Geometric Components Research Articles

Aeroacoustic and Aerodynamic Investigation of a Wingtip-Mounted Tractor Propeller

The wingtip-mounted propeller configuration is widely used in many aircraft, particularly owing to the emergence of urban air mobility. This paper focuses on analyzing the aeroacoustic properties of a wingtip-mounted tractor propeller by understanding the aerodynamic interaction between the two geometric components. Computational fluid dynamics based on Reynolds-averaged Navier–Stokes equations were used to calculate the flow field and aerodynamic loads on a wingtip-mounted propeller model, and the results were compared with experimental data for validation. The resulting surface pressure was fed as input data for the acoustic analysis performed using a Ffowcs Williams–Hawkings equationbased acoustic solver at multiple angles of attack. The presence of the wing significantly increased the propeller noise along the rotational axis. With increasing angle of attack, the propeller noise increased further. By contrast, the wing noise decreased with the angle of attack due to propeller wake dissipation, leading to only a small increase in the maximum total noise.

DIFFRACTION OF A SPHERICAL WAVE BY A HARD HALF-PLANE: POLYNOMIAL FORMULATION OF EDGE-DIFFRACTED FIELD IN THE FREQUENCY DOMAIN

The problem of diffraction of a spherical sound wave by a thin hard half-plane is considered. The expression of the total field at any position in the space around the half-plane is composed of two geometrical components and a third one which originating from the edge of the half-plane. This paper takes the expression of the edge-diffracted field due to a sound doublet, as formulated in the Biot-Tolstoy theory of diffraction, BTD, but rearranged for the Dirac-like pulse by Medwin. The present paper presents a development in the frequency domain of the Fourier transform of the exact expression of the edge-diffracted field as given in the time domain. This solution is composed of a serial development, expressed in simple trigonometric integral functions, and which away from the geometrical optics boundaries shows a quite rapid convergence to the numerical Fourier transform of the exact time-domain expression. The presented solution may be used as a good approximation in simulations and in real case predictions of sound scattering by thin straight-edged noise barriers.

Geometrical Images in Lexis and Phraseology of Modern Russian Language

The article reviews geometrical objects as a factor forming the image system of modern Russian language, and explores the lexical units motivated by the concept of geometrical objects and phraseological units with geometrical components. This approach reveals multiplicity of geometrical objects participating in the process: there are three-dimensional (sphere, spatial angle, etc.), two-dimensional (circle), one-dimensional (line, etc.) and geometrical objects without dimension (point). When considering the language material the author uses the concept of the inner form of the word. Numerous examples are given demonstrating the process of geometric metaphorization. The analysis has shown that circle and spatial angle demonstrate high activity in forming lexical and phraseological units under consideration. Many of those geometrical images have an ancient origin. The article also touches on the issue of national characteristics of the perception of angles and circles. Some examples given by the author indicate the further development of language phenomena motivated by the concept of those geometrical objects in our time. Modern trends in the development of geometric imagery in the Russian language have been identified. The role of such geometric objects as a point, line, edge, etc. in the modern process of enriching the figurative structure of the Russian language is noted. The issues of lexical compatibility of the studied words are considered, the tendency of its change and expansion is traced. Modern trends of development of geometrical imagery in Russian language as a systematic process reflecting essential features of national view of the world are revealed.

