Dense Elements Research Articles

On maximal nowhere dense sublocales

The aim of this paper is to study some variants of nowhere dense sublocales called maximal nowhere dense and homogeneous maximal nowhere dense sublocales. These concepts were initially introduced by Veksler in classical topology. We give some general properties of these sublocales and further examine their relationship with both inaccessible sublocales and remote sublocales. It turns out that a locale has all of its non-void nowhere dense sublocales maximal nowhere dense precisely when all of its its non-void nowhere dense sublocales are inaccessible. We show that the Booleanization of a locale is inaccessible with respect to every dense and open sublocale. In connection to remote sublocales, we prove that, if the supplement of an open dense sublocale S is homogeneous maximal nowhere dense, then every S#-remote sublocale is *-remote from S. Every open localic map that sends dense elements to dense elements preserves and reflects maximal nowhere dense sublocales. If such a localic map is further injective, then it sends homogeneous maximal nowhere dense sublocales back and forth.

Enhanced buoyancy and propulsion in 3D printed swimming micro-robots based on a hydrophobic nano-fibrillated cellulose aerogel and porous lead-free piezoelectric ceramics

This paper provides the first demonstration of additively manufactured swimming micro-robots which combine a hydrophobic nanofibrillated cellulose aerogel, to provide long-term buoyancy, with a low acoustic impedance porous piezoelectric ceramic for improved propulsion. The hydrophobic nanocellulose aerogel is shown to exhibit a high and stable contact angle that was maintained for extended periods of time, which facilitates long-term and stable buoyancy of the micro-robot. To quantify the benefits of introducing porosity into the active piezoelectric element, a new analysis model was developed to inform material design and maximize the acoustic propulsion force. Detailed characterisation and modelling of the swimming robots demonstrated that a swimming robot based on a lead-free porous Ba0.85Ca0.15Zr0.1Ti0.9O3 (BCZT) ceramic exhibited a higher acoustic radiation propulsion force and a faster swimming speed compared to a robot fabricated using a dense ceramic element. These benefits were associated with the lower elastic modulus, density and acoustic impedance of the porous piezoelectric material. The lower dielectric constant, reduced device capacitance, and lower resonant frequency of the porous piezoelectric element also significantly reduced the driving current and power requirements of the robot. This work therefore provides new insights on the impact of hydrophobic and acoustically matched piezoelectric materials on the performance of swimming micro-robots, and successfully demonstrates the use of porosity to improve acoustic impedance matching of resonant piezoelectric devices, such as micro-robots and ultrasonic transducers.

A variable-node element model and its application to damage analysis of RAC using the 2D base force element method

The existing methods find it difficult to resolve the inconsistency in the nodal displacements of nodes at the interface of dense and sparse element models. Therefore, this paper proposes a new variable-node element model using the base force element method (BFEM) and successfully applies it to study the mechanical properties of recycled aggregate concrete (RAC). First, the variable-node element model with an arbitrary change of node number in the mid-edges was established, and the explicit expressions of the 2 × 2 nodal compliance matrix and nodal displacements were given. Subsequently, the triangular and quadrilateral elements of single-sides and double-sides of hanging element models were developed based on the variable-node element model. In addition, a double-notched model of RAC with different aggregate types but the same aggregate distribution position was established, and numerical simulations of uniaxial tension were performed. The results show that the compliance matrix and nodal displacement are independent of the element characteristic without Gaussian integration. The variable-node hanging element model has high numerical accuracy and applicability, and the nodes between the sparse and dense meshes do not require any construction measures. The variable-node elements ensure the coordination of the nodal displacement at the interfaces. The aggregate shape has a significant effect on the damage mode, maximum principal strain, principal stress distribution, and stress concentration, while has a negligible effect on RAC tensile strength when the aggregate distribution is the same.

Free Spectra of Equivalential Algebras with Conjunction on Dense Elements

We construct free algebras in the variety generated by the equivalential algebra with conjunction on dense elements and compute the formula for the free spectrum of this variety. Moreover, we describe the decomposition of free algebras into directly indecomposable factors.

Neural networks-based spring element for second-order analysis of pile-supported structures with nonlinear soil- structure interaction

This paper proposes a novel structural analysis approach, the neural networks-based spring element (NNSE) method, to synergize machine learning (ML) techniques with the line finite element method (LFEM) for the second-order analysis method of pile-supported structures. Traditional LFEM, widely used in upper structure design, showcases limitations in efficiently modeling complex Soil-Structure Interaction (SSI) along piles since it requires dense element mesh for accuracy. Conversely, ML offers a mesh-free alternative for analyzing single piles but struggles in simulating pile-supported structures as the training sample collection for large-scale problems might be unbearable. This paper addresses these challenges by proposing a new analysis framework to utilize the neural network (NN) model, which only describes structural responses of single piles, for the simulation of entire pile-supported structures. In the proposed method, the NN model is not directly used for structural analysis but employed to formulate a new spring element named the NNSE to model single piles in pile-supported structures. This NNSE can be seamlessly implemented within the existing LFEM framework to analyze pile-supported structures, eliminating the dense mesh requirement for single piles and thereby significantly improving the computational efficiency. Extensive examples are provided to verify the effectiveness of the proposed method, indicating its potential in promoting the second-order analysis method to the design of pile-supported structures.

