Full Matrix Research Articles

Strain-induced modification in thermal properties of monolayer 1T-ZrS2 and ZrS2/ZrSe2 heterojunction.

This paper systematically analyzes the phonon dispersion curves of single-layer ZrS2, ZrSe2, and ZrS2/ZrSe2 heterostructures under different strains. The phonon spectra and thermal parameters of the three structures were obtained based on the density functional perturbation theory method. The upper limits of strain that different monolayers and heterojunctions can withstand were studied. The monolayers ZrSe2 and ZrS2 can withstand up to 8% biaxial tensile strain, and the ZrS2/ZrSe2 heterojunction can withstand up to 6% biaxial tensile strain. In addition, the van der Waals force of the heterojunction may cause phonon tearing in the vertical direction. The application of biaxial tensile strain can adjust the thermal properties of the system to a large extent, which is similar to the strain effect in the pristine case. When the temperature rises, the entropy enthalpy of the three structures also gradually increases, the free energy gradually decreases, and the heat capacity of the system gradually increases until it tends to be stable. Taking single-layer ZrS2 as an example, we analyzed the change curve of thermal properties of single-layer ZrS2 under tensile strain. The results show that with the gradual increase of strain, the crystal's entropy, enthalpy, and free energy change differently. In addition, the heat capacity increases slowly under high temperatures. When all systems reach the limit strain, the phonon spectrum appears to have an imaginary frequency, and the thermal properties decrease significantly. This paper uses the first-principle calculation method based on density functional theory, and the PBE exchange-correlation function based on generalized gradient approximation (GGA) is selected for a specific calculation. The density functional perturbation theory (DFPT) calculates the full kinetic matrix. Because the lattice constants of ZrS2 and ZrSe2 are similar and have similar periodicity, the corresponding unit cells are used for structural optimization and property calculation. The Brillouin zone is integrated using the K points generated by the Monkhorst-pack method. For single-layers ZrS2 and ZrSe2, 8 × 8 × 1K-point grid is selected, and for ZrS2/ZrSe2 heterojunction, 8 × 8 × 2K-point grid is selected. A vacuum layer of 30Å was added in the vertical direction to avoid interlayer interaction. The non-conservative pseudopotential method is used to optimize the structure, and the optimization convergence is set as follows: the cutoff energy is set to 700eV, the convergence threshold of the maximum force between atoms is 0.01eV/Å, the convergence threshold of the maximum energy change is set to 1 × 10-9eV, and the convergence threshold of the maximum displacement is 0.001Å.

How do wavelength correlations affect transmission spectra? Application of a new fast and flexible 2D Gaussian process framework to transiting exoplanet spectroscopy

The use of Gaussian processes (GPs) is a common approach to account for correlated noise in exoplanet time series, particularly for transmission and emission spectroscopy. This analysis has typically been performed for each wavelength channel separately, with the retrieved uncertainties in the transmission spectrum assumed to be independent. However, the presence of noise correlated in wavelength could cause these uncertainties to be correlated, which could significantly affect the results of atmospheric retrievals. We present a method that uses a GP to model noise correlated in both wavelength and time simultaneously for the full spectroscopic dataset. To make this analysis computationally tractable, we introduce a new fast and flexible GP method that can analyse 2D datasets when the input points lie on a (potentially non-uniform) 2D grid - in our case a time by wavelength grid - and the kernel function has a Kronecker product structure. This simultaneously fits all light curves and enables the retrieval of the full covariance matrix of the transmission spectrum. Our new method can avoid the use of a `common-mode' correction, which is known to produce an offset to the transmission spectrum. Through testing on synthetic datasets, we demonstrate that our new approach can reliably recover atmospheric features contaminated by noise correlated in time and wavelength. In contrast, fitting each spectroscopic light curve separately performed poorly when wavelength-correlated noise was present. It frequently underestimated the uncertainty of the scattering slope and overestimated the uncertainty in the strength of sharp absorption peaks in transmission spectra. Two archival VLT/FORS2 transit observations of WASP-31b were used to compare these approaches on real observations. Our method strongly constrained the presence of wavelength-correlated noise in both datasets, and significantly different constraints on atmospheric features such as the scattering slope and strength of sodium and potassium features were recovered.

