Geometric Relationship Research Articles

Thermal expansion properties of double concave arrow honeycomb structure with double materials

This article proposes a kind of double concave double-arrow cell. The equivalent thermal expansion coefficient is obtained by using the geometric relation of deformation. The theoretical results agree well with the finite element results. The effect of material matching and geometry size on the equivalent thermal expansion coefficient is discussed. Based on the proposed two-material double-arrow cell, a two-material honeycomb structure is constructed. The thermal expansion coefficient, equivalent elastic modulus and Poisson’s ratio of the structure under thermal load are numerically discussed. It is found that the thermal expansion coefficient of the structure increases with the increase of the thermal expansion coefficient of the material, and the thermal expansion coefficient of the up arrow has a greater effect on the thermal expansion performance of the structure than that of the down arrow. Compared with the single material honeycomb structure, the double-material concave honeycomb structure does not produce the deformation mode of surrounding diffusion, and its longitudinal expansion is smaller. It shows that zero expansion can be achieved by adjusting the material and geometric parameters, and this structure provides a new idea for the design of other zero expansion structures.

Research on Multi Beam Sideline Model Based on Geometric Relationships

Research on Multi Beam Sideline Model Based on Geometric Relationships

Key indicators of caprock sealing assessment with consideration of faults in potential CO2 geological storage sites in Subei Basin, China

Good caprock sealing is crucial for ensuring the long-term safety and security of carbon dioxide (CO2) geological storage. However, concealed faults within caprocks and reservoirs can impact the transport and accumulation of CO2 plumes. Due to the uncertainties associated with the geometric structure, physical properties, and combined relationships among reservoir, caprock and fault, accurately evaluating caprock sealing is challenging. To address the challenge of identifying key indicators for caprock sealing considering faults, this study focuses on the one potential CO2 geological storage field in the Subei Basin, China. First, this study establishes a hydraulic-mechanical (HM) coupled finite element model considering a combination of caprock, reservoir and fault. Then, 22 research indicators, including fault offset, fault dip, caprock thickness, burial depth, permeability and mechanical properties, are analysed to evaluate their influence on caprock sealing via the tornado analysis and response surface methods. Finally, key indicators are determined based on evaluation criteria, such as pore pressure increment (ΔPP) and Coulomb failure stress (CFS), in the fault plane. The research results indicate that fault dip, fault offset, fault permeability, burial depth, and reservoir permeability are key indicators. The caprock thickness, caprock permeability, and caprock Young's modulus significantly influence the caprock sealing capacity. The ΔPP and CFS increase with increasing fault dip and offset. When the fault dip exceeds 45°, the ΔPP and CFS reach maximum values at the interface between the reservoir and caprock. Fault permeability has a greater impact than reservoir permeability and caprock permeability. The research results may provide guidance for the evaluation of caprock sealing capacity for CO2 geological storage.

Performance Improvement of Three-Spring Quasi-Zero-Stiffness Isolator by Shape Memory Alloy Damper

Quasi-zero stiffness vibration isolators (QZSI) can effectively resolve the contradiction between the load bearing and the vibration isolation for low-frequency vibration systems. The three-spring QZSI is a classical QZSI. However, constrained by its geometrical relationship, the working stroke of the QZSI is limited, and the isolation performance will deteriorate when the displacement response is significant. To solve this question, the shape memory alloy (SMA) damper, characterized by lower secondary stiffness, partially replaces the positive-stiffness spring of the three-spring QZS isolator to widen its effective working stroke, which forms a novel SMA-QZSI. Based on a piecewise linear constitutive model of SMA, a theoretical model of the force–displacement relationship of SMA-QZSI is established. Subsequently, the approximate analytic amplitude–frequency response equation of the non-smooth nonlinear SMA-QZSI system under harmonic excitation is obtained by the average method and verified numerically. In addition, the effects of mechanical parameters of SMA springs and external excitation parameters on mechanical behaviors and low-frequency isolation performance of the SMA-QZSI isolator are discussed. Finally, the static and dynamic experiments of SMA-QZSI are conducted to verify its force–displacement relationship and isolation performance. The results show that the proposed SMA-QZSI has remarkable low-frequency vibration isolation performance.