Room temperature imprinting of water-based microparticulate inks for realizing glass microfluidic channels

The combination of imprinting and extrusion overprinting of composite glass materials offers a pathway for the fabrication of fully integrated functional microfluidic devices. Utilizing novel low-temperature phosphate glasses, originally developed for 3D extrusion printing, imprinting now has been achieved with soft stamps. The current hybrid process demonstrates superior resolution compared to previously reported extrusion techniques, presenting possibilities for applications such as open microfluidic channels that can subsequently be sealed by extrusion printing. The water-based microparticle glass-ink enables patterning at room temperature and its solidification occurring through water evaporation within the glass particle scaffold. Following the demolding, sintering is conducted at a temperature of 485 °C, resulting in dense glass elements with porosity levels below 1 %. For straightforward microfluidic channel structures featuring channels ranging from 100-200 µm in width, the shape is fully preserved during demolding and sequential annealing. The shrinkage observed is almost isotropic. The channels were successfully tested in an open microfluidic setup and initial tests were performed with the closed channels.

Deep learning-assisted dual-modal tomography for phase flow rate estimation in two-phase oil-water flow systems

Accurately estimating phase flow rates in multiphase systems is crucial for many industries, where precise measurements are essential for operational efficiency and safety. Addressing this issue, this paper introduces an approach that employs deep learning-assisted dual-modal electromagnetic flow tomography (EMFT) and electrical tomography (ET) to predict both oil and water flow rates in two-phase oil-water flows. To facilitate the generation of the data, we first simulate diverse flow conditions using COMSOL Multiphysics software and the convection–diffusion equation, aiming to create a realistic representation of two-phase oil-water flows. The dual-modal system measurement data, generated from these simulations and simulated by using a dense finite element mesh, provide reliable inputs for the deep learning model. Moreover, this study also integrates experimental data into both the training and testing phases, improving the ability of the proposed approach to estimate flow rates accurately in practical investigations. The results from laboratory experiments demonstrate the potential of the deep learning-assisted dual-modal ET and EMFT approach in effectively resolving the challenges of estimating flow rates in two-phase oil-water flow systems. By combining the deep learning capabilities with dual-modal tomography, this study offers valuable insights for future applications and represents a significant step forward in the field of multiphase flow rate estimation.

A hybrid formulation for determining the input power in a stiffened plate over a wide frequency range

A hybrid analytical/numerical formulation is presented for determining the input power in a stiffened plate over a wide frequency range. A Component Mode Synthesis (CMS) approach is used for developing the hybrid formulation. The structure is divided into a local substructure in the vicinity of the excitation and non-local substructures representing the remaining system. It is considered that the excitation is applied at a small number of discrete locations, therefore the local substructure is a small portion of the overall system. The computational efficiency originates from using an analytical approach and periodic structure theory for determining the dynamic modes and natural frequencies for the non-local substructures. Finite elements are used for determining the static modes for the non-local substructures and also for both the dynamic and static modes of the local substructure. The CMS matrices for the non-local substructures are condensed to their common interface degrees of freedom with the local substructures. In this manner, the non-local substructures are eventually represented as boundary conditions on the local substructure. Results from the hybrid formulation are compared with results from dense finite element models in order to demonstrate the validity and the efficiency of the hybrid method.

Enhancing artistic analysis through deep learning: a graphic art element recognition model based on SSD and FPT.

For the analysis of art works, accurate identification of various elements of works through deep learning methods is helpful for artists to appreciate and learn works. In this study, we leverage deep learning methodologies to precisely identify the diverse elements within graphic art designs, aiding artists in their appreciation and learning process. Our approach involves integrating the attention mechanism into an enhanced Single Shot MultiBox Detector (SSD) model to refine the recognition of artistic design elements. Additionally, we improve the feature fusion structure of the SSD model by incorporating long-range attention mechanism information, thus enhancing target detection accuracy. Moreover, we refine the Feature Pyramid Transformer (FPT) attention mechanism model to ensure the output feature map aligns effectively with the requirements of object detection. Our empirical findings demonstrate that our refined approach outperforms the original SSD algorithm across all four evaluation metrics, exhibiting improvements of 1.52%, 1.89%, 3.09%, and 2.57%, respectively. Qualitative tests further illustrate the accuracy, robustness, and universality of our proposed method, particularly in scenarios characterized by dense artistic elements and challenging-to-distinguish categories within art compositions.

