Geometric Elements Research Articles

One-dimensional Carrollian fluids. Part I. Carroll-Galilei duality

Galilean and Carrollian algebras acting on two-dimensional Newton-Cartan and Carrollian manifolds are isomorphic. A consequence of this property is a duality correspondence between one-dimensional Galilean and Carrollian fluids. We describe the dynamics of these systems as they emerge from the relevant limits of Lorentzian hydrodynamics, and explore the advertised duality relationship. This interchanges longitudinal and transverse directions with respect to the flow velocity, and permutes equilibrium and out-of-equilibrium observables, unveiling specific features of Carrollian physics. We investigate the action of local hydrodynamic-frame transformations in the Galilean and Carrollian configurations, i.e. dual Galilean and Carrollian local boosts, and comment on their potential breaking. Emphasis is laid on the additional geometric elements that are necessary to attain complete systems of hydrodynamic equations in Newton-Cartan and Carroll spacetimes. Our analysis is conducted in general Cartan frames as well as in more explicit coordinates, specifically suited to Galilean or Carrollian use.

Asymmetric phase-split axicon masks for a improved Bessel beam-based glass stealth dicing

The precision glass micromachining technology employing ultrashort laser pulses has reached a state of maturity. This technology enables the precise drilling, cutting, or ablation of various types of glass, achieving accuracy up to a few microns. As laser sources continue to advance in average power and repetition rate, the efficient utilization of laser beam irradiation patterns becomes increasingly crucial. The Bessel beam, known for its ability to create elongated channels in transparent materials because of its invariant focal zone, gains significance in this context. The elongated focal zone of the Bessel beam proves advantageous for expeditious glass cutting, surpassing the efficiency of using a standard Gaussian beam. This study delves into the glass-cutting process by studying asymmetric phase-split diffractive axicon masks to generate such Bessel beams. For this purpose, geometric phase optical elements are created using transparent nanogratings inscribed in the volume of glass. This approach allows high-power asymmetric Bessel-like beams to be generated and experimentally used to investigate beam-shaping performance, ultimately determining the optimal parameter set for applications such as glass stealth dicing.

Study on the Deviation Characteristics of Driving Trajectories for Autonomous Vehicles and the Design of Dedicated Lane Widths

The vehicular trajectory offset represents a critical controlling element in the design of lane width. In light of the paucity of extant research on the lane widths for dedicated autonomous vehicle lanes, this study deployed the PreScan-Simulink co-simulation platform. Based on the established typical lateral and longitudinal control methods for autonomous vehicles, we initially identified the primary factors influencing trajectory offset through multifactorial coupled analysis. Subsequently, we conducted quantitative research on vehicle trajectory offset using S-shaped curves to elucidate the patterns in geometric elements’ impact on trajectory offset. Following this, we established a model of the relationship between design speed and trajectory offset under different vehicle types. Ultimately, we calculated the lane width values for scenarios involving varying positions and numbers of dedicated lanes. The results demonstrate that vehicle speed significantly impacts the trajectory offsets of autonomous vehicles. For passenger cars, the mean offset at speeds between 60 and 130 km/h is approximately 10 cm. At higher speeds of 140–150 km/h, the offset is more variable. The range of offset exhibited by trucks at speeds between 60 and 100 km/h is [8 cm, 16 cm]. In the case of a single dedicated lane, the width of the inner lanes intended for passenger cars is [2.60 m, 3.00 m], while the outer lanes designed to accommodate trucks have a width of [3.00 m, 3.20 m]. In scenarios with two dedicated lanes, the width of lanes for passenger cars can be reduced further, whereas the required lane width for trucks remains largely unchanged compared to that for single-lane setups. The conclusions show that the width of lanes adapted to autonomous vehicles could be reduced, which could help to optimize the use of road space, thus potentially reducing the occupation of land resources, reducing the environmental impact of road construction, and contributing to sustainable development. This study also provides valuable insights for the design of lanes dedicated to autonomous vehicles.