Approaching code-compliant Non-Destructive Testing of carbon steel weld using Total Focusing Method technique

The Total Focusing Method (TFM) technique is an advanced Non-Destructive Testing (NDT) Ultrasonic Testing (UT) technique. It is usually used together with special acquisition configurations such as Full Matrix Capture (FMC) or Plane Wave Imaging (PWI) and can supply synthetic post-processing results based on a quantity of ultrasonic signals. It is believed that it will accelerate the UT technique revolution toward the artificial intelligence era. Compared to the conventional UT technique, or even advanced UT techniques, such like Time of Flight Diffraction (TOFD) and Phased Array (PA) techniques, this advanced UT technique is well known for its easy-to-interpret and high-resolution representative images. For these reasons, it is used more and more in the flaw sizing and characterization assessment. Following the publication of the standard ISO 23864, TFM technique become a member among all standardized weld inspection techniques. This article presents some related study results toward a code-compliant weld inspection regarding the related standards, dealing especially with the sensitivity calibration which is a key point for the applicability of amplitude-based acceptance criteria.

Lie centralizing mappings on generalized matrix algebras through two-sided zero products

Let [Formula: see text] be a generalized matrix algebra defined by the Morita context [Formula: see text] and [Formula: see text] the center of [Formula: see text]. In this paper, under some certain conditions on [Formula: see text], we prove that if [Formula: see text] is an additive map satisfying [Formula: see text] for any [Formula: see text] with [Formula: see text], then [Formula: see text] has the form [Formula: see text] for all [Formula: see text], where [Formula: see text] and [Formula: see text] is an additive map from [Formula: see text] into [Formula: see text]. Finally as its applications, we characterize Lie centralizer maps and generalized Lie derivations on [Formula: see text]. Moreover we prove that the similar conclusions remain valid on full matrix algebras, triangular algebras, upper triangular matrix algebras.

Stationary Points of a Shallow Neural Network with Quadratic Activations and the Global Optimality of the Gradient Descent Algorithm

We consider the problem of training a shallow neural network with quadratic activation functions and the generalization power of such trained networks. Assuming that the samples are generated by a full rank matrix [Formula: see text] of the hidden network node weights, we obtain the following results. We establish that all full-rank approximately stationary solutions of the risk minimization problem are also approximate global optimums of the risk (in-sample and population). As a consequence, we establish that, when trained on polynomially many samples, the gradient descent algorithm converges to the global optimum of the risk minimization problem regardless of the width of the network when it is initialized at some value [Formula: see text], which we compute. Furthermore, the network produced by the gradient descent has a near zero generalization error. Next, we establish that initializing the gradient descent algorithm below [Formula: see text] is easily achieved when the weights of the ground truth matrix [Formula: see text] are randomly generated and the matrix is sufficiently overparameterized. Finally, we identify a simple necessary and sufficient geometric condition on the size of the training set under which any global minimizer of the empirical risk has necessarily zero generalization error. Funding: The research of E. C. Kizildag is supported by Columbia University, with the Distinguished Postdoctoral Fellowship in Statistics. Support from the National Science Foundation [Grant DMS-2015517] is gratefully acknowledged.

A quasi‐31‐vibrator method for the characterization of piezoelectric full matrix parameters using a single sample

AbstractThe full matrix parameters of a piezoelectric material are crucial for designing and evaluating piezoelectric devices. However, due to their inverse problematic nature, commonly used single‐sample characterization methods heavily depend on the accuracy of initial values and mode matching. In this paper, we propose a quasi‐31‐vibrator method to directly evaluate these parameters by designing the sample geometry and establishing the relationship equation between the parameters. This approach completely bypasses the need for characteristic spectrum simulation and mode identification processes. Subsequently, we tested the full matrix parameters of PZT‐5H ceramics and compared the simulated impedance spectra with the measured ones. The presence of well‐fitting spectra validates the feasibility of the method. This method will contribute to characterize the parameters of new piezoelectric materials and advance the intelligent implementation of measuring full matrix parameters.