From λ-hollow frames to λ-repletions in W: I. The scaffolding of a completely regular frame

We hollow out a given completely regular frame L by removing, for an uncountable regular cardinal number κ, the dense κ-cozero elements of L. This we do by passing to the cointersection of the proper dense open κ-cozero quotients of L. The quotient frame is κ-hollow, i.e., it has no proper dense κ-cozero elements, and this passage is a bireflection in the category of frames with skeletal morphisms. Thus each frame L has a descending sequence of dense quotient frames of increasing hollowness, indexed by the uncountable regular cardinal numbers, culminating in the classical minimal dense quotient of L.Our purpose is to shed light on the structure of a given frame L by examining the collection of quotients and sub-κ-frames which arise in its hollowing sequence, to which we refer collectively as the scaffolding of L.

Efficient numerical implementation for nonlinear analysis of pile-supported structures during soil liquefaction through adaptive pile element formulations

The structural behavior of pile-supported structures during soil liquefaction is sometimes insufficiently investigated properly due to the inefficiency in the existing line finite element method (LFEM), which is widely used in practice. The traditional LFEM to simulate pile response requires dense element mesh for accurate results, as it simplifies the continuous surrounding soil as discrete spring elements, resulting in high computational costs, especially for pile-supported structures with a significant number of piles. Additionally, analyzing pile-supported structures in different stages of soil liquefaction requires repetitive updating of p-y curves and tedious starting-over iteration processes. To address these issues, an innovative line element formulation named the pile element formulation is employed and improved to adaptively simulate the surrounding soil conditions at different stages during liquefaction within the element formulation, eliminating the need to model discrete soil springs and significantly improving computational efficiency. The adaptive pile element formulation is then implemented within a refined Newton-Raphson iteration procedure that is proposed for a more effective nonlinear analysis process to consider soil liquefaction without repetitive iteration processes from starting over. Through several examples, the computational efficiency of the proposed method is validated, which requires only 20% of the computational cost compared to traditional LFEM while still providing accurate results, highlighting the application potential of the present study.

Synthesis of Large Ultrawideband Sparse Planar Arrays by Utilizing a Cooperative Coevolutionary Iterative Fourier Transform

This letter introduces a cooperative coevolutionary iterative Fourier transform (CCIFT) technique to extend the conventional IFT to large ultra-wideband (UWB) sparse planar array synthesis. In the proposed CCIFT, a dense initial element position grid such as a spacing of half a wavelength at the highest frequency is adopted to avoid the presence of grating lobes at high frequency band, and a probability-assisted element selection mechanism is presented to guarantee the obtained array layout to meet a preset minimum spacing constraint, enabling the placement of physical UWB antenna elements. In addition, a cooperative coevolutionary strategy is presented to avoid prematurity by establishing the information interaction between different excitation distributions from multiple parallel IFT procedures. Two examples are conducted and results show that the CCIFT can achieve a considerably lower peak sidelobe level (PSL) than some state-of-art algorithms within an acceptable CPU time, which demonstrates its effectiveness and superiority.

3D Printing and processing of miniaturized transducers with near-pristine piezoelectric ceramics for localized cavitation

The performance of ultrasonic transducers is largely determined by the piezoelectric properties and geometries of their active elements. Due to the brittle nature of piezoceramics, existing processing tools for piezoelectric elements only achieve simple geometries, including flat disks, cylinders, cubes and rings. While advances in additive manufacturing give rise to free-form fabrication of piezoceramics, the resultant transducers suffer from high porosity, weak piezoelectric responses, and limited geometrical flexibility. We introduce optimized piezoceramic printing and processing strategies to produce highly responsive piezoelectric microtransducers that operate at ultrasonic frequencies. The 3D printed dense piezoelectric elements achieve high piezoelectric coefficients and complex architectures. The resulting piezoelectric charge constant, d33, and coupling factor, kt, of the 3D printed piezoceramic reach 583 pC/N and 0.57, approaching the properties of pristine ceramics. The integrated printing of transducer packaging materials and 3D printed piezoceramics with microarchitectures create opportunities for miniaturized piezoelectric ultrasound transducers capable of acoustic focusing and localized cavitation within millimeter-sized channels, leading to miniaturized ultrasonic devices that enable a wide range of biomedical applications.

