Coefficients Of Linear Combination Research Articles

N-Euler mathematical modelling and numerical simulation of liquid–gas–solid flows

Three phase flows are omnipresent in industrial as well as natural configurations. Understanding the behaviour of solid particles interacting with liquid–air flows can be of great interest for both topics. In this paper we present a new liquid–gas–solid modelling technique based on the hybrid method combining liquid–gas two-fluid phase-average approach and probability density function (PDF) methods for solid dispersed phases. The PDF approach is based on single particle dynamic equation taking into account its interaction with more than one fluid and separate stochastic Lagrangian equations for each fluid phase velocity seen by the particles. This method does not assume the carrier phases typology. The solid particles can interact with bubbles, droplets, pockets and stratified flow through drag only (other interaction forces are supposed to be negligible for our cases). In this work, it is assumed that the total drag applied to the particle is a linear combination of the drags computed if the particles were interacting separately with each fluid phases. Finding the linear combination coefficient represent the main modelling step. Particle collisions and particle turbulent dispersion are taken into account in the model. Dispersed bubbles can undergo coalescence and fragmentation. The effect of all these sub-models is studied in the comparison with experimental data.The fluid and particle equations are first derived before introducing the appropriate coupling terms. Then, the closure terms for turbulence and multiphase drag are introduced. The model is implemented in neptune_cfd, a finite volume solver developed by EDF, CEA, IRSN and Framatome which allows for the numerical resolution of separate Eulerian equations (mass, momentum and energy) for n phases coupled by interfacial transfer terms. The model is then compared against experimental data obtained in a bubble column charged with particles. The results obtained with it are satisfactory and enable us to study more in details its hypothesis and to confirm comments made in the first section. Eventually, the model is tested on an industrial case which shows its efficiency.

Numerical scattering amplitudes with pySecDec

We present a major update of the program pySecDec, a toolbox for the evaluation of dimensionally regulated parameter integrals. The new version enables the evaluation of multi-loop integrals as well as amplitudes in a highly distributed and flexible way, optionally on GPUs. The program has been optimised and runs up to an order of magnitude faster than the previous release. A new integration procedure that utilises construction-free median Quasi-Monte Carlo rules is implemented. The median lattice rules can outperform our previous component-by-component rules by a factor of 5 and remove the limitation on the maximum number of sampling points. The expansion by regions procedures have been extended to support Feynman integrals with numerators, and functions for automatically determining when and how analytic regulators should be introduced are now available. The new features and performance are illustrated with several examples. Program summaryProgram Title: pySecDecCPC Library link to program files:https://doi.org/10.17632/dnrkf5jxzh.4Developer's repository link:https://github.com/gudrunhe/secdec, https://secdec.readthedocs.io (Online documentation)Licensing provisions: GNU Public License v3Programming language: Python, Form, C++, CudaExternal routines/libraries:GSL [1], NumPy [2], SymPy [3], Nauty [4], Cuba [5], Form [6], GiNaC and CLN [7], Normaliz [8], GMP [9].Journal reference of previous version: Comput. Phys. Commun. 273 (2022) 108267 [1].Does the new version supersede the previous version?: Yes.Nature of problem: Scattering amplitudes at higher orders in perturbation theory are typically represented as a linear combination of coefficients — containing the kinematic invariants and the space-time dimension — multiplied with loop integrals which contain singularities and whose analytic representation might be unknown.Solution method: Extraction of singularities in the dimensional regularization parameter as well as in analytic regulators for potential spurious singularities is done using sector decomposition. The combined evaluation of the integrals with their coefficients is performed in an efficient way.Restrictions: Depending on the complexity of the problem, limited by memory and CPU/GPU time.

