Multiscale Geometries Research Articles

PathNet: Path-Selective Point Cloud Denoising.

Current point cloud denoising (PCD) models optimize single networks, trying to make their parameters adaptive to each point in a large pool of point clouds. Such a denoising network paradigm neglects that different points are often corrupted by different levels of noise and they may convey different geometric structures. Thus, the intricacy of both noise and geometry poses side effects including remnant noise, wrongly-smoothed edges, and distorted shape after denoising. We propose PathNet, a path-selective PCD paradigm based on reinforcement learning (RL). Unlike existing efforts, PathNet enables dynamic selection of the most appropriate denoising path for each point, best moving it onto its underlying surface. We have two more contributions besides the proposed framework of path-selective PCD for the first time. First, to leverage geometry expertise and benefit from training data, we propose a noise- and geometry-aware reward function to train the routing agent in RL. Second, the routing agent and the denoising network are trained jointly to avoid under- and over-smoothing. Extensive experiments show promising improvements of PathNet over its competitors, in terms of the effectiveness for removing different levels of noise and preserving multi-scale surface geometries. Furthermore, PathNet generalizes itself more smoothly to real scans than cutting-edge models.

Scalar transport after a high-resolution solitary fractal tree based on large-eddy simulation: Implication to urban green infrastructure

Scalar transport is one of the most concerned issues in the urban environment (e.g., pollutants, pollens, and aeolian transport). Vegetations are commonly regarded as scalar-moderation structures in urban areas by influencing airflows, avoiding aeolian erosion and pollution. The morphological multi-scale branch structures of the single tree were usually neglected in previous studies, which, however, can lead to highly inhomogeneous wake. The turbulence generation through the multi-scale branches is not yet clear. The corresponding spatial details of scalar distribution and its mechanism need to be further examined. In this study, the wake after a single fractal tree is investigated using the large-eddy simulation (LES). The spatial characteristics of the wakes are illustrated, indicating susceptible zones in the canopy, first-generation levels of branches, and recirculation regions. Higher-order moments signify the rare, extreme events with strong upward acceleration, removing air masses likely to occur at the canopy shear layer within 3h downstream where h is the characteristic tree height. The quadrant analysis elucidates the scalar transport potential. The scalar distribution and its transport mechanism are visualized, showing dilution and accumulation by the streamwise and vertical velocities. Involving the multi-scale geometries of the tree can provide guidance for urban green infrastructure (UGI) planning, advancing environmental and sustainability development.

Biomimetic Chiral Nanomaterials with Selective Catalysis Activity.

Chiral nanomaterials with unique chiral configurations and biocompatible ligands have been booming over the past decade for their interesting chiroptical effect, unique catalytical activity, and related bioapplications. The catalytic activity and selectivity of chiral nanomaterials have emerged as important topics, that can be potentially controlled and optimized by the rational biochemical design of nanomaterials. In this review, chiral nanomaterials synthesis, composition, and catalytic performances of different biohybrid chiral nanomaterials are discussed. The construction of chiral nanomaterials with multiscale chiral geometries along with the underlying principles for enhancing chiroptical responses are highlighted. Various biochemical approaches to regulate the selectivity and catalytic activity of chiral nanomaterials for biocatalysis are also summarized. Furthermore, attention is paid to specific chiral ligands, materials compositions, structure characteristics, and so on for introducing selective catalytic activities of representative chiral nanomaterials, with emphasis on substrates including small molecules, biological macromolecule, and in-site catalysis in living systems. Promising progress has also been emphasized in chiral nanomaterials featuring structural versatility and improved chiral responses that gave rise to unprecedented chances to utilize light for biocatalytic applications. In summary, the challenges, future trends, and prospects associated with chiral nanomaterials for catalysis are comprehensively proposed.

Biomimetic Coupling Structure Increases the Noise Friction and Sound Absorption Effect.