Towards an in-process ultrasonic phased array inspection method for narrow-gap welds

The marriage of welding and Non-Destructive Testing (NDT) processes at the point of manufacture has enabled the detection and correction of defects during the welding process. This has demonstrated clear financial and production benefits by reducing weld rework and ensuring schedule certainty, however this is yet to be demonstrated for use with narrow-groove welding practises. Narrow-groove welds are notoriously difficult to inspect using traditional Phased Array Ultrasonic Testing (PAUT) techniques due to large thicknesses and the vertical nature of Lack-of-Sidewall Fusion (LOSWF) defects. This is further complicated by the presence of partially-filled weld geometries during in-process inspection, which cause geometric reflections which can mask or falsely indicate the presence of a defect. A solution to this is proposed in this work, by adapting a dual-tandem phased array imaging system for the imaging of LOSWF defects in a partial weld geometry. This considers a two array system utilising a phased array probe on each weld side, coupled with an advanced dual-aperture Full Matrix Capture (FMC) acquisition technique. Advanced multi-mode image processing algorithms such as the Total Focusing Method (TFM) and Phase Coherence Imaging (PCI), with adaptive delay law calculation, have shown high sensitivity to LOSWF defects in a mock partial weld geometry. Additionally, an adaptive Probe Centre Spacing (PCS) technique is defined for in-process inspection based on amplitude and phase coherence sensitivity in partial weld geometries, with the effects of partial weld reflections analysed and discussed. These results have demonstrated the effectiveness of a dual-tandem phased array approach to imagine LOSWF defects during the in-process inspection of narrow-gap welds.

A mixed Fourier-variational approach to solve differential or integro-differential wave equations for magnetised plasmas

The All ORders Spectral Algorithm (AORSA) wave equation solver by Jaeger (Jaeger et al 2001 Phys. Plasmas 8 1573) solves the integro-differential wave equation relevant for the radio frequency (RF) domain and for fusion-relevant conditions in tokamaks or stellarators, retaining all finite Larmor radius corrections by substituting the continuous Fourier integrals by a sum over a discrete set of modes. Its strength is also its weakness: the simplicity of the method results in significant computational effort, a full matrix needing to be inverted to solve the associated linear system. Based on the notion that modes are gradually more independent if their eigenvalues differ, the present paper proposes a straightforward numerical method to partly alleviate this need, allowing to substitute the full system matrix by a banded one. The adopted method can be applied to a wide variety of equations. A few 1D examples—of relevance for solving the wave equation in the RF domain of frequencies—are provided: the tunneling equation is used to illustrate the potential of the method, and the all-FLR wave equation (retaining all Finite Larmor Radius corrections in the dielectric response) adopted by Jaeger is solved comparing the solutions found to those based on simpler models (a cold plasma and a ‘tepid plasma’ - i.e. a kinetic model truncated at zero order in Larmor radius—description).

Accelerating structural dynamics simulations with localised phenomena through matrix compression and projection‐based model order reduction

AbstractIn this work, a novel approach is introduced for accelerating the solution of structural dynamics problems in the presence of localised phenomena, such as cracks. For this category of problems, conventional projection‐based Model Order Reduction (MOR) methods are either limited with respect to the range of system configurations that can be represented or require frequent solutions of the Full Order Model (FOM) to update the low‐dimensional spaces, in which solutions are represented. In the proposed approach, low‐dimensional spaces, constructed for the healthy structure, are enriched with appropriately selected columns of the flexibility matrix of the system. It can be shown that these spaces contain the solution to the original problem for the static case, while their dimension is much smaller. In order to allow their online construction for arbitrary localised features, the full flexibility matrix of the system should be available. To this end, a hierarchical representation is used for the matrices involved, allowing to compute the flexibility matrix efficiently and with reduced memory requirements. The resulting method offers significant speedups, without sacrificing the flexibility and accuracy of the full order model. The performance and limitations of the approach are studied through a series of examples in structural dynamics.

