Flat Geometry Research Articles

Monolithic U-shaped crystal design for TOF-DOI detectors: a flat top vs. a tapered top.

For brain-dedicated positron emission tomography (PET) scanners, depth-of-interaction (DOI) information is essential to achieve uniform spatial resolution across the field-of-view (FOV) by minimizing parallax error. Time-of-flight (TOF) information can enhance the image quality. In this study, we proposed a novel monolithic U-shaped crystal design that had a tapered geometry to achieve good coincidence timing resolution (CTR) and DOI resolution simultaneously. We compared a novel tapered U-shaped crystal design with a conventional flat-top geometry for PET detectors. Each crystal had outer dimensions of 5.85 × 2.75 × 15 mm³, with a 0.2 mm central gap forming physically isolated bottom surfaces (2.85 × 2.75 mm²). The novel U-shape crystal design with tapered top roof resulted in the best CTR of 201±3 ps, and DOI resolution of 3.1±0.6 mm, which were better than flat top geometry. In the next study, we plan to optimize the crystal surface treatment and reflector to further improve the CTR and DOI resolution.

Observation of NMR signals from samples with flat geometry: Application to in-situ analysis of a direct ethanol fuel cell.

Most NMR samples are cylindrical, which is ideal for obtaining high-resolution NMR spectra, especially in superconducting magnets with a vertical bore. However, expanding NMR applicability to samples that are not necessarily cylindrical requires a new approach. In this study, we introduce a method for obtaining solution NMR signals from flat samples, such as flat containers or layered structures like a fuel cell. A flat rectangular NMR coil was developed for RF application and sensitive signal detection, while biplanar shim coils were designed using Bfieldtools and manufactured on multilayered printed circuit boards to improve NMR resolution. Water and ethanol molecules in flat rectangular and flat circular containers, as well as in a direct ethanol fuel cell, were observed with narrow NMR linewidths. We believe that our spectrometer design will enable NMR analysis of samples that need to be contained in flat structures and support in-situ analysis of various devices.

Analisis Kemampuan Pemahaman dan Pemecahan Masalah pada Siswa Kelas VIII UPT SMP Negeri 27 Medan Terhadap Materi Bangun Datar dan Ruang

This study is a descriptive study with a qualitative approach that aims to analyze the errors made by students in solving mathematics problems, especially on flat and solid geometry materials using the Newman Theory approach. The subjects in this study were 30 seventh grade students at SMP Negeri 27 Medan. The method of collecting data or information was carried out through a written test of 3 (three) descriptive questions and interviews with selected subjects. The information obtained was then analyzed based on the Newman analysis procedure which is divided into 5 (five) stages of errors, namely reading, understanding, transformation, process skills, and writing answers. The results of the analysis showed that the most significant errors occurred at the transformation stage, with a percentage of 83.3%, categorized as very high. On the other hand, errors in process skills were classified as very low, namely 16.6%. This finding shows the importance of developing more effective learning methods to help students understand and solve mathematics problems, especially those related to geometric concepts.

Superconducting DC busbar with low resistive joints for all-electric aircraft propulsion system

High-temperature superconductors (HTS) can carry high currents with almost zero loss when transmitting direct current (DC). Their compact size and lower weight make them suitable for the application of all-electric aircraft. However, the current carrying capability of a single HTS tape is limited to a few hundred amps; therefore, for high-current applications, multiple HTS tapes need to be connected in parallel. The flat geometry of HTS tape and its critical current (IC) dependence on strain complicate grouping them in parallel. Furthermore, the length of HTS tape is limited by its crystal structure, necessitating low-resistance joints for extended applications. A superconducting busbar design for high-current applications is developed and tested to address these challenges. The superconducting busbar is designed in a way that it helps to reduce the effect of the self-field on critical current and also ride through the fault events. Yttrium barium copper oxide (YBCO) tapes are used to develop the busbar prototype, tested against DC currents in a liquid nitrogen environment. Joint optimization is carried out to determine the required length for efficiently joining HTS tapes. Two busbar prototypes are developed with 180° and 90° joints to join 5 HTS tapes and tested in self-field. A joint resistance of 100 nΩ is measured at self-field for the 180° joint busbar, and 800 nΩ is measured for the 90° joint busbar. Both busbar prototypes are subjected to power cycling and thermal cycling to assess joint performance in self-field and any degradation of the joint electrical parameters during testing.