The radiative and geometric properties of melting first-year landfast sea ice in the Arctic

Abstract. In polar regions, sea ice is a crucial mediator of the interaction between Earth's atmosphere and oceans. Its formation and breakup is intimately connected with large-scale climatic processes, local weather patterns, and the use of sea ice in coastal Arctic regions by Indigenous people. In order to investigate the physical phenomena at the heart of this process, a set of targeted, intensive observations were made over spring sea ice melt and breakup in Kotzebue Sound, Alaska. These observations were planned and executed through a collaborative effort in which an Indigenous Elder advisory council from Kotzebue and scientists participated in co-production of hypotheses and observational research, including a stronger understanding of the physical properties of sea ice during spring melt. Here we present the results of observations performed using high-endurance, fixed-wing uncrewed aerial vehicles (UAVs) containing custom-built scientific payloads. Repeated flights over the measurement period captured the early stages of the transition from a white, snow-covered state to a broken-up, bare blue-green state. We found that the reflectance of sea ice features depends strongly on their size. Snow patches get darker as they get smaller, an effect owed to the geometric relationship between the bright interior and the darker, melting feature edges. Conversely, bare patches get darker as they get larger. For the largest ice features observed, bare blue-green ice patches were found to be ≈ 20 % less reflective than average across all observational cases, while large snowy white ice patches were found to be ≈ 20 % more reflective than that same average.

Monge Surfaces. Generation, Discretisation and Application in Architecture

AbstractThis paper describes a revision of so-called Monge surfaces through using digital graphic tools, based on the synthetic conception exposed by Gaspard Monge in the 18th and 19th centuries, through their geometric relation with polar surface. As a starting point, we propose a graphical system that integrally solves the generation of these kind of surfaces, their rationalization and discretization, with the objective of their specific application in architecture. The geometric system described allows the generation of a type of surface in which the pair of curves -generatrix and directrix- give rise to the network of principal lines of curvature (LCP) of the final surface. In this way, we propose a process that follows a bottom-up generative system based on Monge surfaces, which offers wide possibilities of formal exploration, while imposing geometrical-constructive properties that are very useful in fabrication and assembly processes.

Trajectory design based on frictional resistance of deflector in a hydraulic radial drilling system

The trajectory design is a key factor affecting the frictional resistance of the deflector, which is crucial for the drilling ability of the hydraulic radial drilling system. In this research, the trajectory design model and geometric constraints model of a deflector are established by analyzing the geometric relationship of the deflector and considering the geometric constraints of the casing. According to the actual contact form between the high-pressure hose and the deflector, the theoretical model of frictional resistance is built based on segmental rigidization and micro-element methods. The theoretical model is verified by the deflector friction experiment. The results demonstrate a good agreement between the experimental results of friction resistance of different sizes of high-pressure hoses and the theoretical results, with an error of less than 7%. The influence of critical parameters of deflector trajectory on the friction resistance is studied by coupling the geometric constraints model and the frictional resistance theoretical model of the deflector. The findings show that the deflector’s frictional resistance increases with the inclination angle β of the inclined-straight section and decreases with the increase in the radius R of the bending segment, the inclination angle ω of the straightening segment, and the channel radius of r deflector. A new trajectory parameters of the deflector are presented by taking a five-inch casing as an example, they are β = 9°, R = 92 mm, ω = 108°, r = 17 mm. The research results provide a theoretical rationale for designing a low-frictional resistance deflector.