Integrally Bladed Rotor Modal Identification Under Traveling Wave Excitation With High Density Measurement Points

Abstract Vibration testing of an integrally bladed rotor (IBR) is often completed through traveling wave excitation (TWE) bench tests composed of multiple, simultaneously excited inputs. Often, each blade has many output locations. For IBRs with many blades, as often found in the high pressure compressor, the total number of outputs can be several orders of magnitude. Formulation of a full output spectral density matrix from all measurements will then contain an exponential number of values at each frequency bin that can be detrimental to computational resources during the spectral density matrix formulation as well as down-stream system identification algorithms. An online algorithm is proposed for collecting and analyzing TWE data to reduce the large, computationally burdensome datasets into a manageable number of subsets for subsequent system identification. Furthermore, a frequency domain decomposition technique is also proposed for system identification that also attempts to reduce the data size through singular value decomposition. Identified system poles can be averaged from each subset, but mode shapes require stitching each subset together to identify the full mode shape at all output locations. The developed approaches are tested on synthetic TWE data and compared to baseline system identification results obtained using the full spectral density matrix. Results indicate the data subsets accurately compare to the baseline without much loss in accuracy.

Genetic Parameters for Limousine Interbeef Genetic Evaluation of Calving Traits.

The aim of this study was to estimate across-country genetic correlations for calving traits (birth weight, calving ease) in the Limousine breed. Correlations were estimated for eight populations (Czech Republic, joint population of Denmark, Finland, and Sweden, France, Great Britain, Ireland, Slovenia, Switzerland, and Estonia). An animal model on raw performance accounting for across-country interactions (AMACI) was used. (Co)variance components were estimated for pairwise combinations of countries. Fixed and random effects were defined by each country according to its national genetic evaluation system. The average across-country genetic correlation for the direct genetic effect was 0.85 for birth weight (0.69-0.96) and 0.75 for calving ease (0.62-0.94). The average correlation for the maternal genetic effect was 0.57 for birth weight and 0.61 for calving ease. After the estimation of genetic parameters, the weighted bending procedure was used to compute the full Interbeef genetic correlation matrix. After bending, direct genetic correlations ranged from 0.62 to 0.84 (with an average of 0.73) for birth weight and from 0.58 to 0.82 (with an average of 0.68) for calving ease.

Adaptive Sampling of 3D Spatial Correlations for Focus+Context Visualization.

Visualizing spatial correlations in 3D ensembles is challenging due to the vast amounts of information that need to be conveyed. Memory and time constraints make it unfeasible to pre-compute and store the correlations between all pairs of domain points. We propose the embedding of adaptive correlation sampling into chord diagrams with hierarchical edge bundling to alleviate these constraints. Entities representing spatial regions are arranged along the circular chord layout via a space-filling curve, and Bayesian optimal sampling is used to efficiently estimate the maximum occurring correlation between any two points from different regions. Hierarchical edge bundling reduces visual clutter and emphasizes the major correlation structures. By selecting an edge, the user triggers a focus diagram in which only the two regions connected via this edge are refined and arranged in a specific way in a second chord layout. For visualizing correlations between two different variables, which are not symmetric anymore, we switch to showing a full correlation matrix. This avoids drawing the same edges twice with different correlation values. We introduce GPU implementations of both linear and non-linear correlation measures to further reduce the time that is required to generate the context and focus views, and to even enable the analysis of correlations in a 1000-member ensemble.