ВИЗНАЧЕННЯ ТА ОЦІНКА ЗМІНИ ТИПІВ ЖИВЛЕННЯ РІЧОК БАСЕЙНУ Р. ГОРИНЬ

Using the Horyn River Basin rivers as an example the hydrograph separation algorithm was defined. The results of calculating different river feeding types values were given in the paper. Also, were analyzed their long-term dynamics. Ukrainian rivers are characterized by snow, rain, and ground (soil and underground) types of rivers feeding. The amount of snow and rain rivers feeding is determined by taking into account the characteristics of atmospheric precipitation and their correlation with water runoff characteristics. In the paper, the ground rivers feeding amount, in particular underground feeding, was established using an analytical (calculation) method. The key principles for river feeding amount determination such as graphic and geometric components of the hydrograph separation method application were described. Examples of using computer software for elementary figures areas calculating were considered. The total amount of separated hydrographs was 480. Daily observation data from 8 hydrological stations (water discharges) and 15 meteorological stations (air temperature, precipitation and snow cover height) were used for the research. Meteorological characteristics were correlated to the corresponding watersheds by determining the weight coefficient. The GIS system tools – ArcGIS were used for the catchment areas construction and their further division into separate areas of each weather station influence (Thiessen polygons). The resulting contours of the catchments were further refined on maps with a scale of 1: 50000. In general, for the period 1961-2020, it was established that the Horyn River Basin ground feeding values were from 31.6% to 68.4%; the share of snow feeding ranged from 19.7% (Horyn – Ozhenyn) to 41.6% (Smilka – Susly), and the average long-term values of the rain feeding share were ranged from 11% (Horyn – Derazhne) to 26.8% (Smilka – Susly). For Horyn River Basin rivers feeding types changes were assessed for two representative periods – 1961-1990 and 1991-2020. In general, for the Horyn River Basin in the present period (1991-2020) it was revealed a decrease in the relative values of the snow and rain feeding share by 8.4% and 1.6%, respectively, and an increase in the underground and soil feeding share by 5.7% and 4.3%, respectively.

Liquid Crystal-Based Geometric Phase-Enhanced Platform for Polarization and Wavefront Analysis Techniques with the Short-TeraHertz FEL Oscillator TerRa@BriXSinO

In this work, we propose to design a liquid crystal–based modular and extendable platform of cutting-edge optical technologies for studying materials based on the analysis of polarization and wavefront of light in the wavelength range of 10–50 μm, which is considered to work even in the longer wavelengths range. This platform will be driven by the future THz-FEL source TerRa@BriXSinO that produces high power radiation in THz-range from 6 THz up to 30 THz (Mid-/Far-IR). The lack of optical infrastructures in this range has been tackled by fabricating liquid crystal–based geometric phase components that have been specifically designed for this purpose. This is in order to optimally exploit all the source’s potential for maximum accuracy and efficiency in determining polarization- and wavefront-sensitive properties of materials. We present an overview of a few experiments for characterizing bulk inhomogeneities, dielectric anisotropy, surface roughness, cracks, impact damages, and stress and strain effects with special emphasis on non-destructive tests on composite structures. The tools for wavefront shaping developed within our platform will be exploited to add a further degree of freedom, i.e., orbital angular momentum, to nonlinear optics techniques, such as Terahertz Hyper-Raman spectroscopy, for investigating chiral agents’ properties.

Architected Low-Tortuosity Electrodes with Tunable Porosity from Nonequilibrium Soft-Matter Processing.

Mass transport is performance-defining across energy storage devices, often causing limitations at high current rates. To optimize and balance the device-scale energy and power density for a given energy storage demand, tailored electrode architectures with precisely controllable phase dimensions are needed in combination with low-tortuosity channels that maximize the geometric component of diffusion and species flux. A material-agnostic nonequilibrium soft-matter process is reported to fabricate free-standing inorganic composite electrodes with adjustable thicknesses of 100s ofµm, featuring straight and accessible channels ranging in diameter from 5-30µm, coupled with tunable material-to-pore ratios. Such architected anode and cathode electrodes exhibit electrochemical and architectural stability over extended cycling in a full-cell battery. Further, mass-transport constraints appear at high current densities, and the lithiation step is identified as rate-performance limiting, a result of insufficient lithium-ion supply and concentration polarization. The results demonstrate the need for and feasibility of tailored electrode architectures where dimensional ratios between low-tortuosity channels, the charge-storing matrix, and electrode thickness are tunable to meet coupled power and energy-storage requirements.

