Equal Area Research Articles

Melting and Heat Transfer Characteristics of Phase Change Material: A Comparative Study on Wire Mesh Finned Structure and Other Fin Configurations

Abstract In the present paper, a two-dimensional transient numerical study has been performed to investigate the influence of different fin designs on the melting and heat transfer characteristics of a phase change material (PCM), i.e., Paraffin wax, filled in square enclosures equipped with fin structures. Five distinct fin designs were examined: single rectangular, double rectangular, double triangular, double angled, and wire mesh. It is worth noting that all these fin designs have the equal heat transfer area. An isothermal heat source of temperature 350 K is provided at the left wall of the square enclosure and the remaining walls are assumed to be adiabatic. Six parameters were evaluated to determine the best fin configurations: melting time, enhancement ratio (ER), time savings, energy stored, mean power, and Nusselt number. The results show that all the fin designs outperformed as compared to model 1 (no fin configuration). Among the finned configurations, model 2 had the poorest performance, taking 1314 s to complete the melting, while model 6 had the most efficient fin design, with a melting time reduced by 67.53% compared to model 1. Model 6 also had the highest ER and mean power, i.e., 70.43% and 199.51%, respectively and as the melting process continued, the Nusselt number decreased. In addition to the above, we optimized the element size of the wire-mesh fin design using RSM methodology. This optimized design decreases the melting period by 70.04%. Overall, present study provides a comprehensive analysis of different finned configurations for improving the melting performance of the PCM in square enclosures and found wire-mesh fin design most appropriate and promising.

Transient Synchronous Stability Analysis of Grid-Forming Photovoltaic Grid-Connected Inverters during Asymmetrical Grid Faults

Compared with the traditional grid-following photovoltaic grid-connected converter (GFL-PGC), the grid-forming photovoltaic grid-connected converter (GFM-PGC) can provide voltage and frequency support for power systems, which can effectively enhance the stability of power electronic power systems. Consequently, GFM-PGCs have attracted great attention in recent years. When an asymmetrical short-circuit fault occurs in the power grid, GFM-PGC systems may experience transient instability, which has been less studied so far. In this paper, a GFM-PGC system is investigated under asymmetrical short-circuit fault conditions. A novel Q-V droop control structure is proposed by improving the traditional droop control. The proposed control structure enables the system to accurately control the positive- and negative-sequence reactive current without switching the control strategy during the low-voltage ride-through (LVRT) period so that it can meet the requirements of the renewable energy grid code. In addition, a dual-loop control structure model of positive- and negative-sequence voltage and current is established for the GFM-PGC system under asymmetrical short-circuit fault conditions. Based on the symmetrical component method, the composite sequence network of the system is obtained under asymmetrical short-circuit fault conditions, and positive- and negative-sequence power-angle characteristic curves are analyzed. The influence law of system parameters on the transient synchronous stability of positive- and negative-sequence systems is quantitatively analyzed through the equal area criterion. Finally, the correctness of the theoretical analysis is verified by simulation and hardware-in-the-loop experiments.

Neopolyploidy-induced changes in giant duckweed (Spirodela polyrhiza) alter herbivore preference and performance and plant population performance.

Polyploidy is a widespread mutational process in angiosperms that may alter population performance of not only plants but also their interacting species. Yet, knowledge of whether polyploidy affects plant-herbivore dynamics is scarce. Here, we tested whether aphid herbivores exhibit preference for diploid or neopolyploid plants, whether polyploidy impacts plant and herbivore performance, and whether these interactions depend on the plant genetic background. Using independently synthesized neotetraploid strains paired with their diploid progenitors of greater duckweed (Spirodela polyrhiza), we evaluated the effect of neopolyploidy on duckweed's interaction with the water-lily aphid (Rhopalosiphum nymphaeae). Using paired-choice experiments, we evaluated feeding preference of the herbivore. We then evaluated the consequences of polyploidy on aphid and plant performance by measuring population growth over multiple generations. Aphids preferred neopolyploids when plants were provided at equal abundances but not at equal surface areas, suggesting the role of plant population surface area in driving this preference. Additionally, neopolyploidy increased aphid population performance, but this result was dependent on the plant's genetic lineage. Lastly, the impact of herbivory on neopolyploid vs. diploid duckweed varied greatly with genetic lineage, where neopolyploids appeared to be variably tolerant compared to diploids, sometimes mirroring the effect on herbivore performance. By experimentally testing the impacts of polyploidy on trophic species interactions, we showed that polyploidization can impact the preference and performance of herbivores on their plant hosts. These results have significant implications for the establishment and persistence of plants and herbivores in the face of plant polyploidy.