Synthetic Robust Model Predictive Control With Input Mapping for Constrained Visual Servoing

This paper proposes a synthetic robust model predictive control method with input mapping for the image-based visual servoing problem with constraints, where the novel control law is constructed by the robust control law designed offline and the online linear compensation of the past data. This proposed method can overcome the conservatism of robust model predictive control and reduce the online computational burden. The input mapping method is suitable for the image-based visual servoing system with no requirement of the slow time-varying model or time-invariant model as most adaptive control methods need. Its linear combination coefficients can be online optimized by solving a quadratic programming problem. The stability of the visual servoing system under our proposed method is proven, and its convergence speed is demonstrated to be faster than the traditional robust model predictive control. A real-time experiment on a six-degree-of-freedom manipulator with eye-in-hand construction is designed to evaluate the proposed method. The results indicate that besides the ability to handle the constraint and the singularity problem, our proposed method provides a faster convergence rate than several classic robust control methods, and improves the computational efficiency by an order of magnitude compared with the online robust predictive control method.

The method of fundamental solutions for electromagnetic scattering by a perfect conductor in chiral environment

The electromagnetic scattering problem for a time-harmonic plane wave by a perfectly conductive body embedded in a chiral medium is considered. Potentials in terms of the fundamental solution in dyadic form for chiral media are defined. The well-posedness of the scattering problem is studied using defined potentials in terms of the fundamental solution for chiral environment and the boundary integral operators associated with them. An extension of the method of fundamental solutions for electromagnetic scattering in chiral media is applied in order to approximate the solution. The electric scattered field is approximated by a finite linear combination of the dyadic fundamental solutions of the equation governing the problem for singularities placed on an auxiliary surface outside the domain of the problem and for unknown coefficients determined by the boundary conditions. Density properties on the surface of the scatterer are proven for a defined system of functions consisting of the tangential components of the dyadic fundamental solution. These density properties together with the well-posedness of the scattering problem are used to reduce the approximation of the solution to the approximation of the known boundary data. The linear system obtained from the boundary conditions in order to determine the appropriate unknown coefficients of the finite linear combination is presented. Using these results we approximate the far-field patterns and the scattering cross section. Numerical results for the special case of a spherical scatterer and an ellipsoidal scatterer are presented.

RILS-ROLS: robust symbolic regression via iterated local search and ordinary least squares

In this paper, we solve the well-known symbolic regression problem that has been intensively studied and has a wide range of applications. To solve it, we propose an efficient metaheuristic-based approach, called RILS-ROLS. RILS-ROLS is based on the following two elements: (i) iterated local search, which is the method backbone, mainly solving combinatorial and some continuous aspects of the problem; (ii) ordinary least squares method, which focuses on the continuous aspect of the search space—it efficiently determines the best—fitting coefficients of linear combinations within solution equations. In addition, we introduce a novel fitness function that combines important model quality measures: R^2 score, RMSE score, size of the model (or model complexity), and carefully designed local search, which allows systematic search in proximity to candidate solution. Experiments are conducted on the two well-known ground-truth benchmark sets from literature: Feynman and Strogatz. RILS-ROLS was compared to 14 other competitors from the literature. Our method outperformed all 14 competitors with respect to the symbolic solution rate under varying levels of noise. We observed the robustness of the method with respect to noise, as the symbolic solution rate decreases relatively slowly with increasing noise. Statistical analysis of the obtained experimental results confirmed that RILS-ROLS is a new state-of-the-art method for solving the problem of symbolic regression on datasets whose target variable is modelled as a closed-form equation with allowed operators. In addition to evaluation on known ground-truth datasets, we introduced a new randomly generated set of problem instances. The goal of this set of instances was to test the sensitivity of our method with respect to incremental equation sizes under different levels of noise. We have also proposed a parallelized extension of RILS-ROLS that has proven adequate in solving several very large instances with 1 million records and up to 15 input variables.

Feynman integrals of Grassmannians

We embed Feynman integrals in the subvarieties of Grassmannians through homogenization of the integrands in projective space, then obtain Gel'fand-Kapranov-Zelevinsky systems satisfied by those scalar integrals. The Feynman integral can be written as linear combinations of the hypergeometric functions of a fundamental solution system in neighborhoods of regular singularities of the Gel'fand-Kapranov-Zelevinsky system, whose linear combination coefficients are determined by the integral on an ordinary point or some regular singularities. Taking some Feynman diagrams as examples, we elucidate in detail how to obtain the fundamental solution systems of Feynman integrals in neighborhoods of regular singularities. Furthermore we also present the parametric representations of Feynman integrals of the two-loop self-energy diagrams that are convenient to embed in the subvarieties of Grassmannians.

