Search Results (92)

Addressing the challenges of bulky, low-efficiency sound-insulation materials at low frequencies, this work proposes an acoustic metamaterial based on curve fractal channels. Each unit cell comprises a concentric circular-ring channel recursively iterated: as the fractal order increases, the channel path length grows exponentially, enabling outstanding sound-insulation performance within a deep-subwavelength thickness. Finite-element and transfer-matrix analyses show that increasing the fractal order from one to three raises the number of bandgaps from three to five and expands total stop-band coverage from 17% to over 40% within a deep-subwavelength thickness. Four-microphone impedance-tube measurements on the third-order sample validate a peak transmission loss of 75 dB at 495 Hz, in excellent agreement with simulations. Compared to conventional zigzag and Hilbert-maze designs, this curve fractal architecture delivers enhanced low-frequency broadband insulation, structural lightweighting, and ease of fabrication, making it a promising solution for noise control in machine rooms, ducting systems, and traffic environments. The method proposed in this paper can be applied to noise reduction of transmission parts for ceramic automation production. Full article

This paper addresses the critical challenge of point cloud down-sampling for digital twin creation, where reducing data volume while preserving geometric fidelity remains an ongoing research problem. We propose a novel down-sampling approach that combines Low-Discrepancy Sequences (LDS) with Hilbert curve ordering to create a method that preserves both global distribution characteristics and local geometric features. Unlike traditional methods that impose uniform density or rely on computationally intensive feature detection, our LDS-Hilbert approach leverages the complementary mathematical properties of Low-Discrepancy Sequences and space-filling curves to achieve balanced sampling that respects the original density distribution while ensuring comprehensive coverage. Through four comprehensive experiments covering parametric surface fitting, mesh reconstruction from basic closed geometries, complex CAD models, and real-world laser scans, we demonstrate that LDS-Hilbert consistently outperforms established methods, including Simple Random Sampling (SRS), Farthest Point Sampling (FPS), and Voxel Grid Filtering (Voxel). Results show parameter recovery improvements often exceeding 50% for parametric models compared to the FPS and Voxel methods, nearly 50% better shape preservation as measured by the Point-to-Mesh Distance (than FPS) and up to 160% as measured by the Viewpoint Feature Histogram Distance (than SRS) on complex real-world scans. The method achieves these improvements without requiring feature-specific calculations, extensive pre-processing, or task-specific training data, making it a practical advance for enhancing digital twin fidelity across diverse application domains. Full article

Perfusable microvasculature is critical for advancing in vitro tissue models, particularly for neural applications where limited diffusion impairs organoid growth and fails to replicate neurovascular function. This study presents a versatile fabrication platform that integrates mesh-driven design, two-photon lithography (TPL), and modular interfacing to create multi-material, perfusable 3D microvasculatures. Various 2D and 3D capillary paths were test-printed using both polygonal and lattice support strategies. A double-layered capillary scaffold based on the Hilbert curve was used for comparative materials testing. Methods for printing rigid (OrmoComp), moderately stiff hydrogel (polyethylene glycol diacrylate, PEGDA 700), and soft elastomeric (photocurable polydimethylsiloxane, PDMS) materials were developed and evaluated. Cone support structures enabled high-fidelity printing of the softer materials. A compact heat-shrink tubing interface provided leak-free perfusion without bulky fittings. Physiologically relevant flow velocities and Dextran diffusion through the scaffold were successfully demonstrated. Cytocompatibility assays confirmed that all TPL-printed scaffold materials supported human neural stem cell viability. Among peripheral components, lids fabricated via fused deposition modeling designed to hold microfluidic needle adapters exhibited good biocompatibility, while those made using liquid crystal display-based photopolymerization showed significant cytotoxicity despite indirect exposure. Overall, this platform enables creation of multi-material microvascular systems facilitated by TPL technology for complex, 3D neurovascular modeling, blood–brain barrier studies, and integration into vascularized organ-on-chip applications. Full article

A composite-coated inclusion is embedded in a matrix, where the conductivity (permittivity) of the phases is assumed to be complex-valued. The purpose of this paper is to demonstrate that a non-zero flux can arise under specific conditions related to the conductivities of the components in the absence of external sources. These conditions are unattainable with conventional positive conductivities but can be satisfied when the conductivities are negative or complex—a scenario achievable in the context of metamaterials. The problem is formulated as a spectral boundary value problem for the Laplace equation, featuring a linear conjugation condition defined on a smooth curve L. This curve divides the plane ${\mathbb{R}}^2$ into two regions, $D^{+}$ and $D^{-}\ni \infty$. The spectral parameter appears in the boundary condition, drawing parallels with the Steklov eigenvalue problem. The case of a circular annulus is analyzed using the method of functional equations. The complete set of eigenvalues is derived by applying the classical theory of self-adjoint operators in Hilbert space. Full article