Joule Thomson expansion, Maxwell equal area law and topological interpretation of Phantom RN AdS black holes

This paper is devoted to study the thermodynamic topological defects, Joule–Thomson (J−T) and Maxwell’s equal area law of Phantom RN AdS black holes (BHs). The inversion temperatures and inversion curves are obtained and by using the isenthalpic curves in the temperature–pressure (T−P) plane to locate the cooling and heating regions. Using Maxwell’s equal-area law, we select different independent conjugate variables to study the phase transitions of Phantom RN AdS BHs. We find that phase transition rely on the electric potential and horizon radius of the BH when its charge is constant. Phase transition of Phantom RN AdS BH are proportional to the ratio of event horizon to its cosmological constant, where the latter is assumed to be constant. Moreover, we consider the Phantom RN AdS BH as defects with a topological nature within thermodynamic domain and examine the local and global topology by computing the winding numbers at the defects, which concludes that the overall topological charge is either equal to 0 or 1.

Seismic fragility analysis of high‐strength concrete frame structures reinforced with high‐strength steel bars

SummaryTo investigate the influence of using high‐strength steel bars in columns on the seismic resistance capacity and seismic resilience of frame structures, seismic fragility evaluation of three 8‐story reinforced concrete (RC) frame structures was conducted based on the incremental dynamic analysis (IDA) using 11 ground motion records. The main parameter is the longitudinal reinforcement configuration in the frame columns, where the first structure is reinforced with HRB 600 grade steel bars in the columns, the second structure is replaced with equal area ultra‐high‐strength (UHS) steel bars (i.e., with a yield strength of approximately 1425 MPa), and the third structure is replaced with equal strength UHS steel bars. A numerical model of the RC frame structure was developed and then validated using previous experimental results. The exceeding probabilities at various performance limit states were calculated based on two typical engineering demand parameters (EDPs) of maximum interstory drift and residual interstory drift. The results showed that using UHS longitudinal steel bars instead of HRB 600 grade steel bars in frame columns could reduce the energy dissipation capacity of the structure, inevitably leading to an increase in the maximum interstory response of the frame. However, much lower exceedance probability was observed in the UHS‐enhanced frame under the repair available limit state based on the residual interstory drift, indicating that the UHS‐enhanced RC frame had higher seismic resilience. In addition, compared to equal area substitution, equal strength substitution is a more ideal design method that can use fewer UHS steel bars to achieve comparable reparability and a smaller increase in maximum interstory drift.

Recovery of consistency in thermodynamics of regular black holes in Einstein's gravity coupled with nonlinear electrodynamics

As one of candidate theories in the construction of regular black holes, Einstein's gravity coupled with nonlinear electrodynamics has been a topic of great concerns. Owing to the coupling between Einstein's gravity and nonlinear electromagnetic fields, we need to reconsider the first law of thermodynamics, which will lead to a new thermodynamic phase space. In such a phase space, the equation of state accurately describes the complete phase transition process of regular black holes. The Maxwell equal area law strictly holds when the phase transition occurs, and the entropy obeys the Bekenstein-Hawking area formula, which is compatible with the situation in Einstein's gravity.

Generalized Maxwell equal area law and black holes in complex free energy

Maxwell equal area law is an important and traditional analytical tool in thermodynamic phase transition, especially in the calculation of gas-liquid phase transition, which reconciles the theoretical calculation with the experimental results. Undoubtedly, its importance is also self-evident for the black hole thermodynamic system. In this study, we construct a generalized Maxwell equal area law, which allows different states of thermodynamic systems to be within the generalized free energy. The black hole thermodynamic characteristics are spontaneously emerged in the free energy landscape. Furthermore, by analytic continuation, we utilize the properties of analytical functions to investigate some universal characteristics of thermodynamic phase transitions in black holes, and preliminarily establish the counterpart of thermodynamic phase transitions in the complex domain.