Modelling Method and Meshing Characteristics of a Novel Curve-Surface Conjugate Internal Gear Drive

Space exploration has become a major focus in the field of technology, with gear transmissions in aerospace equipment playing a crucial role. In the extreme environment of space, gear transmissions face challenges like large temperature differentials, deformation and maintenance difficulties, which will severely impact transmission accuracy and service life. To meet the growing demands for high-performance gear transmissions with high transmission efficiency and error adaptability in the aerospace field, this paper proposes a novel curve-surface conjugate internal gear drive consisting of an involute internal gear and a curve-surface gear. The fundamental theory of curve-surface conjugation is introduced, and the construction method for curve-surface gear based on a selected contact path and meshing tube is presented. The analysis models including induced curvature, sliding ratio and tooth contact analysis with errors (ETCA) are simulated to evaluate the meshing characteristics. Additionally, prototypes are manufactured and experimental setups are established to validate the transmission performance. These results indicate that as the rotational speed increases, the transmission efficiency of the curve-surface conjugate internal gear drive improves, which is contrary to the trend observed in involute gear drives. And the transmission efficiency of the curve-surface conjugate internal gear drive surpasses that of the involute gear drive at higher rotational speeds. Moreover, this novel gear drive exhibits excellent error adaptability, maintaining intact contact paths and high transmission efficiency even in the presence of assembly errors. This study provides new ideas for the design and manufacture of high-performance gear transmissions from the perspective of spatial geometric elements.

Design and Implementation of a Geographic Scenario Computation System Based on Knowledge Base

Abstract. The promotion and expansion of Geographic Information System (GIS) applications have increased the complexity of geocomputation. The concept of a geographic scene, which encompasses both geographic entities and complex spatial interaction relationships, serves as a means of organizing and expressing geographic information. Existing methods of organizing and computing geographic scenes often focus on single geometric elements or single-category objects, neglecting the complexity of the geocomputation process and leading to biased results. To address this issue, this study designs and implements a geographic scenario computation system based on WebGIS to overcome the lack of integration of knowledge elements in traditional geographic scenario computation methods. The system consists of a data management module, a geographic scenario visualization module, and a geographic scenario computation module. It not only realizes the visualization of geographic scenarios but also introduces a knowledge base into the geographic scenario computation process, enabling accurate management of geographic scenarios. This paper uses a farmland scenario in Shandong Province, China, as a case study to verify the effectiveness and feasibility of the system. The application of this system provides new technical support for the computation process of geographic scenarios, promoting the refinement and intelligent development of geographic scenario management. This method can also be applied to similar applications of intelligent sensors and the Internet of Things in the organization and management of sensing information in the future.

Flotation Performance of Coal: Investigating the Synergistic Effects of Particle Size and Shape, and the Influence of Geometric Elements

Flotation Performance of Coal: Investigating the Synergistic Effects of Particle Size and Shape, and the Influence of Geometric Elements

Eksplorasi Etnomatematika Geometri Bangun Datar Segitiga pada Pakaian Tradisonal Sortopi Khas Suku Batak Toba

Exploration of ethnomathematics in the context of flat geometry, especially triangles, in traditional Batak Toba clothing, is an interesting and important study. This study aims to reveal the relationship between mathematical concepts and local culture, and how geometric elements can be found in the design of Sortopi traditional clothing. This research method uses a qualitative approach with data sources, namely library studies, from several literature reviews according to the topic and purpose of the study. The results of the study show that Sortopi is a complement to traditional Batak clothing used by men as a crown or headband. The shape of Sortopi contains elements of isosceles triangle flat geometry, thus showing that cultural elements are inseparable from mathematics.

On the Structure of Early Neolithic Societies of the Forest Tobol-Ishim Area: morphology and ornamentation of the pottery