Environmental noise pollution is a growing challenge worldwide, necessitating effective sound absorption strategies to improve acoustic environments. Materials that draw inspiration from nature's structural design principles can provide enhanced functionalities. Wood exhibits an intricate multi-scale porous architecture that can dissipate acoustic energy. This study investigates a biomimetic sound-absorbing structure composed of hierarchical pores inspired by the vascular networks within wood cells. The perforated resonators induce complementary frequency responses and porous propagation effects for broadband attenuation. Samples were fabricated using 3D printing for systematic testing. The pore size, porosity, number of layers, and order of the layers were controlled as experimental variables. Acoustic impedance tube characterization demonstrated that optimizing these architectural parameters enables absorption coefficients approaching unity across a broad frequency range. The tuned multi-layer porous architectures outperformed single pore baselines, achieving up to a 25-35% increase in the average absorption. The bio-inspired coupled pore designs also exhibited a 95% broader working bandwidth. These enhancements result from the increased viscous losses and tailored impedance matching generated by the hierarchical porosity. This work elucidates structure-property guidelines for designing biomimetic acoustic metamaterials derived from the porous morphology of wood. The results show significant promise for leveraging such multi-scale cellular geometries in future materials and devices for noise control and dissipative engineering applications across diverse sectors.

Formation of Multiscale Pattern Structures by Combined Patterning of Nanotransfer Printing and Laser Micromachining.

Various lithography techniques have been widely used for the fabrication of next-generation device applications. Micro/nanoscale pattern structures formed by lithographic methods significantly improve the performance capabilities of the devices. Here, we introduce a novel method that combines the patterning of nanotransfer printing (nTP) and laser micromachining to fabricate multiscale pattern structures on a wide range of scales. Prior to the formation of various nano-in-micro-in-millimeter (NMM) patterns, the nTP process is employed to obtain periodic nanoscale patterns on the target substrates. Then, an optimum laser-based patterning that effectively engraves various nanopatterned surfaces, in this case, spin-cast soft polymer film, rigid polymer film, a stainless still plate, and a Si substrate, is established. We demonstrate the formation of well-defined square and dot-shaped multiscale NMM-patterned structures by the combined patterning method of nTP and laser processes. Furthermore, we present the generation of unusual text-shaped NMM pattern structures on colorless polyimide (CPI) film, showing optically excellent rainbow luminescence based on the configuration of multiscale patterns from nanoscale to milliscale. We expect that this combined patterning strategy will be extendable to other nano-to-micro fabrication processes for application to various nano/microdevices with complex multiscale pattern geometries.

Analytic Preconditioners for Decoupled Potential Integral Equations and Wideband Analysis of Scattering From PEC Objects

Many integral equations used to analyze scattering, such as the standard combined field integral equation (CFIE), are not well-conditioned for a wide range of frequencies and multi-scale geometries. There has been significant effort to alleviate this problem. A more recent one is using a set of decoupled potential integral equations (DPIE). These equations have been shown to be robust at low frequencies and immune to topology breakdown. But they mimic the ill-conditioning behavior of CFIE at high frequencies. This paper addresses this deficiency through new Calderón-type identities derived from the Vector Potential Integral Equation (VPIE). We construct novel analytic preconditioners for the vector potential integral equation (VPIE) and scalar potential integral equation (SPIE) constrained to perfect electric conductors (PEC). These new formulations are wide-band well-conditioned and converge rapidly for multi-scale geometries. This is demonstrated though a number of examples that use analytic and piecewise basis sets.

Discontinuous Galerkin Integral Equation Approach for Electromagnetic Modeling of Realistic and Complex Radiating Systems

An electric field integral equation (EFIE) discontinuous Galerkin (DG) formulation for the electromagnetic radiation analysis of realistic antennas is presented. Radiation problems are known to be computationally challenging, involving complex multiscale geometries often made up of a collection of closed and open surfaces. This complexity points to the convenience of separately building and meshing parts with different characteristics, either physical or geometric. This piecewise modelling approach is also desirable in the context of design optimization processes. The proposed formulation fits perfectly into this context by enabling the assembly of independently-meshed surfaces, yet without the need to enforce mesh conformity along the junction contours. The continuity of the normal components of the equivalent current at junctions is enforced using the interior penalty (IP) concept, which is extended to multiple conducting surfaces meeting at a junction.