Development of a lab-based In situ XCT oven for vacuum-bag processing of prepreg laminates

Real-time 3D microstructure changes in prepreg laminates during curing was observed using widely available X-ray Computed Tomography (XCT) hardware at high temporal resolution (2 min) and spatial resolution (25 µm voxel size). The methodology was demonstrated in a cylindrical convection oven with an internal diameter of 100 mm, a heating rate of 2°C/min, a maximum operating temperature of 135°C, and an integrated vacuum line. The technique was applied to three representative carbon fibre reinforced epoxy prepreg samples having flat, tapered and corner geometries. The increasingly complex geometries lead to higher void mobility and thickness changes that were captured in 40-50 mm size samples. Image processing of the XCT data was enhanced by the use of deep learning semantic segmentation for feature extraction. Uninterrupted microstructure evolution was visualised in larger samples and more realistic processing conditions than previous lab-based In Situ XCT studies.

Analisis Perkembangan Berpikir Kreatif Siswa dalam Menyelesaikan Masalah Matematika yang Melibatkan Pengetahuan Awal

This study aims to analyze the development of students' creative thinking skills in solving mathematical problems, particularly in the context of flat geometry. The research was conducted at SMP Buq’atun Mubarakah, involving two eighth-grade students as subjects. A qualitative descriptive method was used, with data collected through written tests and interviews to understand the students' thinking processes. Data were analyzed using descriptive and thematic analysis techniques, evaluating students' answers based on indicators of creative thinking skills, such as fluency, flexibility, originality, and elaboration. The results indicate that students can generally understand problems but still face difficulties in applying mathematical concepts, especially in measurements and the perimeter of flat shapes. Students tend to make mistakes in interpreting and solving more complex problems, indicating a need to enhance their creative thinking skills. The implications of this study highlight the importance of strong instructional support and teaching methods that encourage exploration, the use of varied strategies, and technology integration to improve students' creative thinking abilities.

Exploration of Ethnomathematics in Traditional Javanese Cakes

Mathematical concepts are used to explore the existence of mathematics in Javanese culture, expecially in traditional Javanese food. Given the current research that discusses traditional Javanese food/cakes is very rare and there is still a lack of public knowledge about ethnomathematics. This study aims to explore the concept of geometry contained in traditional Javanese cakes. This study is qualitative research was conducted in Prapat Janji Village, Buntu Pane District. The instruments used are human instruments. Researchers communicate directly with the object of research and actively participate in data collection, both in literature studies, interviews, documentation, surveys, and observations. The results of this study showed that the traditional Javanese cake there is the concept of flat Geometry on Getuk (Rhombus), Wajik (Parallelogram), Serabi (Circle), Lupis (Triangle), Kue Lumpur (Cylinder), Lemper (Cylinder), Kue Jadah (Cube), Klepon (Sphere), Kue Lapis (Cuboid). Ethnomathematics in traditional Javanese cakes can be used as a source of learning mathematics geometry material.

Global Thermal Instability in the Spherical Interstellar Clouds

Thermal instability (TI) is a trigger mechanism, which can explain the formation of small condensations through some regions of the interstellar clouds. The instability criterion for flat geometry approximations has been investigated in previous works. Here, we focus on spherical perturbations in the spherical clouds. Our goal here is to examine the conditions for the occurrence of TI through the thermally dominated (i.e., gravitationally stable) quasi-static spherical interstellar clouds. First, we obtain the profiles of density, temperature, pressure, and enclosed mass of a symmetric spherical cloud. Then, we use the perturbation method to investigate the linear regime of instability and find its growth rate. Considering spherical perturbations on the quasi-static spherical cloud, instead of a thermal and dynamical equilibrium flat cloud, changes the instability criterion so that we can conclude that sphericalness can increase the occurrence of TI. The results show that in the spherical clouds, perturbations with shorter wavelengths have more chance to grow via TI (i.e., greater growth rates).