Fastener hole inspection using 2D phased array

Fastener hole cracks, resulting from stress concentration around the hole, are potential sources of failure in mechanical structures. Traditionally, inspection involves manually moving a single ultrasonic probe around the hole or using an eddy current probe to move through the hole. However, single ultrasonic probe inspection is time-consuming and needs skilful operators. Eddy current inspection requires the removal of the fastener in advance and does not allow easy crack sizing and visualization. This paper proposes a novel approach that combines a 2D phased array with a coupling block to enable complete fastener hole inspection from a single array position. A single full matrix capture (FMC) data set is collected, from which 3D volumetric images are formed. To obtain clear images of the geometry and potential defects, half-skip and multi-skip total focusing method imaging algorithms are investigated together with transmitter–receiver pairs selection methods to detect different target features. Experimental results demonstrate that the proposed inspection approach can eliminate dead zone problems and capture all target information from a single inspection position. These methods show great potential in enhancing the efficiency and reliability of fastener hole inspections.

Ultrasonic evaluation of wire-to-terminal joints: integrating XGBoost machine learning with finite element feature analysis

ABSTRACT A new scheme for ultrasonic non-destructive evaluation of wire-to-terminal joints was developed in this study. A finite element simulation model of 2D porous media based on X-CT images of an NG sample was proposed to analyse acoustic scattering. The simulation signal features were extracted in the time domain, frequency domain, and time-frequency domain, and entropy analysis was conducted to explore the relationship between different characteristic values and porosity, thereby revealing prominent trends in these features. By controlling parameters, 28 welding samples labelled OK and NG were produced, and their echoes were acquired by an ultrasonic Full Matrix Capture (FMC) system. Features of the full matrix signals were extracted, and the combined XGBoost machine learning was used to classify the quality and order the attribution of features. The result highlighted the significance of the waveform factor, margin factor, and kurtosis which are consistent with simulation results. The accuracy of weld quality identification can reach 84%. The three factors may be performance criteria for ultrasonically welded wire-to-terminal joints.

Coupling transport equations to mechanics in the material point method using an approximate full capacity matrix inverse

Coupling solutions of one or more transport equations to mechanics modeling in the material point method (MPM), extends MPM to a platform for solving multi-physics problems. Unfortunately, the standard MPM approach to transport equations using a lumped transport capacity matrix is prone to large oscillations in particle values especially near interfaces, cracks, or rapid changes in transport value. Switching from lumped capacity matrix methods to an approximate full capacity matrix approach can eliminate those oscillations. Although this switch can cause unwanted numerical diffusion, that problem can be suppressed using periodic or blending options. Several examples illustrate the new methods for heat conduction, solvent transport, poroelasticity, and phase field fracture simulations. In thermal calculations, the new methods improve accuracy for tracking thermodynamics state functions.

The Exact Stochastic Process of the Haploid Multi-Allelic Wright-Fisher Mutation Model.

Diffusion models are widely applied in population genetics, but their approximate solutions may not accurately capture the exact stochastic process. Nevertheless, this practice was necessary due to computing limitations, particularly for large populations. In this article, we develop the exact Markov chain algebra (MCA) for a discrete haploid multi-allelic Wright-Fisher model (MA-WFM) with a full mutation matrix to address this challenge. A special case of nonzero mutations between multiple alleles have not been captured by previous bi-allelic models. We formulated the mean allele frequencies for asymptotic equilibrium analytically for the tri- and quad-allelic case. We also evaluated the exact time-dependent Markov model numerically, presenting it concisely in terms of diffusion variables. The convergence with increasing population size to a diffusion limit is demonstrated for the population composition distribution. Our model shows that there will never be exact irreversible extinction when there are nonzero mutation rates into each allele and never be an exact irreversible fixation when there are nonzero mutation rates out of each allele. We only present results where there is no complete extinction and no complete fixation. Finally, we present detailed computations for the full Markov process, exposing the behavior near the boundaries for the compositional domains, which are non-singular boundaries according to diffusion theory.