To address a key issue in functional time series analysis on testing the randomness of an observed series, we propose an IID test for functional time series by generalizing the Brock–Dechert–Scheinkman (BDS) test, which is commonly used for testing nonlinear independence. Similarly to the BDS test, the proposed functional BDS test can be used to evaluate the suitability of prediction models as a model specification test and to detect nonlinear structures as a nonlinearity test. We establish asymptotic results for the test statistic of the proposed test in a generic separate Hilbert space and show that it enjoys the same asymptotic properties as those for the univariate case. To address the practical issue of selecting hyperparameters, we provide the recommended range of the hyperparameters. Using empirical data on the VIX index, empirical studies are conducted that feature the applications of the proposed test to evaluate the adequacy of the fAR$\left(1\right)$ and fGARCH$(1,1)$ models in fitting the daily curves of cumulative intraday returns (CIDR) of the index. The results reveal that the proposed test remedies some shortcomings of the existing independence test. Specifically, the proposed test can detect nonlinear temporal structures, while the existing test can only detect linear structures. Full article

We study a separable Hilbert space of smooth curves taking values in the Segal–Bergmann space of analytic functions in the complex plane, and two of its subspaces that are the domains of unbounded non self-adjoint linear partial differential operators of the first and second order. We show how to build a Hilbert basis for this space. We study these first- and second-order partial derivation non-self-adjoint operators defined on this space, showing that these operators are defined on dense subspaces of the initial space of smooth curves; we determine their respective adjoints, compute their respective commutators, determine their eigenvalues and, under some normalisation conditions on the eigenvectors, we present examples of a discrete set of eigenvalues. Using these derivation operators, we study a Schrödinger-type equation, building particular solutions given by their representation as smooth curves on the Segal–Bergmann space, and we show the existence of general solutions using an Fourier–Hilbert base of the space of smooth curves. We point out the existence of self-adjoint operators in the space of smooth curves that are obtained by the composition of the partial derivation operators with multiplication operators, showing that these operators admit simple sequences of eigenvalues and eigenvectors. We present two applications of the Schrödinger-type equation studied. In the first one, we consider a wave associated with an object having the mass of an electron, showing that two waves, when considered as having only a free real space variable, are entangled, in the sense that the probability densities in the real variable are almost perfectly correlated. In the second application, after postulating that a usual package of information may have a mass of the order of magnitude of the neutron’s mass attributed to it—and so well into the domain of possible quantisation—we explore some consequences of the model. Full article

In this paper, we study $(i)$-curves with $i\in \{-1,0,1\}$ in the blown-up projective space ${\mathbb{P}}^r$ in general points. The notion of $(-1)$-curves was analyzed in the early days of mirror symmetry by Kontsevich, with the motivation of counting curves on a Calabi–Yau threefold. In dimension two, Nagata studied planar $(-1)$-curves in order to construct a counterexample to Hilbert’s 14th problem. We introduce the notion of classes of $(0)$- and $(1)$-curves in ${\mathbb{P}}^r$ with s points blown up, and we prove that their number is finite if and only if the space is a Mori Dream Space. We further introduce a bilinear form on a space of curves and a unique symmetric Weyl-invariant class, F (which we will refer to as the anticanonical curve class). For Mori Dream Spaces, we prove that $(-1)$-curves can be defined arithmetically by the linear and quadratic invariants determined by the bilinear form. Moreover, $(0)$- and $(1)$-Weyl lines give the extremal rays for the cone of movable curves in ${\mathbb{P}}^r$ with $r+3$ points blown up. As an application, we use the technique of movable curves to reprove that if $F^2\le 0$ then Y is not a Mori Dream Space, and we propose to apply this technique to other spaces. Full article

