A set of criteria are presented for the global exponential stability and the existence of periodic solutions of delayed cellular neural networks (DCNNs) by constructing suitable Lyapunov functionals, introducing many ...A set of criteria are presented for the global exponential stability and the existence of periodic solutions of delayed cellular neural networks (DCNNs) by constructing suitable Lyapunov functionals, introducing many parametersq ij * ,r ij * ,q ij ,r ij ∈R andW i >0 (i, j=1, 2,…,n) and combining them with the elementary inequality 2ab≤a 2+b 2 technique. These criteria have important significance in the design and applications of globally stable DCNNs and periodic oscillatory DCNNs. In addition, the results in literature are extended and improved. Two examples are given to illustrate the theory.展开更多
Two types of activated carbon, namely, Filtrasorb 400 and Nuchar SA, were functionalized by quaternary ammonium salts （quats）, as to enhance perchlorate adsorption. Results showed that the adsorption of quats on Nuc...Two types of activated carbon, namely, Filtrasorb 400 and Nuchar SA, were functionalized by quaternary ammonium salts （quats）, as to enhance perchlorate adsorption. Results showed that the adsorption of quats on Nuchar SA increased with increase in chain length （hydrophobicity） of quats. Filtrasorb 400, however, had limited uptake of long-chain quats such as dodecyl- trimethylammonium and hexadecyltrimethylammoium （HDTMA）. Results indicated that perchlorate removal by the functionalized activated carbon was directly related to the chain length of the modifying quats. Perchlorate removal by functionalized activated carbon increased with increase in chain length of the modifying quats and became less pH-dependent. Modified Nuchar SA had higher overall perchlorate removal capacity than the modified Filtrasorb F400, but was more strongly affected by pH than Filtrasorb 400. Activated carbon treated with HDTMA exhibited the best perchlorate removal capacity among all quats studied. Results indicated that tailoring the activated carbon surface with HDTMA rendered the activated carbon surface positively charged, which resulted in substantial increase in perchlorate removal compared to unfunctionalized activated carbons.展开更多
Considerable efforts are being made to transition current lithium-ion and sodium-ion batteries towards the use of solid-state electrolytes.Computational methods,specifically nudged elastic band(NEB)and molecular dynam...Considerable efforts are being made to transition current lithium-ion and sodium-ion batteries towards the use of solid-state electrolytes.Computational methods,specifically nudged elastic band(NEB)and molecular dynamics(MD)methods,provide powerful tools for the design of solid-state electrolytes.The MD method is usually the choice for studying the materials involving complex multiple diffusion paths or having disordered structures.However,it relies on simulations at temperatures much higher than working temperature.This paper studies the reliability of the MD method using the system of Na diffusion in MgO as a benchmark.We carefully study the convergence behavior of the MD method and demonstrate that total effective simulation time of 12 ns can converge the calculated diffusion barrier to about 0.01 eV.The calculated diffusion barrier is 0.31 eV from both methods.The diffusion coefficients at room temperature are 4.3×10^(-9) cm^(2)⋅s^(−1) and 2.2×10^(-9) cm^(2)⋅s^(−1),respectively,from the NEB and MD methods.Our results justify the reliability of the MD method,even though high temperature simulations have to be employed to overcome the limitation on simulation time.展开更多
The adsorption of 1,1-diamino-2,2-dinitroethylene （FOX-7） molecule on the AI（I 11） surface was investigated by the generalized gradient approximation （GGA） of density functional theory （DFT）. The calculations ...The adsorption of 1,1-diamino-2,2-dinitroethylene （FOX-7） molecule on the AI（I 11） surface was investigated by the generalized gradient approximation （GGA） of density functional theory （DFT）. The calculations employ a supercell （4 × 4 × 2） slab model and three-dimensional periodic boundary conditions. The strong attractive forces between oxygen and aluminum atoms induce the N--O bond breaking of the FOX-7. Subsequently, the dissociated oxygen atoms and radical fragment of FOX-7 oxidize the AI surface. The largest adsorption energy is --940.5 kJ/mol. Most of charge transfer is 3.3 le from the A1 surface to the fragment of FOX-7 molecule. We also investi- gated the adsorption and decomposition mechanism of FOX-7 molecule on the AI（111） surface. The activation en- ergy for the dissociation steps of P2 configuration is as large as 428.8 kJ/mol, while activation energies of other configurations are much smaller, in range of 2.4 to 147.7 kJ/mol.展开更多
