Scale Geometry Research Articles

Joint Observation of a Series of Magnetic Holes by Tianwen-1 and MAVEN on Mars

Magnetic holes (MHs) are transient magnetic structures responsible for energy conversion in space plasma. Using single-spacecraft measurements from Mars Atmosphere and Volatile EvolutioN (MAVEN), the existence of MHs on Mars has been confirmed. However, due to the limitations of single-spacecraft observations, significant uncertainty also arises on the identification of the spatial scale and 3D geometry of MHs. In this study, we report a series of MHs successively detected by Tianwen-1 near the high-latitude magnetopause and by the MAVEN spacecraft near the subsolar magnetopause. The large separation between Tianwen-1 and MAVEN (∼4 R M) suggests these MHs are macroscale structures extending along the axial direction. Additionally, we observe whistler waves generated by electron perpendicular anisotropy in one of the macroscale MHs. This study is the first joint observation of Martian MHs, shedding light on the research of transient magnetic structures on Mars.

Conceptual Model of Graph-based Individual Tree and Its Utilization in Digital Twin and Metaverse of Urban Forest

Abstract. 3D city models are an important cornerstone in the development of digital twin cities, allowing for various analyses and simulations. CityGML, as an open standard for 3D city models, emphasizes five main aspects: scale or level of detail (LoD), semantics, geometry, topology, and appearance. One of the important elements in CityGML 3D city models is representation of vegetation. Vegetation in CityGML, especially individual trees, is still limited in terms of detail and resolution, reducing its effectiveness for specific applications. This paper proposes a graph-based conceptual model for individual trees that conforms to the CityGML v2.0 specification. The model refers to the morphological structure of a tree consisting of roots, trunk, and crown (including branches, twigs, and leaves), and considers the five main aspects of CityGML. By enhancing semantic information and geometric details, the model aims to provide an information-rich and realistic representation of individual trees in a 3D city environment. The 3D tree model created based on this conceptual model may be applicable in the development of digital twin urban forests and virtual forest simulations that utilize immersive technologies such as the metaverse. This research opens up new opportunities in the development of solitary vegetation objects through CityGML ADE by including more detailed semantic and topological information.

Resonance Testing Data Evaluation Approaches for Scaling Onset Detection in Pipelines

Most industries dealing with pipelines face problems resulting from the buildup of deposits therein, such as reduced efficiency, downtime and increased maintenance costs. Although solutions to this issue have been sought for decades, no widely employed technique for monitoring growth of inorganic deposits (or ‘scaling’) in pipelines exists. In this research, a means of detecting the onset of scaling growth, by processing resonance testing data, was sought. For the resonance testing measurements the pipeline segment of interest is equipped with acceleration sensors which record signals generated by impacting the pipeline with a steel tip. The signals are Fourier transformed and analysed in the frequency domain, where a clear shift in frequency peak positions can be observed as the scaling thickness changes. How best to extract quantitative information from the generated frequency data is an open question. In this research, two data analysis approaches for scaling thickness prediction are compared: a supervised (binary classification) machine learning approach as well as a comparison-based change detection approach using cross-correlation. The supervised machine learning approach yields generalizable results for different acceleration sensors and impactor diameters whilst the change detection approach is sensitive from a scaling thickness of 0.5 mm. Whilst this research is specific to the pipe–scaling geometry—and type used in the experiments conducted, resonance testing can be applied to any pipe–scaling combination. The robustness of the data processing approaches presented in this work, when applied to other pipe–scaling materials and geometries, is the next point of research.

Flow-through microfluidic relative permittivity sensor using highly-doped silicon sidewall electrodes

Abstract This paper reports a flow-through sensor for the real-time measurement of the relative permittivity of a flowing fluid. The proposed sensor contains multiple parallel microchannels. Each channel acts as a parallel plate capacitor in which the electrodes are isolated from the fluid. This approach results in a low pressure drop and high sensitivity while the internal volume is only 50 nl. The fabrication technology allows for controllable scaling of the channel geometry. Equally deep microchannels with widths varying between 5 µm and 50 μ m are fabricated. The fabrication technology is compatible with other flow-through sensors, enabling further on-chip integration. The sensor has been characterised using 10 different fluids with relative permittivity values ranging from 1 to 80—including water and water-containing mixtures—at a measurement frequency of 300 kHz. The results show an accuracy within 3% of full scale and the repeated measurements with nitrogen and water show standard deviations of 1.20 and 1.03, respectively.