Fluid–structure interaction introduces critical failure modes due to varying stiffness and changing contact states in rotor-stator systems. This is further aggravated by stress fluctuations due to shaft impact with a fixed stator when the shaft rotates. In this paper, the investigation of imbalance and rotor-stator contact on a rotating shaft was carried out in viscous fluid. The shaft was modelled as a vertical elastic rotor system based on a vertically oriented elastic rotor operating in an incompressible medium. Implicit representation of the rotating system including the rotor-stator contact and the hydrodynamic resistance was formulated for the coupled system using the energy principle and the Navier–Stokes equations. Additionally, the monolithic approach included an implicit strategy of the rotor-stator fluid interaction interface conditions in the solution methodology. Advanced time-frequency methods, such as Hilbert transform, continuous wavelet transform, and estimated instantaneous frequency maps, were applied to extract the vibration features of the dynamic response of the faulted rotor. Time-varying stiffness due to friction is thought to be the main reason for the frequency fluctuation, as indicated by historical records of the vibration displacement, whirling orbit patterns of the centre shaft, and the amplitude–frequency curve. It has also been demonstrated that the augmented mass associated with the rotor and stator decreases the natural frequencies, while the amplitude signal remains relatively constant. This behaviour indicates a quasi-steady-state oscillatory condition, which minimises the energy fluctuations caused by viscous effects. Full article

At present, researchers in the field of pipeline inspection focus on pipe wall defects while neglecting pipeline defects in special situations such as welds. This poses a threat to the safe operation of projects. In this paper, a multi-node fusion and modal projection algorithm of steel pipes based on guided wave technology is proposed. Through an ANSYS numerical simulation, research is conducted to achieve the identification, localization, and quantification of axial cracks on the surface of straight pipelines and internal cracks in circumferential welds. The propagation characteristics and vibration law of ultrasonic guided waves are theoretically solved by the semi-analytical finite element method in the pipeline. The model section is discretized in one-dimensional polar coordinates to obtain the dispersion curve of the steel pipe. The T(0,1) mode, which is modulated by the Hanning window, is selected to simulate the axial crack of the pipeline and the L(0,2) mode to simulate the crack in the weld, and the correctness of the dispersion curve is verified. The results show that the T(0,1) and L(0,2) modes are successfully excited, and they are sensitive to axial and circumferential cracks. The time–frequency diagram of wavelet transform and the time domain diagram of the crack signal of Hilbert transform are used to identify the echo signal. The first wave packet peak point and group velocity are used to locate the crack. The pure signal of the crack is extracted from the simulation data, and the variation law between the reflection coefficient and the circumferential and radial dimensions of the defect is calculated to evaluate the size of the defect. This provides a new and feasible method for steel pipe defect detection. Full article

Spatiotemporal big data contain information in multiple dimensions such as space and time. Spatiotemporal data have the characteristics of large volume, intricate spatiotemporal relationship, and uneven spatiotemporal distribution. Index structure is one of the most important technologies used to improve system data analysis and workload. However, it is difficult to dynamically adjust with data density, resulting in increased maintenance costs and retrieval complexity. At the same time, maintaining the proximity of spatiotemporal data in spatial or temporal dimensions is crucial for efficient spatiotemporal analysis. To address these challenges, this paper proposes a learned index method, GLMI (Geohash and piecewise linear model-based index for spatiotemporal data). GLMI uses dynamic space partitioning based on the Hilbert curve to reduce the impact of data skew on index performance. In the time dimension, a piecewise linear model was constructed using the ShrinkingCone algorithm, and a buffer was designed to support the fast writing of spatiotemporal data. Compared with the current mainstream traditional high-dimensional indexes and the ZM index, GLMI has a smaller space consumption and shorter construction time compared to high-dimensional learned indexes on real traffic itinerary and trajectory record datasets. Meanwhile, GLMI also has an advantage in query efficiency. Full article

Echocardiography (ECG) is a noninvasive technology that is widely used for recording heartbeats and diagnosing cardiac arrhythmias. However, interpreting ECG signals is challenging and may require substantial time from medical specialists. The evolution of technology and artificial intelligence has led to advances in the study and development of automatic arrhythmia classification systems to aid in medical diagnoses. Within this context, this paper introduces a framework for classifying cardiac arrhythmias on the basis of a multimodal convolutional neural network (CNN) with an adaptive attention mechanism. ECG signal segments are transformed into images via the Hilbert space-filling curve (HSFC) and recurrence plot (RP) techniques. The framework is developed and evaluated using the MIT-BIH public database in alignment with AAMI guidelines (ANSI/AAMI EC57). The evaluations accounted for interpatient and intrapatient paradigms, considering variations in the input structure related to the number of ECG leads (lead MLII and V1 + MLII). The results indicate that the framework is competitive with those in state-of-the-art studies, particularly for two ECG leads. The accuracy, precision, sensitivity, specificity and F1 score are 98.48%, 94.15%, 80.23%, 96.34% and 81.91%, respectively, for the interpatient paradigm and 99.70%, 98.01%, 97.26%, 99.28% and 97.64%, respectively, for the intrapatient paradigm. Full article

