Linear Solution Research Articles

NOUVELLE SOLUTION D'ACTIONNEUR LINÉAIRE À FORCE ÉLEVÉE À AIMANTS PERMANENTS

This paper presents a new design, numerical modeling, and experimental validation of a high-force linear actuator with permanent magnets. The proposed linear actuator solution is designed similarly to a classical electromagnet but is equipped with NdFeB permanent magnets and an auxiliary magnetic circuit. These auxiliary components produce a high static holding force when the actuator functions in one of its main operating positions. Like most linear actuators, the new solution has two operating positions: maximum air gap (open position) and minimum air gap (close position). This article aims to present the novel design, the working principle, and the implementation and experimental results of the actuator. The numerical solution of the actuator was obtained using the FEMM package, in which the electromagnetic parameters were computed. The force produced by the actuator was determined using the LUA script incorporated in FEMM. Numerical integration obtained other mechanical parameters (acceleration, work, and speed) with MATLAB.

Deposition patterns formed by the evaporation of linear diblock copolymer solution nanodroplets on solid surfaces.

The evaporation-induced deposition pattern of the linear diblock copolymer solution has attracted attention in recent years. Given its critical applications, we study deposition patterns of the linear diblock copolymer solution nanodroplet on a solid surface (the wall) by molecular dynamics simulations. This study focuses on the influence of the nonbonded interaction strength, including the interaction between the wall and polymer blocks (ɛAW and ɛBW), the interaction between the solvent and the wall (ɛSW), and the interaction between polymer blocks (ɛAB). Conditions leading to diverse deposition patterns are explored, including the coffee-ring and the volcano-like structures. The formation of the coffee-ring structure is attributed to receding interfaces, the heterogeneity inside the droplet, and the self-assembly of polymer chains. This study contributes to the establishment of guidelines for designing deposition patterns of the linear diblock copolymer solution nanodroplet, which facilitates practical applications such as inkjet printing.

Dynamic examination of closed cylindrical shells utilizing the differential transform method

This article presents an innovative approach using the Differential Transform Method (DTM) to analyze the vibration characteristics of cylindrical shells, integrating Taylor's series with Sander's classical theory. It demonstrates DTM's efficiency, accuracy, and potential as an alternative method. The study introduces a novel application of the DTM in exploring the free vibration of cylindrical shells, detailing a technique to address challenges such as normalization, linear solution methodologies, and parameter derivative modifications. A dimensionless parameter analysis evaluates the impact of length, radius, thickness, and modulus of elasticity. Comparative analysis with Hybrid Finite Element Method (FEM) data and validation against existing literature highlights DTM's precision and reliability. In conclusion, DTM offers a robust solution for the eigenvalue problem in coupled differential equations, providing accurate vibration parameters. Additionally, an important relationship between the modulus of elasticity and frequency in the dimensionless state was obtained.

A generative adversarial network based on an efficient transformer for high-fidelity flow field reconstruction

The reconstruction of high-fidelity flow fields from low-fidelity data has attracted considerable attention in fluid dynamics but poses many challenges to existing deep learning methods due to the spatiotemporal complexity of flows and the lack of standardized benchmark datasets. In this study, we generate a low- and high-fidelity dataset containing 25 600 snapshots of four representative flow dynamics simulations using eight different numerical-precision and grid-resolution configurations. Using this dataset, we develop a physics-guided transformer-based generative adversarial network (PgTransGAN) for concurrently handling numerical-precision and grid-resolution enhancement. PgTransGAN leverages a dual-discriminator-based generative adversarial network for capturing continuous spatial and temporal dynamics of flows and applies a soft-constraint approach to enforce physical consistency in the reconstructed data using gradient information. An efficient transformer model is also developed to obtain the long-term temporal dependencies and further alleviate storage constraints. We compare the performance of PgTransGAN against standard linear interpolation and solutions based solely on convolutional neural networks or generative adversarial networks, and demonstrate that our method achieves better reconstruction quality at the data, image, and physics levels with an upscaling factor of 4 or even 8 in each grid dimension.