Expression of concern“On the same origin of quantum physics and general relativity from Riemannian geometry and Planck scale formalism” Astroparticle Physics, Volume 164, 103036.

Expression of concern“On the same origin of quantum physics and general relativity from Riemannian geometry and Planck scale formalism” Astroparticle Physics, Volume 164, 103036.

SHIFT: a spatial-heterogeneity improvement in DEM-based mapping of global geomorphic floodplains

Abstract. Floodplains are a vital part of the global riverine system. Among all the global floodplain delineation strategies empowered by remote sensing, digital elevation model (DEM)-based delineation is considered to be computationally efficient with relatively low uncertainties, but the parsimonious model struggles with incorporating the basin-level spatial heterogeneity of the hydrological and geomorphic influences into the map. In this study, we propose a globally applicable thresholding scheme for DEM-based floodplain delineation to improve the representation of spatial heterogeneity. Specifically, we develop a stepwise approach to estimate the floodplain hydraulic geometry (FHG) scaling parameters for river basins worldwide at the scale of the level-3 HydroBASINS to best respect the scaling law while approximating the spatial extent of two publicly available global flood maps derived from hydrodynamic modeling. The estimated FHG exponent exhibits a significant positive relationship with the basins' hydroclimatic conditions, particularly in 33 of the world's major river basins, indicating the ability of the approach to capture fingerprints from heterogeneous hydrological and geomorphic influences. Based on the spatially varying FHG parameters, a ∼ 90 m resolution global floodplain map named the Spatial Heterogeneity Improved Floodplain by Terrain analysis (SHIFT) is delineated, which takes the hydrologically corrected MERIT Hydro dataset as the DEM inputs and the height above nearest drainage (HAND) as the terrain attribute. Our results demonstrate that SHIFT validates better with reference maps than both hydrodynamic-modeling- and DEM-based approaches with universal parameters. The improved delineation mainly includes better differentiation between main streams and tributaries in major basins and a more comprehensive representation of stream networks in aggregated river basins. SHIFT estimates the global floodplain area to be 9.91×106 km2, representing 6.6 % of the world's total land area. SHIFT data layers are available at two spatial resolutions (90 m and 1 km), along with the updated parameters, at https://doi.org/10.5281/zenodo.11835133 (Zheng et al., 2024). We anticipate that SHIFT will be used to support applications requiring boundary delineations of the global geomorphic floodplains.

On the same origin of quantum physics and general relativity from Riemannian geometry and Planck scale formalism

It has been a long time to reconcile quantum physics and general relativity. To date, no globally accepted theory has been proposed to explain all physical observations. In this work, we reformulated the Riemannian geometry in terms of curvature and energy tensors using the Planck scale formalism. The proposed equation can be transformed into Dirac equations in electrodynamic and chromodynamic fields with a reduction in the background curvature. We redefined the mass and charge of leptons in terms of the interactions between the energy of the field and the curvature of the spacetime. The obtained equation is covariant in space–time and invariant with respect to any Planck scale. Therefore, the constants of the universe can be reduced to only two quantities: Planck length and Planck time. We proved that the Einstein field equation from general relativity is actually a relativistic quantum mechanical equation. We further modeled the universe using the equation with Einstein's lambda formalism and found that the universe dynamics could be considered as harmonic oscillators entangled with lambda curvature. This equation can be used to describe the energy transfer between two entangled spacetimes between the same universe and between any two universes (ER=EPR). The singularity of black holes can be avoided at the Planck scale, because space and time are no longer entangled. This equation predicts that information of light from the entangled universe can be transferred to our universe. The gravitational wave background was predicted, and its spectrum was close to that of the observation.