Cross-region feature fusion with geometrical relationship for OCR-based image captioning

Automatically generating a readable sentence that describes the text-contained image is a challenging task. Compared to traditional image captioning algorithms, OCR-based image captioning focuses on reading OCR tokens in images and understanding them with the image content to generate descriptions. However, existing research mainly concentrate on improving the quantity and quality of obtaining OCR tokens and exploring their spatial relationships while lacking investigation into how to effectively join OCR tokens with image content. This paper proposes a cross-region feature fusion with a geometrical relationship Transformer(CFGR-Transformer) for OCR-based image captioning. The network first establishes the associations between the OCR and object regions of the image by constructing relative geometric relationships, including width/height difference, distance, IOU(Intersection over Union), inclusion relationships, and angles offset, and then incorporates intra-region and cross-region features to aggregate entities from different modalities by a multi-head attention mechanism based on relative relationships. Benefiting from the guidance of the relative relationship, visual entities like OCR tokens and object regions can consider multiple relative relationships as the attention weight for feature fusion within each subspace. Extensive experiments conducted on the TextCaps dataset demonstrate the effectiveness of the proposed CFGR-Transformer method. In particular, our results on the online testing of TextCaps achieve an improvement in CIDEr score from 93.0% to 98.2%.

Cotunneling Effects in the Geometric Statistics of a Nonequilibrium Spin‐Resolved Junction

AbstractIn the nonequilibrium steady state of electronic transport across a spin‐resolved quantronic junction, the role of cotunneling on the emergent statistics under phase‐different adiabatic modulation of the reservoirs' chemical potentials is investigated. By explicitly identifying the sequential and inelastic cotunneling rates, the geometric or Pancharatnam–Berry contribution to the spin exchange flux between the spin system and the right reservoir is numerically evaluated. The relevant conditions wherein the sequential and cotunneling processes compete and selectively influence the total geometric flux upshot are identified. The Fock space coherences are found to suppress the cotunneling effects when the system reservoir couplings are comparable. The cotunneling contribution to the total geometric flux can be made comparable to the sequential contribution by creating a right‐sided asymmetrically stronger system‐reservoir coupling strength. Using a recently proposed geometric thermodynamic uncertainty relationship, the total rate of minimal entropy production is estimated. The geometric flux and the minimum entropy is found to be nonlinear as a function of the interaction energy of the junctions' spin orbitals.

Semantic segmentation for large-scale point clouds based on hybrid attention and dynamic fusion

This paper investigates the semantic segmentation problem for large-scale point clouds. Recent segmentation methods usually employ an encoder–decoder architecture. However, these methods may not effectively extract neighboring information in the encoder. Additionally, they typically use nearest neighbor interpolation and skip connections in the decoder, overlooking the semantic gap between encoder and decoder features. To resolve these issues, we propose HADF-Net, which consists of a Hybrid Attention Encoder (HAE), an Edge Dynamic Fusion module (EDF), and a Dynamic Cross-attention Decoder (DCD). HAE leverages the distinctive properties of geometric and semantic relations to aggregate local features at different stages. EDF aims to alleviate information loss during decoder upsampling by dynamically integrating the neighboring information. DCD employs an enhanced fusion mechanism with spatial-wise cross-attention to bridge the semantic gap between encoder and decoder features. Experimental results on 4 datasets demonstrate that our HADF-Net achieves superior performance.

A method for extracting P‐SV‐converted wave angle‐domain common‐image gathers based on elastic‐wave reverse‐time migration