Single- and multi-objective optimization of an aircraft hot-air anti-icing system based on Reduced Order Method

Geometric optimization of piccolo tube provides a cost-effective approach to shorten the design circle of hot-air anti-icing system and maximize the utilization efficiency of bleed air. An optimization methodology for aircraft hot-air anti-icing systems based on Reduced Order Method (ROM) is developed. ROM based on Proper Orthogonal Decomposition (POD) and Radial Basis Function neural network (RBF) is constructed to evaluate objective and constraint functions of single- and multi-objective optimizations. POD is adopted for data compression and characteristics extraction for the anti-icing performance snapshot matrix. Then, a lower-dimensional approximation for the snapshot matrix is derived from the projection subspace consisting of a set of basis modes. RBF neural network is introduced to construct the mapping between the design variables of piccolo tube geometric configuration samples and the linear combination coefficients of basis modes. The piccolo tube is parameterized by five design variables and is optimized by the developed methodology. The predicted results indicate that the constructed ROM can provide the distributions of surface temperature and runback water with high accuracy and computational efficiency. The optimal results indicate that the developed optimization methodology is efficient and reliable for handling single- and multi-objective design problems of aircraft piccolo tube hot-air anti-icing systems.

PCA-Based Adaptive Training-Feedback Scheme in Time-Varying FDD Massive MIMO Systems

For massive multiple-input multiple-output (MIMO) systems, the real-time channel state information (CSI) acquisition is crucial but difficult in fast time-varying scenarios, especially for downlink (DL) channels in frequency division duplex (FDD) systems. This paper proposes an adaptive training-feedback scheme to estimate the CSI of DL channels. Specifically, first, base station (BS) determines a subspace containing uplink (UL) channel and an orthogonal normal basis of this subspace by using received signals in UL channel and the principle component analysis (PCA) technique. Second, by using the spatial reciprocity, it is found that the obtained subspace above also contains the DL channel vector. Thus, regarding the basis as pilots, the BS transmits pilots to mobile user (MU), and the user estimates received signals, feeds back them to the BS. Finally, according to information of the feedback, the BS can construct the DL channel vector. In this scheme, the pilots are adaptive to the change of the UL channel. Furthermore, the times of training is the dimension of the subspace, and feedback overhead is the coefficients of linear combination of DL channel vector under the basis only. Thus, cost of training and feedback can be greatly reduced. The simulation results show that the performance of the proposed scheme can approach the optimal scheme with very few training times and feedback overhead at high speed.

Quantum Gaussian filter for exploring ground-state properties

Filter methods realize a projection from a superposed quantum state onto a target state, which can be efficient if two states have sufficient overlap. Here we propose a quantum Gaussian filter (QGF) with the filter operator being a Gaussian function of the system Hamiltonian. A hybrid quantum-classical algorithm feasible on near-term quantum computers is developed, which implements the quantum Gaussian filter as a linear combination of Hamiltonian evolution at various times. Remarkably, the linear combination coefficients are determined classically and can be optimized in the postprocessing procedure. Compared to the existing filter algorithms whose coefficients are given in advance, our method is more flexible in practice under given quantum resources with the help of postprocessing on classical computers. We demonstrate the quantum Gaussian filter algorithm for the quantum Ising model with numeral simulations under noises. We also propose an alternative full quantum approach that implements a QGF with an ancillary continuous-variable mode.

A rate-sensitive and pressure-dependent failure criterion for hail ice

Hail is a common natural threat to humans, constructions, and any facilities exposed to it, while there appears to be limited models that are able to accurately capture the mechanical behavior of hail ice, especially its dynamic response to impact. To address this, a rate-sensitive pressure-dependent failure criterion was proposed using a linear combination of the rate-dependent von-Mises equivalent stress and the hydrostatic pressure. After determining the linear combination coefficient via comparison between a series of simulations and experiments, the proposed criterion was used to predict the peak force during impact, for ice balls of different diameters and impact speeds. Both the peak forces and failure patterns during impact predicted using the proposed criterion correlate with experimental results reasonably well, indicating that the proposed criterion is able to accurately capture the dynamic response of ice to impact.

