Geometric Scatter Research Articles

Metabarriers for mitigating traffic-induced surface waves: Mechanism dependence on buried arrangements

Locally resonant metamaterials provide exceptional wave manipulation capabilities in the low-frequency regime. This study introduces a buried metabarrier, which can simultaneously harness both resonant and geometric scatterings, to attenuate surface Rayleigh waves at both low and high frequencies induced by traffic. In particular, how the buried arrangements of metabarriers influence their resonant- and geometric-scattering mechanisms is investigated by considering the metabarrier units buried vertically and horizontally in the ground. To this purpose, a numerical finite element model, which is verified through comparisons with existing studies, is developed to analyze the attenuation performance of the metabarrier. Using this model, we perform parametric studies to examine the effects of the material properties and dimensions of the metabarriers on their attenuation behavior. Due to resonant scattering, low-frequency Rayleigh waves are mainly reflected by the vertical metabarriers; in contrast, they are predominantly converted into refracted bulk waves by the horizontal metabarriers. Additionally, the geometric scattering of horizontal metabarriers yields Bragg effects, which can reflect more high-frequency Rayleigh waves and induce a partial mode conversion to transverse bulk waves. Our systematic investigations will, to some extent, facilitate the future design of a well-performing metabarrier attenuating broadband Rayleigh waves.

Numerical Study of Low Engine Order Excitations due to Manufacturing Variability Part 1: Characterization of the Geometric Scatter and its Effect on Forced Response

Abstract The geometric scatter in the surfaces of blades and vanes due to manufacturing variability has an impact on the dynamics but also on the aerodynamics. The loss of the spatial periodicity of the flow due to the geometric variations generates an aerodynamic forcing with a wave number different from the airfoil count on the adjacent rows. In this paper, deviations from the nominal geometry are obtained from a set of scanned parts. The average manufactured geometry is computed through the point-by-point deviations between the scanned parts and the nominal geometry. Then, Principal Component Analysis is applied to the deviations from the average geometry to find a way to describe them in a simple manner. The cold geometries are reconstructed using the mean geometry and the PCA geometric modes; afterwards, a cold-to-hot process is applied to obtain the hot geometry, and finally the resulting aerodynamics are obtained using an in-house CFD solver. The described method is applied to a representative row constituted by packets of vanes. Firstly, the average packet geometry is used to analyze the aerodynamic forcing associated to the geometric variation of the airfoils inside the vane packet. After that, a conceptual study is carried out under some simplified assumptions in order to relate the geometric variability to random low engine order disturbances, using the geometric modes obtained from the PCA analysis. In both cases, the induced vibrations on the adjacent rotor row are comparable to the excitation due to the nominal blade-passing.

Understanding Graph Neural Networks with Generalized Geometric Scattering Transforms

Understanding Graph Neural Networks with Generalized Geometric Scattering Transforms

Investigative analysis of selected FSO models with varying wavelengths for tropical weather

In this paper, an investigation of some selected Mie and geometric Scattering models for free space optical (FSO) communication was done on available atmospheric data in Nigeria. The Kim and Kruse models have been established for the temperate region. In this work, the models were examined using the visibility data from the year 2008 to 2019. The models were examined under the 2% and 5% transmission threshold and under the wavelengths 780nm, 850nm, 1100nm, and 1550nm. The results indicates a higher attenuation at 780nm, supporting what is available in literature. The Suriza et al, ITU-R(Carbonneau) and Gailani et al  models were investigated using the rain intensity data. The Suriza et al model indicates a reduced attenuation compared to the other two models.

Facial Expression Recognition with Geometric Scattering on 3D Point Clouds.

As one of the pioneering data representations, the point cloud has shown its straightforward capacity to depict fine geometry in many applications, including computer graphics, molecular structurology, modern sensing signal processing, and more. However, unlike computer graphs obtained with auxiliary regularization techniques or from syntheses, raw sensor/scanner (metric) data often contain natural random noise caused by multiple extrinsic factors, especially in the case of high-speed imaging scenarios. On the other hand, grid-like imaging techniques (e.g., RGB images or video frames) tend to entangle interesting aspects with environmental variations such as pose/illuminations with Euclidean sampling/processing pipelines. As one such typical problem, 3D Facial Expression Recognition (3D FER) has been developed into a new stage, with remaining difficulties involving the implementation of efficient feature abstraction methods for high dimensional observations and of stabilizing methods to obtain adequate robustness in cases of random exterior variations. In this paper, a localized and smoothed overlapping kernel is proposed to extract discriminative inherent geometric features. By association between the induced deformation stability and certain types of exterior perturbations through manifold scattering transform, we provide a novel framework that directly consumes point cloud coordinates for FER while requiring no predefined meshes or other features/signals. As a result, our compact framework achieves 78.33% accuracy on the Bosphorus dataset for expression recognition challenge and 77.55% on 3D-BUFE.