On the Accuracy of Transport Spatial Discretization Methods for Diffusive Regimes

An infinite-medium analysis is performed for neutron transport spatial discretization methods in planar geometry. Angular flux solutions of the spatially continuous transport equation, which are driven by a linear (or quadratic) source, are shown to vary linearly (or quadratically) in space and angle; these are used to assess whether the discretized transport equations preserve certain cell-averaged and edge quantities. Each of the continuous angular flux solutions has a scalar flux that satisfies the standard diffusion equation; our analysis predicts whether the transport discretizations yield an accurate diffusion coefficient and (diffusion) spatial differencing scheme. The linear moment–based discretization methods under consideration, which are found to preserve certain features of the linear (or quadratic) infinite-medium angular flux solutions, are the familiar linear discontinuous (LD), lumped linear discontinuous (LLD), and linear characteristic (LC) schemes. The step characteristic scheme, which yields an unphysically large diffusion coefficient, is revisited and shown to possess, for diffusive problems, a solution error that would occur if an unphysical anisotropic scattering term had been included in the starting discretized S N transport equations. The numerical results verify the theoretical predictions and demonstrate the accuracy of the LD, LLD, and LC schemes in highly scattering problems that are optically thick. Our numerical results also illustrate the impact of inaccuracies in the diffusion coefficient on the numerical solutions of eigenvalue problems. The analysis in this paper has practical implications in the choice of spatial schemes used to solve realistic eigenvalue problems.

Moment Problems and Integral Equations

The first part of this work provides explicit solutions for two integral equations; both are solved by means of Fourier transform. In the second part of this paper, sufficient conditions for the existence and uniqueness of the solutions satisfying sandwich constraints for two types of full moment problems are provided. The only given data are the moments of all positive integer orders of the solution and two other linear, not necessarily positive, constraints on it. Under natural assumptions, all the linear solutions are continuous. With their value in the subspace of polynomials being given by the moment conditions, the uniqueness follows. When the involved linear solutions and constraints are positive, the sufficient conditions mentioned above are also necessary. This is achieved in the third part of the paper. All these conditions are written in terms of quadratic expressions.

A geometrically nonlinear Hellinger–Reissner shell element for the postbuckling analysis of variable stiffness composite laminate structures

Variable stiffness (VS) composite laminates provide larger freedom to design thin-walled structures than constant stiffness (CS) composite laminates. They showed to allow the redistributing of stresses, improving buckling and post-buckling performance and, therefore, reducing material weight and costs. This work extends a recently developed mixed shell element, MISS-4C, to the postbuckling analysis of VS composite laminate structures. MISS-4C has a linear elastic closed-form solution for the stress interpolation of symmetric composite materials. Its stress field interpolation is obtained by the minimum number of parameters, making it an isostatic element. Moreover, its kinematic is only assumed along its contour, leading to an efficient evaluation of all operators obtained through analytical integration along the element contour. MISS-4C uses a corotational approach within a fast multi-modal Koiter algorithm to efficiently obtain the initial post-buckling response of VS composite laminate structures.First, the element performance is investigated by analysing a carbon fibre VS composite laminate plate subjected to compressive stresses. Numerical results obtained with MISS-4C are compared with those obtained with the MISS-4 element, showing good accuracy and a high convergence rate. Subsequently, the structural response of a glass fibre VS composite laminate girder of a short-length bridge is optimised through a multi-objective optimisation that exploits the robustness of the MISS-4C element and the efficiency of the multi-modal Koiter algorithm.

Effect of isothermal aging on Poly(N-isopropylacrylamide): Correlation between chemical structure and phase transition temperature property

Poly(N-isopropylacrylamide) (PNIPAm) is a stimuli-responsive polymer with wide applications as a scaffold in biomedical applications. This study presents the PNIPAm's thermoresponsive behavior during storage and its stability in potential pharmaceutical formulations as a drug delivery excipient. Therefore, the turbidity curves of linear PNIPAm aqueous solutions are investigated before and after its thermal oxidation under air at 120°C and 130°C. First, PNIPAm aqueous phase separation diagram is determined for unaged polymer and then compared to thermally aged samples at two distinct points (1 and 10%(w/w)). After isothermal aging, the transition temperature has increased with a shift up to 4°C. The correlation between PNIPAm's chemical structure and phase transition temperature properties is illustrated in terms of chemical modifications, macromolecular changes as well as the polar/non-polar groups balance. It is observed that the water affinity and glass transition temperature (Tg) have increased at the macromolecular level. In addition, chains scissions are highlighted and seem to explain the shift of transition temperature. Chemical changes have revealed the presence of supplementary polar groups induced by aging. This multiscale study suggests a possible mechanism for the partial thermal oxidation based on all the observations.

