Arbitrary Structure Research Articles

Generation of arbitrarily structured optical vortex arrays based on the epicycle model.

Optical vortex arrays (OVAs) are complex light fields with versatile structures that have been widely studied in large-capacity optical communications, optical tweezers, and optical measurements. However, generating OVAs with arbitrary structures without explicit analytical expressions remains a challenge. To address this issue, we propose an alternative scheme for customizing OVAs with arbitrary structures using an epicycle model and vortex localization techniques. This method can accurately generate an OVA with an arbitrary structure by pre-designing the positions of each vortex. The influence of the number and coordinates of the locating points on customized OVAs is discussed. Finally, the structures of the OVA and each vortex are individually shaped into specifically formed fractal shapes by combining cross-phase techniques. This unique OVA will open up novel potential applications, such as the complex manipulation of multiparticle systems and optical communication based on optical angular momentum.

Direct Discrepancy Dynamic Fit Index Cutoffs for Arbitrary Covariance Structure Models

Despite the popularity of traditional fit index cutoffs like RMSEA ≤ .06 and CFI ≥ .95, several studies have noted issues with overgeneralizing traditional cutoffs. Computational methods have been proposed to avoid overgeneralization by deriving cutoffs specifically tailored to the characteristics of the model being evaluated. Simulations show favorable performance of these methods; however, these methods support a narrow set of scenarios (e.g., certain models or response scales) and the interpretation of cutoffs is not always standardized, which affects empirical researchers’ ability to confidently and broadly adopt these methods to evaluate model fit. In this paper, we propose an extension to one recently developed computational method—dynamic fit index cutoffs—that (a) permits application to any covariance structure model (e.g., CFA, mediation, bifactor), (b) standardizes interpretation of cutoffs across any covariance structure model, and (c) supports normal, nonnormal, categorical, and missing data. Software is provided to facilitate implementation of the method.

An adaptive multi-patch isogeometric phase-field model for fatigue fracture

Fatigue fracture is one of the main causes of structural failure under cyclic loading, so accurate evaluation of fatigue fracture is very important for the design of structures subjected to cyclic loading. In this work, we propose an adaptive fatigue phase-field model within the framework of multi-patch isogeometric analysis to simulate crack nucleation and propagation in brittle materials under cyclic loading. Multiple non-uniform rational B-splines (NURBS) patches are used to exactly represent complex structures, and the Nitsche’s method is adopted to enforce the compatibility of the displacements, stresses and phase-field variables between two patches. The coupled governing equations of fatigue phase-field model are established based on the Nitsche’s method, and the selection of Nitsche’s parameters are determined from numerical experiments. A refinement-correction adaptive approach based on locally refined non-uniform rational B-splines (LR NURBS) structured mesh refinement strategy is developed to alleviate the computational burden caused by the requirement of small element size around crack surface and the large number of fatigue loading. The proposed multi-patch isogeometric phase-field model can deal with the coupling between equal/unequal length interfaces, thus the fatigue crack propagation simulation in arbitrary complex structure can be implemented. Several numerical examples are investigated to verify the practicality of the multi-patch isogeometric phase-field model and the effectiveness of the adaptive scheme.

Modifying the false discovery rate procedure based on the information theory under arbitrary correlation structure and its performance in high-dimensional genomic data

BackgroundControlling the False Discovery Rate (FDR) in Multiple Comparison Procedures (MCPs) has widespread applications in many scientific fields. Previous studies show that the correlation structure between test statistics increases the variance and bias of FDR. The objective of this study is to modify the effect of correlation in MCPs based on the information theory. We proposed three modified procedures (M1, M2, and M3) under strong, moderate, and mild assumptions based on the conditional Fisher Information of the consecutive sorted test statistics for controlling the false discovery rate under arbitrary correlation structure. The performance of the proposed procedures was compared with the Benjamini–Hochberg (BH) and Benjamini–Yekutieli (BY) procedures in simulation study and real high-dimensional data of colorectal cancer gene expressions. In the simulation study, we generated 1000 differential multivariate Gaussian features with different levels of the correlation structure and screened the significance features by the FDR controlling procedures, with strong control on the Family Wise Error Rates.ResultsWhen there was no correlation between 1000 simulated features, the performance of the BH procedure was similar to the three proposed procedures. In low to medium correlation structures the BY procedure is too conservative. The BH procedure is too liberal, and the mean number of screened features was constant at the different levels of the correlation between features. The mean number of screened features by proposed procedures was between BY and BH procedures and reduced when the correlations increased. Where the features are highly correlated the number of screened features by proposed procedures reached the Bonferroni (BF) procedure, as expected. In real data analysis the BY, BH, M1, M2, and M3 procedures were done to screen gene expressions of colorectal cancer. To fit a predictive model based on the screened features the Efficient Bayesian Logistic Regression (EBLR) model was used. The fitted EBLR models based on the screened features by M1 and M2 procedures have minimum entropies and are more efficient than BY and BH procedures.ConclusionThe modified proposed procedures based on information theory, are much more flexible than BH and BY procedures for the amount of correlation between test statistics. The modified procedures avoided screening the non-informative features and so the number of screened features reduced with the increase in the level of correlation.