Numerical Investigation and Response Surface Optimization of the Effective Modulus and Electrical and Thermal Conductivities of the Borophene Nanoplatelet-Reinforced PEDOT:PSS Nanocomposite for Energy Storage Application.

Conductive organic nanocomposites have been widely employed to achieve a variety of purposes, particularly for energy storage applications, making it necessary to investigate transport properties such as electron and heat transport qualities based on geometric shapes and component materials. Due to the solid B-B bonds, unique atomic structure, and energy storage potential, borophene has received significant attention due to its reported ultrahigh mechanical modulus and metallic conduction. Herein, we investigated the effect and interaction of content materials (volume fraction) and geometric parameters such as the aspect ratio and orientation of borophene nanoplatelet (BNP) inclusions on the mechanical integrity and transport features (electrical and thermal conductivities) of a poly(3,4-ethylene dioxythiophene):poly(4-styrene sulfonate) (PEDOT:PSS) electrode. The boundary condition is crucial in developing the predictive models for the optimized mechanical and transport properties of the composites. The effective modulus, electrical conductivity, and thermal conductivity of the BNP-reinforced PEDOT:PSS-based nanocomposite are evaluated using the periodic boundary condition, the representative volume element-based finite element homogenization, and statistical analysis response surface techniques. The optimal parameters for the PEDOT:PSS/BNP nanocomposite for energy storage application are predicted based on the desirability function to have a 13.96% volume fraction of BNPs, having an aspect ratio of 0.04 at 45° inclination. The desirability value achieved for the material hinges was 0.78 with a predicted Young's modulus of 6.73 GPa, the electrical conductivity was 633.85 S/cm, and the thermal conductivity was 1.96 W/m K at a generally high predictive performance of <0.03 error. The effective thermal conductivity of the nanocomposite was determined by considering Kapitsa nanoeffects, which exhibit an interfacial thermal resistance of 2.42 × 10-9 m2 K/W. Based on these improved findings, the enhanced PEDOT:PSS/BNP nanocomposite electrode would be a promising material for metal-ion batteries.

Type Synthesis of Modular Polyhedral Mechanisms Based on the Generalized Mechanism Models of Regular Polyhedron

Abstract An integrated type synthesis method for polyhedral mechanisms based on polyhedron is proposed. The properties of the polyhedron are considered and the corresponding generalized mechanism is built based on strategies that geometric components are regarded as construction members. Topological graph and configuration matrix are used to describe the generalized mechanism. The target mechanism and its descriptions are obtained from the generalized mechanism via designing the construction members appropriately. Possible types are then enumerated using set operations according to the configuration matrix. The axes of the kinematic pairs are set based on the geometric properties of the polyhedron. Degrees-of-freedom (DOFs) of those possible types are calculated using the modified G–K criterion based on screw theory, and the type synthesis results with DOF more than 0 are obtained. Tetrahedral mechanisms with revolute and sliding pairs are synthesized, and they have 135 configuration results with lower-mobility, which validates the accuracy and effectiveness of the proposed method. Some application examples of the tetrahedral mechanisms are further illustrated for potential values of synthesized mechanisms in robot field.

Multiscale topology optimization with stress, buckling and dynamic constraints using adaptive geometric components

This research focuses on the multiscale topology optimization (TO) of structures to meet stress, stability, and vibration requirements. The compliance minimization problems of multiscale structures under the global stress constraints, critical buckling load factor, and natural frequencies are established and solved by employing a method using adaptive geometric components (AGCs). During the TO process, the dynamic and stability frequency gap constraints are added to the optimal model to prevent mode switches. The maximum stress is measured using the global p-norm stress aggregation. The concurrent material modeling technique, which involves AGCs, illustrates the macrostructure and microstructure of material under multiple constraints simultaneously, which are optimized by focusing on the AGC parameters under multiple constraints. Benchmark numerical tests are presented and investigated to validate the applicability of the proposed approach.

