In view of the fact that impulsive differential equations have the discreteness due to the impulse phenomenon, this article proposes a single hidden layer neural networkmethod-based extreme learning machine and a phys...
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In view of the fact that impulsive differential equations have the discreteness due to the impulse phenomenon, this article proposes a single hidden layer neural networkmethod-based extreme learning machine and a physics-informed neural network method combined with learning rate attenuation strategy to solve linear impulsive differential equations and nonlinear impulsive differential equations, respectively. For the linear impulsive differential equations, first, the interval is segmented according to the impulse points, and a single hidden layer neural network model is constructed, the weight parameters of the hidden layer are randomly set, the optimal output parameters, and solution of the first segment are obtained by the extreme learning machine algorithm, then we calculate the initial value of the second segment according to the jumping equation and the remaining segments are solved in turn in the same way. Although the single hidden layer neural network method proposed can solve linear equations with high accuracy, it is not suitable for solving nonlinear equations. Therefore, we propose the physics-informed neural network combined with a learning rate attenuation strategy to solve the nonlinear impulsive differential equations, then the Adam algorithm and L-BFGS algorithm are combined to find the optimal approximate solution of each segment. Numerical examples show that the single hidden layer neural network method with Legendre polynomials as the activation function and the physics-informed neural network method combined with learning rate attenuation strategy can solve linear and nonlinear impulsive differential equations with higher accuracy. Impact Statement-It is difficult to obtain the analytical solutions of impulsive differential equations because of the existence of impulse points, and the current numerical methods are complicated and demanding. In recent years, artificial neural network methods have been widely used due to its simplicity and efficie
The Tungsten-Rhenium(W-Re) alloys,celebrated for their high melting point,strength at elevated temperatures,electrical resistivity,and radiation resistance,have been widely utilized in high-temperature components,aero...
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The Tungsten-Rhenium(W-Re) alloys,celebrated for their high melting point,strength at elevated temperatures,electrical resistivity,and radiation resistance,have been widely utilized in high-temperature components,aerospace,electronics,and nuclear *** constituents of the topologically close-packed(TCP) phases,the sigma phase(σ) and chi phase(χ) formed within W-Re alloys wield considerable influence on the mechanical properties and the stability of the *** calculations were utilized in the present work to explore the structural,thermodynamic,and electronic properties of both ordered and disordered configurations within the σ and χ phases,culminating in a systematic elucidation of the higher phase stability exhibited by the ordered *** is found that the bulk modulus of these two phases is directly proportional to the concentration of Re in the alloy,while the equilibrium volume is inversely *** thermodynamic parameters of the σ and χ phases are calculated via the mean-field potential *** similar trends observed in the isobaric heat capacity,enthalpy increment,and entropy change curves for these two phases suggest they possess comparable thermodynamic *** is noteworthy that the contribution of ionic vibrations predominantly affects the isobaric heat capacity,while the contribution of thermal electronic excitations increases linearly with *** the structure and thermodynamic properties of TCP phases in W-Re alloys at low temperatures has profound significance for optimizing material performance,microstructures features,establishing theoretical foundations,and predicting material behavior.
In this paper,we investigate the vanishing viscosity limit of the 3D incompressible micropolar equations in bounded domains with boundary *** is shown that there exist global weak solutions of the micropolar equations...
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In this paper,we investigate the vanishing viscosity limit of the 3D incompressible micropolar equations in bounded domains with boundary *** is shown that there exist global weak solutions of the micropolar equations in a general bounded smooth *** particular,we establish the uniform estimate of the strong solutions for when the boundary is ***,we obtain the rate of convergence of viscosity solutions to the inviscid solutions as the viscosities tend to zero(i.e.,(ε,χ,γ,κ)→0).
Pt-Ir alloy is potential superalloys used above 1300℃because of their high strength and creep ***,the ductility of Pt-Ir alloy has rapidly deteriorated with the increase of Ir,resulting in poor *** work quantitativel...