AbstractMulticomponent seismic technology utilizes the kinematic and dynamic characteristics of reflected P‐waves and converted S‐waves to reduce ambiguity in seismic exploration. The imaging and inversion accuracy of P‐SV‐converted waves are important in determining whether multicomponent seismic exploration can achieve higher exploration accuracy than conventional P‐wave exploration. Pre‐stack inversion of P‐SV‐converted waves requires precise input of P‐SV‐converted wave angle‐domain common‐image gathers. Consequently, the P‐SV‐converted wave angle‐domain common‐image gather extraction accuracy will significantly affect the P‐SV‐converted wave inversion accuracy. However, existing methods for extracting P‐SV‐converted wave angle‐domain common‐image gathers are constrained by issues such as the P‐ and S‐wave crosstalk artefacts, low‐frequency noises and inaccurate calculation of P‐wave incident angles, leading to poor imaging accuracy. We study an angle‐domain cross‐correlation imaging condition and address three key issues based on this condition: the decoupling of P‐ and S‐waves, the separation of up‐going and down‐going waves and the precise calculation of P‐wave incident angles. Our strategies facilitate high‐precision extraction of P‐SV‐converted wave angle‐domain common‐image gathers using elastic wave reverse‐time migration. In this paper, first, we employ the first‐order velocity‐dilatation‐rotation elastic wave equations to decouple P‐ and S‐waves automatically during source and receiver wavefield extrapolations. Second, we calculate the optical flow vectors of P‐ and S‐waves to ensure stable calculations of wave propagation directions. Based on this, we obtain up‐going and down‐going waves of P‐ and S‐waves. Meanwhile, we calculate the incident angle of the source P‐wave using geometric relations. Lastly, we apply the angle‐domain imaging condition to achieve high‐precision extraction of P‐SV‐converted wave angle‐domain common‐image gathers. Model examples demonstrate the effectiveness and advantages of the proposed method.

Analysis, optimization, and testing of a tilt-body aircraft

This paper proposes a new multidisciplinary design optimization framework for tilt-bodies to obtain the optimal combination of geometry and powertrain, achieving both long endurance and low transition power consumption at a 5 kg takeoff weight. A low-fidelity vortex lattice method is used to derive the aerodynamic coefficients. The tandem wings are trimmed using an optimization-based method, considering the effect of distributed propulsion on the trim solution through aero-propulsive interaction at low flight speed. Detailed powertrain parameters are fitted with fewer design variables to calculate power consumption. By analyzing the unique constraints of tilt-bodies, the optimization problem is established as a simultaneous analysis and design architecture, and solved with different numbers of rotors. The impact of the relative geometric relationship between the front and rear wings on aerodynamic performance and constraints is analyzed. Results demonstrate the full angle-of-attack flight capability of tilt-bodies. The optimal design can save nearly 1000 W in transition, with a pure cruise endurance of over 1 hour, which is competitive among other configurations. With an empty weight of only 2 kg, a portion of the battery can be allocated to a heavier payload. High-fidelity computational fluid dynamics corrects the errors of the vortex lattice method on non-lifting components, including the fuselage, nacelles, and landing gear. Finally, the feasibility of the optimal design and the accuracy of the framework are validated by wind tunnel tests and in-flight drag measurements on a test platform.

Measurement Approach for the Pose of Flanges in Cabin Assemblies through Distributed Vision.

The relative rotation angle between two cabins should be automatically and precisely obtained during automated assembly processes for spacecraft and aircraft. This paper introduces a method to solve this problem based on distributed vision, where two groups of cameras are employed to take images of mating features, such as dowel pins and holes, in oblique directions. Then, the relative rotation between the mating flanges of two cabins is calculated. The key point is the registration of the distributed cameras; thus, a simple and practical registration process is designed. It is assumed that there are rigid and scaling transformations among the world coordinate systems (WCS) of each camera. Therefore, the rigid-correct and scaling-correct matrices are adopted to register the cameras. An auxiliary registration device with known features is designed and moved in the cameras' field of view (FOV) to obtain the matrix parameters so that each camera acquires traces of every feature. The parameters can be solved using a genetic algorithm based on the known geometric relationships between the trajectories on the registration devices. This paper designs a prototype to verify the method. The precision reaches 0.02° in the measuring space of 340 mm.