Transient resonance of sloshing liquid with time-varying mass

This study examines the sloshing of liquid with time-varying mass in a tank. A set of innovative experiments is carried out involving a shaking table supporting a water tank equipped with a drain pipe. Physical evidence of transient resonance is observed for the first time. Transient resonance occurs under specific excitation conditions when the instantaneous average water level (AWL) approaches a critical depth. During transient resonance, the oscillatory amplitude of the free-surface elevation increases sharply and then decreases in an envelope pattern. A bifurcation of the frequency band is first found in the Morlet-wavelet time–frequency spectrum, coinciding with the appearance of the maximum oscillatory amplitude. How the excitation conditions, drainage rate, and initial water depth affect transient resonance is recognized. Two mathematical models—one based on linear modal theory and the other based on nonlinear asymptotic theory and the Bateman–Luke variational principle—are derived to replicate the physical observations, by which application scopes of both models have been greatly broadened. The linear solution fails to predict the key feature of transient resonance, namely, the asymmetric envelopes of the oscillatory component about the AWL. By contrast, the nonlinear asymptotic solution captures this asymmetric feature accurately, and predicts both the steady and maximum oscillatory amplitudes well. The nonlinear solution is decomposed into terms of order 1/3, 2/3, and 1 using an asymptotic series for component analyses. A special nonlinear jump behavior is observed. The effects of draining and filling on transient resonance are compared.

Performance of Linear Algebra Factorization in Multi-Accelerator Architectures

Hardware and software are required to effectively solve problems in many domains. The idea of creating a hybrid architecture based on graphics processors arose to meet the increasing demands of modern scientific problems. Most of these problems are reduced to solving linear algebra problems. A set of efficient linear solutions has been successfully used to solve important scientific problems for many years. Factorizations play a crucial role in solving linear algebra problems. This work presents implementations of LU, QR and Cholesky factorizations on two graphics processors using the MAGMA 2.6.0 library. Their performances are given for matrices with real and complex numbers in single and double precision.

A novel sparse-based approach for joint radio frequency fingerprint and channel estimation

Radio Frequency Fingerprint (RFF) plays a pivotal role in specific emitter identification (SEI) and enhancing the physical layer security of wireless networks. However, past research on RFF extraction has encountered significant challenges, including algorithm instability in the presence of multi-path channels, disparities between actual RFF and proposed models, and the need to compensate for receiver RFF. In this study, we introduce an innovative algorithm designed to simultaneously estimate the transmitter's RFF and the non-line-of-sight (NLOS) channel state in the presence of receivers’ antenna effect. Moreover, we introduce the transmitter antenna feeding current as a modified RFF, accounting for transimtter components such as power amplifier (PA) nonlinearity, in-phase quadrature (IQ) modulator imbalance. Our approach commences with an exploration of wave propagation theory fundamentals, followed by a transformation of the inverse scattering equations into linear equations for joint channel and RFF estimation. Due to the non-convex nature of the derived equation, we employ the sparse lift method to render the problem convex. Leveraging the sparsity of channel coefficients, we devise a compressive sensing linear solution, denoted as the sparse-based approach for joint (SBJ) RFF and channel estimator. Additionally, we propose a calibration method to mitigate the effect of the receiver antennas on the estimated RFF of the transmitter. Through simulation, we demonstrate a 10 dB enhancement in RFF estimation accuracy compared to existing methods. Furthermore, our results indicate that the SBJ algorithm remains robust when faced with the combined effect of transmitter components, whereas previous models exhibit diminished precision as additional component effects are considered.

Survey Data and Subjective Beliefs in Business Cycle Models

Abstract This paper develops a theory of subjective beliefs that departs from rational expectations, and shows that biases in household beliefs have quantitatively large effects on macroeconomic aggregates. The departures are formalized using model-consistent notions of pessimism and optimism which are supported by extensive time-series and cross-sectional evidence from household surveys. The role subjective beliefs play in aggregate fluctuations is quantified in a business cycle model with goods and labour market frictions. Consistent with the survey evidence, an increase in pessimism generates upward biases in unemployment and inflation forecasts and lowers economic activity. The underlying belief distortions reduce aggregate demand and propagate through frictional goods and labour markets. As a by-product of the analysis, solution techniques that preserve the effects of time-varying belief distortions in the class of linear solutions are developed.

