Revealing the coupling correlations between stiffness nonlinearity and magneto-electro-mechanical effect in multi-point impacts contributes significantly to the advancement of intelligent morphing structures. Multi-po...
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In this paper, we propose a novel second-order dynamical low-rank mass-lumped finite element method for solving the Allen-Cahn (AC) equation, a semilinear parabolic partial differential equation. The matrix differenti...
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Interparticle interactions with multiple length scales play a pivotal role in the formation and stability of quasicrystals. Choosing a minimal set of length scales to stabilize a given quasicrystal is a challenging pr...
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Interparticle interactions with multiple length scales play a pivotal role in the formation and stability of quasicrystals. Choosing a minimal set of length scales to stabilize a given quasicrystal is a challenging problem. To address this challenge, we propose a symmetry-preserving screening method (SPSM) to design a Landau theory with a minimal number of length scales—referred to as the minimal Landau theory—that includes only the essential length scales necessary to stabilize quasicrystals. Based on a generalized multiple-length-scale Landau theory, SPSM first evaluates various spectral configurations of candidate structures under a hard constraint. It then identifies the configuration with the lowest free energy. Using this optimal configuration, SPSM calculates phase diagrams to explore the thermodynamic stability of desired quasicrystals. SPSM can design a minimal Landau theory capable of stabilizing the desired quasicrystals by incrementally increasing the number of length scales. Our application of SPSM has not only confirmed known behaviors in 10- and 12-fold quasicrystals but also led to a significant prediction that quasicrystals with 8-, 14-, 16-, and 18-fold symmetry could be stable within three-length-scale Landau models.
This paper introduces a generalized fractional Halanay-type coupled inequality, which serves as a robust tool for characterizing the asymptotic stability of diverse time fractional functional differential equations, p...
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The solution of nonsymmetric positive definite (NSPD) systems for advection-diffusion problems is an important research topic in science and engineering. The adaptive BDDC method is a significant class of non-overlapp...
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The four-roll mill has been traditionally viewed as a device generating simple extensional flow with a central stagnation point. Our systematic investigation using a two-relaxation-time regularized lattice Boltzmann (...
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The seepage law under a magnetic field is obtained by up-scaling the flow at the pore scale of rigid porous media,and the macroscopic equivalent model is also *** is proved that the macroscopic mass flow depends on th...
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The seepage law under a magnetic field is obtained by up-scaling the flow at the pore scale of rigid porous media,and the macroscopic equivalent model is also *** is proved that the macroscopic mass flow depends on the macroscopic magnetic force and the gradients of pressure and of magnetic pressure,as Zahn and Rosensweig have described in their *** permeability tensor is symmetric and positive.
In this paper, we propose a deep learning-enhanced multigrid solver for high-frequency and heterogeneous Helmholtz equations. By applying spectral analysis, we categorize the iteration error into characteristic and no...
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This paper explores the application of kernel learning methods for parameter prediction and evaluation in the Algebraic Multigrid Method (AMG), focusing on several Partial Differential Equation (PDE) problems. AMG is ...
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In this paper,we study the role of mesh quality on the accuracy of linear finite element *** derive a more detailed error estimate,which shows explicitly how the shape and size of elements,and symmetry structure of me...
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In this paper,we study the role of mesh quality on the accuracy of linear finite element *** derive a more detailed error estimate,which shows explicitly how the shape and size of elements,and symmetry structure of mesh effect on the error of numerical *** computable parameters Ge and Gv are given to depict the cell geometry property and symmetry structure of the *** compare with the standard a priori error estimates,which only yield information on the asymptotic error behaviour in a global sense,our proposed error estimate considers the effect of local element geometry properties,and is thus more *** certain conditions,the traditional error estimates and supercovergence results can be derived from the proposed error ***,the estimators Ge and Gv are computable and thus can be used for predicting the variation of *** tests are presented to illustrate the performance of the proposed parameters Ge and Gv.
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