In the presence of external forces depending only on the time and space variables, the Boltzmann-Enskog equation formally conserves only the mass of the . system, and its entropy functional is also nonincreasing. Cor...In the presence of external forces depending only on the time and space variables, the Boltzmann-Enskog equation formally conserves only the mass of the . system, and its entropy functional is also nonincreasing. Corresponding to this type of equation, we first give some hypotheses of its bicharacteristic equations and then get some results about the stablity of its global solution with the help of two new Lyapunov functionals： one is to describe interactions between particles with different velocities and the other is to measure the L1 distance between two mild solutions. The former Lyapunov functional yields the time-asymptotic convergence of global classical solutions to the collision free motion while the latter is applied into the veri-fication of the L1 stability of global mild solutions to the Boltzmann-Enskog equation for a moderately or highly dense gas in the influence of external forces.展开更多
In this paper, a predator-prey chain system with impulsive effects and Beddington-DeAngelis functional response is studied. We investigate the existence of periodic solu-tion by coincidence degree theory. Sufficient c...In this paper, a predator-prey chain system with impulsive effects and Beddington-DeAngelis functional response is studied. We investigate the existence of periodic solu-tion by coincidence degree theory. Sufficient conditions are obtained for the existence of periodic solution.展开更多
Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model describe...Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model described by the Poisson- Boltzmann （PB）/Poisson-Nernst-Planck （PNP） equations has made great contributions towards simulation of these pro- cesses. However, the model has shortcomings in its commonly used form and cannot capture （or cannot accurately capture） some important physical properties of the biological systems. Considerable efforts have been made to improve the con- tinuum model to account for discrete particle interactions and to make progress in numerical methods to provide accurate and efficient simulations. This review will summarize recent main improvements in continuum modeling for biomolecu- lar systems, with focus on the size-modified models, the coupling of the classical density functional theory and the PNP equations, the coupling of polar and nonpolar interactions, and numerical progress.展开更多
In this paper, the almost periodic predator-prey-mutualist model with Holling type II functional response is discussed. A set of sufficient condi- tions which guarantee the uniform persistence and the global attractiv...In this paper, the almost periodic predator-prey-mutualist model with Holling type II functional response is discussed. A set of sufficient condi- tions which guarantee the uniform persistence and the global attractivity of the system are obtained. For the almost periodic case, by constructing a suit- able Lyapunov function, sufficient conditions which guarantee the existence of a unique globally attractive positive almost periodic solution of the system are obtained. An example together with its numerical simulations shows the feasibility of the main results.展开更多
Starting with the many-body SchrSdinger Hamiltonian in R2, we prove that the ground state energy of a two-dimensional interacting Bose gas with the pairwise attractive interaction approaches to the minimum of the Gros...Starting with the many-body SchrSdinger Hamiltonian in R2, we prove that the ground state energy of a two-dimensional interacting Bose gas with the pairwise attractive interaction approaches to the minimum of the Gross-Pitaevskii energy functional in the mean- field regime, as the particle number N → ∞ and however the scattering length → 0. By fixing N｜k｜, this leads to the mean-field approximation of Bose-Einstein condensates with attractive interactions in R^2.展开更多
文摘A set of criteria are presented for the global exponential stability and the existence of periodic solutions of delayed cellular neural networks (DCNNs) by constructing suitable Lyapunov functionals, introducing many parametersq ij * ,r ij * ,q ij ,r ij ∈R andW i >0 (i, j=1, 2,…,n) and combining them with the elementary inequality 2ab≤a 2+b 2 technique. These criteria have important significance in the design and applications of globally stable DCNNs and periodic oscillatory DCNNs. In addition, the results in literature are extended and improved. Two examples are given to illustrate the theory.