Investigation of anisotropic characteristics in ultra-precision grinding of sapphire crystal planes and strategies for suppression

Sapphire has been extensively utilized due to its excellent infrared transmittance. The demand for sapphire optical components has transitioned from flat geometries to more complex curved geometries. This transition necessitates the processing of sapphire from a single crystal plane to multiple crystal planes, presenting a significant challenge. To gain a comprehensive understanding of the anisotropy present in the machining of sapphire multiple crystal planes and to explore strategies for its suppression, various grinding wheels were employed for ultra-precision grinding of the sapphire A-plane, C-plane, M-plane, N-plane, and R-plane. This investigation encompassed multiple facets, including surface roughness, surface topography, residual stress, acoustic emission time-frequency characteristics, and infrared transmittance. A thorough analysis was conducted on the morphology of corrosion damage and the anisotropic mechanisms involved in sapphire ultra-precision grinding, as well as the resulting grinding quality following the implementation of suppression strategies. The findings indicate that the A-plane, C-plane, and M-plane of sapphire exhibit significant anisotropic characteristics when ground with the D25 resin bond grinding wheel, whereas the N-plane and R-plane do not display such characteristics. Furthermore, the application of the D3 ceramic bond grinding wheel effectively suppresses the anisotropy in the grinding of different sapphire crystal planes, achieving a high-quality surface finish with a ductile domain exceeding 90 %, and ensuring high uniformity in the ultra-precision grinding of various sapphire crystal planes.

Development of CABATAR Learning Media on Plane Geometry Material to Improve Numeracy Skills of 4th Grade Students at SDN Susukan 04 Pagi

This research develops the CABATAR learning media based on the Canva application to improve the numeracy skills of fourth-grade students on flat geometry material at SDN Susukan 04 Pagi. The research uses a Research and Development (R&D) approach, with both qualitative and quantitative methods. Data was collected through interviews, questionnaires, and validation by media and material experts. The study found that the CABATAR media was validated with 91.25% by media experts and 94.16% by material experts, both categorized as "Very Feasible." A small group of 10 students and a larger group of 31 students were involved in the trial, with student responses reaching an average of 90% and 89% from teachers, all categorized as "Very Feasible." Additionally, the pretest-posttest results showed a moderate improvement in numeracy skills, with an N-gain value of 0.62. The findings indicate that CABATAR media is an effective tool for enhancing numeracy skills in elementary school students and can be a valuable addition to flat geometry material in mathematics lessons.

Flat-Slab Mechanics Transforming Double-Arc Expressions Along the Middle America Trench

The southeast–northwest variation in the trench–volcano distance along the Middle America subduction zone is widely recognised to be due to the horizontal (flat) geometry of the descending Cocos plate (slab) in its northwestern part. In the topographic and gravitational expressions, the southeastern segment forms doubled low–high (i.e. trench–continental shelf edge–oceanic basin–volcanic arc) belts, whereas the northwestern segment forms wide doubled low–high belts. To define their attribution, the surface uplift rates were computed from a two-dimensional dislocation-based subduction model with hypocentre-based plate interface geometries. The trench-perpendicular plate-interface profiles exhibited similar curvature compositions, which were reflected in three (shallow, moderate depth and deep) convexities (downward bends) and one concavity (upward bend) between the moderate-depth and deep convex sections. The steady subduction along the first and second positive curvatures (shallow and moderate-depth convexities) in the southeastern and northwestern segments could serve as mechanical sources of short-wavelength double-arc formation. The latter two (negative and third positive) curvatures (concavity and deep convexity) in the northwestern segment produced distinct features including the narrow continental shelf, large trench–volcanic-arc distance and relevant long-wavelength double arcs. This was attributed to the direct contact of the flat elastic slab with the overriding plate.

The observational evidence that all microflares that accelerate electrons to high energies are rooted in sunspots