Arbitrary Triangle Structure Adaptive Mean PCA and Image Recognition

Arbitrary Triangle Structure Adaptive Mean PCA and Image Recognition

Fabrication of high aspect ratio, non-line-of-sight vias in silicon carbide by a two-photon absorption method

The future of Moore’s Law for high-performance integrated circuits (ICs) is going to be driven more by advanced packaging and three-dimensional (3D) integration than by simply decreasing transistor size. 3D ICs offer low-power consumption, high-performance and a smaller footprint compared to conventional 2D ICs. The key enabling technology to 3D integration is the interposer that provides interconnects to route signals between the chiplets that comprise the IC. However, the fabrication of high-aspect ratio through wafer vias (TWVs), that provide electrical and mechanical connection between chiplets on the top and bottom of the interposer, is one of the important challenges that limit interposer performance. Current fabrication technologies are limited by tapering effects and the need for direct line of sight to the fabrication surface. These limit the possible aspect ratios of vias and require large, complicated surface traces to connect the vias to the chiplets. Here, we demonstrate the fabrication of high-aspect ratio, non-line-of-sight TWVs in silicon carbide (SiC). SiC provides better mechanical, chemical, and thermal performance than silicon (Si). The technique uses an electro-chemical etch process that utilizes two-photon absorption to create any arbitrary 3D structure in SiC allowing for direct, subsurface routing between chiplets.

Development and testing of WEASEL for least-squares neutron spectrum adjustment

A new least-squares adjustment program called WEASEL has been developed. WEASEL is implemented in Python and uses standard ASCII interfaces for user input and output, and HDF5 interfaces for cross section, covariance data, and weighting function data. WEASEL allows the user to supply a trial neutron spectrum in an arbitrary group structure. The trial neutron spectrum is re-binned into a group structure consistent with the covariance data using a weighting function that can either be read from the data library or supplied as input by the user. WEASEL performs least-squares adjustments of a single irradiation environment. The adjusted neutron spectrum, covariance matrices, and other derived quantities can then be plotted and interrogated with standard software packages.

A novel design employing arbitrary tree structure for adaptive thrsholding discrete wavelet packet transformation

A novel design employing arbitrary tree structure for adaptive thrsholding discrete wavelet packet transformation

Q-deformed rainbows: a universal simulator of free entanglement spectra

The behavior of correlations across a bipartition is an indispensable tool in diagnosing quantum phases of matter. Here we present a spin chain with position-dependent XX couplings and magnetic fields, that can reproduce arbitrary structure of free fermion correlations across a bipartition. In particular, by choosing appropriately the strength of the magnetic fields we can obtain any single particle energies of the entanglement spectrum with high fidelity. The resulting ground state can be elegantly formulated in terms of q-deformed singlets. To demonstrate the versatility of our method we consider certain examples, such as a system with homogeneous correlations and a system with correlations that follow a prime number decomposition. Hence, our entanglement simulator can be easily employed for the generation of arbitrary entanglement spectra with possible applications in quantum technologies and condensed matter physics.

Numerical Optimization Technique of Multilayer SERS Substrates

A numerical optimization technique of a three-dimensional (3D) SERS substrate with finite element analysis is proposed. Using the optical reciprocity theorem, we have shown that instead of the well-known local field enhancement criterion, it is more correct to use the Purcell factor as an objective function that determines the quality of the SERS substrate. This allows us to take into account the detail inhomogeneity of local fields in an arbitrary three-dimensional structure containing multiple emitters. We have theoretically shown that employment of a 3D CNT structure as a nanoparticle substrate instead of a nanoparticle monolayer allows one to achieve the enhancement of the SERS signal.