Predicting partition coefficients for the SAMPL7 physical property challenge using the ClassicalGSG method.

The prediction of log P values is one part of the statistical assessment of the modeling of proteins and ligands (SAMPL) blind challenges. Here, we use a molecular graph representation method called Geometric Scattering for Graphs (GSG) to transform atomic attributes to molecular features. The atomic attributes used here are parameters from classical molecular force fields including partial charges and Lennard-Jones interaction parameters. The molecular features from GSG are used as inputs to neural networks that are trained using a “master” dataset comprised of over 41, 000 unique log P values. The specific molecular targets in the SAMPL7 log P prediction challenge were unique in that they all contained a sulfonyl moeity. This motivated a set of ClassicalGSG submissions where predictors were trained on different subsets of the master dataset that are filtered according to chemical types and/or the presence of the sulfonyl moeity. We find that our ranked prediction obtained 5th place with an RMSE of 0.77 log P units and an MAE of 0.62, while one of our non-ranked predictions achieved first place among all submissions with an RMSE of 0.55 and an MAE of 0.44. After the conclusion of the challenge we also examined the performance of open-source force field parameters that allow for an end-to-end log P predictor model: General AMBER Force Field (GAFF), Universal Force Field (UFF), Merck Molecular Force Field 94 (MMFF94) and Ghemical. We find that ClassicalGSG models trained with atomic attributes from MMFF94 can yield more accurate predictions compared to those trained with CGenFF atomic attributes.

GEOMETRIC SCATTERING ATTENTION NETWORKS.

Geometric scattering has recently gained recognition in graph representation learning, and recent work has shown that integrating scattering features in graph convolution networks (GCNs) can alleviate the typical oversmoothing of features in node representation learning. However, scattering often relies on handcrafted design, requiring careful selection of frequency bands via a cascade of wavelet transforms, as well as an effective weight sharing scheme to combine low- and band-pass information. Here, we introduce a new attention-based architecture to produce adaptive task-driven node representations by implicitly learning node-wise weights for combining multiple scattering and GCN channels in the network. We show the resulting geometric scattering attention network (GSAN) outperforms previous networks in semi-supervised node classification, while also enabling a spectral study of extracted information by examining node-wise attention weights.

The Impact of Manufacturing Variations on Performance of a Transonic Axial Compressor Rotor

Abstract In this paper, the impact of manufacturing variations on performance of an axial compressor rotor is evaluated at design rotational speed. The geometric variations from the design intent obtained from measurements were used to evaluate the impact of manufacturing variations on performance and the flow field in the rotor. The complete blisk is simulated using 3D computational fluid dynamics calculations, allowing for a detailed analysis of the impact of geometric variations on the flow. It is shown that the mean shift of the geometry from the design intent is responsible for the majority of the change in performance in terms of mass flow and total pressure ratio for this specific blisk. In terms of polytropic efficiency, the measured geometric scatter is shown to have a higher influence than the geometric mean deviation. The geometric scatter around the mean is shown to impact the pressure along the leading edge and the shock position. Furthermore, a blisk is analyzed with one blade deviating substantially from the design intent. It is shown that the impact of this blade on the flow is largely limited to the blade passages that it is directly a part of. It is also shown that the impact of this blade on the flow field can be represented by a simulation including three blade passages. In terms of loss, using five blade passages is shown to give a close estimate for the relative change in loss for the blade deviating substantially from the design intent and for the neighboring blades.

A Geometric Scattering Model for Circularly Polarized Indoor Channels

Wireless systems are being deployed in evermore complex environments, ones that can introduce multipath resulting in not only severe frequency selective fading but also signal depolarization. Polarization diversity is a known technique to mitigate such fades. To date, primarily linearly polarized (LP) systems have been used for indoor communications, but recently circularly polarized (CP) systems have received attention. As such there is motivation to better understand how both linearly and CP systems perform in depolarizing environments. In this article, we present a 3-D geometry-based stochastic channel model (GBSCM) for dual-polarized systems to evaluate circular and LP in cluttered settings. Using a Poisson distribution, the model generates a number of multipath scatterers. Measurements have been conducted at 2.4 GHz to validate the model. Leveraging parameters extracted from measured data, linear and circular polarization conditions are simulated for both line-of-sight (LOS) and non-LOS (NLOS) conditions. cross-polarization discrimination (XPD) and 1% link margins are considered as performance metrics. These metrics applied to both simulated and empirical data are both within 1 dB of each other.