Context. In general, large solar flares are more efficient at accelerating high-energy electrons than microflares. Nonetheless, sometimes microflares that accelerate electrons to high energies are observed. Their origin is unclear. Aims. We statistically characterized microflares with strikingly hard spectra in the hard X-ray (HXR) range, which means that they are efficient at accelerating high-energy electrons. We refer to these events as “hard microflares”. Methods. We selected 39 hard microflares, based on their spectral hardness estimated from the Solar Orbiter/STIX HXR quicklook light curves in two energy bands. The statistical analysis is built on spectral and imaging information from STIX combined with extreme ultraviolet (EUV) and magnetic field maps from SDO/AIA and SDO/HMI. Results. The key observational result is that all hard microflares in this dataset have one of the footpoint rooted directly within a sunspot (either in the umbra or the penumbra). This clearly indicates that the underlying magnetic flux densities are large. For the events with the classic two-footpoints morphology, the absolute value of the mean line-of-sight magnetic flux density (and vector magnetic field strength) at the footpoint rooted within the sunspot ranges from 600 to 1800 G (1500 to 2500 G), whereas the outer footpoint measures from 10 to 200 G (100 to 400 G), therefore about ten times weaker. In addition, approximately 78% of the hard microflares, which exhibited two HXR footpoints, have similar or even stronger HXR flux from the footpoint rooted within the sunspot. This contradicts the magnetic mirroring scenario. The median footpoint separation, measured through HXR observations, is approximately 24 Mm, which aligns with regular events of similar GOES classes. In addition, about 74% of the events could be approximated by a single-loop geometry, demonstrating that hard microflares typically have a relatively simple morphology. Out of these events, around 54% exhibit a relatively flat flare loop geometry. Conclusions. We conclude that all hard microflares are rooted in sunspots, which implies that the magnetic field strength plays a key role in efficiently accelerating high-energy electrons, with hard HXR spectra associated with strong fields. This key result will allow us to further constrain our understanding of the electron acceleration mechanisms in flares and space plasmas.

Optimization of Tip Seal Grooves for Aerodynamic and Durability Improvements of Small-Core Turbines

Abstract While the gap between the turbine rotor tip and the outer case in a gas turbine engine is necessary for engine function, the gap is kept as small as possible due to the detrimental effect of the flow over the turbine tip. With the increased investments in ultra-high bypass turbofans, blade tip clearances are increasing in relative size to the turbine rotor, as engines move towards smaller cores. In this work, an optimization of a rotor tip seal with discrete axisymmetric grooves was explored computationally using RANS simulations. The optimization was applied at two tip clearances representing a nominal and small-core-scaled geometry, and with both flat- and squealer-tipped blades. The multi-objective optimization was designed to maximize rotor efficiency and minimize tip heat load. Several casing designs were identified for each tip configuration that both increased efficiency and reduced the heat load into the rotor tip. However, some optimal tip seal designs were composed of grooves that were demonstrated to be detrimental in prior work. Furthermore, grooves were more effective at increasing efficiency when applied to flat tipped geometries – increasing efficiency by 0.9 points over the ungrooved baseline with flat tipped blades, as opposed to 0.25 points over the ungrooved case with squealer tipped blades. Finally, optimal seal geometries that were obtained from the small-core scaled clearance gap optimizations maintained near optimal performance when evaluated at the design tip clearance, while those geometries developed at the design clearance experienced greater tip gap sensitivity.

Scalable electrospinning using a desktop, high throughput, self-contained system

Electrospinning is a specialized processing technique for the formation of submicron diameter fibers of polymeric and ceramic materials using an electrostatic field. The process has multiple advantages over other nano- and micro- fiber synthesis methods; however, generally suffers from very low fabrication speeds, making it undesirable for scalability. This work assesses the performance of a needle-less, self-contained, high throughput electrospinning system. It further compares the fiber fabrication rates obtained versus two single needle setups with different collectors: (i) a conventional single needle and flat plate geometry, and (ii) a single needle with a rotating collector geometry. Polyvinylpyrrolidone (PVP) in ethanol was used as the model material. The fabrication rate of the high throughput system “HTES” was measured at about 2.6 g/h and was about 15 times that collected of the flat plate. Comparing it to other systems reported in the literature also proved it to be a viable option for high throughput, lab scale electrospinning.

Study of halogen interactions in dichlorovinyldiazenes: Structural analysis, DFT simulation and molecular modeling

In recent years, our research group has synthesized about two hundred different dihalogenated vinyldiazenes. The analysis revealed that the type (conformation) of the compounds is the same-"bike stop", but the properties and nature of intermolecular interactions are different. The concepts of the nature of halogen-halogen relationships recommended by IUPAC (2013) do not explain the nature of the observed intermolecular interactions in the synthesized systems. In this paper, for the first time, using the examples of the compounds presented below, an algorithm is built for the relationship between the structure of synthesized compounds and their properties, and the nature of non-covalent interactions involving the chlorine atom.The molecules presented in this paper were studied by the DFT method using the hybrid potential of B3LYP with the Gaussian 09 software package. The extended basis 6-311++G(d,p) with polarization and diffusion functions was used for calculations. Conducted NBO analysis of atomic charge populations. Calculations of the structural parameters of the synthesized systems were carried out in order to study the reactivity, molecular properties and identify the nature of non-covalent interactions involving the halogen atom. It has been established that the Cl–C–Cl triad has a flat geometry and is capable of forming atypical non-covalent interactions both with each other and with various coplanar systems.