Estimation of extreme multivariate expectiles with functional covariates

The present article is devoted to the semi-parametric estimation of multivariate expectiles for extreme levels. The considered multivariate risk measures also include the possible conditioning with respect to a functional covariate, belonging to an infinite-dimensional space. By using the first order optimality condition, we interpret these expectiles as solutions of a multidimensional nonlinear optimum problem. Then the inference is based on a minimization algorithm of gradient descent type, coupled with consistent kernel estimations of our key statistical quantities such as conditional quantiles, conditional tail index and conditional tail dependence functions. The method is valid for equivalently heavy-tailed marginals and under a multivariate regular variation condition on the underlying unknown random vector with arbitrary dependence structure. Our main result establishes the consistency in probability of the optimum approximated solution vectors with a speed rate. This allows us to estimate the global computational cost of the whole procedure according to the data sample size. The finite-sample performance of our methodology is provided via a numerical illustration of simulated datasets.

An improved algorithm for solving inverse problems of the dynamics of robotic devices at SCAS KIDYM

The paper presents the results of studies of an analytical algorithm for constructing a resolving system of linear equations to determine the driving forces and moments in the links of robotic devices of arbitrary structure during movement. This algorithm is implemented as an analytical algorithm in a special computer algebra system (SCAS) KiDyM, on the basis of which numerical calculations of the specified forces and moments are generated in the process of performing work processes, positioning mechanisms in the required positions, parking movements, etc. The KiDyM software package is used to solve mechanics problems of a wide class of discrete mechanical systems of arbitrary structure and type of motion for engineering and scientific calculations. A theoretical justification for the developed new approach, analytical and numerical proof of its effectiveness from the point of view of the process of automatically obtaining resolving equations, computational efficiency and accuracy of results are presented. The proposed algorithm is the result of the development of an algorithm that was previously implemented in SCAS KiDyM and was similar in purpose. Unlike the previously implemented algorithm, which generates a resolving system of equations after constructing the dynamic equations, the new algorithm is built into the process of generating dynamic equations - it sorts the model elements - inertial, dissipative, elastic and force elements of known forces and moments form the right side, and force elements with unknown forces and moments, they form a matrix of the left side of equations that solve the inverse problem of dynamics. The article gives a comparative analytical conclusion of one and another algorithm and shows the coincidence of the resulting equations. Also, using examples of calculations of the inverse problem of the dynamics of a portal crane and two 6-degree manipulators, the advantages of the new approach are shown.

Towards effective information content assessment: Analytical derivation of information loss in the reconstruction of random fields with model uncertainty

Structures are abundant in both natural and human-made environments and usually studied in the form of images or scattering patterns. To characterize structures a huge variety of descriptors is available spanning from porosity to radial and correlation functions. In addition to morphological structural analysis, such descriptors are necessary for stochastic reconstructions, stationarity and representativity analysis. The most important characteristic of any such descriptor is its information content — or its ability to describe the structure at hand. For example, from crystallography it is well known that experimentally measurable S2 correlation function lacks necessary information content to describe majority of structures. The information content of this function can be assessed using Monte-Carlo methods only for very small 2D images due to computational expenses. Some indirect quantitative approaches for this and other correlation function were also proposed. Yet, to date no methodology to obtain information content for arbitrary 2/3D image is available. In this work, we make a step towards developing a general framework to perform such computations analytically. We show, that one can assess the entropy of a perturbed random field and that stochastic perturbation of fields’ correlation function decreases its information content. In addition to analytical expression, we demonstrate that different regions of correlation function are in different extent informative and sensitive for perturbation. Proposed model bridges the gap between descriptor-based heterogeneous media reconstruction and information theory and opens way for computationally effective way to compute information content of any descriptor as applied to arbitrary structure.

Low-cycle fatigue performance and life prediction of a P/M nickel-based superalloy with artificial surface defect at elevated temperature

P/M nickel-based superalloys are widely used in turbine disks, defects such as inclusions and surface scratches inevitably arisen from manufacturing process will exert negative influences on the low-cycle fatigue performance of superalloys and make traditional life prediction method no longer reliable. The residual fatigue life in presence of defect is an important performance index for disc alloy in damage tolerance design criteria. In this work, LCF tests of FGH96 specimens with artificial surface defect were conducted at 600℃, 650℃, 700℃ and room temperature, the size of the defect is determined in accordance with the minimum flaw size which can be detected by NDT technique. The results show that the LCF life of the specimens with artificial surface defect decreases significantly with the increase of temperature and size of defect. Microscopic characterization technique SEM and EDS were executed to investigate the failure mechanism of the specimens, different mechanisms of crack initiation from artificial surface defect at room and elevated temperature were discussed. And then life prediction based on fracture mechanics was carried out by ABAQUS-FRANC3D co-simulation. This method allows that SIF can be conveniently calculated by finite element method and it is applicable to analysis of arbitrary engineering structure. Good life prediction results which fall within double dispersion band of experimental lives were obtained at elevated temperature, but the predicted life is excessively conservative at room temperature because the crack initiation process accounts for a large proportion of fatigue life. It seems that life prediction method based on fracture mechanics is more applicable to specimens with surface defect at elevated temperature due to the shorter crack initiation process. This work has reference significance to the damage tolerance analysis of turbine disks.