(Invited) Metal Corrosion Mitigation in Fine Geometries during Chemical Mechanical Planarization

In the Si semiconductor industry, aggressive device geometry scaling has given rise to new processing challenges to each new technology nodes over the past 6 decades. When the feature size shrinks to nanometer regime, new phenomenon emerges whereby significant loss in metal vias and lines can be observed after CMP.Findings from our previous studies suggest just a few nanometers of metal loss imposes serious yield loss in sub-5nm technology nodes MOL and BEOL metallization. Post CMP clean process can be responsible for ~ 50% of the metal loss after CMP. The phenomenon was observed with W, Co, and Cu alike. It affects conductors as well as liner/barrier metals, and exhibits strong dependence on pattern density, feature size, and even underlying layer. [1, 2]. Properly formulated slurries and post CMP clean chemicals can modulate the amount of metal loss and partially alleviate the issue.In this study, we continue to assess how post CMP clean chemicals and modified de-ionized water can influence the amount of metal loss for Cu interconnects. As a starter, blanket wafers resembling several different Cu/liner/low-k stacks were evaluated. The were subjected to polish with the same alkaline slurry followed by various alkaline post clean chemicals (Clean 1, pH ~ 10.2; Clean 2, pH 9.8). It was observed on the attached figure that brush clean only process with DIW alone can induce small amount of Cu loss. For wafers with polish and post clean, on a comparison basis, Clean1 resulted in slightly more Cu loss than Clean2. However, when dilute NH4OH solution (pH ~ 9.6) was introduced to replace DIW during brush clean with Clean1, the amount of Cu loss is reduced, on par with that of Clean2. The observation suggests NH4OH-treated DIW can help alleviate part of Cu loss during post CMP clean process. Patterned wafers with various combination of liner stacks will be subjected to clean process with various combinations of chemistries and/or NH4OH-treated DIW. The amount of Cu or liner loss will be characterized.

On the scaling of river network biogeochemical function

AbstractRiver networks play a fundamental biogeochemical role in the Earth system by transporting and processing materials from terrestrial to ocean ecosystems. The cumulative biogeochemical function of a watershed of area can broadly be referred to as the total processing rate of material performed by its river network. An important recent research, conducted through network simulations, has revealed that the biogeochemical function of rivers can scale superlinearly with the area under certain scenarios. This finding has significant implications for the role of river networks in regional and global biogeochemical cycles. Here, we demonstrate how such scaling can be derived analytically by combining the power law distribution of drainage area, the universal fractal signature of river networks and the scaling of channel hydraulic geometry, utilising the theory of finite‐size scaling. The results enable the discrimination between linear and superlinear behaviours, as well as the calculation of the exact exponent based on parameters that define how the biogeochemical function and the river width change with river drainage area. Furthermore, we investigate the difference between the scaling of the biogeochemical function with the area of the watershed and with the area of a region drained by multiple river networks, emphasising the implications for upscaling efforts.

Efficient data acquisition and reconstruction for air-coupled ultrasonic robotic NDE

Non-destructive evaluation of complex parts using surface scanning techniques, such as ultrasonic testing and eddy current testing, requires complex manipulation of such sensors to ensure quantitative results. A robotic arm may function as a complex manipulator for surface scanning, controlling the position and tilt between the probe and specimen’s surface. To ensure accuracy in probe manipulation, accurate geometric information of the specimen is required. This article explores a methodology that uses structured light for physical-to-virtual reconstruction, providing submillimeter scale and accurate surface geometries. Reconstruction aids in path planning through a novel ray-triangle intersection array algorithm, establishing movements for the NDE probe to orient itself on the specimen at a constant probe to specimen surface distance, or lift-off. The proposed technique is demonstrated and validated through experimental air-coupled ultrasonic inspection of automotive CFRP composite samples with simulated flaws such as interlaminar delamination. The proposed method employs guided waves and a pitch-catch configuration of air-coupled ultrasonic probes, enabling single-side access scans. A Fanuc 100ib robot arm was used to manipulate the ultrasonic probes along a sample reconstructed with a CR-Scan 01 structured light sensor. The probes were excited at 200khz from a SonoAir system, while also recovering defect vs background information synchronized with the probe’s orientation. Additionally, a framework for potential automation is proposed, with further details to be explored in future works.

