In this paper,we develop a lattice Boltzmann model for a class ofone-dimensional nonlinear wave equations,including the second-order hyperbolictelegraph equation,the nonlinear Klein-Gordon equation,the damped and unda...In this paper,we develop a lattice Boltzmann model for a class ofone-dimensional nonlinear wave equations,including the second-order hyperbolictelegraph equation,the nonlinear Klein-Gordon equation,the damped and undampedsine-Gordon equation and double sine-Gordon equation.By choosing properly theconservation condition between the macroscopic quantity u,and the distributionfunctions and applying the Chapman-Enskog expansion,the governing equation isrecovered correctly from the lattice Boltzmann equation.Moreover,the local equilib-rium distribution function is obtained.The results of numerical examples have beencompared with the analytical solutions to confirm the good accuracy and the applica-bility of our scheme.展开更多
We present the development of a non-reflecting boundary condition,based on the Local One-Dimensional Inviscid(LODI)approach,for Lattice Boltzmann Models working with multi-speed stencils.We test and evaluate the LODI ...We present the development of a non-reflecting boundary condition,based on the Local One-Dimensional Inviscid(LODI)approach,for Lattice Boltzmann Models working with multi-speed stencils.We test and evaluate the LODI implementation with numerical benchmarks,showing significant accuracy gains with respect to the results produced by a simple zerogradient condition.We also implement a simplified approach,which allows handling the unknown distribution functions spanning several layers of nodes in a unified way,still preserving a comparable level of accuracy with respect to the standard formulation.展开更多
Phase transformation is one of the essential topics in the studies on high entropy alloys(HEAs).However,characterization of the nucleation behavior in the phase transformation for HEAs is still challenging through exp...Phase transformation is one of the essential topics in the studies on high entropy alloys(HEAs).However,characterization of the nucleation behavior in the phase transformation for HEAs is still challenging through experimental methods.In the present work,HfNbTaTiZr HEA was chosen as the representative material,and molecular dynamics/Monte Carlo(MD/MC)simulations were performed to investigate the nucleation behavior in temperature-induced BCC-to-HCP transformation for this HEA system.The results indicate that Nb–Ta,Ti–Zr,Hf–Zr and Hf–Ti atom pairs are preferred in the BCC solid solution of HfNbTaTiZr HEA and Hf–Ti–Zr-rich atom cluster with chemical short range order acts as the nucleation site for HCP phase.The nucleation process follows the non-classical two-step nucleation model:BCC-like structure with severe lattice distortion forms first and then HCP structure nucleates from the BCC-like structure.Moreover,at low temperature,the BCC-to-HCP nucleation hardly occurs,and the BCC solid solution is stabilized.The present work provides more atomic details of the nucleation behavior in temperature-induced BCC-to-HCP phase transformation for HEA,and can help in deep understanding of the phase stability for HEAs.展开更多
In this paper, the concepts of probabilistic normed Riesz space and probabilistic Banach lattice are introduced, and their basic properties are studied. In this context, some continuity and convergence theorems are pr...In this paper, the concepts of probabilistic normed Riesz space and probabilistic Banach lattice are introduced, and their basic properties are studied. In this context, some continuity and convergence theorems are proved.展开更多
Suppose X is a Banash lattice, and X* has Radon-Nikodym property. Then the space R(X, L1(μ)) of all bounded regular operators is isometrically isomorphic onto L1 (μ, X). We denote R(X, L1 (μ)) L1 (μ, X).
A method to construct strongly non regular order bounded operators from a classical Banach lattice C into any separable Banach lattice F without Dedekind σ completeness is presented in this paper. A r...A method to construct strongly non regular order bounded operators from a classical Banach lattice C into any separable Banach lattice F without Dedekind σ completeness is presented in this paper. A result concerning the order bounded norm and the regular norm is also contained.展开更多
基金The authors are very thankful to the reviewers for their valuable suggestions toimprove the quality of the paper.This work is supported by National Natural Science Foundation of China(Nos.11101399,11271171,11301234)the Provincial Natural Science Foundation of Jiangxi(Nos.20161ACB20006,20142BCB23009,20151BAB201012).
文摘In this paper,we develop a lattice Boltzmann model for a class ofone-dimensional nonlinear wave equations,including the second-order hyperbolictelegraph equation,the nonlinear Klein-Gordon equation,the damped and undampedsine-Gordon equation and double sine-Gordon equation.By choosing properly theconservation condition between the macroscopic quantity u,and the distributionfunctions and applying the Chapman-Enskog expansion,the governing equation isrecovered correctly from the lattice Boltzmann equation.Moreover,the local equilib-rium distribution function is obtained.The results of numerical examples have beencompared with the analytical solutions to confirm the good accuracy and the applica-bility of our scheme.
文摘We present the development of a non-reflecting boundary condition,based on the Local One-Dimensional Inviscid(LODI)approach,for Lattice Boltzmann Models working with multi-speed stencils.We test and evaluate the LODI implementation with numerical benchmarks,showing significant accuracy gains with respect to the results produced by a simple zerogradient condition.We also implement a simplified approach,which allows handling the unknown distribution functions spanning several layers of nodes in a unified way,still preserving a comparable level of accuracy with respect to the standard formulation.
基金funded by the China Postdoctoral Science Foundation(No.2020M672787)the National Natural Science Foundation of China(Nos.51701125,51801128,52001123)the Guangdong Basic and Applied Basic Research Foundation(No.2021A1515012278)。
文摘Phase transformation is one of the essential topics in the studies on high entropy alloys(HEAs).However,characterization of the nucleation behavior in the phase transformation for HEAs is still challenging through experimental methods.In the present work,HfNbTaTiZr HEA was chosen as the representative material,and molecular dynamics/Monte Carlo(MD/MC)simulations were performed to investigate the nucleation behavior in temperature-induced BCC-to-HCP transformation for this HEA system.The results indicate that Nb–Ta,Ti–Zr,Hf–Zr and Hf–Ti atom pairs are preferred in the BCC solid solution of HfNbTaTiZr HEA and Hf–Ti–Zr-rich atom cluster with chemical short range order acts as the nucleation site for HCP phase.The nucleation process follows the non-classical two-step nucleation model:BCC-like structure with severe lattice distortion forms first and then HCP structure nucleates from the BCC-like structure.Moreover,at low temperature,the BCC-to-HCP nucleation hardly occurs,and the BCC solid solution is stabilized.The present work provides more atomic details of the nucleation behavior in temperature-induced BCC-to-HCP phase transformation for HEA,and can help in deep understanding of the phase stability for HEAs.
文摘In this paper, the concepts of probabilistic normed Riesz space and probabilistic Banach lattice are introduced, and their basic properties are studied. In this context, some continuity and convergence theorems are proved.
基金This research is supported by the National Natural Science Foundation of China(No.19971046).
文摘Suppose X is a Banash lattice, and X* has Radon-Nikodym property. Then the space R(X, L1(μ)) of all bounded regular operators is isometrically isomorphic onto L1 (μ, X). We denote R(X, L1 (μ)) L1 (μ, X).
文摘A method to construct strongly non regular order bounded operators from a classical Banach lattice C into any separable Banach lattice F without Dedekind σ completeness is presented in this paper. A result concerning the order bounded norm and the regular norm is also contained.
