Geometric Components Research Articles

Mm-CasGAN: A cascaded adversarial neural framework for mmWave radar point cloud enhancement

Handling and interpreting sparse 3D point clouds, especially from mmWave radar, presents unique challenges due to the inherent data sparsity and the vast domain difference compared to denser point clouds like those from LiDAR. In this paper, we introduce a novel cascaded generative adversarial network (GAN) approach to bridge this domain gap. The core principle is to progressively refine the radar-based point cloud through a series of GANs, each targeting a higher resolution. By leveraging multi-level features and a hybrid loss function that combines adversarial, geometric, and consistency components, our method ensures a smooth transition from the sparse radar representation to a high-resolution LiDAR-like point cloud. Our cascaded approach operates at a patch level, and the integrated loss function ensures that the generated points not only resemble the target domain but also maintain geometric and structural fidelity. Real-life dataset consisting mostly of moving pedestrians were collected using a system made of Radar, LiDAR, and RGB Camera. Through an extensive experiment on the collected real-world pedestrian dataset, we validate the efficacy of our approach. Inference from the network indicates that our method can upsample mmWave radar point clouds with enhanced density, uniformity, and closer alignment to the ground truth LiDAR point clouds, which is the first of its kind network to do so.

A method for generating case-specific vehicle models from a single-view vehicle image for accurate pedestrian injury reconstructions

Developing vehicle finite element (FE) models that match real accident-involved vehicles is challenging. This is related to the intricate variety of geometric features and components. The current study proposes a novel method to efficiently and accurately generate case-specific buck models for car-to-pedestrian simulations. To achieve this, we implemented the vehicle side-view images to detect the horizontal position and roundness of two wheels to rectify distortions and deviations and then extracted the mid-section profiles for comparative calculations against baseline vehicle models to obtain the transformation matrices. Based on the generic buck model which consists of six key components and corresponding matrices, the case-specific buck model was generated semi-automatically based on the transformation metrics. Utilizing this image-based method, a total of 12 vehicle models representing four vehicle categories including family car (FCR), Roadster (RDS), small Sport Utility Vehicle (SUV), and large SUV were generated for car-to-pedestrian collision FE simulations in this study. The pedestrian head trajectories, total contact forces, head injury criterion (HIC), and brain injury criterion (BrIC) were analyzed comparatively. We found that, even within the same vehicle category and initial conditions, the variation in wrap around distance (WAD) spans 84–165 mm, in HIC ranges from 98 to 336, and in BrIC fluctuates between 1.25 and 1.46. These findings highlight the significant influence of vehicle frontal shape and underscore the necessity of using case-specific vehicle models in crash simulations. The proposed method provides a new approach for further vehicle structure optimization aiming at reducing pedestrian head injury and increasing traffic safety.

Inter-institutional variability of knowledge-based plan prediction of left whole breast irradiation

PurposeWithin a multi-institutional project, we aimed to assess the transferability of knowledge-based (KB) plan prediction models in the case of whole breast irradiation (WBI) for left-side breast irradiation with tangential fields (TF). MethodsEight institutions set KB models, following previously shared common criteria. Plan prediction performance was tested on 16 new patients (2 pts per centre) extracting dose-volume-histogram (DVH) prediction bands of heart, ipsilateral lung, contralateral lung and breast. The inter-institutional variability was quantified by the standard deviations (SDint) of predicted DVHs and mean-dose (Dmean). The transferability of models, for the heart and the ipsilateral lung, was evaluated by the range of geometric Principal Component (PC1) applicability of a model to test patients of the other 7 institutions. ResultsSDint of the DVH was 1.8 % and 1.6 % for the ipsilateral lung and the heart, respectively (20 %-80 % dose range); concerning Dmean, SDint was 0.9 Gy and 0.6 Gy for the ipsilateral lung and the heart, respectively (<0.2 Gy for contralateral organs). Mean predicted doses ranged between 4.3 and 5.9 Gy for the ipsilateral lung and 1.1–2.3 Gy for the heart. PC1 analysis suggested no relevant differences among models, except for one centre showing a systematic larger sparing of the heart, concomitant to a worse PTV coverage, due to high priority in sparing the left anterior descending coronary artery. ConclusionsResults showed high transferability among models and low inter-institutional variability of 2% for plan prediction. These findings encourage the building of benchmark models in the case of TF-WBI.