Accounting for Geometric Scatter within Manufacturing Tolerances on the Natural Frequency Values of Compressor Rotor Blade during Its Detuning from Dangerous Resonances

Computational research is carried out of the effect of geometric scatter within the manufacturing tolerances on the natural frequency values of a low pressure compressor blade. The first stage blade natural frequencies are estimated and compared considering various distribution laws of dimensions within the manufacturing tolerances. The joint approach to the blade natural frequency optimization and robust design is presented. The obtained blade design is less sensitive to geometric dimension scattering compared to the original design.

Geometric Scattering for Schrödinger Operators with Asymptotically Homogeneous Potentials of Order Zero

In this paper we consider Schr\"oodinger operators with potentials of order zero on asymptotically conic manifolds. We prove the existence and the completeness of the wave operators with a naturally defined free Hamiltonian.

A Three-Dimensional Geometrical Scattering Model for Cellular Communication Environment

Geometrical channel modeling has been one of the hot topics in wireless communication systems since the last two decades. It has been used for variety of scattering model characterizations like spatial and temporal statistical behavior of the channel, level crossing rate of the fading channel along with the analysis of average fade duration etc. In this paper, we propose a three dimensional (3D) semi-ellipsoid geometric scattering model for cellular mobile communication systems, where, elevated base station is considered in scattering free region while the mobile station is assumed to be surrounded by uniformly distributed scatterers in the proposed geometrical shape. Exploiting the proposed geometry, expressions for the joint and marginal probability density functions for angle-of-arrival and time-of-arrival in azimuth and elevation planes are derived. This model is suitable for macro-cellular environment.

High resolution time-delay estimation of underwater target geometric scattering

The geometric scatterings carry the information of the shape of an underwater target. While the time-delay of the weak geometric scattering exists in the received signal cannot be obtained accurately by the conventional time-delay estimation methods because of the limit of the main-lobe width and the interferences from the side-lobe. In this paper, we propose a high resolution time-delay estimation (HRTDE) scheme consisting of two steps. Firstly, when a linear-frequency-modulated (LFM) pulse is transmitted by sonar, the dechirping method transforms the geometric scatterings with different time-delays into multiple single-frequency components respectively, in which the frequency of the dechirped signal shows a linear relationship with the time-delay of the geometric scattering. Then the multiple signal classification (MUSIC) algorithm is adopted to increase the spectrum resolution when multiple single-frequency signals exist in the dechirped signal and the frequency interval is smaller than the frequency resolution limit of the Fourier transform. Simulation results show that the main lobe of the proposed scheme is sharper and with less interference from the side-lobe, compared with the conventional time-delay estimation methods. The results from the anechoic pool experiment demonstrate that the proposed scheme achieves a better time-delay estimation performance for the weak geometric scattering generated by the bottom edge of the underwater target model than match filter based methods.

New methods for pre- and post-processing of stochastic simulations

The aim of numerical simulation is a reliable prediction of real system’s behaviour, which is influenced by numerous uncertainties. In this work, a modelling process is developed for spatially localised modelling of uncertainties by random fields. The developed differential scale-space representation allows the derivation of a stochastic model that can be used to generate synthetic realisations based on a given sample. The post-processing of such stochastic simulation results is usually performed by means of statistic methods. However, this way only values of selected points in space and time can be evaluated and the associativity to the geometric model is lost. To overcome these limitations, a new concept to visualise geometric scatter and dependent statistic measures from stochastic simulation results is developed. The visualisation of the expected value geometry with statistic measures of dependent variables as well as surrounding probability envelopes by superimposed transparent geometry constitutes a holistic approach to evaluate stochastic simulation results.

On Angle-of-Arrival and Time-of-Arrival Statistics of Geometric Scattering Channels

This paper proposes a hyperbolic distribution to model the distribution of random scatterers between a base station (BS) and the user equipment (UE) in multipath mobile environments. New hyperbolic angle-of-arrival (AoA) probability density function (pdf), power azimuth spectrum (PAS), time-of-arrival (ToA) pdf, and power delay spectrum (PDS) are derived. The effectiveness of Gaussian, Janaswamy, and hyperbolic scatterer distributions is assessed by estimating their fitting errors to a given empirical data set. New 3-D simulation results on the Gaussian and hyperbolic PAS and PDS are given and discussed. The line-of-sight (LoS) distance <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> (in kilometers) between the BS and the UE and the propagation path distance mu (in kilometers) can be related mathematically.