Hardware, methodology and applications of 2+D backscatter Mössbauer spectroscopy with simultaneous x-ray and γ-ray detection

A unique method is presented for the acquisition and analysis of 57Fe backscatter Mössbauer spectra with simultaneous detection of the resonant 14.4 keV γ-rays and the characteristic 6.4 keV x-rays, using a custom-built multi-parameter analyser constructed on the basis of commercial analogue to digital converters and high-speed digital latches. The system allows for the simultaneous registration of Doppler-modulation velocities and photon energies, with up to 4096 and 8192 digital channels respectively. This arrangement is in contrast to most related systems, which detect at a single narrow energy window per detector. Samples of arbitrary atomic structure, morphology and surface topography can be studied without altering the setup or the analysis procedure, provided that the samples are at least micrometre sized. The hardware and software that are used to acquire data with minimal dead time are described and the custom and self-contained methods for post-measurement energy discrimination, background correction and velocity-axis folding are discussed. The data are fit using a general Hamiltonian model for the nuclear energy levels of 57Fe and a quantum mechanical description of the angular momentum coupling is utilised, with consideration of the crystalline and chemical disorder of the sample under examination. Three examples of distinct magnetic systems, with thicknesses ranging from m to 6 mm, that were studied using this method are presented, these are: an amorphous CoFeB-based ribbon with ultra-soft coercivity for high-frequency applications, magnetically hard Nd-Fe-B thick films on Si substrates, examined in both as-deposited and annealed states, and a sample from the nickel-rich iron meteorite NWA 6259 that contains the atomically ordered, elevated coercivity, phase of FeNi, tetrataenite. The wide applicability and usefulness of this method is thus demonstrated on three distinct sample morphologies that required little to no surface preparation prior to examination.

Multi-node wind speed forecasting based on a novel dynamic spatial–temporal graph network

Providing reliable and accurate wind speed predictions for the power system ensures a stable power output. However, the high wind speed uncertainty and the complex spatial–temporal correlation between wind turbines still make wind speed prediction a significant challenge. This paper proposes a novel dynamic spatial–temporal graph network (DSTGN) to make wind speed predictions by accurately capturing the dynamic dependencies of multi-turbine on an arbitrary graph structure. DSTGN adopts an extensible and serialized structure consisting of stacked dynamic spatial–temporal blocks to model dependencies. In spatial dependency extraction, a graph generation module is used in the spatial block to produce static and dynamic spatial information. A parameterized adjacency matrix expands the spatial hypothesis space rather than being limited by the distance between turbines. In temporal dependency extraction, the multi-head attention mechanism models temporal associations of diverse time horizons. Based on publicly available wind datasets, extensive experimental results showed that the proposed model significantly improves performance. Compared to recent state-of-the-art models, MAE, RMSE and MAPE are improved over 4.57%, 4.25% and 8.31%, respectively. Furthermore, through ablation studies, we verified the benefits of each component of the proposed model, especially the positive role of graph sampling in improving performance.

Method and finite element verification of indentation calculation for a novel air-spring mattress: for estimating spinal alignment in sleep postures

PurposeThis study aimed to develop a method to calculate the mattress indentation for further estimating spinal alignment.Design/methodology/approachA universal indentation calculation model is derived based on the system theory, and the deformation characteristics of each component are analyzed by the finite element (FE) model of a partial air-spring mattress under the initial air pressure of 0.01–0.025 MPa. Finally, the calculation error of the model is verified.FindingsThe results indicate that the indentation calculation model could describe the stain of a mattress given the load and the constitutive model of each element. In addition, the FE model of a partial air-spring mattress can be used for further simulation analysis with an error of 1.47–3.42 mm. Furthermore, the deformation of the series system is mainly contributed by the air spring and the components directly in contact with it, while the top component is mainly deflection deformation. In addition, the error of the calculation model is 2.17–5.59 mm on the condition of 0.01–0.025 MPa, satisfying the engineering application. Finally, the supine spinal alignment is successfully extracted from the mattress indentation.Research limitations/implicationsThe limitation of this study is that it needs to verify the practicality of the indentation calculation model for the Bonnier spiral spring mattress. The main feature of the Bonnier spring mattress is that all springs are connected, so the mattress deflection and neighborhood effect are more significant than those of the air-spring mattress. Therefore, the applicability of the model needs to be tested. Moreover, it is worth further research to reduce the deformation error of each component.Practical implicationsAs part of the series of studies on the intelligent air-spring mattress, the indentation-based evaluation method of spinal alignment in sleep postures will be studied for hardness and intelligent regulation based on this study.Social implicationsThe results of this research are ultimately used for the intelligent adjustment of air-spring mattresses, which automatically adjusts the hardness according to the user's sleep postures and spinal alignment, thus maintaining optimal spinal biomechanics. The successful application of this result could improve the sleep health of the general public.Originality/valueBased on the series system theory, an indentation calculation model for mattresses with arbitrary structure is proposed, overcoming the dependence of parameters on materials and their combinations when fitting the Burgers model. Further, the spinal alignment in supine posture is extracted from the indentation, laying a theoretical foundation for further recognition and adjustment of the spinal alignment of the intelligent mattress.

