Small-scale Geometry Research Articles

Toward accurate prediction of partial-penetration laser weld performance informed by three-dimensional characterization – Part II: μCT based finite element simulations

The mechanical behavior of partial-penetration laser welds exhibits significant variability in engineering quantities such as strength and apparent ductility. Understanding the root cause of this variability is important when using such welds in engineering designs. In Part II of this work, we develop finite element simulations with geometry derived from micro-computed tomography (μCT) scans of partial-penetration 304L stainless steel laser welds that were analyzed in Part I. We use these models to study the effects of the welds’ small-scale geometry, including porosity and weld depth variability, on the structural performance metrics of weld ductility and strength under quasi-static tensile loading. We show that this small-scale geometry is the primary cause of the observed variability for these mechanical response quantities. Additionally, we explore the sensitivity of model results to the conversion of the μCT data to discretized model geometry using different segmentation algorithms, and to the effect of small-scale geometry simplifications for pore shape and weld root texture. The modeling approach outlined and results of this work may be applicable to other material systems with small-scale geometric features and defects, such as additively manufactured materials.

Characteristics of recoil leaders as observed by LOFAR

Lightning dart leaders and recoil leaders are current pulses that propagate along previously established lightning channels reionizing the channel. They are poorly understood since it is not known how a previously ionized channel can undergo dielectric breakdown multiple times. In this work we investigate five recoil leaders on two different channels using lightning observations of the LOFAR radio telescope in vhf (where we observe 30--80 MHz) using our TRI-D interferometric imaging algorithm. We show that while recoil leaders do slow down over time on average, they can also clearly accelerate. In addition, the vhf power emitted by the recoil leader is closely correlated with speed. We also investigate the vhf-emitting width of the recoil leaders and show that it is thinner than our meter-scale resolution. This shows that recoil leaders have significant streamer activity in their channel core or at most very inner region of the corona sheath, and that there is either very little, or weakly vhf-emitting, streamer activity in the majority of the corona sheath. Finally, we show that recoil leaders can have small microsecond-scale fluctuations in emitted vhf power that can occur in the same spot across subsequent recoil leaders on the same channel, demonstrating that recoil leader propagation is affected by small-scale channel geometry.

Comb-based multispectral LiDAR providing reflectance and distance spectra.

Multispectral LiDAR enables joint observations of the 3D geometry and material properties of natural targets by combining ToF-based distance measurements with remote spectroscopy. Established multispectral LiDAR solutions provide mm-level range resolution and reflectance estimates of the target material over some tens of spectral channels. We propose a novel multispectral LiDAR approach based on an ultra-broadband frequency comb that enables enhanced remote spectroscopy by resolving relative delays in addition to reflectance. The spectrally-resolved delay and power measurements are transformed into distance and reflectance spectra by differential observations to a common reference object and adequate system calibration. These distance and reflectance spectra encode material information related to the surface and sub-surface composition and small-scale geometry. We develop the proposed comb-based multispectral LiDAR on an implementation covering the spectral range between 580 nm and 900 nm on 2 different spectral configurations with 7 and 33 channels of different spectral width. The performance assessment of the implemented system demonstrates a distance measurement precision better than 0.1 mm on most channels. Table-top probing results on five material specimens show that both the distance and the reflectance spectra alone enable discrimination of material specimens, while the novel distance signature particularly complements reflectance and increases classification accuracy when the material surface exhibits significant reflectance inhomogeneity. Material classification results using a support vector machine with radial basis function kernel demonstrate the potential of this approach for enhanced material classification by combining both signature dimensions.

Design and performance evaluation of a submerged floating tidal current power generation device

Due to the difficulty and high cost of offshore power supply, there are still many remote islands which have not been fully developed and utilized. In order to solve this kind of problem, a new type of marine current turbine (MCT) power generation device was designed for Tuoji Island, Changdao County, Shandong Province, which is convenient for installation and maintenance. This paper presents both the prototype design and model test verification work. Limited by the size of circulating water channel, the test model was modeled and manufactured under the scale of 3:100, which means the turbine model is not able to meet the small scale geometry similarity and gravity equivalent at the same time. A light circular plate was designed to replace the resistance of the turbine as equal by means of CFD. Then it combines the main body and the equivalent disc to complete the mooring test, observing the attitude response of the device under different angles of current. On the basis, the hydrodynamic performance of the whole device model was observed under different inflow speeds and angles. The results of the model tests indicated that the prototype is relatively stable under the design condition.