Morita equivalence of two $\ell^p$ Roe-type algebras

Given a metric space with bounded geometry, one may associate with it the \ell^{p} uniform Roe algebra and the \ell^{p} uniform algebra, both containing information about the large scale geometry of the metric space. We show that these two Banach algebras are Morita equivalent in the sense of Lafforgue for 1\leq p<\infty . As a consequence, these two Banach algebras have the same K -theory. We then define an \ell^{p} uniform coarse assembly map taking values in the K -theory of the \ell^{p} uniform Roe algebra and show that it is not always surjective.

Investigating the Effect of the Separation of Scales in Reduced Order Battery Modelling: Implications on the Validity of the Newman Model

Modelling lithium-ion battery behavior is essential for performance prediction and design improvement. However, this task is challenging due to processes spanning many length scales, leading to computationally expensive models. Reduced order models have been developed to address this, assuming a “separation of scales” between micro- and macroscales. This study compares two approaches: direct microstructure-resolved 3D domain electrochemical modelling and a simplified 1D homogenized model, similar to the Doyle-Fuller-Newman model. The research investigates the validity of the scale separation assumption in continuum electrode-level models by varying scale separation factors, boundary conditions, and geometries. The findings reveal increases in deviation between the 3D models and 1D models for more tortuous, less porous microstructures, especially under higher discharge rates. However, under realistic conditions, with an electrode featuring eight particles across its thickness and typical transport properties, the 3D model predicts only a slight (2%) increase in current compared to the 1D model at a high rate of 7C (approximately j ≈ 350 Am−2). These results suggest that the separation of scales assumption in the DFN model is generally suitable for a wide range of operating conditions. However, 1D models may overlook local variations in electrolyte concentration and potential, crucial for understanding degradation mechanisms.

Expedited re-design of multi-band passive microwave circuits using orthogonal scaling directions and gradient-based tuning

Geometry scaling of microwave circuits is an essential but challenging task. In particular, the employment of a given passive structure in a different application area often requires re-adjustment of the operating frequencies/bands while maintaining top performance. Achieving this necessitates the utilization of numerical optimization methods. Nonetheless, if the intended frequencies are distant from the ones at the starting point, local search procedures tend to fail, whereas global search algorithms are computationally expensive. As recently demonstrated, a combination of large-scale concurrent geometry parameter scaling with intermittent local tuning allows for dependable re-design of high-frequency circuits at low CPU costs. Unfortunately, the procedure is only applicable to single-band structures due to synchronized modifications of all operating bands under scaling. This article discusses a novel procedure that leverages a similar overall concept, but allows for independent control of all center frequencies. To achieve this goal, an automated decision-making procedure is developed in which a set of orthogonal scaling directions are determined based on their effect on individual circuit bands, and using auxiliary optimization sub-problems. The scaling range is then automatically computed by solving an appropriately-defined least-square design relocation problem. The methodology introduced in the work is illustrated using two planar passive devices. In both cases, wide-range operating frequency re-design has been demonstrated and favorably compared to conventional gradient-based tuning. Furthermore, the presented procedure has been shown to be computationally efficient. It is also easy to implement and integrate with a variety of gradient-based optimization procedures of a descent type.

Experimental investigation of countercurrent flow limitation (CCFL) in a 1/19 scale of VVER-1000 geometry

Countercurrent flow limitation (CCFL) has been experimentally considered in a VVER-1000 hot-leg. The proposed test facility consists of a hot-leg pipe, a reactor vessel simulator (RVs), and a steam generator simulator (SGs). It was designed and constructed based on power-to-volume scaling approach by preserving the Froud number in the hot leg. The scaling ratio was considered 1/19 of the Bushehr NPP (VVER-1000) geometry. The hot leg of the proposed facility provides good optical observation of the gas/liquid interface. The SG simulator has also a side view for optical observation. Experimental results were captured at atmospheric pressure with air/water as fluid. CCFL was obtained by analyzing the pressure differences between RV and SG simulators.This CCFL data was compared with empirical data and correlations available in the literature. With increasing liquid superficial velocity, the gas superficial velocity curve is continuously decreased, which is consistent with Navarro's results. In this study, an experimental correlation is proposed and compared to other correlations. It was very close to the Navarro and Richter correlations.The results of experimental investigations clarified the onset of the CCFL phenomenon in a Bushehr NPP (VVER-1000) hot-leg geometry. Moreover, the achieved patterns and behaviors of the air/water mixture would be used in computational fluid dynamics (CFD) code validations.