An Optima Combination Method of Three-Frequency Real-Time Cycle Slip Detection for Non-Normal Ionospheric Variation Data

Linear combinations of triple-frequency help improve the performance of cycle slip detection for high-precision positioning using a single receiver; however, the position can be easily misjudged under ionospheric scintillation conditions or low sampling rates. We propose a method, which is developed specially for the datasets under ionospheric scintillation conditions or low sampling rates, to detect the triple-frequency cycle slips in real-time based on optimal linear combination coefficients and ionospheric range delay. Detection formulas are derived from the triple-frequency geometry-free code-phase combination, and ionospheric range delay is estimated by the wide lane combination. In addition, the principle used to select an optimal linear phase combination coefficient is derived, and the optimal linear coefficient suitable under high ionospheric activity conditions is provided. Finally, the data collected from self-build stations JYPS and NQ01 are used to test the performance of the method. The results demonstrate that the improved method can be used to detect all combinations of cycle slips in real-time, even under conditions of ionospheric scintillation or a sampling period exceeding 10 s.

Factor Research Based on Multi-index Gray Correlation Analysis Correlation Analysis

Breast cancer is one of the most common and fatal cancers in the world. Therefore, this paper uses data mining and prediction technology, which is of great significance. In this paper, firstly, the relevant data were collected, and the Pearson correlation coefficients of 729 molecular descriptors in 1974 compounds were calculated respectively, and the correlation coefficient distribution map was obtained. Through observation, all the molecular descriptors were 0 elements. Then the grey correlation analysis method was used to analyze the correlation degree, and the grey correlation value between the information of 729 molecular descriptors and the bioactivity value of ER α was obtained. Then, making use of the advantage of canonical correlation analysis in feature extraction, according to the feature selection of linear combination coefficient, the molecular descriptors with the most significant effect on biological activity were selected.

Analysis of Biphenylene and Benzo{3,4}cyclobuta{1,2-c}thiophene Molecular Orbital Structure using the Huckel Method

The Huckel method is an old fashion method to predict the molecular orbital and energies of  electrons in a conjugated molecule. Although Huckel`s theory`s approximations are relatively crude, its general results are still reasonable compared to the advanced computing method and experimental results for many molecules. This paper describes the Huckel calculation of biphenylene and benzo{3,4}cyclobuta{1,2-c}thiophene using the HuLis software. The benzo{3,4}cyclobuta{1,2-c}thiophene is a derivative of biphenylene, in which case one of the benzene rings is replaced by a thiophene ring. This change produces new electronic properties that are interesting to study. This work focused on calculating those molecules on energy levels diagrams, linear combination coefficient of molecular orbitals, molecular orbital shape, energy gap, resonance energy, bond-order, bond length, and charge distribution (π electron population). Besides, we calculate the harmonic oscillator measure of aromaticity (HOMA) parameter to study the Huckel method`s validity.

A GROUND MOTION SYNTHESIS METHOD FOR MATCHING MULTI-OBJECTIVE PARAMETERS

Ground motion synthesis methods provide input time histories for structural seismic design and performance evaluation. The existing synthesis methods can only match the target spectrum to consider the frequency spectrum and amplitude of the ground motion, but cannot consider the duration characteristics. To synthesize ground motions which matches the three elements of ground motions for a specific area, a method that incorporates machine learning is proposed. In this method, the data-driven principal component analysis is used to extract the characteristic mother waves from the actual ground motion database of the target area. The target response spectrum and duration are obtained by the ground motion prediction equation of the region. The multi-objective genetic algorithm is applied to solve the linear combination coefficient of the mother waves, so that the combined ground motion can match the preset error standard and the multi-objective parameters of the regional ground motion. The method is verified for the 2019 Ms 6.0 Changning earthquake in Sichuan Province. The results show that, because the proposed method is driven by the actual ground motion data in the target area, the synthetic ground motion matches the demand of the target spectrum and the duration characteristics of regional ground motions, which can provide more reasonable ground motion inputs for seismic analyses considering regional seismic characteristics.