A Python implementation in graphic processing unit of a lattice Boltzmann model for unstable three-dimensional flows in immersed permeable media

The implementation of a lattice Boltzmann model for three-dimensional permeable media with localized drag forces is presented. The model was previously introduced for two-dimensional geometries and follows the basics of the immersed boundary method. Permeable flows are much less stable than their counterparts in porous media and generally produce large coherent flow structures, such as vortex lines, rolls, and wakes. In addition, in permeable media, the small-scale geometry often needs to be represented to a high degree of detail in order to capture certain transport phenomena, such as micro-convection or pollination. Hence, both calculation speed and memory requirements are under strain. The present model was implemented in a graphic processing unit showing excellent performance in the calculation of stable and unstable flows in a rectangular channel partially obstructed by an array of parallel wires. In particular, the model is able to deal with small and medium spatial scales without losing the heterogeneous nature of permeable flows in the homogenization process. The algorithm to manage memory issues is described in detail, and the results of the test case for stable and unstable conditions show the capability of the method to simulate these types of flows.

Velocity-inverted Three-dimensional Distribution of the Gas Clouds in the Type 2 AGN NGC 1068

Abstract Spatially resolved velocity maps at high resolutions of 1–10 pc are becoming available for many nearby active galactic nuclei (AGNs) in both optical/infrared atomic emission lines and submillimeter molecular lines. For the former, it is known that a linear relationship appears to exist between the velocity of the ionized gas clouds and the distance from the nucleus in the inner ∼100 pc region, where these clouds are outflowing. Here we demonstrate that, in such a case, we can actually derive the three-dimensional (3D) geometrical distribution of the clouds directly from the velocity map. Revisiting such a velocity map taken by the Hubble Space Telescope for the prototypical Type 2 AGN NGC 1068, we implement the visualization of the 3D distribution derived from the map, and show that this inner narrow-line region has indeed a hollow-cone structure, consistent with previous modeling results. Quite possibly, this is the outer extended part of the polar elongated dusty material seen in the recent mid-infrared interferometry at parsec scale. Conversely, the latter small-scale geometry is inferred to have a hollow-cone outflowing structure as the inward extension of the derived 3D distribution above. The AGN obscuring “torus” is argued to be the inner optically thick part of this hollow-cone outflow, and its shadowed side would probably be associated with the molecular outflow seen in certain submillimeter lines. We discuss the nature of the linear velocity field, which could be from an episodic acceleration that occurred ∼105 yr ago.

Learning-Based Inverse Bi-Scale Material Fitting From Tabular BRDFs.

Relating small-scale structures to large-scale appearance is a key element in material appearance design. Bi-scale material design requires finding small-scale structures - meso-scale geometry and micro-scale BRDFs - that produce a desired large-scale appearance expressed as a macro-scale BRDF. The adjustment of small-scale geometry and reflectances to achieve a desired appearance can become a tedious trial-and-error process. We present a learning-based solution to fit a target macro-scale BRDF with a combination of a meso-scale geometry and micro-scale BRDF. We confront challenges in representation at both scales. At the large scale we need macro-scale BRDFs that are both compact and expressive. At the small scale we need diverse combinations of geometric patterns and potentially spatially varying micro-BRDFs. For large-scale macro-BRDFs, we propose a novel 2D subset of a tabular BRDF representation that well preserves important appearance features for learning. For small-scale details, we represent geometries and BRDFs in different categories with different physical parameters to define multiple independent continuous search spaces. To build the mapping between large-scale macro-BRDFs and small-scale details, we propose an end-to-end model that takes the subset BRDF as input and performs classification and parameter estimation on small-scale details to find an accurate reconstruction. Compared with other fitting methods, our learning-based solution provides higher reconstruction accuracy and covers a wider gamut of appearance.