High‐Pressure Cell for In Situ Grazing Incidence XAS Characterization of Model Catalysts on Planar Supports

AbstractThe growing interest in physically deposited model catalysts for uncovering complex structure‐activity relationships is spurred by the possibility of depositing nanoparticles of precise atomic structure and composition using cluster‐beam sources. However, the limitations accompanying these synthesis techniques, such as low deposition rates and flat sample geometry, present a challenge for in situ structural characterization using bulk‐sensitive methods, such as X‐ray absorption spectroscopy (XAS), especially at elevated pressures (1–100 bar). To overcome this challenge, we constructed an in situ XAS cell operating in a grazing incidence (GI) geometry. The GIXAS cell was used to investigate the structure of cluster‐beam‐generated Pd and Au0.3Ag0.7 nanoparticles under CO2‐to‐methanol hydrogenation conditions (230 °C, 20 bar, CO2:H2=1 : 3). These nanoparticles, with metal loading of 0.96–10 μg cm−2, demonstrated stability and resistance to sintering upon activation in H2 at 120 °C and catalytic conditions, revealed by in situ XAS. The promising results from our work will help bridge the gap in the investigation of model catalytic materials produced by gas‐phase cluster deposition at industrially relevant pressures and temperatures, which is vital for a mechanistic understanding of catalytic processes.

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.

The common solution space of general relativity

We review the solution space for the field equations of Einstein's General Relativity for various static, spherically symmetric spacetimes. We consider the vacuum case, represented by the Schwarzschild black hole; the de Sitter-Schwarzschild geometry, which includes a cosmological constant; the Reissner-Nordström geometry, which accounts for the presence of charge. Additionally we consider the homogenenous and anisotropic locally rotational Bianchi II spacetime in the vacuum. Our analysis reveals that the field equations for these scenarios share a common three-dimensional group of point transformations, with the generators being the elements of the D⊗sT2 Lie algebra, known as the semidirect product of dilations and translations in the plane. Due to this algebraic property the field equations for the aforementioned gravitational models can be expressed in the equivalent form of the null geodesic equations for conformally flat geometries. Consequently, the solution space for the field equations is common, and it is the solution space for the free particle in a flat space. This approach open new directions on the construction of analytic solutions in gravitational physics and cosmology.

Friction stir processing: A thermomechanical processing tool for high pressure die cast Al-alloys for vehicle light-weighting

This study uses friction stir processing (FSP) for thermomechanical processing of high-pressure die-casting (HPDC) to modify microstructure and improve mechanical properties. FSP is carried out on two different HPDC aluminum alloys: (a) general-purpose, high-iron, HPDC A380 alloy and (b) premium quality, low-iron HPDC Aural-5 alloy in thin wall, flat plate geometry. Subsequent mechanical testing shows ∼30 % and ∼65 % enhancement in yield strength and tensile ductility. In addition, FSP leads to ∼10 times improvement in fatigue life for A380 alloy and ∼70 % improvement in fracture toughness for Aural-5 alloy. These findings emphasize the capability of FSP to modify the microstructure of HPDC Al-alloys-based structural components so that they can demonstrate a good combination of strength, ductility, fracture toughness, and high fatigue properties for long-term durability and reliability.

The harmonic background paradigm, or why gravity is attractive

In a work by Visser, Bassett and Liberati (VBL) (Nucl Phys B Proc Suppl 88:267, 2000) a relation was suggested between a null energy condition and the censorship of superluminal behaviour. Their result was soon challenged by Gao and Wald (Class Quantum Grav 17:4999, 2000) who argued that this relation is gauge dependent and therefore not appropriate to find such connections. In this paper, we clear up this controversy by showing that both papers are correct but need to be interpreted in distinct paradigms. In this context, we introduce a new paradigm to interpret gravitational phenomena, which we call the Harmonic Background Paradigm. This harmonic background paradigm starts from the idea that there exists a more fundamental background causality provided by a flat spacetime geometry. One of the consequences of this paradigm is that the VBL relation can provide an explanation of why gravity is attractive in all standard weak-field situations.