Nonlocal strain gradient-based nonlinear vibration analysis of nonlinear FG three-phase HJCNT/MWCNT/epoxy composite microbeam resonators using a modified micromechanical model

This paper aims to study nonlinear dynamic behavior of functionally graded (FG) three-phase composite microbeam resonators made of an epoxy matrix and two reinforcements namely multi-walled carbon nanotubes (MWCNTs) and hetero-junction carbon nanotubes (HJCNTs). The effective mechanical properties of the composite microbeam are obtained using the modified Halpin-Tsai micromechanical model. The microbeam surrounding medium is simulated using a two-parameter elastic foundation. The von-Karman’s geometric nonlinearity relations are incorporated and the equations of motion are derived based on the nonlocal strain gradient Euler–Bernoulli beam model. A new closed-form analytical solution is obtained using the homotopy perturbation method. The effects of vibration amplitude, nanofiber volume fraction, nanofiber distribution pattern, small-scale parameters and the foundation parameters on the nonlinear frequency and deflection of the FG three-phase composite microbeams are studied in detail. The findings of the paper are valuable for researchers in the field of microbeam resonators.

Theoretical and observational implications of Planck’s constant as a running fine structure constant

This paper explores how a reinterpretation of the generalized uncertainty principle as an effective variation of Planck’s constant provides a physical explanation for a number of fundamental quantities and couplings. In this context, a running fine structure constant is naturally emergent and the cosmological constant problem is solved, yielding a novel connection between gravitation and quantum field theories. The model could potentially clarify the recent experimental observations by the DESI Collaboration that could imply a fading of dark energy over time. When applied to quantum systems and their characteristic length scales, a simple geometric relationship between energy and entropy is disclosed. Lastly, a mass–radius relation for both quantum and classical systems reveals a phase transition-like behavior similar to thermodynamical systems, which we speculate to be a consequence of topological defects in the universe.

Geometric relationship between the projected surface area and mass of a plastic particle

The quantification of the mass of meso/microplastic (MMP) particles is crucial for assessing the global inventory of ocean plastics and assessing environmental and human health risks. Herein, linear regression models between mass and projected surface area on a log scale were established by directly measuring the masses of 4390 MMP particles collected at 35 sites in 17 Japanese rivers with an ultramicrobalance. The linear regression models estimated mass concentrations more accurately than any previous method based on geometric volume assuming several three-dimensional shapes. Additionally, linear regression models were quite reasonable for determining the geometric relationships of idealized cuboid particles. The slope of the linear regression models was dependent on the three-dimensional shapes of the particles, and their intercept was determined according to their third dimension. Moreover, the third dimension led to uncertainty in the mass estimation of particles; thus, the accuracies of the previous methods were relatively poor. Nevertheless, two limitations for mass measurement by linear regression models were identified, which determined the size range of the MMP particles on the projected surface area (ranging from 10−4 mm2 to 102 mm2) that is applicable for mass estimation of the particles collected from riverine and marine environments. Our results could be used to accurately estimate the mass concentrations in aquatic environments and provide insights into the geometric relationships between the mass and size of MMP particles.

Rethinking Feature Mining for Light Field Salient Object Detection

Light field salient object detection (LF SOD) has recently received increasing attention. However, most current works typically rely on an individual focal stack backbone for feature extraction. This manner ignores the characteristic of blurred saliency-related regions and contour within focal slices, resulting in insufficient or even inaccurate saliency responses. Aiming at addressing this issue, we rethink the feature mining (i.e., exploration) within focal slices, and focus on exploiting informative focal slice features and fully leveraging contour information for accurate LF SOD. First, we observe that the geometric relation between different regions within the focal slices is conducive to useful saliency feature mining if utilized properly. In light of this, we propose an implicit graph learning (IGL) approach. The IGL constructs graph structures to propagate informative geometric relations within the focal slices and all-focus features, and promotes crucial and discriminative focal stack feature mining via graph feature distillation. Second, unlike previous works that rarely utilize contour information, we propose a reciprocal refinement fusion (RRF) strategy. This strategy encourages saliency features and object contour cues to effectively complement each other. Furthermore, a contour hint injection mechanism is introduced to refine the feature expressions. Extensive experiments showcase the superiority of our approach over previous state-of-the-art models with an efficient real-time inference speed. Codes are available at: https://github.com/gbliao/IRNet .