Transient stability enhancement control strategy based on grid dispatching for multi-paralleled grid forming inverters during LVRT

In this article, the transient synchronization process of multi-paralleled grid forming (GFM) inverters is studied detailly. Firstly, based on the multi-paralleled inverters control structure and complementary cluster center of inertia relative motion (CCCOI-RM), the single machine infinite bus (SMIB) system is proposed. Subsequently, the power angle characteristic (PAC) equation of multi-paralleled inverters for different dispatching strategies with simplified damping coefficient is built. Meanwhile, a grid dispatching strategy considering communication delay is proposed, which avoiding the cascading failures of grid faults. Furthermore, according to the grid dispatching strategy, a cluster control strategy optimization method including critical cluster identification (CCI) method and transient stability prediction analysis method is designed, which is proposed to identify unstable cluster in multi-paralleled inverters. In addition, the synchronization stability criteria for dispatching strategies of multi-paralleled inverters are obtained based on the PAC equation, in which the transient instability phenomenon and mechanism for different fault stages is explained by extended equal area criterion (EEAC) method. Finally, the simulations results validate the effectiveness of the theoretical analysis and proposed method.

A New Method for the Compaction Quality Inspection of High Rockfill Dams Based on 3D Laser Scanning Technology

The compaction quality is directly related to the deformation and stability of the rockfill dam. Measuring the test pit volume efficiently and accurately is the most critical step during the compaction quality inspection. A new method for calculating the test pit volume based on point cloud data is proposed. An auxiliary device that can change the scanning distance and angle of the handheld 3D laser scanner is developed to collect the initial point cloud. The segmentation method of the initial point cloud data including the test pit and the compaction surface outside the pit is to divide the data into two parts according to the order number of the segmentation point, after slicing and sorting point clouds, which is the key to ensuring the computational precision. The segmentation points are the adjacent two points with the greatest order number difference in these point clouds whose distance from the line connecting the end points of the slicing point clouds is less than dz. The compaction surface point clouds are used to construct a plane by the least-squares algorithm so that the closed three-dimensional model is formed by registering it with the test pit point clouds. After converting the test pit surface to the horizontal plane by the Rodrigues formula, the test pit point clouds are divided into n2 parts with equal projection areas on the horizontal plane, and n2 prisms are constructed using them and their projection areas. The test pit volume is the sum of the intersection space volumes of all prisms and the test pit model, and the intersection space is determined by comparing the Z-values of point clouds. The new method was programmed in MATLAB and applied to the Shuangjiangkou rockfill dam with a height of 315 m. The relative error of volume results between the new method and the old water-filling method is 0.14–2.31%. The cause of the error is analyzed, and it is proved that the results of the new method are closer to the real volume of the test pit in theory. This method reduces the inspection cost but greatly improves the level of precision, efficiency, and intelligence for compaction quality inspection.

Phase Correction of the Channels of a Fully Populated Randomized Multielement Therapeutic Array Using the Acoustic Holography Method

The acoustic holography method was used to characterize a therapeutic focused fully populated 256-element ultrasonic transducer array. Elements of the array with the shape of equal area polygons are densely arranged in an irregular pattern on a spherically concave surface with a radius of curvature of 150 mm and a diameter of 200 mm. The array has a central frequency of 1.2 MHz and is designed to operate in water. The performance of individual array elements was studied based on the holographically reconstructed normal velocity distribution over the array surface. It was shown that with the same electrical signals applied to the elements, their acoustic responses had a phase deviation relative to the nominal values, which can be caused either by the asphericity of the array surface, or by the introduction of additional phase delays by the electrical matching network. To compensate for the detected parasitic phase shifts of the elements and restore the effective sphericity of the radiating surface, the Verasonics V-1 control system was used. The hologram measured after making the correction, as well as the shape of the focal region and acoustic pressure magnitude at the focus, separately measured by a hydrophone, showed that the proposed method reconstructed the nominal operating parameters of the array with high accuracy.

