Trapezoidal Shape Research Articles

Dual Temperature- and pH-Responsive Layered Hydrogels Synthesized via Halogen Bond-Based Solid Phase Radical Polymerization.

Stimuli-responsive shape-changing layered hydrogels were, for the first time, prepared via solid-phase polymerization, where halogen bond-based solid-phase radical polymerization was utilized. Monomer cocrystals were assembled to form predetermined layered structures before polymerization, and all layers are polymerized at one time. AB bilayer and ABA and ABC trilayer hydrogel sheets that consisted of temperature- and pH-responsive layers were prepared. The obtained layered sheets were responsive to temperature and pH in dual manners at relatively wide ranges of temperature (5-65 °C) and pH (2.0-11.0). The bilayer sheets exhibited bending upon stimuli. The bending angle was tunable, and the bending direction (negative and positive directions) was also switchable in response to temperature and pH. The trilayer sheets exhibited switchable concave, trapezoid, and convex shape changes with modulated angles, which were unprecedented shape changes. Because of the ease of operation and wide monomer scope (using radical polymerization and halogen bonding), the present method offers a facile and versatile approach to fabricate stimuli-responsive shape-changing hydrogel materials.

Image-Based Analysis of Correlation Between Valve Stent Deformation and Valve Function in Transcatheter Aortic Valve Replacement.

Currently, there remains a paucity of research on the deformation and valve function of transcatheter heart valves (THV) in patients with aortic regurgitation (AR) following transcatheter aortic valve replacement (TAVR). This study aimed to thoroughly explore the correlation between THV deformation and postoperative hemodynamics in these patients. In this study, we assessed 39 AR patients treated with the J-Valve THV system during TAVR. We utilized postoperative cardiac-enhanced computed tomography angiography (CTA) to examine the extent of stent deformation, correlating these measurements with concurrent echocardiographic data. Among patients with AR, the J-Valve exhibited three distinct configurations: rectangular, trapezoidal, and inverted trapezoidal shapes. The rectangular configuration showed a trend toward a larger effective orifice area (EOA) compared to the trapezoidal and inverted trapezoidal configurations (rectangular: 2.20 ± 0.11 cm², trapezoidal: 1.88 ± 0.08 cm², inverted trapezoidal: 2.04 ± 0.08 cm²; p = 0.068). Stratified analysis of the degree of inclined commissural posts indicated that THVs with all three commissural angles < 5° exhibited the highest standard EOA (sEOA). An increase in the number and degree of inclined commissural posts correlated with a decrease in sEOA. Furthermore, a higher EOA was observed when the expansion in the mid and transition level exceeded 80%. During the TAVR procedure, ensuring sufficient expansion in the mid and transition level of the stent, maintaining the stent in a rectangular configuration, and avoiding tilting of the commissural posts contribute to achieving favorable postoperative hemodynamics.

Selecting analytical method of leakage inductance calculation for optimizing high-voltage test transformer design

AN ACTUAL PROBLEM in transformer design is to optimize its design, since it allows you to create a competitive transformer. One of the objective functions in optimization algorithms for high-voltage test transformers is the ratio of the leakage inductive reactance of the transformer, reduced to the secondary side, to the load capacitance. Since the objective functions in the optimization procedure must be found many times, it is advisable to use approximate analytical calculation methods to calculate the leakage inductance. THE PURPOSE of the article is to analyze the error of the traditional analytical method for calculating the leakage inductance of power transformers with a rectangular axial cross-sections of the windings, and to develop a refined analytical method that takes into account the main design feature of high-voltage test transformers, which consists in the trapezoidal shape of the secondary winding cross-section. The refined method takes into account the change in the number of turns in the radial direction while maintaining the basic assumptions of the traditional method. METHODS. The error is studied by comparing the calculation results using these methods with the results of a numerical calculation of leakage inductance based on a 3D magnetostatic field, which are accepted as accurate. RESULTS. It is shown that the calculation error using the method proposed in the article is significantly reduced compared to the error of the method developed for power transformers with rectangular winding cross-sections. The ranges of changes in the relative geometric parameters of the base transformer have been determined, in which the error of this calculation method does not exceed 10%. The TGI 50/100 transformer, whose rated power is 5 kVA, was chosen as the base transformer. The developed analytical method is recommended for high-voltage test transformers optimization algorithms.