Sparse sampling photoacoustic reconstruction with a graph regularization group sparse dictionary

Photoacoustic tomography (PAT) has emerged as a promising biomedical imaging technique. The combination of optical contrast and ultrasound spatial resolution in photoacoustic tomography overcomes the limitations of optical scattering, enabling clear imaging of tissue structures. However, achieving high-resolution photoacoustic images typically requires a large number of sensor detection elements for sufficient angular coverage. This demand for extensive data acquisition and processing raises concerns about efficiency and system complexity. While sparse sampling strategies can improve efficiency, preserving detailed structural information becomes challenging with a minimal number of detectors. To address the challenges of sparse sampling, compressed sensing (CS) techniques have been successfully applied for image reconstructions in 2D and 3D photoacoustic embodiments. In this context, we propose a joint graph regularization group sparse dictionary and total variational regularization (GRGS-TV) algorithm based on our previous work of a group sparse dictionary. It preserves structured information and geometric relationships among dictionary atoms. Moreover, TV regularization effectively preserves edge structures while exhibiting a certain degree of robustness and flexibility. Numerical simulations and in vivo experiments on mice validate the effectiveness of this method in improving photoacoustic image quality and suppressing artifacts. Comparative evaluations against other algorithms show enhanced performance in terms of image reconstruction evaluation indices. This innovative approach holds promise for advancing photoacoustic imaging in biomedical research and clinical diagnostics.

An analytical method to estimate the accuracy representation index of circular and elliptical disc models for rectangular fractures with application to seepage analysis

Constructing a suitable discrete fracture network (DFN) to represent rock fractures proves vital for tackling engineering projects involving rock masses. Among the commonly used models for constructing DFN, the circular disc model (CDM) and elliptical disc model (EDM) stand out. The selection between these models has been facilitated by the introduction of the Accuracy Representation Index (ARI), which quantitatively assesses their suitability. The existing methods for calculating ARI based on Monte Carlo simulations are time-consuming. In order to quickly estimate the ARI for CDM and EDM concerning any length-width ratio (kr) of rectangular fracture, the paper derives analytical formulas based on the geometric relationships between circles and ellipses with rectangles. These formulas show that: (a) for the CDM, ARI is only related to kr, and its value decreases as kr increases; (b) for the EDM, ARI is dependent on the relationship between kr and the long-short axis length ratio (ke) of the ellipse, and it has been theoretically proven that ARI reaches its maximum value of 0.91 when kr is equal to ke. Moreover, we apply ARI to the study of rock mass seepage characteristics, and the results show that ARI could reflect the error rate of permeability of the CDM and EDM for rock masses with rectangular fractures.

Graph Embedded Ensemble Deep Randomized Network for Diagnosis of Alzheimer's Disease.

Randomized shallow/deep neural networks with closed form solution avoid the shortcomings that exist in the back propagation (BP) based trained neural networks. Ensemble deep random vector functional link (edRVFL) network utilize the strength of two growing fields, i.e., deep learning and ensemble learning. However, edRVFL model doesn't consider the geometrical relationship of the data while calculating the final output parameters corresponding to each layer considered as base model. In the literature, graph embedded frameworks have been successfully used to describe the geometrical relationship within data. In this paper, we propose an extended graph embedded RVFL (EGERVFL) model that, unlike standard RVFL, employs both intrinsic and penalty subspace learning (SL) criteria under the graph embedded framework in its optimization process to calculate the model's output parameters. The proposed shallow EGERVFL model has only single hidden layer and hence, has less representation learning. Therefore, we further develop an ensemble deep EGERVFL (edEGERVFL) model that can be considered a variant of edRVFL model. Unlike edRVFL, the proposed edEGERVFL model solves graph embedded based optimization problem in each layer and hence, has better generalization performance than edRVFL model. We evaluated the proposed approaches for the diagnosis of Alzheimer's disease and furthermore on UCI datasets. The experimental results demonstrate that the proposed models perform better than baseline models. The source code of the proposed models is available at https://github.com/mtanveer1/.