Space–Time Adaptive Modeling and Shape Optimization of Microwave Structures With Applications to Metasurface Design

This article presents a time-domain modeling and shape optimization framework for microwave structures, including metasurfaces, based on a nodal discontinuous Galerkin time-domain (DGTD) method. In particular, we employ an unstructured mesh and the inherent mesh refinement ability of DGTD to model multiscale geometries via adaptive mesh refinement. More importantly, we integrate a multitier local time-stepping technique into the time integration of DGTD, which significantly alleviates the cost introduced by mesh refinement. We further present a flexible parameterization approach by defining the contours of metasurface unit cells by B-spline curves, which allows us to explore a wide range of smooth shapes by only a few design variables. Besides, we adopt a polynomial chaos-Kriging (PCK) surrogate method to approximate the full-wave DGTD model, reducing the computational cost for optimization problems that require time-consuming simulations by three orders of magnitude. The B-spline parameterization and the PCK surrogate model are combined with a pattern search-based Pareto front algorithm to optimize metasurfaces for multiple design objectives. The proposed optimization framework is also applicable to other microwave structures. We demonstrate the effectiveness of our approach through the optimization of an omega-bianisotropic Huygens’ metasurface unit cell and an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$E$ </tex-math></inline-formula> -plane microwave T-junction.

Multiscale Progressive Failure Analysis of 3D Woven Composites.

Application of three-dimensional (3D) woven composites is growing as an alternative to the use of ply-based composite materials. However, the design, analysis, modeling, and optimization of these materials is more challenging due to their complex and inherently multiscale geometries. Herein, a multiscale modeling procedure, based on efficient, semi-analytical micromechanical theories rather than the traditional finite element approach, is presented and applied to a 3D woven carbon–epoxy composite. A crack-band progressive damage model was employed for the matrix constituent to capture the globally observed nonlinear response. Realistic microstructural dimensions and tow-fiber volume fractions were determined from detailed X-ray computed tomography (CT) and scanning electron microscopy data. Pre-existing binder-tow disbonds and weft-tow waviness, observed in X-ray CT scans of the composite, were also included in the model. The results were compared with experimental data for the in-plane tensile and shear behavior of the composite. The tensile predictions exhibited good correlations with the test data. While the model was able to capture the less brittle nature of the in-plane shear response, quantitative measures were underpredicted to some degree.

A coupled 3D-1D multiscale Keller-Segel model of chemotaxis and its application to cancer invasion

&lt;p style='text-indent:20px;'&gt;Many problems arising in biology display a complex system dynamics at different scales of space and time. For this reason, multiscale mathematical models have attracted a great attention as they enable to take into account phenomena evolving at several characteristic lengths. However, they require advanced model reduction techniques to reduce the computational cost of solving all the scales.&lt;/p&gt;&lt;p style='text-indent:20px;'&gt;In this work, we present a novel version of the Keller-Segel model of chemotaxis on embedded multiscale geometries, &lt;i&gt;i.e.&lt;/i&gt;, one-dimensional networks embedded in three-dimensional bulk domains. Applying a model reduction technique based on spatial averaging for geometrical order reduction, we reduce a fully three-dimensional Keller-Segel system to a coupled 3D-1D multiscale model. In the reduced model, the dynamics of the cellular population evolves on a one-dimensional network and its migration is influenced by a three-dimensional chemical signal evolving in the bulk domain. We propose the multiscale version of the Keller-Segel model as a realistic approach to describe the invasion of malignant cancer cells along the collagen fibers that constitute the extracellular matrix. Performing several numerical simulations, we investigate how the invasive abilities of the cells are affected by the topology of the network (&lt;i&gt;i.e.&lt;/i&gt;, matrix fibers orientation and alignment) as well as by three-dimensional spatial effects. We discuss these results in light of biological evidences.&lt;/p&gt;

Broadband Analysis of Multiscale Electromagnetic Problems: Novel Incomplete-Leaf MLFMA for Potential Integral Equations

Recently introduced incomplete tree structures for the magnetic-field integral equation are modified and used in conjunction with the mixed-form multilevel fast multipole algorithm (MLFMA) to employ a novel broadband incomplete-leaf MLFMA (IL-MLFMA) to the solution of potential integral equations (PIEs) for scattering/radiation from multiscale open and closed surfaces. This population-based algorithm deploys a nonuniform clustering that enables to use deep levels safely and, when necessary, without compromising the accuracy resulting in an improved efficiency and a significant reduction for the memory requirements (order of magnitudes), while the error is controllable. The superiority of the algorithm is demonstrated in several canonical and real-life multiscale geometries.