Impact performance of unconventional trigger holes

Abstract Crash boxes in vehicles are one of the passive safety measures that aim to reduce injury to passengers and damage to the vehicle during a collision. Their function is to absorb the mechanical energy resulting from a collision by deforming plastically. Considering human safety, not only the energy must be damped, but also the forces acting on the passengers must be controlled. This force control can be adjusted to some extent using trigger mechanisms. There is a wide variety of research on hole type triggers, but they concentrated on traditional shapes; unique or hybrid shapes have not been sufficiently tested. This study examined the effects of various hole profiles with equal areas on dynamic mechanical performances of Al 6063-T6 rectangular crash boxes. Four types of trigger shapes were formed: upward keyhole, downward keyhole, U-shaped, and S-shaped. The dynamic performance evaluation was carried out experimentally by testing five types of geometries, the fifth one being the geometry without any trigger. In addition, dynamic Finite element analyses were conducted and validated using the experimental data, with the aim of employing the Finite element models in future geometry improvement studies. The experimental results were interpreted with some common evaluation parameters: peak force, crash force efficiency, mean crash force, and total energy absorption. The downward keyhole profile generally gave the best results, while the lowest peak force was observed in the U-shaped profile.

The Spherical Cap Discrepancy of Healpix Points

In this paper we show that the spherical cap discrepancy of the point set given by centers of pixels in the HEALPix tessellation (short for Hierarchical, Equal Area and iso-Latitude Pixelation) of the unit 2-sphere is lower and upper bounded by order square root of the number of points, and compute explicit constants. This adds to the currently known (short) collection of explicitly constructed sets whose discrepancy converges with order 𝑁−1/2, matching the asymptotic order for i.i.d. random point sets. We describe the HEALPix framework in more detail and give explicit formulas for the boundaries and pixel centers. We then introduce the notion of an 𝑛-convex curve and prove an upper bound on how many fundamental domains are intersected by such curves, and in particular we show that boundaries of spherical caps have this property. Lastly, we mention briefly that a jittered sampling technique works in the HEALPix framework as well.

Particle Swarm Optimization-Based Unconstrained Polygonal Fitting of 2D Shapes

In this paper, we present a general version of polygonal fitting problem called Unconstrained Polygonal Fitting (UPF). Our goal is to represent a given 2D shape S with an N-vertex polygonal curve P with a known number of vertices, so that the Intersection over Union (IoU) metric between S and P is maximized without any assumption or prior knowledge of the object structure and the location of the N-vertices of P that can be placed anywhere in the 2D space. The search space of the UPF problem is a superset of the classical polygonal approximation (PA) problem, where the vertices are constrained to belong in the boundary of the given 2D shape. Therefore, the resulting solutions of the UPF may better approximate the given curve than the solutions of the PA problem. For a given number of vertices N, a Particle Swarm Optimization (PSO) method is used to maximize the IoU metric, which yields almost optimal solutions. Furthermore, the proposed method has also been implemented under the equal area principle so that the total area covered by P is equal to the area of the original 2D shape to measure how this constraint affects IoU metric. The quantitative results obtained on more than 2800 2D shapes included in two standard datasets quantify the performance of the proposed methods and illustrate that their solutions outperform baselines from the literature.

In vivo exposure of the bladder using a non-invasive high intensity focused ultrasound toroidal transducer

A toroidal high-intensity focused ultrasound (HIFU) transducer was used to expose normal bladder wall tissues non-invasively in vivo in a porcine model in order to investigate the potential to treat bladder tumors. The transducer was divided into 32 concentric rings with equal surface areas, operating at 2.5 MHz. Eight animals were split into two groups of 4. In the first group, post-mortem evaluation was performed immediately after ultrasound exposure. In the second group, animals survived for up to seven days before post-mortem evaluation. The ultrasound imaging guided HIFU device was hand-held during the procedure using optical tracking to ensure correct targeting. One thermal lesion in each animal was created using a 40 s exposure at 80 acoustic Watts (free-field) in the trigone region of the bladder wall. The average (±Standard Deviation) abdominal wall and bladder wall thicknesses were 10.3 ± 1.4 mm and 1.1 ± 0.4 mm respectively. The longest and shortest axes of the HIFU ablations were 7.7 ± 2.9 mm and 6.0 ± 1.8 mm, respectively, resulting in an ablation of the whole thickness of the bladder wall in most cases. Ablation were performed at an average depth (distance from the skin surface to the centre of the HIFU lesion) of 42.5 ± 3.8 mm and extended throughout the thickness of the bladder. There were two cases of injury to tissues immediately adjacent to the bladder wall but without signs of perforation, as confirmed by histological analysis. Non-invasive HIFU ablation using a hand-held toroidal transducer was successfully performed to destroy regions of the bladder wall in vivo.