Riemannian optimization with a preconditioning scheme on the generalized Stiefel manifold

Optimization problems on the generalized Stiefel manifold (and products of it) are prevalent across science and engineering. For example, in computational science they arise in symmetric (generalized) eigenvalue problems, in nonlinear eigenvalue problems, and in electronic structures computations, to name a few problems. In statistics and machine learning, they arise, for example, in various dimensionality reduction techniques such as canonical correlation analysis. In deep learning, regularization and improved stability can be obtained by constraining some layers to have parameter matrices that belong to the Stiefel manifold. Solving problems on the generalized Stiefel manifold can be approached via the tools of Riemannian optimization. However, using the standard geometric components for the generalized Stiefel manifold has two possible shortcomings: computing some of the geometric components can be too expensive and convergence can be rather slow in certain cases. Both shortcomings can be addressed using a technique called Riemannian preconditioning, which amounts to using geometric components derived by a preconditioner that defines a Riemannian metric on the constraint manifold. In this paper we develop the geometric components required to perform Riemannian optimization on the generalized Stiefel manifold equipped with a non-standard metric, and illustrate theoretically and numerically the use of those components and the effect of Riemannian preconditioning for solving optimization problems on the generalized Stiefel manifold.

Generic autonomous system approach to interacting dark energy models

We explore an autonomous system analysis of dark energy models with interactions between dark energy and cold dark matter in a general systematic approach to cosmological fluids. We investigate two types of models such as local and non-local ones. In particular, a local form of interaction is directly proportional to only the energy density, while a non-local interaction is directly proportional to the energy density as well as the Hubble parameter. As a consequence, it is explicitly demonstrated that in both cases there exist the stability points in terms of cosmological parameters. This work aims at obtaining acceleration and stability using interaction models without modifying the matter or geometric component of the Universe.

Automated assembly of reciprocal frame structures using robotics

In this paper, the robotization of structural construction was studied in preference to the undemanding assembly of the reciprocal frame (RF) structures. Formulas were developed to automate the process of geometric forming and component evaluation. Subsequently, the robotic cooperative system was established to assemble the structure according to the positions and orientations of each component from the geometric forming module. The robotic system consists of two robotic arms, two navigating robots, depth cameras, and customized grippers. The structure was made from pultruded glass fibre reinforced polymer (GFRP) members owing to their lightweight, high strength and corrosion resistance. Concepts of temporary connections were also proposed to eliminate the offset generated during the construction. Finally, the comparative studies of the constructions in different light environments and with different ground obstacles were investigated through experimental investigations. The results showed that the structure can be successfully assembled with the proposed robotic system and the assistance of the temporary connection in most of the light conditions and ground obstacles.

Design of Control Schedules for Interturbine Burner Turbofan Engine Considering Ignition and Flameout Characteristics

Abstract The interturbine burner (ITB) engine, which is introduced between high and low pressure turbines (LPTs), is a relatively new concept for increasing specific thrust and lowering high altitude specific fuel consumption (SFC) than engine with afterburner (AB). Although ITB engines have outstanding performance improvements, they also present a challenge to the design of control laws for ITB engines under unknown matching mechanisms and multiple constraints. This study proposes a self-scheduling control law design method for ITB engine mode transition that considers ITB ignition and flameout characteristics, as well as cooling air volume. This method derives the control law based on the global optimal algorithm and shapley additive explanation (SHAP)-value analysis method, which avoids manual analysis and reduces the number of adjustment of variable geometric components. An ITB transient model is established to verify the control laws under the transition of ignition and flameout modes. During the mode transition process of opening and closing the ITB, the flow fluctuation of the precritical point and rear-critical point does not exceed 2%, and the comprehensive thrust fluctuation index composed of three typical state points does not exceed 5%. Through simulation analysis with constrained constraints, at most one variable geometry component is adjusted.

