approach is based on innovative shape functions able to capture the formation of elasto‐plastic regions at the ends of the beam element. While the proposed shape functions can theoretically handle any cross‐section, in this paper the formulation is developed only for rectangular cross‐sections. Linear geometric behavior is considered. The formulation is validated by comparisons with the upper bound method of plastic limit analysis in terms of ultimate loading, and with simulations using shell FE analyses in terms of load‐displacement response and development of the plastic regions.

Numerical Study of an Improved Non-Circular MC Fuelled with H/Air for Thermo-Photovoltaic (TPV) Applications

In recent years, researchers have paid special attention to wall uniformity temperature and improvement in a micro-combustor (MC) for applications as thermos-photovoltaic (TPV) since they have a direct influence on feasibility and efficiency of the required conversion of energy. Numerous experimentation and numerical studies in the field of micro-combustion have been carried out and published in this respect. This study focuses on the flame and flow behaviour in an improved MC. Utilizing the famous approach of fluid dynamics being computational (CFD), the impact of geometrical flow parameters behaviour and temperature of wall is explored and measured. The generated model is being used to evaluate the effects of Hydrogen (H) mass flow rate (MFR) and H/air equivalency ratios on the flame pattern and outer temperature of wall of conventional and enhanced MCs. Moreover, the influence of various MC cross sections (CS), such as square, circular, and flat, on temperature of wall is examined. The findings reveal that when the MFR rises, the wall outside temperature rises as well. The MC with flat cross-sections (CSs) is found to be more effective in terms of power of emitter and efficiency of emitter.

On the Influence of Linear Energy/Heat Input Coefficient on Hardness and Weld Bead Geometry in Chromium-Rich Stringer GMAW Coatings.

Wear of the working surfaces of machinery parts is a phenomenon that cannot be fully countered, only postponed. Among surface lifecycle elongation techniques, hardfacing is one which is most often used in heavy load applications. Hardfaced coating can be applied using different welding approaches or thermal spraying technologies, which differ when it comes to weld bead dimensional precision, layer thickness, process efficiency and material. In this study the authors examine the geometrical behavior and hardness properties of two distinctive chromium-based Gas Metal Arc Welding (GMAW) cored wires. The stringer beads are applied numerically with five levels of linear energy, being a resultant of typical values of welding speed and wire feed, ranging between 250 mm/s to 1250 mm/s (welding speed) and 2 m/min to 10 m/min (wire feed). The samples were cut, etched and measured using a digital microscope and Vickers indenter, additionally the chemical composition was also examined. Hardness was measured at five points in each cutout, giving 40 measurements per sample. The values were analyzed using an ANOVA test as a statistical background in order to emphasize the divergent behavior of the cored wires. It appeared that, despite having less chromium in its chemical composition, wire DO*351 exhibits higher hardness values; however, DO*332 tends to have a more stable geometry across all of the heat input levels.

Geometric Models and Variation of Weights on Moduli of Parabolic Higgs Bundles over the Riemann Sphere: a Case Study

We construct explicit geometric models for moduli spaces of semi-stable strongly parabolic Higgs bundles over the Riemann sphere, in the case of rank two, four marked points, arbitrary degree, and arbitrary weights. The mechanism of construction relies on elementary geometric and combinatorial techniques, based on a detailed study of orbit stability of (in general non-reductive) bundle automorphism groups on certain carefully crafted spaces. The aforementioned techniques are not exclusive to the case we examine, and this work elucidates a general approach to construct arbitrary moduli spaces of semi-stable parabolic Higgs bundles in genus 0, which is encoded into the combinatorics of weight polytopes. We also present a comprehensive analysis of the geometric models' behavior under variation of parabolic weights and wall-crossing, which is concentrated on their nilpotent cones.

A 1D Reduced-Order Model (ROM) for a Novel Latent Thermal Energy Storage System

Phase change material (PCM)-based thermal energy storage (TES) systems are widely used for repeated intermittent heating and cooling applications. However, such systems typically face some challenges due to the low thermal conductivity and expensive encapsulation process of PCMs. The present study overcomes these challenges by proposing a lightweight, low-cost, and low thermal resistance TES system that realizes a fluid-to-PCM additively manufactured metal-polymer composite heat exchanger (HX), based on our previously developed cross-media approach. A robust and simplified, analytical-based, 1D reduced-order model (ROM) was developed to compute the TES system performance, saving computational time compared to modeling the entire TES system using PCM-related transient CFD modeling. The TES model was reduced to a segment-level model comprising a single PCM-wire cylindrical domain based on the tube-bank geometry formed by the metal fin-wires. A detailed study on the geometric behavior of the cylindrical domain and the effect of overlapped areas, where the overlapped areas represent a deviation from 1D assumption on the TES performance, was conducted. An optimum geometric range of wire-spacings and size was identified. The 1D ROM assumes 1D radial conduction inside the PCM and analytically computes latent energy stored in the single PCM-wire cylindrical domain using thermal resistance and energy conservation principles. The latent energy is then time-integrated for the entire TES, making the 1D ROM computationally efficient. The 1D ROM neglects sensible thermal capacity and is thus applicable for the low Stefan number applications in the present study. The performance parameters of the 1D ROM were then validated with a 2D axisymmetric model, typically used in the literature, using commercially available CFD tools. For validation, a parametric study of a wide range of non-dimensionalized parameters, depending on applications ranging from pulsed-power cooling to peak-load shifting for building cooling application, is included in this paper. The 1D ROM appears to correlate well with the 2D axisymmetric model to within 10%, except at some extreme ranges of a few of the non-dimensional parameters, which lead to the condition of axial conduction inside the PCM, deviating from the 1D ROM.