Fault diagnosis study of hydraulic pump based on improved symplectic geometry reconstruction data enhancement method

Aiming at the problem of poor consistency between the enhanced samples and the original samples in the current data enhancement methods. In this paper, we propose a data enhancement method with improved symplectic geometry reconstruction. The method expands a sufficient number of augmented samples while ensuring high similarity to real fault samples. First, the components to be augmented and their weights are selected from the decomposed symplectic geometric modal components using a random sampling method. Second, a data-weighted scaling criterion is formulated to augment the modal component amplitudes. Then, the summation and reconstruction of all amplitude enhancement components are performed on the basis of ensuring that the statistical characteristics of the enhanced samples remain consistent with the original samples. Finally, the proposed method is combined with the deep residual network, and the experimental dataset of hydraulic pump failure simulation is utilized to verify the effectiveness of the proposed method in obtaining the enhanced fault sample information. The diagnostic results show that the fault diagnosis model established by the method has higher accuracy and convergence ability in hydraulic pump data imbalance fault diagnosis compared with other comparative models.

Micro/nanopositioning coplanar stage with real-time compensation of volumetric error

A micro/nanopositioning coplanar stage is designed with real-time compensation of volumetric error. According to the topological structure of the stage, it has 13 geometric error components. Furthermore, there are positional shifts of a functional point from the displacement feedback point and the measurement point of geometric errors. To improve the positional accuracy, it is crucial to real-time measure, model, and compensate for the volumetric error at the functional point. Therefore, a volumetric error measuring unit (VEMU) is designed to simultaneously real-time measure 13 geometric error components. A volumetric error model is established using the Abbe and Bryan principles. A control unit with two backpropagation neural networks-based PID controllers combines with the VEMU and volumetric error model to realize the real-time compensation of the volumetric error. The positional error of the micro/nanopositioning coplanar stage is reduced approximately 97.6 %, from which the effectiveness and applicability of the proposed methods are verified.

Anisotropic extensions of Tolman IV through decoupling in energy–momentum squared gravity

This paper is dedicated to the precise computation of anisotropic extensions for the Tolman IV solution. These extensions are achieved through the utilization of the extended gravitational decoupling scheme within the framework of [Formula: see text] gravity, where R is the Ricci scalar and [Formula: see text] is the contraction of energy–momentum tensor. In this context, we select a linear model characterized by the expression [Formula: see text], where the parameter [Formula: see text] establishes a connection between the geometric and matter components. The extended gravitational decoupling technique incorporates a decoupling parameter that governs the extent of the induced anisotropy. Deformations in the radial and temporal metric components lead to the decomposition of the field equations into two distinct subsystems. One of these sets pertains to the isotropic solution, while the other is addressed by implementing the extra constraints. We examine the outcomes through graphical analysis and investigate the viability and stability of the obtained anisotropic solutions for the celestial object. Moreover, we study the mass, compactness and surface redshift of the system to gain a comprehensive understanding of its characteristics. It is concluded that this technique in this modified gravity yields physically acceptable solutions.