Modeling scalability of impurity precipitation in downstream biomanufacturing.

Precipitation during the viral inactivation, neutralization and depth filtration step of a monoclonal antibody (mAb) purification process can provide quantifiable and potentially significant impurity reduction. However, robust commercial implementation of this unit operation is limited due to the lack of a representative scale-down model to characterize the removal of impurities. The objective of this work is to compare isoelectric impurity precipitation behavior for a monoclonal antibody product across scales, from benchtop to pilot manufacturing. Scaling parameters such as agitation and vessel geometry were investigated, with the precipitate amount and particle size distribution (PSD) characterized via turbidity and flow imaging microscopy. Qualitative analysis of the data shows that maintaining a consistent energy dissipation rate (EDR) could be used for approximate scaling of vessel geometry and agitator speeds in the absence of more detailed simulation. For a more rigorous approach, however, agitation was simulated via computational fluid dynamics (CFD) and these results were applied alongside a population balance model to simulate the trajectory of the size distribution of precipitate. CFD results were analyzed within a framework of a two-compartment mixing model comprising regions of high- and low-energy agitation, with material exchange between the two. Rate terms accounting for particle formation, growth and breakage within each region were defined, accounting for dependence on turbulence. This bifurcated model was successful in capturing the variability in particle sizes over time across scales. Such an approach enhances the mechanistic understanding of impurity precipitation and provides additional tools for model-assisted prediction for process scaling.

Geometry Scaling for Externally Balanced Cascade Deterministic Lateral Displacement Microfluidic Separation of Multi-Size Particles.

To non-invasively monitor personal biological and environmental samples in Internet of Things (IoT)-based wearable microfluidic sensing applications, the particle size could be key to sensing, which emphasizes the need for particle size fractionation. Deterministic lateral displacement (DLD) is a microfluidic structure that has shown great potential for the size fractionation of micro- and nano-sized particles. This paper introduces a new externally balanced multi-section cascade DLD approach with a section-scaling technique aimed at expanding the dynamic range of particle size separation. To analyze the design tradeoffs of this new approach, a robust model that also accounts for practical fabrication limits is presented, enabling designers to visualize compromises between the overall device size and the achievement of various performance goals. Furthermore, results show that a wide variety of size fractionation ranges and size separation resolutions can be achieved by cascading multiple sections of an increasingly smaller gap size and critical separation dimension. Model results based on DLD theoretical equations are first presented, followed by model results that apply the scaling restrictions associated with the second order of effects, including practical fabrication limits, the gap/pillar size ratio, and pillar shape.

Interface frictional anisotropy of dilative sand.

Understanding direction-dependent friction anisotropy is necessary to optimize interface shear resistance across soil-structure. Previous studies estimated interface frictional anisotropy quantitatively using contractive sands. However, no studies have explored how sand with a high dilative tendency around the structural surface affects the interface shear response. In this study, a series of interface direct shear tests are conducted with selected French standard sand and snakeskin-inspired surfaces under three vertical stresses (50, 100, and 200kPa) and two shearing directions (cranial → caudal or caudal → cranial). First, the sand-sand test observes a higher dilative response, and a significant difference between the peak and residual friction angles (ϕpeak - ϕres = 8°) is obtained at even a lower initial relative density Dr = 40%. In addition, the interface test results show that (1) shearing against the scales (cranial shearing) mobilizes a larger shear resistance and produces a dilative response than shearing along the scales (caudal shearing), (2) a higher scale height or shorter scale length exhibits a higher dilative tendency and produces a higher interface friction angle, and (3) the interface anisotropy response is more pronounced during cranial shearing in all cases. Further analysis reveals that the interface friction angle and dilation angle are decreased with the scale geometry ratio (L/H). For L/H values between 16.67 and 60, the interface dilation angle varies between 9° and 4° for cranial first shearing and 3.9°-2.6° for caudal first shearing. However, the difference in dilation angle within the same shearing direction is less than 1°.