Extending bubble measuremenets below 20 μm: in memory of Ralph Goodman’s contributions.

No matter which aspect of underwater acoustics we worked on, conversations with Ralph Goodman invariably added insight and often motivated new lines of investigation. This was certainly true of our interest in measuring bubble size distributions. We discuss the extension of acoustical measurement of bubbles to radii below 20 μm, a topic of particular relevance to the study of optical scatter in the ocean. Extending the frequency range of a resonator to 1 Mhz would in principle allow measurement down to ∼3 μm, but significant challenges arise due to the confounding effects of geometric scatter from larger bubbles. This problem becomes greater for measurements of smaller bubbles, requiring a careful analysis of the accuracy limits imposed on the inversion procedure. Preliminary steps along this path are discussed with examples drawn from recent field measurements.

Comparison of penetration and scatter effects on defect contrast for GE and Siemens LEHR collimators in myocardial perfusion SPECT-a simulation study

The goal of this paper was to evaluate the effects of collimator penetration and scatter on myocardial SPECT image quality. We chose two designs: a LEHR collimator for GE Millennium VG with a longer bore and thicker septa, and a LEHR collimator for Siemens E.CAM with a shorter bore and thinner septa. These two collimators have similar resolution properties, but very different penetration fractions. In particular, the Siemens collimator has higher detection efficiency. We used Monte Carlo (MC) simulation to simulate projection data from the three-dimensional (3-D) NCAT phantom. For each collimator, we generated three sets of projection data: the first one included only the geometric components of the collimator response, the second one included both the geometric and penetration components, and the third one included geometric, penetration and collimator scatter components. The resulting projections were reconstructed with the OSEM algorithm including attenuation and geometric response compensation. For each collimator and reconstruction, we computed the defect contrast in a short-axis slice. We found very small differences in defect contrast between the two collimators with and without penetration and collimator-scattered photons. Since the collimator with higher penetration had greater detection efficiency and showed little loss in defect contrast, a collimator with higher penetration fraction may be acceptable for use in Tc-99 m myocardial perfusion imaging.

Complex Powers and Non-compact Manifolds

We study the complex powers A z of an elliptic, strictly positive pseudodifferential operator A using an axiomatic method that combines the approaches of Guillemin and Seeley. In particular, we introduce a class of algebras, called “Guillemin algebras, ” whose definition was inspired by Guillemin [Guillemin, V. (1985). A new proof of Weyl's formula on the asymptotic distribution of eigenvalues. Adv. in Math. 55:131–160]. A Guillemin algebra can be thought of as an algebra of “abstract pseudodifferential operators.” Most algebras of pseudodifferential operators belong to this class. Several results typical for algebras of pseudodifferential operators (asymptotic completeness, construction of Sobolev spaces, boundedness between appropriate Sobolev spaces,…) generalize to Guillemin algebras. Most important, this class of algebras provides a convenient framework to obtain precise estimates at infinity for A z , when A > 0 is elliptic and defined on a non-compact manifold, provided that a suitable ideal of regularizing operators is specified (a submultiplicative Ψ*-algebra). We shall use these results in a forthcoming paper to study pseudodifferential operators and Sobolev spaces on manifolds with a Lie structure at infinity (a certain class of non-compact manifolds that has emerged from Melrose's work on geometric scattering theory [Melrose, R. B. (1995). Geometric Scattering Theory. Stanford Lectures. Cambridge: Cambridge University Press]).

Extended molecules and geometric scattering resonances in optical lattices.

We develop a theory describing neutral atom scattering at low energies in an optical lattice. We show that, for a repulsive interaction, as the microscopic scattering length increases the effective scattering amplitude approaches a limiting value which depends only on the lattice parameters. In the case of attractive interaction a geometric resonance occurs before reaching this limit. Close to the resonance, the effective interaction becomes repulsive and supports a weakly bound state, which can extend over several lattice sites.

515 均質化法に基づく圧電粒子分散複合材料の特性評価

The macroscopic piezo-electroelastic properties of piezoelectric particles-dispersed composites are affected by the geometric scatter of particles. In this study, a multi-scale finite element analysis based on homogenization method is proposed to estimate the macroscopic piezo-electroelastic properties considering the geometric scatter of particles. As an example, the effects of scatters in diameter and aspect ratio of particle have been investigated numerically for piezoelectric composite consisting of PZT particles and epoxy resin. It was recognized that the scatter of diameter has lager influence on macroscopic properties than one of aspect ratio.