Eigenfaces-Based Steganography.

In this paper we propose a novel transform domain steganography technique—hiding a message in components of linear combination of high order eigenfaces vectors. By high order we mean eigenvectors responsible for dimensions with low amount of overall image variance, which are usually related to high-frequency parameters of image (details). The study found that when the method was trained on large enough data sets, image quality was nearly unaffected by modification of some linear combination coefficients used as PCA-based features. The proposed method is only limited to facial images, but in the era of overwhelming influence of social media, hundreds of thousands of selfies uploaded every day to social networks do not arouse any suspicion as a potential steganography communication channel. From our best knowledge there is no description of any popular steganography method that utilizes eigenfaces image domain. Due to this fact we have performed extensive evaluation of our method using at least 200,000 facial images for training and robustness evaluation of proposed approach. The obtained results are very promising. What is more, our numerical comparison with other state-of-the-art algorithms proved that eigenfaces-based steganography is among most robust methods against compression attack. The proposed research can be reproduced because we use publicly accessible data set and our implementation can be downloaded.

Generalized canonical transform method for radio occultation sounding with improved retrieval in the presence of horizontal gradients

Abstract. By now, a series of advanced wave optical approaches to the processing of radio occultation (RO) observations are widely used. In particular, the canonical transform (CT) method and its further developments need to be mentioned. The latter include the full spectrum inversion (FSI) method, the geometric optical phase matching (PM) method, and the general approach based on the Fourier integral operators (FIOs), also referred to as the CT type 2 (CT2) method. The general idea of these methods is the application of a canonical transform that changes the coordinates in the phase space from time and Doppler frequency to impact parameter and bending angle. For the spherically symmetric atmosphere, the impact parameter, being invariant for each ray, is a unique coordinate of the ray manifold. Therefore, the derivative of the phase of the wave field in the transformed space is directly linked to the bending angle as a single-valued function of the impact parameter. However, in the presence of horizontal gradients, this approach may not work. Here we introduce a further generalization of the CT methods in order to reduce the errors due to horizontal gradients. We describe, in particular, the modified CT2 method, denoted CT2A, which complements the former with one more affine transform: a new coordinate that is a linear combination of the impact parameter and bending angle. The linear combination coefficient is a tunable parameter. We derive the explicit formulas for the CT2A and develop the updated numerical algorithm. For testing the method, we performed statistical analyses based on RO retrievals from data acquired by the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) and collocated analysis profiles of the European Centre for Medium-Range Weather Forecasts (ECMWF). We demonstrate that it is possible to find a reasonably optimal value of the new tunable CT2A parameter that minimizes the root mean square difference between the RO retrieved and the ECMWF refractivity in the lower troposphere and allows the practical realization of the improved capability to cope with horizontal gradients and serve as the basis of a new quality control procedure.

A Neural Network Based on the Johnson S U Translation System and Related Application to Electromyogram Classification

Electromyogram (EMG) classification is a key technique in EMG-based control systems. Existing EMG classification methods, which do not consider EMG features that have distribution with skewness and kurtosis, have limitations such as the requirement to tune hyperparameters. In this paper, we propose a neural network based on the Johnson SU translation system that is capable of representing distributions with skewness and kurtosis. The Johnson system is a normalizing translation that transforms non-normal distribution data into normal distribution data, thereby enabling the representation of a wide range of distributions. In this study, a discriminative model based on the multivariate Johnson SU translation system is transformed into a linear combination of coefficients and input vectors using log-linearization; then, it is incorporated into a neural network structure. This allows the calculation of the posterior probability of each class given the input vectors and the determination of model parameters as weight coefficients of the network. The uniqueness of convergence of the network learning is theoretically guaranteed. In the experiments, the suitability of the proposed network for distributions including skewness and kurtosis was evaluated using artificially generated data. Its applicability to real biological data was also evaluated via EMG classification experiments. The results showed that the proposed network achieved high classification performance (e.g., 99.973% accuracy using Khushaba’s dataset) without the need for hyperparameter optimization.