A study of structural effect on the spectral property of metallic cross-hole array in mid-infrared wavelengths

Based on the earlier success in developing multichannel detection in long (8–14 μm) infrared wavelengths, this paper reports our recent progress for spectral filters in the mid-infrared band of 4–10 μm by introducing a new design with metallic cross annular hole array. The effects of structural dimensions on filtering performance were investigated by numerical simulations with the finite-difference time-domain method and experimentally verified by optical characterizations of fabricated filters made by electron beam lithography. The transmission peaks were optimized with the maximum transmittance of 62%. The existing problem of low spectral resolution of transmittances was tackled by using a thick Au film for the filter, which remains a big challenge for conventional electron beam lithography. By modeling ice lithography in amorphous solid water for constructing the filter, it was found that ice lithography certainly possesses significant advantage in replicating nanoscale features with high aspect ratio. The proposed ice lithography in this work provides an effective solution for the nanofabrication of high performance filters with dense elements in an array in the mid-infrared wavelengths.

A Full-Vectorial Spectral Element Method With Generalized Sheet Transition Conditions for High-Efficiency Metasurface/Metafilm Simulation

Recently, metasurfaces as 2-D metamaterials have been widely applied due to their advantages in low loss, ease of fabrication, and tunability in the phase, magnitude, and polarization of incident electromagnetic waves. However, due to the subwavelength-thickness properties of metasurfaces, their direct modeling and simulation are challenging because of the heavy computational burden. In this work, a high-efficiency spectral element method with generalized sheet transition conditions (SEM-GSTCs) is proposed by replacing finite thickness metasurfaces with zero-thickness equivalent boundary conditions to avoid dense elements and the associated enormous number of unknowns. Moreover, both the scalar and the full-vectorial SEM-GSTC are implemented. Some illustrative numerical examples are shown to verify that the proposed SEM-GSTC not only can obtain highly accurate numerical results but also is effective in addressing complex functions ranging from isotropic to fully bianisotropic metasurfaces.

Algebraic frames in which dense elements are above dense compact elements

Algebraic frames in which dense elements are above dense compact elements

Equivalential Algebras with Conjunction on Dense Elements

We study the variety generated by the three-element equivalential algebra with conjunction on the dense elements. We prove the representation theorem which let us construct the free algebras in this variety.

A fast direct solver for non-intrusive reduced order modeling of vibroacoustic problems

This paper proposes a fast model order reduction method for large-scale three-dimensional vibro-acoustic coupling problems, which proceeds in three perspectives. Firstly, part of the coupling matrices is neglected and another part of the coupling matrices is treated as the partial right-hand side of the Schur complement of the corresponding subsystem in order to implement model reduction quickly. Secondly, the proposed fast method does not require the use of the underlying complex-valued and dense boundary element full-order model for the construction of a global orthonormal basis in the offline phase. Rather, its sparse approximation is exploited, which benefits from the consistent amplitude decay property of the kernel functions. This way it can be regarded as a non-intrusive method. Lastly, in addition to structural loads, acoustic loads, such as the load from incident waves impinging on the flexible structure from the outside, can be handled as well. Application of this solution method to the frequency sweep analyses of coupled structural acoustic systems, i.e. simple sphere and complex geometrical model submerged in an infinite fluid with the number of degrees of freedom ranging from hundreds of thousands up to millions, shows the improved computational efficiency and reduced memory requirement as compared to the brute force approach based on the direct evaluation of original high-dimensional models and also the previous acceleration scheme.

ASFF-YOLOv5: Multielement Detection Method for Road Traffic in UAV Images Based on Multiscale Feature Fusion

Road traffic elements are important components of roads and the main elements of structuring basic traffic geographic information databases. However, the following problems still exist in the detection and recognition of road traffic elements: dense elements, poor detection effect of multi-scale objects, and small objects being easily affected by occlusion factors. Therefore, an adaptive spatial feature fusion (ASFF) YOLOv5 network (ASFF-YOLOv5) was proposed for the automatic recognition and detection of multiple multiscale road traffic elements. First, the K-means++ algorithm was used to make clustering statistics on the range of multiscale road traffic elements, and the size of the candidate box suitable for the dataset was obtained. Then, a spatial pyramid pooling fast (SPPF) structure was used to improve the classification accuracy and speed while achieving richer feature information extraction. An ASFF strategy based on a receptive field block (RFB) was proposed to improve the feature scale invariance and enhance the detection effect of small objects. Finally, the experimental effect was evaluated by calculating the mean average precision (mAP). Experimental results showed that the mAP value of the proposed method was 93.1%, which is 19.2% higher than that of the original YOLOv5 model.

Dense Elements in B-Almost Distributive Fuzzy Lattices

In this paper we define the concept of a dense element in a B-Almost Distributive Fuzzy Lattice BADFL and prove that the set of all dense elements of is an implicative filter of . Also, we establish a fuzzy epimorphism of into the set of all closed elements ofand prove the existence of an fuzzy epimorphism of into . We prove that and are fuzzy isomorphic.