A bearing fault diagnosis method with improved symplectic geometry mode decomposition and feature selection

A rolling bearing fault diagnosis method based on improved symplectic geometry mode decomposition (SGMD) and feature selection was proposed to solve the problem of low fault identification due to the influence of noise on early bearing fault features. First, the SGMD SGMD is improved to enhance its robustness in decomposing signals with noise, then the time domain, frequency domain, and time-frequency features of each symplectic geometric component are extracted as feature vectors. Second, a comprehensive feature selection strategy is proposed to select the optimal subset of features that are conducive to fault classification. Finally, considering the problem of low classification accuracy of a single machine learning model, the AdaBoost-WSO-SVM model is constructed for fault classification using the AdaBoost algorithm of integrated learning. Experimental decomposition of complex signals with noise indicates that the improved SGMD is more effective compared to traditional SGMD. Subsequently, multiple experiments were conducted using the bearing datasets from Case Western Reserve University (CWRU) and Jiangnan University (JNU). The experimental results reveal that, after comprehensive feature selection and ensemble learning pattern recognition experiments on the CWRU dataset, the average accuracy of fault diagnosis can reach 99.67%. On the JNU dataset, the proposed fault diagnosis method achieves an average accuracy of 95.03%. This suggests that, compared to other feature selection methods and classification models, the proposed approach in this paper exhibits higher accuracy and generalization capabilities.

A generalized indicator of the efficiency of the use of the spacecraft radar to solve the remote sensing of earth problems by synthesizing the aperture. Part 1. Methodological foundations

The importance of the article is determined by the following factors: the increasing use of spacecraft radars and, at the same time, the extension of the range of tasks to be solved for remote sensing of the Earth; using a wide range of orbits for the output of remote sensing radars of the spacecraft; a large number of parameters of the remote sensing radar of the spacecraft, which determines the purposive characteristics in accordance with the tasks to be solved; conflicting requirements for parameter values when solving various remote sensing tasks. Under these conditions, the substantiation of the parameters of the onboard radar of the spacecraft, as well as any complex technical system, is impossible without a generalized indicator that takes into account heterogeneous and often contradictory requirements for their values. The methodological basis for the formation of a generalized indicator of the effectiveness of the use of space radar is to take into account the main objective characteristics of the remote sensing spacecraft, including: the area of the observed surface of the Earth per unit of time (productivity); spatial resolution along and across the path line; radiometric sensitivity, radiometric resolution. Using the specified objective characteristics and variable indicators of the degree to which each of them is built, a generalized indicator of the efficiency of the spacecraft is formed in the form of multipliers. The number of multipliers is equal to the number of objective characteristics. The first and second factors represent a weighted ratio (taking into account the corresponding exponents) of the first and second objective characteristics and determine the geometric component of the received volume of radar information. The third and fourth factors determine the possibility of radar discrimination of objects on the ground in terms of their reflectivity and represent a weighted ratio of radiometric sensitivity and radiometric resolution. On the basis of the radar equation, taking into account the relationship of the parameters of the spacecraft radar with the objective characteristics, analytical relations are obtained linking the parameters of the space radar and a generalized indicator of the effectiveness of the use of the space-based radar for remote sensing of Earth. This makes it possible to determine the requirements for the main resources of the on-board radar complex, namely, the radiated power and dimensions of the antenna system of the on-board radar.

ПОСТРОЕНИЕ ПЕРСПЕКТИВЫ ПРЯМОЙ ПО КАРТИННОМУ СЛЕДУ И ТОЧКЕ СХОДА

The article is exclusively applied and methodical in nature and is intended for the study of constructions in the section "Perspective". The paper considers the construction of the perspective of a straight line of the general position with the help of a picture trace and a vanishing point. In perspective, the traces of a straight line are the points of intersection with the picture and subject planes. Vanishing point – the perspective of an improper point of a straight line. The article discusses the picture trail, the vanishing point and the construction of a straight line segment by means of these perspective points. In textbooks for builders, such a task is not set at all and is not considered. Three authors have solutions in textbooks for architects: A.G. Klimukhin, Yu.I. Koroev and T.S. Timrot. However, they also have some disadvantages, which are discussed in this article. In the work proposed to the reader, such an arrangement of geometric components is performed that there is neither parallelism nor perpendicularity between them, that is, they are all located at acute angles to each other, which means that a general case of construction is proposed for consideration. So, we have a right angle only between the horizontal and frontal planes of projections, as well as between the picture and object (horizontal plane of projections) planes. The angles between the other geometric components are exceptionally sharp: a straight line of general position in the P1/P2 system is taken, it is also a straight line of general position in the P1/K system. Thus, the article considers, unlike other textbooks, the general case of a direct task.