The Early Neolithic complexes located in Western Siberia are characterized by the following common determinant features: chronological position within the end of 7,000 – turn of 6,000 cal BC, flat-bottomed vessels, design layouts of vessel necks (lips, rims, collars), and geometric and tree-like ornamental elements. The ceramic complexes are distinguished by different qualitative and quantitative ratios of the types of pottery (Boborykino, Koshkino, Satyga (with rims), comb ceramics, etc.) identified by researchers. When found in the same occupation layer, such a variety of ceramics might be evidence of an unequal sociocultural structure of the Neolithic population groups. The author stand for the concept that ceramic production and new stone processing skills and technologies were introduced (Zach, 2018, 2020) to the indigenous groups with Mesolithic traditions. It resulted in the interaction of autochthonous groups and newcomers and the subsequent merging of their structures, which ran differently in different territories. The author tend to consider the development of “syncretistic” societies in the first stages of such interaction in the Tobol-Ishim Rivers area as a process of transition from the Mesolithic to the Neolithic. Various types of pottery have been recorded at Boborykino complexes. The variety increases at Koshkino complexes, in different settlements and different proportions, which apparently reflects the formation of a new stable cultural tradition. The Kozlovo ceramics became such a tradition, being characterized by round-bottomed vessels with sags in the interior of the rim and a combination of ornaments in mainly incised-receding and comb techniques.

Study on the Influence of Laser Power on the Heat–Flow Multi-Field Coupling of Laser Cladding Incoloy 926 on Stainless Steel Surface

In order to explore the influence of laser power on the evolution of molten pool and convective heat transfer of laser cladding Incoloy 926 on stainless steel surface, a three-dimensional thermal fluid multi-field coupled laser cladding numerical model was established in this paper. The variation of latent heat during solid-liquid phase transformation was treated by apparent heat capacity method. The change in the gas–liquid interface was tracked using the mesh growth method in real time. The instantaneous evolution of temperature field and velocity flow field of laser cladding Incoloy 926 on a stainless steel surface under different laser power was discussed. The solidification characteristic parameters of the cladding layer were calculated based on the temperature-time variation curves at different nodes. The mechanism of the impact of laser power on the microstructure of the cladding layer was revealed. The experiment of laser cladding Incoloy 926 on 316L surface was carried out under different laser power. Combined with the numerical simulation results, the effects of laser power on the geometrical morphology, microstructure and element distribution of the cladding layer were compared and analyzed. The results show that with the increase in laser power, the peak temperature and flow velocity of the molten pool surface both increase significantly. The thermal influence of the molten pool center on the edge is enhanced. The temperature gradient, solidification rate, and cooling rate increased gradually. The microstructure parameters (G/R) are relatively small when the laser power is 1000 W. In the experimental range, the dilution rate and wetting angle of the cladding layer both increase with the increase in laser power. When the laser power is 1000 W, the alloying elements of the cladding layer are more evenly distributed and the microstructure is finer. The experimental results are in good agreement with the simulation results.

The safety impacts of paved shoulder width in Indian four-lane rural highways

The shoulder width, as a geometric element, plays a crucial role in enhancing highway safety. Research from high-income countries indicates that improving shoulders on highways leads to substantial safety benefits. However, the safety effectiveness of paved shoulders for low- and middle-income countries (LMICs) highway contexts has limited evidence. This study evaluated the safety effectiveness of the paved shoulder width on 61 km, four-lane, divided rural intercity highways in India. The first objective was to evaluate highway crash patterns using data from 2016 to 2019. The second objective was to evaluate the safety effectiveness of paved shoulder width using the case-control approach. The findings of this study demonstrate a consistent decline in the likelihood of crashes as the shoulder’s width increases within the range of zero to 2.5 m for the 100 m segment length and zero to 1.7 m for the 500 m segment length. Nevertheless, model estimates indicate an increased crash risk for shoulders wider than 2.5 m. The results also suggested that the odds ratio for paved shoulder widths ranging from no shoulder to 2.5 m is likely to follow the crash modification factor from the highway safety manual. The findings of this study hold significant implications for the design policy of shoulder width on rural highways in LMICs.