Calculation of rubber-metal silent-blocks under quasi-static loading

Abstract. In this paper, an algorithm for calculating rubber-metal silent blocks (hinges) under the action of a lateral quasi-static load is presented. Silent blocks of a welded type made of new brands of rubbers, which are widely used in vibration machines of various types as elastic links, are considered. A calculation is given for a very long hinge, for which the length is large compared to its outer diameter. In the calculation, it was assumed that there are no axial displacements, and the angular and radial displacements can be represented as a product of arbitrary functions of the radial coordinate and the sine and cosine of the angular coordinate, respectively. The relationship between these functions is obtained from the condition of rubber incompressibility. From the condition of the minimum total energy of the system, we have a linear inhomogeneous differential equation of the third order for one of these functions. By solving it under known boundary conditions, we obtain final expressions for the radial and angular displacement, and, consequently, for the displacement of the inner cage. With taking these expressions into account, a solution was also obtained for the hinge, the length of which cannot be considered infinite in comparison with its diameter. In this case, axial displacements should also be considered. Besides, it is assumed that the functions of the radial coordinate for the radial and angular displacement can be represented as a linear combination of the corresponding functions for the long hinge. The corresponding function for axial displacement can be found from the condition of volume constancy. The linear combination coefficients are obtained from a system of two linear algebraic equations, to which the minimum condition for the total energy of the system leads. The exact expression for the movement for the short hinge is rather cumbersome. But for the most common sizes of rubber-metal hinges, you can use a series expansion of the expression for displacement and thus get a fairly simple formula. By comparing the resulting expression with the expression for displacement of the long hinge, you can see that the formula for the infinitely long hinge can only be used if a certain condition is met that binds the dimensions of the hinge. At the end of the paper, an example of calculating a rubber-metal element ШРМ-102, which is under the action of a radial load, is given. The rubber layer in it is made of a new medium-filled rubber made of natural rubber. The obtained value of the displacement of the inner cage is in good agreement with the experimental data.

Application of Supporting Integral Curves and Generalized Invariant Unbiased Estimation for the Study of a Multidimensional Dynamical System

The well-known methods of supporting integral curves and generalized invariant unbiased estimation are used to find numerical-analytical representations of the solution to an equation describing a dynamical system and its measured output and to compute optimal values of continuous linear functionals (numerical characteristics) of measured parameters based on incorrect data involving both a fluctuation error and a singular disturbance. A two-step method is developed for this purpose. Numerical-analytical representations depending continuously on all parameters of the system are formed at the first stage, and numerical characteristics of the system that are invariant under the singular disturbance are estimated at the second stage. The method ensures the maximum possible decomposition of the numerical procedures involved; moreover, it does not require traditional linearization or initial guess choice and does not involve the computation of spectral coefficients in finite linear combinations (with given basis functions) describing the integral curves, measured parameters, and the singular disturbance. The random and systematic errors are analyzed, an illustrative example is given, and recommendations on practical application of the results are made.

A novel B-spline method to analyze convection-diffusion-reaction problems in anisotropic inhomogeneous medium

We present a B-spline based semi-analytical technique for solving 2D convection-diffusion-reaction equations. The main feature of the presented technique is to separate the satisfaction of the conditions on the boundary and the elliptic partial differential equation inside. To be more precise, we transform the original equation into the problem with homogeneous boundary conditions and seek the approximate solution as a sum of the modified B-spline tensor products which satisfy the homogeneous boundary conditions of the problem. The cubic and quintic B-spline are used in the framework of the method. The coefficients of linear combination are determined to satisfy the governing equation. Eight numerical examples have been studied to demonstrate the high effectivity of the presented technique in solving 2D convection-diffusion-reaction problems in single and multi-connected domains.