Design of acceleration control schedule for adaptive cycle engine based on direct simulation model

To design the optimum acceleration control schedule for the Adaptive Cycle Engine (ACE) in the full flight envelope, this paper establishes a direct simulation model of the ACE transient state. In this model, geometric parameters are used to replace the component state parameters. The corresponding relationship between geometric parameters and component state parameters is determined by sensitivity analysis. The geometric variables are controlled when the geometric adjustment speed exceeds the limit, and at the same time the corresponding component state parameters are iterated. The gradient optimization algorism is used to optimize the ground acceleration process of ACE, and the control schedule in terms of operating point of compression components and corrected acceleration rate is used as the full-envelope acceleration control schedule based on the similarity principle. The acceleration control schedules of the triple-bypass mode and the double-bypass mode are designed in this paper. The acceleration processes under various flight conditions are simulated using the acceleration control schedules. Compared with the acceleration process with the linear geometric adjustment schedule, the acceleration performance of ACE is improved by the acceleration control schedule, with the impulse of the acceleration process of the triple-bypass mode being increased by 8.7%–12.3% and the impulse of the double-bypass mode acceleration process being increased by 11.8%–14.1%.

Recreating horizontal alignments of existing railways with a hybrid analytic and harmony search algorithm

After operating a long time, existing railway tracks gradually deviate from their initially designed alignments due to the wheel-track interaction, thereby compromising operational performance and safety. Therefore, existing railway alignments should be recreated through periodic maintenance to enhance train operations and guarantee operational safety. Currently, most methods in this field first identify tangent alignment sections and then curves based on measured points along the railway. Afterward, these identified geometric components are optimized to fit the actual alignment. However, for existing railways that are fairly circuitous, the above strategy is limited since the curves’ geometric characteristics dominate those of tangents in recreating alignments. Thus, the precision of geometric identification is reduced and the recreated alignment may significantly deviate from the actual railway. To solve this problem, a three-stage optimization method is proposed. At the first stage, a dynamic threshold method is developed to flexibly identify the geometric attributions of all measured points based on the existing railway. For the second stage, an adaptive analytic method is proposed which combines two geometric recreation approaches that are devised for curves and tangents to determine a preliminarily recreated horizontal alignment. Moreover, to enhance the recreation accuracy of local alignment sections, a harmony search algorithm is customized as the third stage to further optimize the recreated alignment. Finally, the effectiveness of the proposed method is verified through detailed data and sensitivity analyses applied to a real-world case.

Exploration of Ethnomathematics Houses Malay ‘Limas Potong’ The Batam Islands of Riau

Ethnomathematics is the study of how a group of individuals in a particular culture understand, communicate, and use cultural ideas and practices that researchers identify as mathematics. To return cultural heritage of traditional house in Batam, Riau Islands, and to further explore the idea of mathematical geometry inherent in the traditional house, so this research aims to explore the ethnomathematics in the Malay Traditional House 'Limas Potong'. This study applied a qualitative approach that was conducted in the Malay Traditional House 'Limas Potong', specifically in the Kampung Melayu neighborhood of Batam City's Nongsa District in the Riau Archipelago. The data used in this research was obtained from these explorations or already-published articles. Observation, interviews, and documentation were used as data collection methods. In this research, data analysis was carried out in two stages: data analysis in the field and data combining. According to the research findings, each decorative and structural part of the Malay Traditional House 'Limas Potong' incorporates mathematical ideas in geometrical shapes and components. Measurement, architectural design, mathematics learning, and application of learning are all related to ethnomathematics in the Malay Traditional House 'Limas Potong'. The construction of the Malay Traditional House 'Limas Potong' can be utilized as a learning resource for students, especially in geometry material, according to some mathematical ideas contained in the structure of the traditional house. Ethnomathematics exploration will inspire teachers to make this a new alternative to developing creativity in students' mathematics learning.