Continuous evolution of oceanic crustal structure following an eruption at Axial Seamount, Juan de Fuca Ridge

Abstract We present the first continuous observations of the temporal evolution of oceanic crustal shear velocity beneath Axial Seamount, a submarine volcano on the Juan de Fuca Ridge (offshore northwestern North America). Weekly values of seafloor compliance, the periodic deformation of the seafloor under ocean waves, were estimated over the time period between December 2014 and May 2018 using data from two cabled broadband ocean-bottom seismometers with collocated absolute pressure sensors. We inverted these measurements for shear-wave velocity within the volcano beneath the two stations as a function of depth and time. Our results, combined with estimates of seismic compressional wave velocity, suggest that the shallow melt reservoir and the lower crust beneath the central caldera contain melt fractions of 14% and at least 4%, respectively. The eruption of April 2015 induced a dramatic drop in shear velocities beneath the central station, primarily in the lower crust, which could have been caused by an increase in melt fraction, a change in small-scale melt geometry, or both. The absence of such a change beneath the eastern flank of the caldera indicates that there is a lower-crustal conduit beneath the caldera center, which is much narrower in cross section (<1 km2) than the overlying melt reservoir (≥42 km2). Our study demonstrates the promise of using continuous data to understand submarine volcanism and crustal accretionary processes.

Free vibration investigation of FG nanoscale plate using nonlocal two variables integral refined plate theory

In this research paper, the free vibrational behavior of the simply supported FG nano-plate is studied using the nonlocal two variables integral refined plate theory. The present model takes into account the small scale effect. The effective\'s properties of the plate change according to the power law variation (P-FGM). The equations of motion of the system are determined and resolved via Hamilton\'s principle and Navier procedure, respectively. The validity and efficiency of the current model are confirmed by comparing the results with those given in the literature. At the last section, several numerical results are presented to show the various parameters influencing the vibrational behavior such as the small-scale effect, geometry ratio, material index and aspect ratio.

Integrated study on the topographic and shallow subsurface expression of the Grote Brogel Fault at the boundary of the Roer Valley Graben, Belgium

The Grote Brogel Fault (GBF) is a major WNW-ESE striking normal fault in Belgium that diverges westward from the NW-SE striking western border fault system of the Roer Valley Graben. The GBF delimits the topographically higher Campine Block from the subsiding Roer Valley Graben, and is expressed in the Digital Terrain Model (DTM) by relief gradients or scarps. By integrating DTM, Electrical Resistivity Tomography (ERT), Cone Penetration Test (CPT) and borehole data, we studied the Quaternary activity of the GBF and its effects on local hydrogeology. In the shallow subsurface (<50m) underneath these scarps, fault splays of the GBF were interpreted on newly acquired ERT profiles at two investigation sites: one on the eastern section and the other on the western section, near the limit of the visible surface trace of the fault. Borehole and CPT data enabled stratigraphic interpretations of the ERT profiles and thereby allowed measuring vertical fault offsets at the base of Pleistocene fluvial deposits of up to 12m. Groundwater measurements in the boreholes and CPTs indicate that the GBF acts as a hydrologic boundary that prevents groundwater flow from the elevated footwall towards the hangingwall, resulting in hydraulic head differences of up to 12.7m. For the two investigation sites, the hydraulic head changes correlate with the relief gradient, which in turn correlates with the Quaternary vertical offset of the GBF. ERT profiles at the eastern site also revealed a local soft-linked stepover in the shallow subsurface, which affects groundwater levels in the different fault blocks, and illustrates the complex small-scale geometry of the GBF.