Recurrence Analysis Applied to Ultrasonic Absorptive Coating

Metasurfaces are, at the actual state-of-the-art, a constant topic for scientific community as they find widespread applications in several fields, including acoustics and aeroacoustics. In this paper, the potential of recurrence analysis was evaluated by applying it to some metasurfaces. These devices effectiveness has been previously demonstrated with a reflection coefficients analysis in the Fourier and Wavelet domains. A novel strategy based on the Recurrence Analysis, which is a no man’s land applied on the metasurfaces, was performed. The evaluation of the recurrence plot and phase space attractors led to interesting results. The results show an introduction of non linearities after the forcing wave interacts with the metasurfaces. In light of that, there is the evidence that the chaotic analysis principles may be a powerful tool to characterize the performance of metasurfaces in particular through the calculation of the chaotic indexes. This method could be integrated with previous ones for the evaluation of more complex and multiscale geometries that nowadays show huge potential in too many fields of application.

Color-complexity enabled exhaustive color-dots identification and spatial patterns testing in images.

Our computational developments and analyses on experimental images are designed to evaluate the effectiveness of chemical spraying via unmanned aerial vehicle (UAV). Our evaluations are in accord with the two perspectives of color-complexity: color variety within a color system and color distributional geometry on an image. First, by working within RGB and HSV color systems, we develop a new color-identification algorithm relying on highly associative relations among three color-coordinates to lead us to exhaustively identify all targeted color-pixels. A color-dot is then identified as one isolated network of connected color-pixel. All identified color-dots vary in shapes and sizes within each image. Such a pixel-based computing algorithm is shown robustly and efficiently accommodating heterogeneity due to shaded regions and lighting conditions. Secondly, all color-dots with varying sizes are categorized into three categories. Since the number of small color-dot is rather large, we spatially divide the entire image into a 2D lattice of rectangular. As such, each rectangle becomes a collective of color-dots of various sizes and is classified with respect to its color-dots intensity. We progressively construct a series of minimum spanning trees (MST) as multiscale 2D distributional spatial geometries in a decreasing-intensity fashion. We extract the distributions of distances among connected rectangle-nodes in the observed MST and simulated MSTs generated under the spatial uniformness assumption. We devise a new algorithm for testing 2D spatial uniformness based on a Hierarchical clustering tree upon all involving MSTs. This new tree-based p-value evaluation has the capacity to become exact.

Additively Manufactured Absorbable Porous Metal Implants – Processing, Alloying and Corrosion Behavior

Treating large bone defects is still a clinical challenge without perfect solution, mainly due to the unavailability of suitable bone implants. Additively manufactured (AM) absorbable porous metals provide unparalleled opportunities to realize the challenging requirements for bone-mimetic implants. Firstly, multi-scale geometries of such implants can be customized to mimic the micro-architecture and mechanical properties of human bone. The interconnected porous structure additionally increases the surface area to facilitate adhesion and proliferation of bone cells. Finally, their absorption properties are tunable to maintain the structural integrity of the implant throughout the bone healing process, ensuring sufficient loadbearing when needed and full disintegration after their job is done. Such a combination of properties paves the way for complete bone regeneration and remodeling. It is important to thoroughly characterize the biodegradation behavior, mechanical properties, and bone regeneration ability when developing ideal porous absorbable metal implants. We review the state-of-the-art of absorbable porous metals manufactured by selective laser melting (SLM), with a focus on geometrical design, material type, processing, and post-treatment. The impact of the latter aspects on absorption behavior, resulting mechanical properties, and cytocompatibility will also be briefly discussed. In comparison to their solid inert counterparts, AM absorbable porous metals (APMs) have shown many unique properties and hold tremendous potential to further optimize their application-specific performance due to their flexible geometrical design. We further highlight challenges in adopting AM APMs for future Orthopedic solutions.