Impact of Vertical Scaling on Normal Probability Density Function Plots.

Probability density function (PDF) curves are among the few charts on a Cartesian coordinate system that are commonly presented without y-axes. This design decision may be due to the lack of relevance of vertical scaling in normal PDFs. In fact, as long as two normal PDFs have the same means and standard deviations (SDs), they can be scaled to occupy different amounts of vertical space while still remaining statistically identical. Because unfxed PDF height increases as SD decreases, visualization designers may fnd themselves tempted to vertically shrink low-SD PDFs to avoid occlusion or save white space in their fgures. Although irregular vertical scaling has been explored in bar and line charts, the visualization community has yet to investigate how this visual manipulation may affect reader comparisons of PDFs. In this paper, we present two preregistered experiments (n = 600, n = 401) that systematically demonstrate that vertical scaling can lead to misinterpretations of PDFs. We also test visual interventions to mitigate misinterpretation. In some contexts, we fnd including a y-axis can help reduce this effect. Overall, we fnd that keeping vertical scaling consistent, and therefore maintaining equal pixel areas under PDF curves, results in the highest likelihood of accurate comparisons. Our fndings provide insights into the impact of vertical scaling on PDFs, and reveal the complicated nature of proportional area comparisons.

Performance evaluation and parameter optimization of a walnut shell–kernel winnowing device

AbstractTo design a walnut shell–kernel winnowing device, the aerodynamic characteristics of walnut shells and kernels were studied by combining theoretical computation and empirical tests. A winnowing method was developed for shell–kernel separation based on an analysis of suspending velocity. The performance of the walnut shell–kernel winnowing device was evaluated based on the screening rate and loss rate. Influences of feeding rate, wind speed, and vibration frequency on the performance of the device were simulated, and the optimal operating parameters were acquired. Research results demonstrated that the suspending velocity ranges of walnut shells and kernels were 8.96–13.89 and 11.81–20.78 m/s, respectively. Vibration frequency was the primary factor that influenced the screening rate of the device, followed by wind speed and then feeding rate. Feeding rate was the primary factor influencing the loss rate of the device, followed by vibration frequency and then wind speed. The optimal operating parameters were as follows: feeding rate = 246.61 g/s, wind speed = 19.77 m/s, and vibration frequency = 41.17 Hz. Under these conditions, the winnowing device's screening rate and loss rate were 79.22% and 7.38%, respectively. The performance of the designed walnut shell–kernel winnowing device conforms to practical operational requirements. This study provides a potential reference for future investigation into the optimization of shell–kernel winnowing devices for other agricultural products.Practical applicationsIn order to explore the influence of each factor on the performance of the device, the windward area of the crushed materials was obtained by Image Processing. Meanwhile the “3σ criterion” was used to establish an equivalent sphere of equal windward area to replace the real shape of the walnut particles, and the range of the suspending velocity of the walnut crushed material was explored. Based on the Computational Fluid Dynamics Discrete Eement Method (CFD‐DEM) coupling method, and taking the screening rate and loss rate as the evaluation indicators, the effects of feed flow, wind speed, and vibration frequency on the performance of the device were simulated and analyzed, and the optimal operating parameter combination was obtained. The performance of the walnut shell–kernel winnowing device designed in this paper meets the actual operation requirements, and the research method can provide a reference for the development and optimization of other agricultural product separation equipments.

Modeling asymmetric cell membranes at all-atom resolution.

Molecular dynamics (MD) simulations are a useful tool when studying the properties of membranes as they allow for a molecular view of lipid interactions with proteins, nucleic acids, or small molecules. While model membranes are usually symmetric in their lipid composition between leaflets and include a small number of lipid components, physiological membranes are highly complex and vary in the level of asymmetry. Simulation studies have shown that changes in leaflet asymmetry can alter the properties of a membrane. It is therefore necessary to carefully build asymmetric membranes to accurately simulate membranes. This chapter carefully describes the different methods for building asymmetric membranes and the advantages/disadvantages of each method. The simplest methods involve building a membrane with either an equal number of lipids per leafletor an equal initial surface area(SA) estimated by the area per lipid. More detailed methods include combining two symmetric membranes of equal SAor altering an asymmetric membrane and adjusting the number of lipids after equilibration to minimize an observable such as differential stress (0-DS). More complex methods that require specific simulation software are also briefly described. The challenges and assumptions are listed for each method which should help guide the researcher to choose the best method for their unique MD simulation of an asymmetric membrane.