Azimuthal Scattering from Elliptical Hair Fibers

The appearance of hair follows from the small-scale geometry of hair fibers, with the cross-sectional shape determining the azimuthal distribution of scattered light. Although previous research has described some of the effects of non-circular cross sections, no accurate scattering models for non-circular fibers exist. This article presents a scattering model for elliptical fibers, which predicts that even small deviations from circularity produce important changes in the scattering distribution and which disagrees with previous approximations for the effects of eccentricity. To confirm the model’s predictions, new scattering measurements of fibers from a wide range of hair types were made, using a new measurement device that provides a more complete and detailed picture of the light scattered by fibers than was previously possible. The measurements show features that conclusively match the model’s predictions, but they also contain an ideal-specular forward-scattering behavior that is not predicted and has not been fully described before. The results of this article indicate that an accurate and efficient method for computing scattering in elliptical cylinders—something not provided in this article—is the correct model to use for realistic hair in the future and that the new specular behavior should be included as well.

Fine structure of connectedness loci

We study distributions of the harmonic and Lebesgue measures on the boundary of the connectedness locus \(\mathcal{M}_{d}\) for uni-critical polynomials \(z^{d}+c\) and dynamical properties which are typical with respect to the harmonic measure. One result is a conformal similarity between \(\mathcal{M}_{d}\) and the corresponding Julia set for almost every point of \(\mathcal{M}_{d}\) with respect to the harmonic measure. It is also shown that the harmonic measure is supported on Lebesgue density points of the complement of \(\mathcal{M}_{d}\) which are not accessible from outside within John angles and at which the boundary of \(\mathcal{M}_{d}\) ‘spirals’ infinitely often in both directions. In the case of quadratic polynomials, we prove that every parameter c from the boundary of the Mandelbrot set \(\mathcal{M}\) that is recurrent under iterates of \(z^{2}+c\) but not infinitely tunable is a Lebesgue weak density point of the complement of \(\mathcal{M}\). A direct consequence of our theory is the Yoccoz local connectivity theorem. A new technical ingredient in the paper is the method of “amplification” which is based on promoting the small scale geometry of the parameter space at a typical point in the sense of harmonic measure to uniform geometry of the corresponding Julia set. The pointwise conformality of the similarity map is derived through inducing techniques and a classical TWB-theory.

Shape optimisation with multiresolution subdivision surfaces and immersed finite elements

We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets, multiresolution surfaces represent the domain boundary using a coarse control mesh and a sequence of detail vectors. Based on the multiresolution decomposition efficient and fast algorithms are available for reconstructing control meshes of varying fineness. During shape optimisation the vertex coordinates of control meshes are updated using the computed shape gradient information. By virtue of the multiresolution editing semantics, updating the coarse control mesh vertex coordinates leads to large-scale geometry changes and, conversely, updating the fine control mesh coordinates leads to small-scale geometry changes. In our computations we start by optimising the coarsest control mesh and refine it each time the cost function reaches a minimum. This approach effectively prevents the appearance of non-physical boundary geometry oscillations and control mesh pathologies, like inverted elements. Independent of the fineness of the control mesh used for optimisation, on the immersed finite element grid the domain boundary is always represented with a relatively fine control mesh of fixed resolution. With the immersed finite element method there is no need to maintain an analysis suitable domain mesh. In some of the presented two and three-dimensional elasticity examples the topology derivative is used for introducing new holes inside the domain. The merging or removing of holes is not considered.

Effect of VOCs-adsorbing particles on the VOCs emission from wood

This study presents the effect of the VOCs-adsorbing particles and air velocity on the transport of volatile organic compounds (VOCs) in a wood in a small-scale geometry. This study aims to show that the use of VOCs-adsorbing particle can enhance significantly the VOCs emission from building indoor materials before they are actually installed in a residential place. A numerical simulation based on two-dimensional computational fluid dynamics model has been performed to investigate the influences of air velocity and particle concentration. Together with air, particles come into the channel on which a wood is laid. Numerical results show that particles in the air blown to the channel drastically decrease VOCs concentration in the air. With an increase in the inlet particle concentration, the volume-averaged VOCs concentration in the airside decreases a lot. The air flow rate has significant impacts on the airside VOCs concentration. An increase in the air flow rate decreases the airside VOCs concentration. Under the same air flow rate at the inlet, larger inlet velocity with smaller channel width yields lower airside VOCs concentration when particles are released into the model. Meanwhile, the VOCs concentration in wood of 5cm thickness decreases a little bit under a situation with high inlet velocity and high inlet particle concentration. When wood thickness is thinner, the VOCs concentration in wood significantly decreased, which means larger increase in the rate of VOCs emission from a thin wood.