Exact Nonlinear Decomposition of Ideal-MHD Waves Using Eigenenergies

In this paper, we introduce a new method for exact decomposition of propagating, nonlinear magnetohydrodynamic (MHD) disturbances into their component eigenenergies associated with the familiar slow, Alfvén, and fast wave eigenmodes, and the entropy and field-divergence pseudoeigenmodes. First, the mathematical formalism is introduced, where it is illustrated how the ideal-MHD eigensystem can be used to construct a decomposition of the time variation of the total energy density into contributions from the eigenmodes. The decomposition method is then demonstrated by applying it to the output of three separate nonlinear MHD simulations. The analysis of the simulations confirms that the component wave modes of a composite wavefield are uniquely identified by the method. The slow, Alfvén, and fast energy densities are shown to evolve in exactly the way expected from comparison with known linear solutions and nonlinear properties, including processes such as mode conversion. Along the way, some potential pitfalls for the numerical implementation of the decomposition method are identified and discussed. We conclude that the exact, nonlinear decomposition method introduced is a powerful and promising tool for understanding the nature of the decomposition of MHD waves as well as analyzing and interpreting the output of dynamic MHD simulations.

Decomposition solutions and Bäcklund transformations of the B-type and C-type Kadomtsev–Petviashvili equations

This paper introduces a modified formal variable separation approach, showcasing a systematic and notably straightforward methodology for analyzing the B-type Kadomtsev–Petviashvili (BKP) equation. Through the application of this approach, we successfully ascertain decomposition solutions, Bäcklund transformations, the Lax pair, and the linear superposition solution associated with the aforementioned equation. Furthermore, we expand the utilization of this technique to the C-type Kadomtsev–Petviashvili (CKP) equation, leading to the derivation of decomposition solutions, Bäcklund transformations, and the Lax pair specific to this equation. The results obtained not only underscore the efficacy of the proposed approach, but also highlight its potential in offering a profound comprehension of integrable behaviors in nonlinear systems. Moreover, this approach demonstrates an efficient framework for establishing interrelations between diverse systems.

Computer Algorithm Design and Linearity Analysis of Its Data Structures

Linearity optimization of data structure is in an important position in the design of computer algorithms, and the study of its optimization measures and strategies can help to promote the research of computer algorithms in depth. This paper introduces the multithreading technology, designs a multithreaded inverted sorted cited table on the basis of the data chain table structure, and prunes and optimizes the data in the table and its distribution repetitions, and puts forward the linearity optimization strategy. And the GaBP parallel computer algorithm for banded linear equations is designed by combining this strategy. The linearity analysis of the optimized data structure reveals that the linearity is significantly improved, and the overall linearity is smooth and reasonably skewed. In the calculation of large-scale numerical values, the running time of the Partition number of 30 is only 3756.9 s. The average linear solution speed is only 0.063 s when solving the satisfiable SAT instances, which is 4.631 s less than that of the Minisat algorithm, and the optimization strategy of the data structure linearity proposed in this paper provides a reference scheme to accelerate the speed of computer algorithms in solving the difficult problems, and the design of the computer parallel algorithm provides a reference scheme to accelerate the speed of computer algorithms in solving the difficult problems. The designed computer parallel algorithm provides an effective method for the field of large-scale numerical processing and SAT problem solving.

On Density-based Local Community Search

Local community search (LCS) finds a community in a given graph G local to a set R of seed nodes by optimizing an objective function. The objective function f(S) for an induced subgraph S encodes the set inclusion criteria of R to a classic community measurement of S such as the conductance and the density. An ideal algorithm for optimizing f(S) is strongly local, that is, the complexity is dependent on R as opposed to G. This paper formulates a general form of objective functions for LCS using configurations and then focuses on a set C of density-based configurations, each corresponding to a density-based LCS objective function. The paper has two main results. i) A constructive classification of C: a configuration in C has a strongly local algorithm for optimizing its corresponding objective function if and only if it is in C L ⊆ C. ii) A linear programming-based general solution for density-based LCS that is strongly local and practically efficient. This solution is different from the existing strongly local LCS algorithms, which are all based on flow networks.