Study on influence of types and numbers of inner-layer shape on failure mechanism of layered alumina ceramic under three-point bending and bending fatigue load

Abstract In this paper, the failure mechanism of Layered Alumina Ceramic (LAC) with different types and numbers of inner-layer shapes is investigated under three-point bending (TPB) and bending fatigue load. Moreover, finite element analysis (FEA) models are established. Results of the experiment and FEA models indicate that specimens with different types and numbers of inner-layer shapes show excellent mechanical behavior. Introducing inner-layer shapes causes crack deflection, improving the bending strength and bending fatigue life of LAC specimens with arched or trapezoidal inner-layer shapes. However, taking the trapezoidal inner-layer shape as an example, if its number is more than or less than 19, the deflection of cracks in the inner layer is hindered, reducing the specimen’s mechanical properties. Furthermore, all LAC specimens show a mixed fracture mode. When a trapezoidal or arched inner-layer shape is adopted, transgranular cracks are significantly increased, improving its mechanical properties. However, the number of transgranular cracks is further reduced by changing the number of trapezoidal inner-layer shapes. Therefore, LAC specimens show poor mechanical behavior. In summary, LAC specimens with 19 arches or trapezoids in the inner layer show excellent mechanical properties. This research offers component design engineers the optimal types and numbers of inner-layer shapes for layered alumina ceramic, thereby enhancing the service life of ceramics.

Numerical simulation, constructal design, and systematic search applied to the geometrical evaluation of hat-stiffened plates under bending

Steel plates have wide structural applications in various engineering sectors due to their combination of lightness, efficiency, and high load-bearing capacity. When stiffeners are added to these structures, the deflections can be significantly minimized. In this study, hat-stiffened plates having box-girder stiffeners with a trapezoidal shape, positioned longitudinally along the plate, are considered to evaluate their influence on the maximum and central deflection of the structure. The analyses in this work are carried out using ANSYS Mechanical APDL software, employing a validated and verified computational model developed with the SHELL281 finite element. Starting from a reference plate without stiffeners, the Constructal Design method was applied, allowing to propose different geometric configurations for plates with longitudinal hat-stiffeners, keeping the total steel volume constant. All these cases were simulated numerically and their results were compared through a Systematic Search technique. Among these 100 different cases investigated, the geometric configuration with 1 hat-stiffener of 250 mm in height and 9.53 mm in thickness achieved the best performance, resulting in a reduction of approximately 86% in maximum and central deflections compared to the reference plate. This highlights its effectiveness in minimizing out-of-plane displacements.

Study on the influence of section shape of underground roadway on ventilation resistance

ABSTRACT Among the parameters that affect the ventilation capacity of an underground mine, the cross-sectional shape of the roadway plays a significant role. When the required airflow is constant, the roadways with different shapes but the same area evidently overcome the different wind resistance. In order to investigate the influence of roadway cross-sectional shape on airflow resistance, this study carried out experimental and Simulation Research on the influence of different cross-section shape and size changes on ventilation resistance. And the Relative Shape Factor (RSF) is established to quantitatively evaluate the influence of cross-section shape on ventilation resistance. Firstly, focusing on the four common types of cross-sectional in the roadway, including circular, rectangular, trapezoidal, and arched, the experimental platform of airflow resistance of the pipe is built, and the effect of the changes of cross-sectional shape on the ventilation resistance is studied. Furthermore, the law of airflow resistance with different scale changes under the same section shape is studied by numerical simulation. Subsequently, the scale-independent coefficient RSF is established through theoretical derivation to characterize the degree to which the section shape deviates from the circle. The further it deviates from the circular shape, the larger the RSF, indicating a greater impact of the cross-section shape on airflow resistance. Comparing the theoretical with the simulation results, the RSF errors of the rectangular, trapezoidal, and arched shapes are 7.3%, 4.01%, and 2.05%, respectively, indicating that the RSF can accurately describe the influence of the cross-section on ventilation resistance. Finally, the range of RSF for common roadway dimensions is summarized, the trapezoidal is 1.131 to 1.187, the arch-shaped is 1.0 to 1.160, and the rectangular is 1.128 to 1.152. The proposed RSF in this paper is intuitive and effective, which provides a reference for the engineering application and a new insight for the selection of the minimum ventilation resistance cross-section of roadway.