Application of the geometric component of a product digital twin when studying its actual geometric parameters

The article analyzes the results of using the digital twin concept to study changes in the geometric parameters (GP) of an aircraft wing during its production. The concept of creating a product digital twin is put into practice by constructing geometric models of the wing console at each key stage of its manufacture. The main attention is focused on studying the change in the GP of the caisson part of the wing console at the following stages: assembling of consoles in an aircraft fixture, assembling of consoles out of an aircraft fixture and final assembling of an aircraft. It is concluded that the first significant changes in wing GP appear at the stage of removing the wing caisson from the aircraft fixture. It is shown that even with acceptable mold forming characteristics of the aircraft fixture, it does not ensure compliance of the actual wing GP with the design data within the permitted tolerances and cannot be a means of controlling GP. It is substantiated the necessity of implementing into a wing caisson manufacturing technological process a procedure for monitoring the geometric shape of the unit after its removal from an aircraft fixture. It is proposed for a comprehensive assessment of isolated units’ geometric parameters to use a digital model of the aircraft, which is formed at each stage of the product manufacturing based on executed models of the units’ actual surfaces.

Two algorithms for reconstructing vertical alignments exploring the neural dynamics model of Adeli and Park

AbstractVertical alignment reconstruction obtains alignment parameters by fitting geometric components to a set of measured points representing the profile of an existing road or railroad, which is essential in alignment consistency analysis and maintenance to ensure safety and comfort. The neural dynamics model of Adeli and Park is explored and improved for reconstructing vertical alignments with constraints. The structure of the dynamics model is modified to include three layers: parameter layer, intermediate layer, and energy layer. The number of nodes in the parameter or intermediate layers corresponds to the number of independent parameters defining a vertical alignment. The number of nodes in the energy layer is the sum of the number of deviations and the number of constraints in the alignment reconstruction problem. The coefficients connecting nodes between the parameter layer and the intermediate layer determine the integral operations, which define the Levenberg–Marquardt algorithm of the dynamics model (LMADM) and the steepest descent algorithm of the dynamics model (SDADM). Both the LMADM and SDADM methods satisfy the Lyapunov stability theorem, but the LMADM method outperforms the SDADM method in its objective function value and computation time. Experiment results demonstrate that there are multiple local optima for a vertical alignment reconstruction, and the solutions obtained by the LMADM method are the best obtained so far, compared with those reported in the literature, with 57.1% and 23.4% decreases of the mean squared error for the highway and the railroad examples, respectively.

M-TAG: A modular teaching-aid for Geant4

Geant4 is a versatile Monte Carlo radiation transport simulation toolkit with a steep learning curve. This work introduces a user-code called M-TAG (Modular Radiation Teaching-Aid for Geant4), built on top of Geant4. M-TAG is designed to help gradually introduce the Geant4 toolkit to new users.The goal of Geant4 is to record quantities from the simulated radiation as it is transported through geometries. M-TAG simplifies the inclusion of new geometric elements and detector components in the simulation by including new classes. M-TAG also provides basic validated examples for some common detector development tasks. Geant4 intercom modules, called messenger classes, manage these classes. To validate M-TAG, simulations were performed to calculate the range of positrons in water. One hundred million decays at the center of a water-filled sphere with a radius of 1 m were allowed for fluorine-18, carbon-11, oxygen-15 and gallium-68. These results were compared to literature values. An inexperienced Geant4 user was tasked with creating a simulation model for a plastic scintillator-based detector and conducting basic tests to assess the effectiveness of M-TAG as a teaching tool. The simulation involved calculating the dose to the detector's sensitive volume using a 2x2 cm planar monoenergetic photon source spanning energies from 20 to 100 keV. One billion particles were simulated twice: once with the actual detector geometry and once with the sensitive volume replaced by water. The validity of M-TAG was also verified by computing dose ratios and comparing them with mass-attenuation ratios obtained from NIST XCOM data sets.The mean positron travel distances were within the distribution of literature values. Simulated positron energy spectra means were within 1.8% of literature means. Simulated dose ratios agreed with literature values within uncertainties.We have developed and verified a modular Geant4 teaching aid called M-TAG. It was used to introduce a new user to Geant4, who used it to perform further validation simulations.