Some Practical Applications of Discretely Tunable Couplers’ Matrix Model

The findings of a research of the practical application of a previously developed model of a decametric waves discrete coupler are presented. Due to the high accuracy achieved in describing the transforming properties of Coupler in the operating frequency range, together with the apparatus of the theory of complex variables, in particular with the method of conformal maps of fractional linear functions, it was possible to solve a number of applied problems. A method for calculating the area of consistent loads of discretely tunable power circuits of arbitrary structure has been developed. For completeness of the result, the case of matching a generator with a complex value of internal resistance with a given quality (with an acceptable value of the traveling wave coefficient) has been considered. The proposed approach to matching assumes that for any possible antenna load there must be appropriate combinations of discretely tunable elements of the Coupler power circuit that ensure matching with a given quality. The design ratio for images of arbitrary circles and straight lines conformally mapped by a matching quadrilateral to a given complex domain (i.e., expressions for calculating the coordinates of the circle center and its radius, as well as coefficients of the equation of straight lines) has been obtained. Studies of the matching properties of various circuits implemented on discrete elements have been carried out. The results of this study are important when choosing the structural design of the Coupler power circuit. Calculation formulas are obtained that allow us to estimate the relative losses of active power in the Coupler power circuit. This contributes to the reasonable choice of the best configuration option from several, similar in quality matching, thereby avoiding complicated temperature settings of the circuit elements. An exhaustive search method of tuning the discrete contour of the Coupler has been proposed, which is extremely simple and does not require heavy calculations with matrices and complex numbers.

3D nanoprinting for fiber-integrated achromatic diffractive lens.

Achromatic performance is crucial for numerous multi-wavelength optical fiber applications, including endoscopic imaging and fiber sensing. This paper presents the design and nanoprinting of a fiber-integrated achromatic diffractive lens within the visible spectrum (450-650 nm). The 3D nanoprinting is achieved by a high-resolution direct laser writing technology, overcoming limitations in the optical performance caused by the lack of an arbitrary 3D structure writing capability and an insufficient feature resolution in the current manufacturing technology for visible light broadband achromatic diffractive lenses. A three-step optimization algorithm is proposed to effectively balance optical performance with writing difficulty. The characterization results demonstrate excellent achromatic focusing performance, paving the way towards the development of nanoprinted flat optical devices for applications such as optical fiber traps, miniature illumination systems, and integrated photonic chips.

Low-Overhead RF Impedance Measurement Using Periodic Structures

Due to the need for higher reliability and performance from RF circuits, multi-port reflectometers are increasingly used as low-overhead impedance monitors. In this work, using periodic structures as multi-ports is proposed. Periodic structures impose a new constraint on the multi-port theory and simplify it significantly. This simplification leads to closed form solution for calibration and measurement procedures. The closed-form solution also shows that any arbitrary periodic structure will always have a unique solution for both procedures. Therefore, the proposed technique does not rely on frequency-dependent behavior of devices, such as directivity and phase shift to measure impedance. This fact leads to increased bandwidth and simplified design procedure. In addition, proposed multi-port structures can be calibrated by using fewer known loads than existing multi-port techniques. This fact, coupled with the closed-form solution, reduces computation overhead and test time. The theory and its robustness against non-idealities, such as part-to-part variation, are verified with Monte-Carlo simulations. A practical embodiment of the technique is demonstrated with EM simulations and hardware experiments. In this embodiment, the multi-port structure is embedded into an LC matching network. Hardware experiments show that the embedded multi-port structure can measure test loads with high accuracy from 1.5 GHz to 3.5 GHz, without degrading matching network performance.