Fluid-Structure Interaction Analysis of Trapezoidal and Arc-Shaped Membranes Mimicking the Organ of Corti.

In a previous study [H. Shintaku etal., Sensors and Actuators A: Physical 158 (2010): 183-192], an artificially developed auditory sensor device showed a frequency selectivity in the range from 6.6 to 19.8 kHz in air and from 1.4 to 4.9 kHz in liquid. Furthermore, the sensor succeeded in obtaining auditory brain-stem responses in deafened guinea pigs [T. Inaoka etal., Proceedings of the National Academy of Sciences of the United States of America 108 (2011): 18390-18395]. Since then, several research groups have developed piezoelectric auditory devices that have the capability of acoustic/electric conversion. However, the piezoelectric devices are required to be optimally designed with respect to the frequency range in liquids. In the present study, focusing on the trapezoidal shape of the piezoelectric membrane, the vibration characteristics are numerically and experimentally investigated. In the numerical analysis, solving a three-dimensional fluid-structure interaction problem, resonant frequencies of the trapezoidal membrane are evaluated. Herein, Young's modulus of the membrane, which is made of polyvinylidene difluoride and is different from that of bulk, is properly determined to reproduce the experimental results measured in air. Using the modified elastic modulus for the membrane, the vibration modes and resonant frequencies in liquid are in good agreement with experimental results. It is also found that the resonant characteristics of the artificial basilar membrane for guinea pigs are quantitatively reproduced, considering the fluid-structure interaction. The present numerical method predicts experimental results and is available to improve the frequency selectivity of the piezoelectric membranes for artificial cochlear devices.

Early Medieval Catacomb Burials of Verkhnii Saltiv with Pendants of the Slavic Circle

As a result of work (1984–1992) at the catacomb burial ground near Verkhnii Saltiv village, bronze plate pendants of a trapezoidal shape were discovered in three burials (catacombs no. 11, VSB-III; no. 42 and no. 49, VSB-I). The pendants are decorated with lines and dots along the perimeter of the item and a circle with a dot in the middle in the central part of the item (fig. 1: 1, 3, 4). Such pendants are a typical attribute of the women’s costume of the population who left monuments of the Smolensk-Polotsk long barrows circle in the 8th—9th centuries — chronicle Kryvichs (fig. 1: 8–19). In the studied Alanian burials, these pendants formed a single set with typical female jewelry of the Saltiv culture. The burial complexes of Verkhnii Saltiv, in which pendants of the Slavic circle were discovered, date back to the second — third quarters of the 9th century. These pendants are added to the range of similar items discovered in the catacomb burials of Verkhnii Saltiv in previous years (catacombs no. 1, 1911; no. 5, 1904; no. 14, 1947; no. 93, VSB-IV) (fig. 1: 5–7). Personal jewelry, which in traditional societies serve as visible signs and symbols of the ethnic, gender, age, social and economic status of a particular person, in our opinion, testifies to the burial of Slavic women in the Saltiv culture catacombs. Slavic women were included in the Saltiv community as full members, considered as wives or concubines. It is possible to assume that these Slavic women were captured during a military raid or purchased from the local elite by representatives of the Khazar Khaganate while gathering tribute. The practice of capturing representatives of the aboriginal population of the forest and forest-steppe zones of Eastern Europe (Slavs, Balts, Finno-Ugrians) for subsequent sale on the Crimean slave markets was a typical feature of the military-political processes of the Khazarian historical and cultural period.