Evaluation of the Implementation Status of the Nepal Rural Road Standards (NRRS) Concerning Geometrical Parameters: A Case Study of Morang District of Nepal

Maintaining the effectiveness of the transportation system is essential to economic growth. Poor road upgrading methods in many developing nations, however, are making it impossible for traffic to flow freely. Nepal developed the Nepal Rural Road Standards (NRRS) of 2055, District Transportation Master Plan (DTMP), and Municipality Transportation Master Plan (MTMP) to regulate the construction of rural road infrastructure. These guidelines provide guidelines for rural road planning, design, building, and maintenance, among other aspects. However, each geometric design has certain features, and parameter requirements depending on the region and location to be applied. This study aims to compare the geometrical features of the rural roads that have been built with the Nepal Rural Road Standards (NRRS) 2055, second revision (2071). Using a random sampling approach, six rural roads in the Morang district were selected for the data collection. To gather geometrical data, field observations and measurements were made at random chainages. This study evaluates various geometric parameters using linear and angular field measurements. Mapping conducted via smart road software ensures road geometry compliance, including aspects such as curve radius, shoulder width, gradient, sight distance, carriageway, and additional widening. The findings demonstrate that strict adherence to established standards substantially enhances road safety. Based on the results of the field observation, the geometric elements have been built according to design specifications, except for the additional widening at shoulder width and horizontal.

The Analysis of Cultural Literacy in Ethnomathematics used by The Animaker Website at The Kramat Buyut Trusmi Mosque

Ethnomatematics is mathematics that connects mathematical concepts with elements of culture or everyday life. This research aims to identify and describe ethnomathematics in the Kramat Buyut Trusmi Mosque building as a learning resource assisted by the animaker website. Animaker is a medium for creating explanatory videos and presentations. The research carried qualitative research with an ethnographic approach where this approach leads to observation and has a role as part of field research. Researcher played the role of planning, collecting information, documenting and also analyzing information or data, who will then choose anyone as a source of data or information. Data analysis through data collection techniques, data reduction, data presentation, and also drawing conclusions. The results of the research showed that several buildings in the Kramat Buyut Trusmi Mosque include Gapura Kori Agung which is an example of a building that contains elements of spatial plane geometry such as a rectangular pyramid on the roof of the building, a tube structure found in a water barrel located not far from the door gate, in the gate there are also geometric elements of transformation such as reflection or mirroring.

Influence of horizontal alignment elements on operating speed of vehicles on two-lane highways

Earlier studies acknowledged that the design speed does not principally assure consistency in the design of highway geometric elements. Methodologies for estimating operating speeds are limited to specific or local traffic conditions and design standards, as in various studies conducted on two-lane and multi-lane highways. The present study develops operating speed models of the vehicle types observed on horizontal curves and tangent sections on two-lane highways in southern parts of India. Geometric features of the curve section and adjacent tangent sections, such as the radius of the curve, curve length, deflection angle, degree of curvature, gradient, carriageway width, and shoulder width, are obtained from the field. The speed data collected at 24 locations on the highway, including curved and tangent gradient sections, are used to analyze and model operating speed. The results indicate that the inverse of the square root of the radius appears to be an influencing parameter for modeling the operating speed of vehicles. The operating speed is sensitive for a curve radius of up to 600 m; thereafter, the operating speed appears insignificant. On tangent sections, the gradient has a larger influence on the operating speeds of all vehicle types. The operating speed models are validated and compared with models available in the literature. The proposed models developed in the present study are helpful to traffic engineers for predicting the operating speed on two-lane highways.

An Efficient Algorithm for Gravity Forward Modeling (GFM) with Masses of Arbitrary Shapes and Density Distributions

Summary Currently, gravimetric forward modelling of mass density structures with arbitrary geometries and density distributions typically involves subdividing the mass body into individual geometric elements (such as rectangular prisms), calculating their gravitational contributions that are then summed up to obtain the gravitational attraction of the whole body. To achieve a more accurate approximation of the true geometric shape and density distribution, this rectangular prism model requires fine dividing, which significantly increases computational load and reduces numerical efficiency. To address this issue, we propose the algorithm for gravimetric forward modeling of arbitrary geometric shapes and density distributions in spectral domain that significantly improves numerical efficiency while preserves computational accuracy. The novelty of our proposed algorithm lies in dividing the masses into multiple layers of equal thickness in the vertical direction, providing constant upper and lower bounds. This allows to extended Parker's formulas and apply the Fast Fourier Transform (FFT) to increase numerical efficiency. The algorithm is tested using synthetic models and then used to compute gravitational effects of topography and sediments using real data from Tibet. Results show high accuracy and numerical efficiency than rectangular prism approach.