DATASET FOR URBAN SCALE BUILDING STOCK MODELLING: IDENTIFICATION AND REVIEW OF POTENTIAL DATA COLLECTION APPROACHES

Abstract. Construction materials play an important role in environmental impacts and make cities big resource consumers. To assess the sustainability of cities, the combined use of Life Cycle Assessment (LCA) and Material Flow Analysis (MFA) is considered effective to analyze construction material stock and flows. However, exhaustive data is required for such analyses, making LCA and MFA difficult to apply at the urban scale. Building information, the essential ingredient, is rarely available openly. Common approaches to gather the required data include both obtaining it directly from available datasets, e.g. open data from official sources, and indirectly generating data based on available data, e.g. using machine learning to fill the missing gaps. This research develops a data collection guideline for buildings’ geometrical features, components and materials at the urban scale in the context of LCA and MFA. First, it identifies the basic steps of urban-scale building stock modelling and the list of data requirements. Second, the factors influencing the data collection are pointed out. In line with these guidelines, this research picks Singapore as a study area, reviewing the relevant authoritative open data sources and methodologies to estimate missing data. Finally, the suggestion on implementation of data collection are provided. When the data collection for urban scale stock modelling is limited by uncertain reality conditions, identifying and combining open datasets and data generation methods for data preparation is a necessity.

Knowledge-based multi-institution plan prediction of whole breast irradiation with tangential fields.

To quantify inter-institute variability of Knowledge-Based (KB) models for right breast cancer patients treated with tangential fields whole breast irradiation (WBI). Ten institutions set KB models by using RapidPlan (Varian Inc.), following previously shared methodologies. Models were tested on 20 new patients from the same institutes, exporting DVH predictions of heart, ipsilateral lung, contralateral lung, and contralateral breast. Inter-institute variability was quantified by the inter-institute SDint of predicted DVHs/Dmean. Association between lung sparing vs PTV coverage strategy was also investigated. The transferability of models was evaluated by the overlap of each model's geometric Principal Component (PC1) when applied to the test patients of the other 9 institutes. The overall inter-institute variability of DVH/Dmean ipsilateral lung dose prediction, was less than 2% (20%-80% dose range) and 0.55Gy respectively (1SD) for a 40Gy in 15 fraction schedule; it was < 0.2Gy for other OARs. Institute 6 showed the lowest mean dose prediction value and no overlap between PTV and ipsilateral lung. Once excluded, the predicted ipsilateral lung Dmean was correlated with median PTV D99% (R2=0.78). PC1 values were always within the range of applicability (90th percentile) for 7 models: for 2 models they were outside in 1/18 cases. For the model of institute 6, it failed in 7/18 cases. The impact of inter-institute variability of dose calculation was tested and found to be almost negligible. Results show limited inter-institute variability of plan prediction models translating in high inter-institute interchangeability, except for one of ten institutes. These results encourage future investigations in generating benchmarks for plan prediction incorporating inter-institute variability.

PlaneSDF-Based Change Detection for Long-Term Dense Mapping

The ability to process environment maps across multiple sessions is critical for robots operating over extended periods of time. Specifically, it is desirable for autonomous agents to detect changes amongst maps of different sessions so as to gain a conflict-free understanding of the current environment. In this paper, we look into the problem of change detection based on a novel map representation, dubbed Plane Signed Distance Fields (PlaneSDF), where dense maps are represented as a collection of planes and their associated geometric components in SDF volumes. Given point clouds of the source and target scenes, we propose a three-step PlaneSDF-based change detection approach: (1) PlaneSDF volumes are instantiated within each scene and registered across scenes using plane poses; 2D height maps and object maps are extracted per volume via height projection and connected component analysis. (2) Height maps are compared and intersected with the object map to produce a 2D change location mask for changed object candidates in the source scene. (3) 3D geometric validation is performed using SDF-derived features per object candidate for change mask refinement. We evaluate our approach on both synthetic and real-world datasets and demonstrate its effectiveness via the task of changed object detection. Supplementary video: https://youtu.be/oh-MQPWTwZI

The City as a Tool for STEAM Education: Problem-Posing in the Context of Math Trails