EXPLORATION OF ETHNOMATHEMATICS IN THE ANRI (NATIONAL ARCHIVES OF THE REPUBLIC INDONESIA) BUILDING WEST JAKARTA

Mathematics and culture have a strong relationship in life. In Indonesia, culture is different from local wisdom, and the culture of certain community groups or tribes that support mathematical activities is called ethnomathematics. One example is cultural heritage buildings, such as the ANRI (National Archives of the Republic of Indonesia) building which was founded in 1750 in DKI Jakarta Province, precisely on Jalan Gajah Mada, West Jakarta. The purpose of the research that we use, which is exploratory with this ethnographic method, is to find and categorize the mathematical concepts contained in the ANRI building which is one of the sources of learning mathematics and efforts to develop ethnomathematics as a basis for mathematics learning. This study focuses on understanding the informal mathematical knowledge acquired by local people from their environment and culture, especially those related to cultural heritage sites, which are referred to as ethnomathematics. The study findings show that the National Archives Building is a significant cultural heritage site with historical and architectural significance. The architectural features of the building, such as the rectangular and trapezoidal shapes of the main structure and roof, reflect various geometric concepts. Overall, this research emphasizes the importance of preserving cultural heritage and documents in the National Archives to retain the historical knowledge contained within. Ethnomathematics provides a valuable framework to explore and appreciate mathematical concepts embedded in cultural artifacts, promoting a deeper understanding of mathematics through real-world activities and cultural practices.

Development of essential oils inclusion complexes: a nanotechnology approach with enhanced thermal and light stability

Essential oils (EOs) are volatile compounds that may have antimicrobial and antioxidant properties. Despite their potential application, low water solubility and chemical instability are limiting factors. Nanoencapsulation processes can overcome this problem, protecting against external factors and promoting a moderate release. Therefore, the objective of the present study was to encapsulate Cymbopogon citratus (CC) and Origanum vulgare (OV) essential oils in β-cyclodextrin (βCD) complexes. Different ratios (w/w) between βCD and EOs (96:4, 92:8, 90:10, 88:12) were tested, seeking greater entrapment efficiency. The particles were characterized by yield, entrapment efficiency, size distribution, morphology, crystallinity, infrared spectroscopy, and thermal behavior. Furthermore, the thermal (70 °C) and photochemical (UV) stability of the free and encapsulated EO was evaluated for 48 h. The results showed that the βCD-CC 90:10 and βCD-OV 90:10 formulations presented greater entrapment efficiency. Crystalline structures of varying sizes (200 to 800 nm), trapezoidal shape, and tendency to aggregation were obtained. Changes in the βCD crystalline organization and the suppression of characteristic free oil absorption bands suggest the EO entrapment. Regarding stability results, βCD-CC remained constant when CC showed losses of 20% (photodegradation) and 60% (thermal degradation) after 48 h of stress exposure. Free OV showed slight variations in absorbance over time, while βCD-OV remained constant over 24 h (thermal degradation) and maintained 60% of oil over 48 h of photo exposure. Furthermore, OV and CC demonstrate color change over time, while βCD-OV and βCD-CC remained constant. The results demonstrate that nanoencapsulation can be an interesting tool for protecting EOs.