Finite element analysis of the mechanical properties of sheet- and skeleton-gyroid Ti6Al4V structures produced by laser powder bed fusion

Additive manufacturing, and laser powder bed fusion (L-PBF) in particular, can produce complex geometric components with high resolution, and is very suitable for manufacturing lightweight triple periodic minimal surface (TPMS) structures to achieve lightweight. With regard to the two forms of the same structure, most of the previous studies focused on sheet-TPMS, but lacked the understanding of the difference between skeleton-TPMS and sheet-TPMS structures. In order to explore the characteristics of these two structures and provide theoretical support for the development of lightweight structure design, this paper compares the manufacturing performance and defect distribution of skeleton-gyroid (GSK) and sheet-gyroid structures (GSH). It employs high-precision finite element analysis (FEA) prediction and experimental verification to compare comprehensively the mechanical properties, failure behavior and energy absorption characteristics of the two structures. The results show that, compared to GSK, the larger specific surface area of GSH leads to more unmelted powder and draping adhesion, without affecting its higher stiffness and strength. Moreover, the more stable failure mode of GSH leads to more gentle stress platform stage and superior energy absorption performance. The results predicted by simulation are highly consistent with the experimental results. This improved understanding allows better prediction of the mechanical properties of the specimens using the Gibson–Ashby theory, which can reduce the experimental cost and time, and improve the resource consumption of TPMS structural performance research. This study can open new possibilities for the design and application of TPMS structures.

Architecting for Mass Transport: It Is More Than Just Tortuosity

Mass transport is performance-defining across energy storage devices. An example of this limitation is evident in energy dense lithium-ion batteries (LIBs), which develop concentration gradients from insufficient transport of lithium-ions (Li-ions) when operated at high current rates. This results in lowered capacity and energy due to underutilized active material and increased overpotential. The movement of Li-ions, or lack thereof is the root cause of the trade-off that exists between energy and power density in LIBs. To alleviate societal demur towards the full adoption of electric vehicles, range anxiety and slow charging are predominant challenges that industry and academia are rushing to overcome. These goals may require reimagined processing methods to move beyond planar electrodes with disorganized and heterogeneous porosity to create architectures that are dense in active material and contain tailored porosity. To maximize the geometric component of diffusion and species flux, porous low-tortuosity channels are a rational design choice, as they act as mass-transport highways for much needed through-plane Li-ion transport.One such innovative process is hybrid inorganic phase inversion (HIPI), a manufacturing method that is scalable, material-agnostic and results in low-tortuosity free-standing and monolithic architectures with tunable material-to-pore ratios. The HIPI process can enable electrodes with adjustable thicknesses of 100s of µm and relevant micro-architectural feature sizes between 5-40 µm, tailored by tuning the gelation temperature and nucleation density of the inorganic suspension during the nonequilibrium HIPI process. Importantly, the use of a soft organogel casting support results in the unhindered accessibility of the low-tortuosity pores present in the HIPI architectures.HIPI-architected anode and cathode electrodes exhibit electrochemical and architectural stability over a 1000 cycles in a full-cell battery. Further, mass-transport constraints appear at high current densities, and we identify the lithiation step as rate-performance limiting, a result of insufficient Li-ion supply and concentration polarization. Thus, for energy and power dense LIBs the answer is not simply mass-transport highways as unoptimized low-tortuosity channels, rather in-plane Li-ion demands must be tethered to the through-plane transport. Our results demonstrate the need for and feasibility of tailored electrode architectures where dimensional ratios between low-tortuosity channels, the charge-storing matrix, and electrode thickness are tunable, to both understand multi-scale structure-performance relationships and meet coupled power and energy-storage requirements.