Pseudo rigid body model for a nonlinear folding compliant mechanism

Folding compliant mechanisms have the potential to be used for innovative designs tailored for specific applications such as energy absorption, shape morphing, or stress relief. This tailorability relies on multiple variables that define the geometric and material behavior. The combined effort of the geometric and material nonlinearity can emphasize certain features in the design that, individually, would not be possible. Folding as a concept is very important in origami engineering and requires careful choice in the design variables when it comes to dimensions and material properties. Finite element analyses for folding at the level of a unit cell, as well as the overall structural design, can be cumbersome and computationally expensive. Therefore, in this work, a segmented pseudo rigid body model that captures a high level of flexibility is developed for both a superelastic material, which is characterized using a shape memory alloy, and a hyperelastic, rubber-like material. By increasing the number of segments, the model allows the structure to undergo large deformations. The results from the segmented model are compared with FEA for the folding compliant mechanism. 3D-printing and experimental testing of the compliant mechanism is also explored.

An empirical data analysis of "price runs" in daily financial indices: Dynamically assessing market geometric distributional behavior.

In financial time series there are time periods in which market indices values or assets prices increase or decrease monotonically. We call those events "price runs", "elementary uninterrupted trends" or just "uninterrupted trends". In this paper we study the distribution of the duration of uninterrupted trends for the daily indices DJIA, NASDAQ, IPC and Nikkei 225 during the period of time from 10/30/1978 to 08/07/2020 and we compare the simple geometric statistical model with [Formula: see text] consistent with the EMH to the empirical data. By a fitting procedure, it is found that the geometric distribution with parameter [Formula: see text] provides a good model for uninterrupted trends of short and medium duration for the more mature markets; however, longest duration events still need to be statistically characterized. Estimated values of the parameter p were also obtained and confirmed by calculating the mean value of p fluctuations from empirical data. Additionally, the observed trend duration distributions for the different studied markets are compared over time by means of the Anderson-Darling (AD) test, to the expected geometric distribution with parameter [Formula: see text] and to a geometric distribution with a free parameter p, making possible to assess and compare different market geometric behavior for different dates as well as to measure the fraction of time runs duration from studied markets are consistent with the geometric distribution with [Formula: see text] and in parametric free way.

Two-step incremental procedure associated with the normal flow technique applied to trusses

To achieve the nonlinear structural behavior, there is a need to trace of their equilibrium path in the space of load-displacement. Truss systems are commonly implemented in several structural systems, including high-span bridges and bracing of the supporting structure of tall buildings. Our study adapts a two-step method with cubic convergence into an incremental-iterative procedure to analyze the geometric nonlinear behavior of trusses. The solution method is combined with the Linear Arc-Length path-following technique. To find the approximate root of nonlinear equation system in the two-step method, two formulas are used. Structures are discretized using the Positional Finite Element Method and all truss bars are assumed to remain linear elastic. The correction of the nodal coordinates subincrement vector is performed using the Normal Flow technique. A computational algorithm was implemented using the free program Scilab. Our numerical results show that, when compared to the standard and modified Newton-Raphson algorithms, the new algorithm decreases the number of iterations and the computing time in the nonlinear analysis of trusses. Equilibrium paths with force and/or displacement limit points are obtained with good precision.

Accelerating scenarios of viscous fluid universe in modified f(T) gravity

In this paper, we have investigated the physical behavior of cosmological models in modified teleparallel gravity with a linear function [Formula: see text] where [Formula: see text] and [Formula: see text] are model parameters and [Formula: see text] is the torsion scalar. We have considered a homogeneous and isotropic Friedman universe filled with bulk viscosity fluid. We have solved the field equations for the scale factor [Formula: see text] and found [Formula: see text] where [Formula: see text] and [Formula: see text] and [Formula: see text] is an integrating constant, [Formula: see text] is the equation of state (EoS) for normal matter and [Formula: see text] is generated from bulk viscosity fluid. We have calculated the several cosmological parameters for this scale factor and studied their physical and geometrical behavior along with the observational data sets [Formula: see text] and Union [Formula: see text] compilation of SNe Ia data sets. We have observed that the [Formula: see text] factor reveals the presence of cosmological constant and for [Formula: see text], the acceleration drives by the bulk viscosity of the fluid and it behaves just like dark energy model without cosmological constant. We have studied the effective EoS [Formula: see text] and found [Formula: see text]. We have evaluated the age of the present universe as [Formula: see text] Gyrs. Also, we have studied the nature of deceleration parameter with the signature-flipping point at [Formula: see text] and the present value of deceleration parameter [Formula: see text] is obtained as [Formula: see text], respectively, for both observational datasets.