Adaptive Ultrasonic Full Matrix Capture Process for the Global Imaging of Complex Components with Curved Surfaces.

This work proposes a new global FD-RTM method to solve the problem of ultrasonic inspection of parts with complex geometric shapes. With this method, the frequency domain reverse time migration (FD-RTM) algorithm is used to adapt to the complex refraction of ultrasonic waves by the surface, while an interface solution algorithm based on tangent fitting is used to solve the interface position with high precision through the full matrix reception data. Based on high-precision interface information, a hybrid extrapolation algorithm and a situation-specific probe movement strategy are used to enable the probe to find the next sampling point according to the direction of the workpiece surface, allowing complex surface topography features to be identified without relying on the workpiece CAD drawing. This makes it possible to achieve the automated inspection of workpieces. To verify the proposed method's effectiveness, an aluminum alloy model with side-drilled holes (SDH) is used. The geometry of the model consists of multiple convex and concave surfaces. By comparing the local FD-RTM imaging with images synthesized using the entire scan path, it is shown that gFD-RTM improved the imaging performance. Compared with FD-RTM, the average signal-to-noise ratio of gFD-RTM was increased by 20%, and the array performance index (API) was reduced by 70%, indicating effective detection coverage.

Coherent signals direction estimation using high-order quantities in the acoustic field

To meet the demands of underwater remote detection technology, the receiving array must be extended to low frequencies by increasing the array aperture required for detection. Furthermore, the base array aperture must be increased owing to the loss of effective array aperture in coherent targets detection using most decoherent algorithms; however, this prevents its use on small platforms, such as autonomous underwater platforms. Thus, reducing the array aperture while ensuring high resolution is required. In this article, high-order quantities in the acoustic field are utilized to construct a full rank covariance matrix to Multiple Signal Classification Method (MUSIC), which achieves high-resolution results for small aperture arrays with small incident angular intervals in low-frequency coherent targets. The correlated noise of each sensor is considered in the small aperture arrays and the gain of each element in the new matrix is derived. The theoretical analysis, numerical simulations, and experimental verifications show the validity of the method.

On the bias in the AUC variance estimate

The area under the Receiver Operating Characteristic (ROC) curve (AUC) is a standard metric for quantifying and comparing binary classifiers. A popular approach to estimating the AUCs and the associated variabilities – the variance of the AUC or the full covariance matrix of multiple correlated AUCs – is the one proposed by DeLong et al. (1988), which is based on the Mann Whitney two-sample U-statistics. The bias of a variance estimator is an important factor in applications such as hypothesis testing and construction of confidence intervals – a negatively biased variance estimator may lead to incorrect conclusions, and a positive bias is conservative hence preferable. In this work, we show that the (co-)variance estimate in DeLong’s approach is always positively biased. More specifically, the difference matrix between the expectation of the estimated covariance and the true covariance is a positive semi-definite matrix. This bias is non-negligible when the sample size is small, and quickly diminishes as the sample size increases. Our method relies on constructing, from the AUC kernel, a random variable whose (co-)variance matrix coincides with the bias, thereby establishing the claim. We also discuss alternative approaches to AUC variance estimation that may potentially reduce the bias.

Superpixels meet essential spectra for fast Raman hyperspectral microimaging.

In the context of spectral unmixing, essential information corresponds to the most linearly dissimilar rows and/or columns of a two-way data matrix which are indispensable to reproduce the full data matrix in a convex linear way. Essential information has recently been shown accessible on-the-fly via a decomposition of the measured spectra in the Fourier domain and has opened new perspectives for fast Raman hyperspectral microimaging. In addition, when some spatial prior is available about the sample, such as the existence of homogeneous objects in the image, further acceleration for the data acquisition procedure can be achieved by using superpixels. The expected gain in acquisition time is shown to be around three order of magnitude on simulated and real data with very limited distortions of the estimated spectrum of each object composing the images.