Study of defect mode characteristics in acoustic metamaterials

The development of novel material architectures incorporating unconventional geometric designs (e.g., microstructural instabilities, multi-length scale geometries), or adaptive constituent elements (e.g., piezo electrics) has created a powerful tool to design metamaterials for efficient dispersion manipulation and precise control of acoustic waves. Various aspects of the acoustic dispersion (e.g., wave speed, damping ratio, band gap position and widths) have been investigated with a primary focus on wave characteristics in the acoustic pass bands, promoting their utility in applications, e.g., wave guiding, energy harvesting. However, recent studies on topological waves, truncation and bandgap resonances have highlighted potential benefits of leveraging acoustic waves in the bandgap, e.g., signal propagation, passive flow control. Motivated by this, we explore the dispersion behavior of finite mass-spring-damper acoustic metamaterial models with material defects. The eigen analysis reveals a (defect) resonance in the acoustic band gap, producing a highly localized defect mode. The dependence of this resonance frequency, the degree of localization and phase response of the eigenmode, on the defect parameters are explored. Subsequently, the potential utility of these defect modes in flow control applications is also explored and presented.

Design and Validation of Miniaturized Repetitive Transcranial Magnetic Stimulation (rTMS) Head Coils.

Repetitive transcranial magnetic stimulation (rTMS) is a rapidly developing therapeutic modality for the safe and effective treatment of neuropsychiatric disorders. However, clinical rTMS driving systems and head coils are large, heavy, and expensive, so miniaturized, affordable rTMS devices may facilitate treatment access for patients at home, in underserved areas, in field and mobile hospitals, on ships and submarines, and in space. The central component of a portable rTMS system is a miniaturized, lightweight coil. Such a coil, when mated to lightweight driving circuits, must be able to induce B and E fields of sufficient intensity for medical use. This paper newly identifies and validates salient theoretical considerations specific to the dimensional scaling and miniaturization of coil geometries, particularly figure-8 coils, and delineates novel, key design criteria. In this context, the essential requirement of matching coil inductance with the characteristic resistance of the driver switches is highlighted. Computer simulations predicted E- and B-fields which were validated via benchtop experiments. Using a miniaturized coil with dimensions of 76 mm × 38 mm and weighing only 12.6 g, the peak E-field was 87 V/m at a distance of 1.5 cm. Practical considerations limited the maximum voltage and current to 350 V and 3.1 kA, respectively; nonetheless, this peak E-field value was well within the intensity range, 60-120 V/m, generally held to be therapeutically relevant. The presented parameters and results delineate coil and circuit guidelines for a future miniaturized, power-scalable rTMS system able to generate pulsed E-fields of sufficient amplitude for potential clinical use.

3D-printed geocells in footing systems: A comprehensive physical and numerical studies on scaling and performance under centric and eccentric loading scenarios

The complexities of scaling have long presented challenges in applying small-scale test results of geocell-reinforced footings to field conditions in geosynthetic engineering. There has been no research that thoroughly examines the scaling of both geometry and material stiffness in geocell-reinforced footing systems although limited studies have attempted to scale geocells using alternative materials with lower strength, such as simile paper, non-woven geotextile etc. Therefore, this is a leading study to address the complexities of scaling using 3D-printing technology, where both geometry and tensile stiffness of geocell were accurately scaled using scaling laws. In the present study, the impact of scaling on the performance of strip footings reinforced with both traditional fabricated and 3D-printed geocells in terms of pressure-settlement response and improvement factors were assessed. The results indicated that 3D-printed geocells offered significant advantages in customization and rapid prototyping of field scale. Specifically, the strip footings reinforced with fabricated geocells showed up to 65% higher improvement factors in both loose and dense soils compared to those using the scaled 3D-printed geocells. Furthermore, the footings reinforced with scaled geocells using 3D-printing technologies closely aligned with existing large-scale test results regarding improvement factors, which were further validated through various numerical analyses. These findings offer new perspectives for optimizing and applying 3D-printed geocells in geotechnical engineering and address the longstanding challenge of scaling geocell-reinforcement systems in small-scale model tests.