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Pt-Ir alloy is potential superalloys used above 1300℃because of their high strength and creep ***,the ductility of Pt-Ir alloy has rapidly deteriorated with the increase of Ir,resulting in poor *** work quantitatively evaluated the solid solution strengthening(SSS)and grain refinement strengthening(GRS)of Pt-Ir alloy using first-principles calculations combined with experimental ***,the stretching force constants in the second nearest neighbor region(SFC^(2nd))of pure Ir(193.7 eV·nm^(-2))are 3.40 times that of pure Pt(57.0 eV·nm^(-2)),i.e.,the interatomic interaction is greatly enhanced with the increase of Ir content,which leads to the decrease of ductility,and modulus misfit plays a dominant role in ***,the physical mechanisms responsible for the hardness(H_(V))of Pt-Ir alloy,using the power-law-scaled function of electron work function coupled SSS and GRS,are attributed to the electron redistribution caused by different Ir ***,a thorough assessment of the thermodynamic characteristics of Pt-Ir binary alloy was conducted,culminating in development of a mapping model that effectively relates enmposition,temperature and *** results revealed that the compressive strength incrcases with the Ir content,and the highest strength was observed in Pt_(0.25)Ir_(0.75).This study provides valuable insights into the Pt-Ir alloy system.
By combination of iteration methods with the partition of unity method(PUM),some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics(MHD)with different physical parameters are pre...
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By combination of iteration methods with the partition of unity method(PUM),some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics(MHD)with different physical parameters are presented and *** algorithms are highly *** first,a global solution is obtained on a coarse grid for all approaches by one of the iteration *** parallelized residual schemes,local corrected solutions are calculated on finer meshes with overlapping *** subdomains can be achieved flexibly by a class of *** proposed algorithm is proved to be uniformly stable and ***,one numerical example is presented to confirm the theoretical findings.
作者：
GUO YixiaoMING PingbingLSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences
University of Chinese Academy of SciencesBeijing 100049China
The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger *** proposed approach combines a newly developed loss function with an innovative neural network architectu...
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The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger *** proposed approach combines a newly developed loss function with an innovative neural network architecture that incorporates prior knowledge of the *** improvements enable the proposed method to handle both high-dimensional problems and problems posed on irregular bounded *** authors successfully compute up to the first 30 eigenvalues for various fractional Schrödinger *** an application,the authors share a conjecture to the fractional order isospectral problem that has not yet been studied.
The Euler characteristic transform (ECT) is a simple to define yet powerful representation of shape. The idea is to encode an embedded shape by tracking how the Euler characteristic, a simple integer-valued topologica...
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In this paper,we study the a posteriori error estimator of SDG method for variable coefficients time-harmonic Maxwell's *** propose two a posteriori error estimators,one is the recovery-type estimator,and the othe...
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In this paper,we study the a posteriori error estimator of SDG method for variable coefficients time-harmonic Maxwell's *** propose two a posteriori error estimators,one is the recovery-type estimator,and the other is the residual-type *** first propose the curl-recovery method for the staggered discontinuous Galerkin method(SDGM),and based on the super-convergence result of the postprocessed solution,an asymptotically exact error estimator is *** residual-type a posteriori error estimator is also proposed,and it's reliability and effectiveness are proved for variable coefficients time-harmonic Maxwell's *** efficiency and robustness of the proposed estimators is demonstrated by the numerical experiments.
This study addresses the deficiencies in the assumptions of the results in Chen and Yang, 2017 [1] due to the lack of uniformity. We first show the missing hypothesis by presenting a counterexample. Then we prove why ...
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Hydride precipitation in zirconium cladding materials can damage their integrity and *** temperature and material defects have a significant effect on the dynamic growth of *** this study,we have developed a phasefiel...
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Hydride precipitation in zirconium cladding materials can damage their integrity and *** temperature and material defects have a significant effect on the dynamic growth of *** this study,we have developed a phasefield model based on the assumption of elastic behaviour within a specific temperature range(613 K-653 K).This model allows us to study the influence of temperature and interfacial effects on the morphology,stress,and average growth rate of zirconium *** results suggest that changes in temperature and interfacial energy influence the length-to-thickness ratio and average growth rate of the hydride *** ultimate determinant of hydride orientation is the loss of interfacial coherency,primarily induced by interfacial dislocation defects and quantifiable by the mismatch degree *** escalation in interfacial coherency loss leads to a transition of hydride growth from horizontal to vertical,accompanied by the onset of redirection ***,redirection occurs at a critical mismatch level,denoted as qc,and remains unaffected by variations in temperature and interfacial ***,this redirection leads to an increase in the maximum stress,which may influence the direction of hydride crack *** research highlights the importance of interfacial coherency and provides valuable insights into the morphology and growth kinetics of hydrides in zirconium alloys.
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