Taking Advantage of the Aesthetic Values of Asiri Art Decorations to Enrich and Sustain the Printing of Modern Women’s Clothing Supplements to Preserve Saudi Heritage Using Artificial Intelligence Techniques

Sustainability is the result of modern-day design philosophy as a result of major industrial developments and many conflicts and wars. This concept is what prompted this research to focus on the possibility of achieving the principles of sustainability practically - in field reality - through the use of artificial intelligence techniques to create contemporary designs derived from the Saudi Asiri heritage and employ them in printing sustainable clothing supplements. Heritage-inspired design has cultural meaning and importance, and its purpose is to transmit our heritage to our emerging generations, and therefore it is considered a type of sustainable thought. The Asir region in the Kingdom of Saudi Arabia has a rich heritage that is greatly influenced by the charming nature of the place. The Asir region is distinguished by the art of the “Asiri Cat,” which consists of engravings, lines, and aesthetic formations engraved by women specialized in this field. They inherited this art from the women who preceded them. Asiri art is distinguished from other arts. The use of bright natural colors such as blue, green, orange, black and white, as the Asir region is considered one of the important heritage and tourist areas within the Kingdom of Saudi Arabia, has played a pivotal role in enriching the cultural and creative stock not only of the Saudi citizen, but also of the Arabian Gulf region. This is what prompted us in the current research to delve into the analysis of the creative and artistic aspects of Asiri art inscriptions and to benefit from the aesthetic values of Asiri art decorations in contemporary artistic designs that achieve sustainability for the purpose of exploiting them in the manufacture of plastic fittings for clothing supplements to serve small industries. Many diverse designs have been implemented using different printing techniques. From (direct drawing method - stencil printing - pictorial screen printing) the use of different types and colors to implement different products to produce clothing accessories that are closely related to the structure of form and content of Al-Qat Al-Asiri art, and depends on its aesthetic philosophy about the heritage and cultural references associated with the place and the artist’s own vision. To revive Saudi heritage. The research aims to take advantage of the geometric and floral decorative elements in Al-Qat Al-Asiri’s artistic engravings as a source for enriching and sustaining printed designs for women’s clothing supplements that are characterized by authenticity and contemporaryness, and preserving popular motifs by reformulating them. In keeping with the times, and preserving its most prominent features, in a way that enhances belonging and preserves the community’s heritage and values. From extinction, endless horizons of creativity and innovation have been achieved in the field of printing clothing supplements, and sustainable plastic repetition, which the designer or art practitioner resorts to in general, and the field of printing in particular, as a creative pluralistic plastic method.The research followed the descriptive and analytical approach in identifying the origins and characteristics of the Asir artistic inscriptions (the cat), analyzing their vocabulary, reformulating them, and drawing inspiration from them to enrich the printed designs of women’s clothing supplements, in addition to the experimental approach in the applied study through the use of different techniques and materials. The results of the study concluded that there are various aesthetic values in the Asiri cat engraving that can be used to create contemporary designs on clothing accessories using different printing techniques, in order to preserve the Asiri heritage in the southern region of the country. The study recommended the need to pay attention to studying heritage and the arts it contains because of its great importance, as it stimulates appreciation of traditional art and preserves it.

Elastic properties identification of a bio-based material in tertiary packaging: Tools and methods development

This study focuses on the use of bio-based materials for structural purposes in the packaging field, which requires the identification of their mechanical properties at a representative scale. The mechanical properties of bio-based materials are more variable than those of traditional composite materials. In a standard characterization approach using elemental coupons under uniaxial loading, the variability depends on the chosen representative elementary volume (REV), free edges, boundary conditions, etc. for elastic properties that are not identified for representative working conditions; this could lead to the ineligibility of these bio-based materials as structural materials. This paper contributes to the debate on how to study the response of bio-based materials within a structure, here a packaging structure as a logistic unit (LU) subjected to a compressive load simulating storage and stacking conditions. In the set of tools and methods for the design of packaging materials made of bio-based materials, an elastic nonlinear geometric finite element model (FEM) and an experimental approach are presented. The FEM allows the numerical identification of zones of interest within the LU. Inevitably, the FEM classically requires input data which are elastic properties of the equivalent homogeneous material. The design of the FEM is based on a calculation-test approach using an existing reference LU and it can be summarized in two main steps. The first step concerns the development of a FEM able to restore the experimental conditions of vertical compression imposed by transport standards for packaging. The second step is based on updating the input properties of the FEM by reverse identification, to achieve the representative working condition properties, using experimental results obtained on the existing reference LU. For the reverse identification a multi-scale investigation is mandatory. For this purpose, the linear elastic part of the load/vertical displacement curves (at the LU stiffness scale) and the displacement and strain fields measured (at the local LU scale) by 3D digital image correlation (3D DIC) are evaluated. Then, FEM property updating is carried out by reducing the deviation of displacement/strain fields between FEM and experimentally measured results (3D DIC). Finally, we explain how FEM and 3D DIC help in decision-making by allowing the recognition of zones of interest in a phase of design of new LUs with the concept of Multi-Instrumented Technological Evaluator (MITE).