An Iterative Equal Area Criterion for Transient Stability Analysis of Grid-Tied Converter Systems With Varying Damping

With the increasing penetration of renewable energy generators, the stability issues of grid-tied converter systems become much more important. However, due to the high nonlinearity and varying damping of converter systems, conventional transient stability analysis methods are not applicable, which may bring to conservativeness or misjudgment on stability assessment. In this paper, the transient stability of grid-tied converter systems with varying damping is investigated to provide stability boundary estimation. Firstly, considering the frequency mutation of the phase-locked loop (PLL) caused by various perturbations, a modified swing equation model of grid-tied converter systems is built, which greatly improves the mathematical model accuracy under transient disturbances. To evaluate the impacts of varying damping and frequency mutation, an iterative equal area criterion (ITEAC) method is proposed with the iterative calculation of the accelerating and decelerating area, which renders stability boundaries with high accuracy. Moreover, the impacts of controller and system parameters on stability boundaries are quantitatively analyzed. Eventually, simulation and hardware-in-loop experiments are performed to verify the effectiveness and superiority of the proposed ITEAC.

СИНТЕТИЧЕСКОЕ ПРЕДСТАВЛЕНИЕ ПРЕОБРАЗОВАНИЯ "КОСАЯ СИММЕТРИЯ" НА ПРИМЕРЕ ПРЕОБРАЗОВАНИЯ ЭЛЛИПСА

Geometric transformations play a pivotal role in computer graphics, determining the position and shape of objects. In machine learning, they are applied for processing and analyzing data, such as in images. In geometric surface modeling, they are utilized for the creation and transformation of three-dimensional forms. In physics, geometric transformations assist in describing the motion of objects in space and time.
 The aim of this work is to analyse and study the geometric transformation known as "oblique symmetry." Primarily, the article seeks to elucidate a number of important properties of this transformation, expanding the field of knowledge in perspective-affine correspondence.
 Throughout the study, the principal directions of oblique symmetry are identified, and their relationship with the axis and direction of the transformation is established. It is crucial to emphasise that the analysis makes it evident that the axis and the direction of symmetry are equivalent and interchangeable. Additionally, the article addresses the challenge of transforming an arbitrary ellipse, defined by its semi-axes, into a circle of equal area. In this context, a method is proposed to determine the axis and direction of oblique symmetry for a given ellipse.
 Based on the results obtained and the analysis conducted, the authors propose a geometric algorithm that provides the capacity to resolve positional problems in the field of descriptive geometry. This algorithm also offers a novel method for constructing ellipses with given semi-axes, which holds practical significance in various engineering and geometric issues.
 In the conclusion of the article, a specific example of applying the developed method is provided, clearly demonstrating its practical value and real capabilities in solving positional problems in the field of descriptive geometry. Moreover, directions for future research in the field of shape formation are suggested, utilising the "oblique symmetry" transformation in the spaces and .

Solid-liquid mixing characteristics in a fractal cut impeller stirred reactor with dense solid loading

The fractal cut impeller (FC impeller) based on fractal iteration of “H” pattern cuts on the impeller blades was introduced in the solid-liquid system with dense solid loading. The solid-liquid mixing characteristics in a stirred tank with pitched blade impeller (PB impeller) and FC impeller were comparatively investigated with experiment and numerical simulation. Results showed that FC impeller exhibited lower power consumption (P) and power number (Np) compared to PB impeller at the same impeller speed. It could be also observed that increasing the fractal iteration number of FC impeller led to a further decrease in P and Np. Meanwhile, FC impeller could reduce the size of impeller tailing vortex, enhance turbulent intensity and turbulent kinetic energy dissipation rate, and improve solid particle suspension quality compared to PB impeller under the constant power consumption, and an increase in fractal iteration number of FC impeller resulted in higher solid particle suspension efficiency. In addition, it was also found that the fractal arrangement of cuts on the impeller blades could increase turbulent intensity, enhance turbulent kinetic energy dissipation rate and facilitate an improvement in solid particle suspension quality as compared to a whole cut on the impeller blades with equal cut area.