Interactive bi-scale editing of highly glossy materials

We present a new technique for bi-scale material editing using Spherical Gaussians (SGs). To represent large-scale appearances, an effective BRDF that is the average reflectance of small-scale details is used. The effective BRDF is calculated from the integral of the product of the Bidirectional Visible Normal Distribution (BVNDF) and BRDFs of small-scale geometry. Our method represents the BVNDF with a sum of SGs, which can be calculated on-the-fly, enabling interactive editing of small-scale geometry. By representing small-scale BRDFs with a sum of SGs, effective BRDFs can be calculated analytically by convolving the SGs for BVNDF and BRDF. We propose a new SG representation based on convolution of two SGs, which allows real-time rendering of effective BRDFs under all-frequency environment lighting and real-time editing of small-scale BRDFs. In contrast to the previous method, our method does not require extensive precomputation time and large volume of precomputed data per single BRDF, which makes it possible to implement our method on a GPU, resulting in real-time rendering.

Stability analysis of nanocones under external pressure and axial compression using a nonlocal shell model

A nonlocal continuum shell model is developed to study the stability of nanocones under combined loading: external pressure and compression force. The nonlinear governing equations of motion of nanocone are obtained using Hamilton's principle and the external loads are considered as prestress. Based on Eringen's nonlocal elasticity theory the small-scale effect is accounted in the governing equations of motion. To obtain the critical loads, the equations are solved using Galerkin technique and the effect of small-scale parameter and geometry on the stability of nanocone is studied.

Physically-based interactive bi-scale material design

We present the first physically-based interactive system to facilitate the appearance design at different scales consistently, through manipulations of both small-scale geometry and materials. The core of our system is a novel reflectance filtering algorithm, which rapidly computes the large-scale appearance from small-scale details, by exploiting the low-rank structures of the Bidirectional Visible Normal Distribution Function and pre-rotated BRDFs in the matrix formulation of our rendering problem. Our algorithm is three orders of magnitude faster than a ground-truth method. We demonstrate various editing results of different small-scale geometry with analytical and measured BRDFs. In addition, we show the applications of our system to physical realization of appearance, as well as modeling of real-world materials using very sparse measurements.

Zig-zag chains and metric equivalences between ultrametric spaces

We study the classification of ultrametric spaces based on their small scale geometry (uniform homeomorphism), large scale geometry (coarse equivalence) and both (bi-uniform equivalences). Using a combinatoric approach we consider every ultrametric space as the end space of a chain and prove that all these equivalences can be characterized by the existence of a common zig-zag chain.

Urban road networks — spatial networks with universal geometric features?

Urban road networks have distinct geometric properties that are partially determined by their (quasi-) two-dimensional structure. In this work, we study these properties for 20 of the largest German cities. We find that the small-scale geometry of all examined road networks is extremely similar. The object-size distributions of road segments and the resulting cellular structures are characterised by heavy tails. As a specific feature, a large degree of rectangularity is observed in all networks, with link angle distributions approximately described by stretched exponential functions. We present a rigorous statistical analysis of the main geometric characteristics and discuss their mutual interrelationships. Our results demonstrate the fundamental importance of cost-efficiency constraints for in time evolution of urban road networks.

Effective large-scale description of lateral diffusions on fluctuating interfaces

The non-linear coupling between lateral diffusions on an interface and the geometry of this interface is studied numerically on a simple 1D model which presents the same kind of non-linearities as fully 2D ones. It is found that small-scale geometry fluctuations influence the diffusion at all scales, including scales much larger than those of the fluctuations. At large enough scales, the diffusion can be approximately described by introducing an effective or renormalized diffusion coefficient. Several theoretical estimates for this coefficient are introduced and compared to the value derived from numerical simulations.