A Method for Recognition and Coordinate Reference of Autonomous Underwater Vehicles to Inspected Objects of Industrial Subsea Structures Using Stereo Images

To date, the development of unmanned technologies using autonomous underwater vehicles (AUVs) has become an urgent demand for solving the problem of inspecting industrial subsea structures. A key issue here is the precise localization of AUVs relative to underwater objects. However, the impossibility of using GPS and the presence of various interferences associated with the dynamics of the underwater environment do not allow high-precision navigation based solely on a standard suite of AUV navigation tools (sonars, etc.). An alternative technology involves the processing of optical images that, at short distances, can provide higher accuracy of AUV navigation compared to the technology of acoustic measurement processing. Although there have been results in this direction, further development of methods for extracting spatial information about objects from images recorded by a camera is necessary in the task of calculating the exact mutual position of the AUV and the object. In this study, in the context of the problem of subsea production system inspection, we propose a technology to recognize underwater objects and provide coordinate references to the AUV based on stereo-image processing. Its distinctive features are the use of a non-standard technique to generate a geometric model of an object from its views (foreshortening) taken from positions of a pre-made overview trajectory, the use of various characteristic geometric elements when recognizing objects, and the original algorithms for comparing visual data of the inspection trajectory with an a priori model of the object. The results of experiments on virtual scenes and with real data showed the effectiveness of the proposed technology.

EXPLORE THE IMPORTANCE OF THE ASPECTS OF SHADOW AND LIGHT AS A FUNDAMENTAL TOOL IN PENCIL DRAWING

In this written article in pencil drawing, which is one of the foundations of fine art, be it household items, geometric elements, landscape or portrait, in all of them the main tool is the light and shadow aspects. Each step is illustrated with drawings.

Eksplorasi etnomatematika dalam kesenian sikambang pada masyarakat kota Sibolga

This study aims to determine the ethnomathematics values contained in Sikambang art, which is the traditional art of the people of Sibolga City, North Sumatra. This research is qualitative research using an ethnographic approach. Research data collection techniques consist of observation, interviews and documentation. The collected data will be analyzed in three stages: data reduction, data submission, and verification. Next, the data will be examined based on four criteria: trustworthiness, transferability, dependability, and certainty. The results show that mathematical concepts are inherent in the culture of the people of Sibolga city, namely Sikambang art which has geometric elements, such as angles (acute, right, obtuse), lines (straight, curved, parallel, intersecting), and flat shapes (triangles, rectangles). , square, and circle). By incorporating ethnomathematics into the school curriculum, students' mathematics learning can become more contextual and meaningful. This study also helps maintain Sikambang art as a local cultural heritage that is increasingly marginalized by contemporary developments.

Notas sobre escultura e Notas sobre escultura, parte 2

The articles “Notes on Sculpture” and “Notes on Sculpture, Part 2” by Robert Morris mark a milestone in the history of sculpture, challenging traditional notions of form and function. The emphasis on basic geometric elements and the understanding of sculpture as a spatial event, rather than a static object, transformed artistic discourse. By proposing an approach centered on the viewer’s experience and the work’s interaction with the environment, Morris paved the way for Minimalism. Through his reflections, the artist significantly expanded the possibilities of sculpture, influencing contemporary art production and criticism in a decisive manner.