This study investigates the impact toughness of 3D-printed PLA structures with Hilbert curve and honeycomb infill patterns at various raster angles. Samples were fabricated using Fused Deposition Modeling (FDM) and tested for impact energy absorption using the Charpy test. The results showed that specimens printed at a 90° raster angle exhibited the highest impact absorption. Hilbert curve patterns demonstrated 20.6% less energy absorption than plain samples with 40% infill and 11% higher energy absorption than plain samples with 100% infill, highlighting the significant role of material utilization in enhancing structural integrity. Full article

Semantic segmentation-based Complex Waterway Scene Understanding has shown great promise in the environmental perception of Unmanned Surface Vehicles. Existing methods struggle with estimating the edges of obstacles under conditions of blurred water surfaces. To address this, we propose the Lightweight Dual-branch Mamba Network (LDMNet), which includes a CNN-based Deep Dual-branch Network for extracting image features and a Mamba-based fusion module for aggregating and integrating global information. Specifically, we improve the Deep Dual-branch Network structure by incorporating multiple Atrous branches for local fusion; we design a Convolution-based Recombine Attention Module, which serves as the gate activation condition for Mamba-2 to enhance feature interaction and global information fusion from both spatial and channel dimensions. Moreover, to tackle the directional sensitivity of image serialization and the impact of the State Space Model’s forgetting strategy on non-causal data modeling, we introduce a Hilbert curve scanning mechanism to achieve multi-scale feature serialization. By stacking feature sequences, we alleviate the local bias of Mamba-2 towards image sequence data. LDMNet integrates the Deep Dual-branch Network, Recombine Attention, and Mamba-2 blocks, effectively capturing the long-range dependencies and multi-scale global context information of Complex Waterway Scene images. The experimental results on four benchmarks show that the proposed LDMNet significantly improves obstacle edge segmentation performance and outperforms existing methods across various performance metrics. Full article

The widespread use of Light Detection and Ranging (LiDAR) technology has led to a surge in three-dimensional point cloud data; although, it also poses challenges in terms of data storage and indexing. Efficient storage and management of LiDAR data are prerequisites for data processing and analysis for various LiDAR-based scientific applications. Traditional relational database management systems and centralized file storage struggle to meet the storage, scaling, and specific query requirements of massive point cloud data. However, NoSQL databases, known for their scalability, speed, and cost-effectiveness, provide a viable solution. In this study, a 3D point cloud indexing strategy for mobile LiDAR point cloud data that integrates Hilbert curves, R*-trees, and B⁺-trees was proposed to support MongoDB-based point cloud storage and querying from the following aspects: (1) partitioning the point cloud using an adaptive space partitioning strategy to improve the I/O efficiency and ensure data locality; (2) encoding partitions using Hilbert curves to construct global indices; (3) constructing local indexes (R*-trees) for each point cloud partition so that MongoDB can natively support indexing of point cloud data; and (4) a MongoDB-oriented storage structure design based on a hierarchical indexing structure. We evaluated the efficacy of chunked point cloud data storage with MongoDB for spatial querying and found that the proposed storage strategy provides higher data encoding, index construction and retrieval speeds, and more scalable storage structures to support efficient point cloud spatial query processing compared to many mainstream point cloud indexing strategies and database systems. Full article

In this study, we investigate the relationship between parameters and the dynamic behavior of traffic flow in road traffic systems, and we propose a segmented cost function to describe the effects of this flow on the dynamic gravity model at different saturation levels. We use single-parameter bifurcation analysis, maximum Lyapunov exponent calculation, and three-parameter bifurcation analysis to reveal the effects of parameter variations on the nonlinear dynamical behaviors of the modified gravity model, and we investigate the evolution laws of the traffic system in depth. In order to solve the problems of low efficiency and poor visualization ability in traditional dynamics analysis techniques, this paper proposes the Hilbert curve dimensionality reduction technique, which can completely retain the original data features. The three-dimensional pseudo-Hilbert curve is used to traverse the three-parameter bifurcation data, realizing the transformation of data from three- to one-dimensional. Then, the two-dimensional pseudo-Hilbert curve is used to traverse the reduced one-dimensional data, and the two-dimensional visualization of the three-parameter bifurcation diagram is successfully realized. The dimensionality reduction technique provides a new way of thinking for parameter analysis in the engineering field. By analyzing the two-dimensional bifurcation plan obtained after this reduction, it is found that the modified gravity model is more stable compared with the original model, and this conclusion is also verified by the wavelet transform results. Finally, a new robustness evaluation index is defined based on the dynamics of the model, and the simulation results reveal the intrinsic correlation between the saturation parameter and road congestion, which provides an important basis for promoting sustainable transportation in the road network. Full article