This study presents an experience that combines problem-posing and Math Trails in the context of future teachers’ instruction. Pre-service teachers in the third year of their studies were faced with the design of tasks to be included in Math Trails for primary school students. The study analyzes, from a quantitative approach, 117 tasks contained in 11 Math Trails. The analysis was performed on the basis of classification variables (grade, mathematical content and object or real element involved in every task) and research variables which provide information about the nature of the tasks (procedural vs. problem-solving, level of cognitive demand, degree of contextualization, openness and creativity). Additionally, relationships between the different categories of analysis have been studied. The results reveal certain biases in the tasks in relation to the contents addressed (an abundance of tasks with a geometric component and a scarcity of tasks involving algebra or probability concepts). Most of the tasks are presented in a real context. However, a higher percentage of procedural tasks than problem-solving tasks is observed, with a predominance of low openness, creativity and cognitive demand. These results provide useful lines of work to address difficulties faced by future teachers in the STEAM field.

Revisiting the Eden Project: The geometry of the Domes

The Eden Project in Cornwall, UK, has probably the largest greenhouse complex in the world, comprehending eight interconnected spherical geodesic domes. The geometric design and optimisation of the double-layered spherical structures focussed primarily on the hexagonal grids of the external dome surfaces, where optimisation consisted of minimising the number of component types, being these components, faces, line lengths and angle combinations at grid nodes. The present article reviews the general geometric definition of the Eden Domes and elaborates, for the first time since the domes design around the year 2000, on their geometric optimisation. The results of this rationalisation are presented in colour images, which were produced with state-of-the-art (2021) software tools 20 years after the design development. The images reveal the geometric ‘economy’ – here, the extreme reduction of geometric component types – and the high symmetrical order of these structural configurations. The aim of the present paper is to present the thorough geometric specification of the Eden Domes in a single document that answers in detail the question of how the Eden Domes grids were geometrically constructed.

Complément to the Thurston 3D-geometrization picture

Geometrization says that “any closed oriented three-manifold which is prime (not a connected sum) carries one of the eight Thurston geometries OR it has incompressible torus walls whose complementary components each carry one of four particular Thurston geometries”. These geometric components have finite volume for the hyperbolic geometries. They also have finite volume for each of the two geometries appearing as Seifert fibrations. The remaining pieces have Euclidean geometries of linear volume growth. Then these vertex geometries are combined topologically to recover the original manifold. This, by cutting off the toroidal ends and then gluing the torus boundaries by affine mappings. The point of this work is to make the affine gluing respect an interpretation of the metric geometry in terms of a new notion of “regional Lie generated geometry”. The vertex regions use four geometries in Lie form combined in the overlap edge regions via affine geometry. The theorem solves, using geometrization, a forty-five-year-old question/approach to the Poincaré conjecture. This was described in a 1976 Princeton Mathematics Department preprint and finally documented by Thurston and the second author (1983).

Plaque Structural Stress: Detection, Determinants and Role in Atherosclerotic Plaque Rupture and Progression.

Atherosclerosis remains a major cause of death worldwide, with most myocardial infarctions being due to rupture or erosion of coronary plaques. Although several imaging modalities can identify features that confer risk, major adverse cardiovascular event (MACE) rates attributable to each plaque are low, such that additional biomarkers are required to improve risk stratification at plaque and patient level. Coronary arteries are exposed to continual mechanical forces, and plaque rupture occurs when plaque structural stress (PSS) exceeds its mechanical strength. Prospective studies have shown that peak PSS is correlated with acute coronary syndrome (ACS) presentation, plaque rupture, and MACE, and provides additional prognostic information to imaging. In addition, PSS incorporates multiple variables, including plaque architecture, plaque material properties, and haemodynamic data into a defined solution, providing a more detailed overview of higher-risk lesions. We review the methods for calculation and determinants of PSS, imaging modalities used for modeling PSS, and idealized models that explore structural and geometric components that affect PSS. We also discuss current experimental and clinical data linking PSS to the natural history of coronary artery disease, and explore potential for refining treatment options and predicting future events.