Chiral Nanoceramics.

The study of different chiral inorganic nanomaterials has been experiencing rapid growth during the past decade, with its primary focus on metals and semiconductors. Ceramic materials can substantially expand the range of mechanical, optical, chemical, electrical, magnetic, and biological properties of chiral nanostructures, further stimulating theoretical, synthetic, and applied research in this area. An ever-expanding toolbox of nanoscale engineering and self-organization provides a chirality-based methodology for engineering of hierarchically organized ceramic materials. However, fundamental discoveries and technological translations of chiral nanoceramics have received substantially smaller attention than counterparts from metals and semiconductors. Findings in this research area are scattered over a variety of sources and subfields. Here, the diversity of chemistries, geometries, and properties found in chiral ceramic nanostructures are summarized. They represent a compelling materials platform for realization of chirality transfer through multiple scales that can result in new forms of ceramic materials. Multiscale chiral geometries and the structural versatility of nanoceramics are complemented by their high chiroptical activity, enantioselectivity, catalytic activity, and biocompatibility. Future development in this field is likely to encompass chiral synthesis, biomedical applications, and optical/electronic devices. The implementation of computationally designed chiral nanoceramics for biomimetic catalysts and quantum information devices may also be expected.

GSIS: An efficient and accurate numerical method to obtain the apparent gas permeability of porous media

The apparent gas permeability (AGP) of a porous medium is an important parameter to predict production of unconventional gas. The Klinkenberg correlation, which states that the ratio of the AGP to the intrinsic permeability is approximately a linear function of reciprocal mean gas pressure, is one of the most popular estimations to quantify AGP. However, due to the difficulty in defining the characteristic flow length in complex porous media where the rarefied gas flow is multiscale, the slope in the Klinkenberg correlation varies significantly for different geometries such that a universal expression seems impossible. In this paper, by solving the gas kinetic equation using the general synthetic iterative scheme (GSIS), we compute the AGP in porous media that are represented by Sierpinski fractals and pore body/throat systems. With the abilities of fast convergence to steady-state solution and asymptotic preserving of Navier-Stokes limit, it is shown that GSIS is a promising tool to simulate low-speed rarefied gas flow through complex multiscale geometries. A new definition of the characteristic flow length is proposed as a function of porosity, tortuosity and intrinsic permeability of porous media, which enables to find a unique slope in the Klinkenberg correlation for all the considered geometries. This research also shows that the lattice Boltzmann method using simple wall scaling for the effective shear viscosity is not able to predict the AGP of porous media.

Ultrafast Laser Processing of Nanostructured Patterns for the Control of Cell Adhesion and Migration on Titanium Alloy.

Femtosecond laser texturing is a promising surface functionalization technology to improve the integration and durability of dental and orthopedic implants. Four different surface topographies were obtained on titanium-6aluminum-4vanadium plates by varying laser processing parameters and strategies: surfaces presenting nanostructures such as laser-induced periodic surface structures (LIPSS) and ‘spikes’, associated or not with more complex multiscale geometries combining micro-pits, nanostructures and stretches of polished areas. After sterilization by heat treatment, LIPSS and spikes were characterized to be highly hydrophobic, whereas the original polished surfaces remained hydrophilic. Human mesenchymal stem cells (hMSCs) grown on simple nanostructured surfaces were found to spread less with an increased motility (velocity, acceleration, tortuosity), while on the complex surfaces, hMSCs decreased their migration when approaching the micro-pits and preferentially positioned their nucleus inside them. Moreover, focal adhesions of hMSCs were notably located on polished zones rather than on neighboring nanostructured areas where the protein adsorption was lower. All these observations indicated that hMSCs were spatially controlled and mechanically strained by the laser-induced topographies. The nanoscale structures influence surface wettability and protein adsorption and thus influence focal adhesions formation and finally induce shape-based mechanical constraints on cells, known to promote osteogenic differentiation.