ТЕПЛООБМЕН ПРИ КОНДЕНСАЦИИ ЧИСТОГО ОЗОНОБЕЗОПАСНОГО ХЛАДАГЕНТА R404A НА ПРОДОЛЬНО-ОРЕБРЕННЫХ ГОРИЗОНТАЛЬНЫХ ТРУБАХ

A method for conducting an experimental study of freon (R404A, etc.) condensation and their oil-freon mixtures on smooth and developed horizontal surfaces has been developed. A smooth and longitudinally finned surface with a trapezoidal fin shape is presented as the heat transfer surface under study. As a result of the conducted experimental studies of the condensation process of ozone-safe pure mixed refrigerant R404A on a longitudinally finned horizontal pipe with short fins in height, the hydrodynamic characteristics of the condensate (condensate film thickness along the fin height, film velocity and condensate flow rate, heat flux density and heat exchange process intensity) of the condensate film gravitationally flowing down the elements of the finned surface have been experimentally established. The dependencies obtained during the experimental studies (heat transfer coefficient on heat flux den-sity; film thickness on heat flux density; film thickness on temperature difference; heat transfer coefficient on temperature difference) show that the experimental data on heat transfer coefficients and condensate film thickness match with the data, calculated using the Nusselt formula.

Multi-crack spatial propagation evolution analysis of 3D-TSV under thermal-electric-mechanical coupling field

Multi-crack spatial propagation evolution analysis of 3D-TSV under thermal-electric-mechanical coupling field

Quasi-static indentation characteristics of foam-filled sandwich composite structures with additively manufactured CFRP and GFRP corrugated cores

This paper presents an experimental investigation on the quasi-static indentation performance of polyurethane (PU) foam-filled carbon fibre-reinforced polymer (CFRP) and glass fibre-reinforced polymer (GFRP) corrugated sandwich composite structures (SCSs) under different indenter tip geometries (conical, trapezoidal, hemispherical, pyramidal, and cylindrical shapes). The SCSs were produced using hybrid manufacturing methods: (1) the facesheets were fabricated using the vacuum-assisted resin infusion (VARI) process, (2) the CFRP and GFRP corrugated cores were additively manufactured using the fused filament fabrication (FFF) process, and (3) the self-expanding PU foam-filled the open spaces in the core. The results elucidated that the indenter tip geometry and core material have a large influence on the indentation performance of SCSs. The cylindrical indenter showed the highest peak load, bending stiffness, and damage severity, while the conical indenter offered the lowest peak load, energy absorption, and damage severity. Among different core materials, CFRP corrugated core SCSs exhibited higher peak loads, specific energy absorption, and damage severity compared to ones with GFRP core. The primary damage modes were observed using an optical microscope, showing facesheet rupture, debonding between facesheets and core, core crushing, foam densification, and shear plugging. Shear plugging is a unique failure mode observed with cylindrical indenter tip geometry due to the blunt edges of the indenter, which induced large damages in SCSs. These findings provide new insight into the design and development of lightweight additively manufactured SCSs, which will benefit a wide range of industries and applications.

Two-Step Chemical Vapor Deposition for Fabrication of FAPbI3 Single-Crystal Microsheets with High Exciton Binding Energy.

Hybrid perovskites exhibit highly efficient optoelectronic properties and find widespread applications in areas such as solar cells, light-emitting diodes, photodetectors, and lasers. Here, we report the innovative synthesis of formamidinium lead iodide (FAPbI3) single-crystal microsheets via a two-step chemical vapor deposition (CVD) method. The microsheets exhibit hexagonal and trapezoidal shapes, with hexagonal FAPbI3 growing parallel to the substrate and trapezoidal FAPbI3 growing perpendicular to the substrate. The dominant role of single-exciton recombination in the photoluminescence (PL) of these microsheets is observed, especially pronounced at low temperatures, attributed to the relatively large exciton binding energies of the samples. Calculations reveal exciton binding energies as high as 110.8 meV for hexagonal and 133.3 meV for trapezoidal FAPbI3 single-crystal microsheets, attributed to reduced rotational freedom of the formamidinium (FA) ions. Further investigation into low-temperature phase transitions indicates lower transition temperatures (around 100 K) for these microsheets, suggesting reduced FA ion rotational freedom and consequently higher exciton binding energies.