The Partial Reconstruction Symplectic Geometry Mode Decomposition and Its Application in Rolling Bearing Fault Diagnosis.

Extracting the fault characteristic information of rolling bearings from intense noise disturbance has been a heated research issue. Symplectic geometry mode decomposition (SGMD) has already been adopted for bearing fault diagnosis due to its advantages of no subjective customization of parameters and the ability to reconstruct existing modes. However, SGMD suffers from rapidly decreasing calculation efficiency as the amount of data increases, in addition to invalid symplectic geometry components affecting decomposition accuracy. The regularized composite multiscale fuzzy entropy (RCMFE) operator is constructed to evaluate the complexity of each initial single component and minimize the residual energy. Combined with the partial reconstruction threshold indicator to filter out specific significant initial single components, the raw signal can be decomposed into multiple physically meaningful symplectic geometric mode components. Therefore, the decomposition efficiency and accuracy can be enhanced. Thus, a rolling bearing fault diagnosis method is proposed based on partial reconstruction symplectic geometry mode decomposition (PRSGMD). Both simulated and experimental analysis results show that PRSGMD can improve the speed of SGMD analysis while increasing the decomposition accuracy, thereby augmenting the robustness and effectiveness of the algorithm.

Electronic and structural behavior of graphene and azulphene nanoflakes under the influence of two-point charges

We have studied the behavior of graphene and azulphene nanoflakes in the presence of two-point charges. The carbon systems geometry was optimized using the DFT method without symmetry constraint. We studied the coronene (7-ring), two azulphene-coronenes (7-ring) with different symmetries, the superbenzene (19-ring), and three azulphene-superbenzenes (19-ring) with also different symmetries and different combinations of five, six, and seven-member rings exposed to an electric field due to two-point charges. In addition, the induced electric dipole and quadrupole were studied as a function of the charge point magnitude and signs.The Stark-lo-Surdo effect in HOMO, LUMO, and total energies was analyzed. The positive (negative) charges decrease (increase) the HOMO, LUMO, and total electronic energies. The contraction and expansion of molecular systems and the induced charge in the molecular plane due to two identical charges were studied. Due to two identical charges, the null net force does not deform the molecular systems out-off the xy-plane at z = 0. Instead, the deformation occurs in the xy-plane at z = 0, and the positive (negative) identical charges expand (contract) the molecular systems. These systems suffer concavation under the presence of the electric field due to two-point charges with opposite signs. The central ring is closer to the positive charge, while the hydrogen atoms belonging to the edges are closer to the negative charge for curved graphene models. The concavation of azulene-based systems is irregular and very intricate.This work aims to generically describe the influence of a pair of ions on the energetic and structural (electronic and geometric) components of two-dimensional carbon nanosystems with five, six, and seven-member rings. Our studies allow understanding of the general behavior to extrapolate to other bidimensional systems with different charge exposition like ions. Despite the complexity of the performance of the electric field due to point charges to systems with many electrons, we can obtain some general behaviors, although difficult to interpret in some cases.

The Influence of Geometry on Continuous and Split Bipolar Electrochemistry Applied to Corrosion Studies

Bipolar electrochemistry provides a wireless approach for driving redox reactions and has been applied in corrosion, electrodeposition, sensing, and electrocoagulation. Despite the extensive study of the method, the significance of geometric aspects of the experimental setup still remain ill-explored, and a justification for geometries used in previous works is missing. The aim of this study is to provide information about how current/potential distributions of a split bipolar electrode in an open configuration are affected by geometric components. Through PDE-constrained optimizations, the most influential parameters are identified to be the bipolar electrode size, electrolyte height, and applied current. It is shown that a general Wagner number may be used to inform the form of the current distribution for bipolar electrochemistry but with limitations. The results also show that the current through the bipolar electrode is directly associated with cell components and higher bipolar current efficiencies will promote the primary current distribution.