Validity of triple-effect model for fluid flow in mismatched, self-affine fractures

Investigation of seepage law of fluid flow through a self-affine, rough fracture has attracted broad attention because of its fundamental importance for complex hydrodynamic problems. Although it is natural to assume that permeability value depends on aperture size, it is hard to determine which is the appropriate relationship between them because of the large number of parameters related to the multi-scale geometries and mismatched behaviors in internal surfaces. Moreover, those parameters are hard to obtain by field observation or laboratory tests. For these, we focused on synthesising mismatched composite topography of natural fractures and numerical simulation of fluid flow through them at pore scale. Firstly, the control mechanism of self-affine property was clarified, and a novel Weierstrass-Mandelbrot (W-M) function was proposed to model self-affine profile as per fractal topography theory. Afterwards, a weighting algorithm was developed to construct the composite topography of fractures accounting for the mismatched behavior. Finally, the effects of mismatched behavior, hydraulic and surface tortuosities on fracture flow were systematically analyzed by numerical simulations using Lattice Boltzmann methods (LBM) at pore scale. Our investigation indicates that the aperture distribution is dominated by the mismatched range between internal surfaces, however the hydraulic and surface tortuosity effects are approximately scaled by 2(H−1) (H is the Hurst exponent) with the mean aperture despite of its distribution. Moreover, it was found that the local surface roughness factor, accounting for effects from surface geometries with size smaller than the value of mean aperture, is stationary at long range and inversely proportional to fracture permeability. Based on above discussions, the validity of triple-effect model for permeability prediction of mismatched self-affine fractures was established.

Effective floating volume: a highly parallelizable mesh-free approach for solving transient multiphysics problems in multi-scale geometries with non-linear material properties

A novel numerical method is proposed for the solution of transient multi-physics problems involving heat conduction, electrical current sharing and Joule heating. The innovation consists of a mesh-free Monte Carlo approach that eliminates or drastically reduces the particle scattering requirements typical of conventional Monte-Carlo methods. The proposed algorithm encapsulates a volume around each point that affects the solution at a given point in the domain; the volume includes other points that represent small perturbations along the path of energy transfer. The proposed method is highly parallelizable and amenable for GPU computing, and its computational performance was substantially increased by the elimination of scattered interpolation. The accuracy and simulation time of the proposed method are compared against a finite element solution and also against experimental results from existing literature. The proposed method provides accuracy comparable to that of finite element methods, achieving an order of magnitude reduction in simulation time.

Hydrocarbon-Phase Behaviors in Shale Nanopore/Fracture Model: Multiscale, Multicomponent, and Multiphase

Summary Hydrocarbon recovery from shale subformations has greatly contributed to the global energy supply and has been constantly reshaping the energy sector. Oil production from shale is a complex process in which multicomponent–fluid mixtures experience multiphase transitions in multiscale volumes (i.e., nanoscale pores are connected to fractures/macropores). Understanding such complicated phenomena plays a critical role in the estimation of ultimate oil recovery, well productivity, and reserves estimation, and ultimately in policy making. In this work, we use density–functional theory (DFT) to explicitly consider fluid/surface interactions, inhomogeneous–density distributions in nanopores, volume partitioning in nanopores, and connected macropores/natural fractures to study the complex multiphase transitions of multicomponent fluids in multiscale volumes. We found that vapor–like and liquid–like phases can coexist in nanopores when pressure is between the bubblepoint and dewpoint pressures of nanoconfined fluids, both of which are much lower than those of the originally injected hydrocarbon mixtures. As the volume ratio of the bulk at the initial condition to pores decreases, both the bubblepoint and the dewpoint in nanopores increase and the pore two–phase region expands. Within the pore two–phase region, both C1 and C3 are released from the nanopores to the bulk phase as pressure declines. Meanwhile, both liquid and vapor phases become denser as pressure drops. By further decreasing pressure below the dewpoint of confined fluids, C3 in the nanopore can be recovered. Throughout the process, the bulk–phase composition varies, which is in line with the field observation. Collectively, this work captures the coupled complexity of multicomponent and multiphase fluids in multiscale geometries that is inherent to shale reservoirs and provides a theoretical foundation for reservoir simulation, which is significant for the accurate prediction of well productivity and ultimate oil recovery in shale reservoirs.