Evolution characteristics of mining-induced fractures in overburden strata under close-multi coal seams mining based on optical fiber monitoring

Evolution characteristics of mining-induced fractures in overburden strata under close-multi coal seams mining based on optical fiber monitoring

Enhancing wind turbine energy efficiency: Tribo-dynamics modeling and shape modification

Enhancing wind turbine energy efficiency: Tribo-dynamics modeling and shape modification

Time-varying displacement excitation and dynamic modeling of angular contact ball bearing with local defects

Angular contact ball bearings will produce fault damage when working for a long time, thus affecting the normal operation of the system. This paper takes angular contact ball bearings with local defects on the outer ring as the research object, proposes a method to distinguish different local defect profiles, establishes a generalized characterization model of time-varying displacement excitation of local defects in angular contact ball bearings, and studies the evolution process of local defects and their displacement excitation mechanism. On this basis, considering the influence of time-varying displacement caused by bearing defects on dynamic characteristics, based on Hertz contact theory, a fault dynamics model of angular contact ball bearings is established, and the correctness of the established model is verified by experiments. In addition, the analysis results show that rectangular local defects will eventually evolve into trapezoidal shapes; the displacement excitation change trends induced by different defect morphologies are different; compared with the length of local defects, the width has a greater impact on displacement excitation. The research results provide a theoretical basis for bearing optimization design and fault diagnosis.

A Mathematical Model for Estimating the Area of a Large Leaf

A mathematical model for estimating the area of large leaves was developed and validated with the leaves of plantain (&amp;lt;i&amp;gt;Musa paradisiaca&amp;lt;/i&amp;gt;). The length of each plantain leaf was characterized by the mid-rib length which was divided into a certain number of equal parts of length. By this divisions, two major geometrical shapes were obtained, viz; trapezoidal shapes bounded by half elliptical shapes at the two ends of the leaf. In this work, the mathematical expression for the surface area of a plantain leaf was obtained by summing the areas of the trapeziums and the two half ellipses. The values of leaf areas as generated from this model for various seizes of plantain leaves converged reasonably well with true values obtained by the weighing method of same plantain leaf seizes. The correlation between these two values was carried out to ascertain the fitness of the mathematical model as developed here showed a linear relationship for the various mid-rib divisions tested in this study. It is thus concluded here that once the calculated area of the large leaf is known for a specific number of divisions with this model, the true area can be estimated. The main advantages of the new method are precision, accuracy, and applicability to determine the area of large leaves far out in the field where electrical weighing balance and large graph papers are not available.

Analysis of mixed traffic flow characteristics based on cellular automata model under lane management measures

Analysis of mixed traffic flow characteristics based on cellular automata model under lane management measures

Selective area epitaxy of in-plane HgTe nanostructures on CdTe(001) substrate

Semiconductor nanowires (NWs) are believed to play a crucial role for future applications in electronics, spintronics and quantum technologies. A potential candidate is HgTe but its sensitivity to nanofabrication processes restrain its development. A way to circumvent this obstacle is the selective area growth technique. Here, in-plane HgTe nanostructures are grown thanks to selective area molecular beam epitaxy on a semi-insulating CdTe substrate covered with a patterned SiO2mask. The shape of these nanostructures is defined by the in-plane orientation of the mask aperture along the <110>, <11¯0>, or <100> direction, the deposited thickness, and the growth temperature (GT). Several micron long in-plane NWs can be achieved as well as more complex nanostructures such as networks, diamond structures or rings. A good selectivity is achieved with very little parasitic growth on the mask even for a GT as low as 140 °C and growth rate up to 0.5 monolayer per second. For <110> oriented NWs, the center of the nanostructure exhibits a trapezoidal shape with {111}B facets and two grains on the sides, while <11¯0> oriented NWs show {111}A facets with adatoms accumulation on the sides of the top surface. Transmission electron microscopy observations reveal a continuous epitaxial relation between the CdTe substrate and the HgTe NW. Measurements of the resistance with four-point scanning tunneling microscopy indicates a good electrical homogeneity along the main NW axis and a thermally activated transport. This growth method paves the way toward the fabrication of complex HgTe-based nanostructures for electronic transport measurements.