Shell analysis by different methods of dynamic relaxation

Shell analysis is a complex process. So far, many equations and theories have been proposed. With the increasing processing power of computers, numerical and approximate solutions were developed. The dynamic relaxation scheme is one of these methods. This procedure is an explicit technique for solving simultaneous equations. The fictitious mass and damping are added to the system of static structural equations in the dynamic relaxation technique to obtain a fictitious dynamic system. In this paper, 12 well-known dynamic relaxation processes were used for the linear analysis of shells. It is found that so far, the ability of many solutions of dynamic relaxation in the linear analysis of shells has not been shown. In each approach, the mass, damping and time step matrices are obtained based on the researchers’ work. Twelve samples are analysed. Most of these are examples of well-known benchmarks in non-linear analysis. The number of iterations and the analysis time gives the score of each technique. Then, the final rank of each method was obtained. Numerical solutions show that minimising the residual energy was the best process for linear shell analysis. Also, minimising the error of displacement, Zhang, Qiang and the power iteration methods behaved very similarly to each other.

Displacement response waveform restoration of simply supported bridge during train passage using measured acceleration integration based on linear vibration theory

This study proposes a method for restoring the displacement waveform during train passage using the acceleration integration based on linear vibration theory and noise cancellation techniques. This method replaces the low-frequency region affected by noise with a linear theoretical solution; however, this method uses the actual measurement data around the natural frequency, where nonlinearities (such as concrete member cracks and the train–bridge interaction) can be observed. The method identifies only the ratio of single axle weight to modal stiffness. Numerical experiments clarify that the method can estimate the maximum displacement of a bridge from acceleration with an error of approximately 5% or less. Improved prediction accuracy can be achieved using the proposed noise cancellation technique not only in the high-speed range but also into the lower-speed ranges as well. Furthermore, the proposed method is applied to acceleration monitoring data, and results show that the displacement waveform can be restored from the acceleration waveform.

Reproducibility of Equatorial Kelvin Waves in a Super‐Parameterized MIROC: 2. Linear Stability Analysis of In‐Model Kelvin Waves

AbstractWhile low‐resolution climate models at present struggle to appropriately simulate convectively coupled large‐scale atmospheric disturbances such as equatorial Kelvin waves (EKWs), superparameterization helps better reproduce such phenomena. To evaluate such model differences based on physical mechanisms, a linearized theoretical framework of convectively coupled EKWs was developed in a form readily applicable to model evaluation by allowing background stability and diabatic heating to have arbitrary vertical profiles rather than assuming simplified ones. A system of linearized equations of convection‐coupled gravity waves was derived as a two‐dimensional model of the convectively coupled EKWs. In this work, the basic states are taken from observations, CTL‐MIROC and SP‐MIROC experiments introduced in Part 1. The tendency of convectively coupled gravity waves to grow faster under top‐heavy heating is confirmed for realistic stratification profiles, as found in previous studies under constant stratifications. A comparison of linear unstable solutions with basic states taken from SP‐MIROC and CTL‐MIROC shows that the top‐heavy heating profile in SP‐MIROC largely contributes to the enhancement of the EKW‐like unstable modes, while subtle differences of stratification profiles considerably affect EKW behaviors. The bottom‐heavy heating bias in the CTL‐MIROC likely originates from insufficient modeling of subgrid stratiform precipitation in tropical organized systems. It is desirable to incorporate such stratiform components in cumulus parameterizations to achieve better EKW reproducibility.

Advanced deep operator networks to predict multiphysics solution fields in materials processing and additive manufacturing

Unlike classical artificial neural networks, which require retraining for each new set of parametric inputs, the Deep Operator Network (DeepONet), a lately introduced deep learning framework, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to complete solution fields. In this paper, two newly devised DeepONet formulations with sequential learning and Residual U-Net (ResUNet) architectures are trained for the first time to simultaneously predict complete thermal and mechanical solution fields under variable loading histories, process parameters, and even variable geometries. Two real-world applications are demonstrated: 1- coupled thermo-mechanical analysis of steel continuous casting with multiple visco-plastic constitutive laws and 2- sequentially coupled directed energy deposition for additive manufacturing. Despite highly challenging spatially variable target distributions, DeepONets can infer reasonably accurate full-field temperature and stress solutions several orders of magnitude faster than traditional and highly optimized finite-element analysis (FEA), even when FEA simulations are run on the latest high-performance computing platforms. The proposed DeepONet model’s ability to provide field predictions almost instantly for unseen input parameters opens the door for future preliminary evaluation and design optimization of these vital industrial processes.