文摘Two types of activated carbon, namely, Filtrasorb 400 and Nuchar SA, were functionalized by quaternary ammonium salts （quats）, as to enhance perchlorate adsorption. Results showed that the adsorption of quats on Nuchar SA increased with increase in chain length （hydrophobicity） of quats. Filtrasorb 400, however, had limited uptake of long-chain quats such as dodecyl- trimethylammonium and hexadecyltrimethylammoium （HDTMA）. Results indicated that perchlorate removal by the functionalized activated carbon was directly related to the chain length of the modifying quats. Perchlorate removal by functionalized activated carbon increased with increase in chain length of the modifying quats and became less pH-dependent. Modified Nuchar SA had higher overall perchlorate removal capacity than the modified Filtrasorb F400, but was more strongly affected by pH than Filtrasorb 400. Activated carbon treated with HDTMA exhibited the best perchlorate removal capacity among all quats studied. Results indicated that tailoring the activated carbon surface with HDTMA rendered the activated carbon surface positively charged, which resulted in substantial increase in perchlorate removal compared to unfunctionalized activated carbons.
基金supported by the National Natural Science Foundation of China (Grant Nos.12164019,11991060,12088101,and U1930402)the Natural Science Foundation of Jiangxi Province of China (Grant No.20212BAB201017).
文摘Considerable efforts are being made to transition current lithium-ion and sodium-ion batteries towards the use of solid-state electrolytes.Computational methods,specifically nudged elastic band(NEB)and molecular dynamics(MD)methods,provide powerful tools for the design of solid-state electrolytes.The MD method is usually the choice for studying the materials involving complex multiple diffusion paths or having disordered structures.However,it relies on simulations at temperatures much higher than working temperature.This paper studies the reliability of the MD method using the system of Na diffusion in MgO as a benchmark.We carefully study the convergence behavior of the MD method and demonstrate that total effective simulation time of 12 ns can converge the calculated diffusion barrier to about 0.01 eV.The calculated diffusion barrier is 0.31 eV from both methods.The diffusion coefficients at room temperature are 4.3×10^(-9) cm^(2)⋅s^(−1) and 2.2×10^(-9) cm^(2)⋅s^(−1),respectively,from the NEB and MD methods.Our results justify the reliability of the MD method,even though high temperature simulations have to be employed to overcome the limitation on simulation time.
文摘The adsorption of 1,1-diamino-2,2-dinitroethylene （FOX-7） molecule on the AI（I 11） surface was investigated by the generalized gradient approximation （GGA） of density functional theory （DFT）. The calculations employ a supercell （4 × 4 × 2） slab model and three-dimensional periodic boundary conditions. The strong attractive forces between oxygen and aluminum atoms induce the N--O bond breaking of the FOX-7. Subsequently, the dissociated oxygen atoms and radical fragment of FOX-7 oxidize the AI surface. The largest adsorption energy is --940.5 kJ/mol. Most of charge transfer is 3.3 le from the A1 surface to the fragment of FOX-7 molecule. We also investi- gated the adsorption and decomposition mechanism of FOX-7 molecule on the AI（111） surface. The activation en- ergy for the dissociation steps of P2 configuration is as large as 428.8 kJ/mol, while activation energies of other configurations are much smaller, in range of 2.4 to 147.7 kJ/mol.
基金The NSF (11171356) of Chinathe Grant (09LGTY45) of Sun Yat-Sen University
文摘In the presence of external forces depending only on the time and space variables, the Boltzmann-Enskog equation formally conserves only the mass of the . system, and its entropy functional is also nonincreasing. Corresponding to this type of equation, we first give some hypotheses of its bicharacteristic equations and then get some results about the stablity of its global solution with the help of two new Lyapunov functionals： one is to describe interactions between particles with different velocities and the other is to measure the L1 distance between two mild solutions. The former Lyapunov functional yields the time-asymptotic convergence of global classical solutions to the collision free motion while the latter is applied into the veri-fication of the L1 stability of global mild solutions to the Boltzmann-Enskog equation for a moderately or highly dense gas in the influence of external forces.
基金Natural Science Foundation of Education Department of AnhuiProvince (KJ2008B236).
文摘In this paper, a predator-prey chain system with impulsive effects and Beddington-DeAngelis functional response is studied. We investigate the existence of periodic solu-tion by coincidence degree theory. Sufficient conditions are obtained for the existence of periodic solution.
基金supported by the National Natural Science Foundation of China(Grant No.91230106)the Chinese Academy of Sciences Program for Cross&Cooperative Team of the Science&Technology Innovation
文摘Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model described by the Poisson- Boltzmann （PB）/Poisson-Nernst-Planck （PNP） equations has made great contributions towards simulation of these pro- cesses. However, the model has shortcomings in its commonly used form and cannot capture （or cannot accurately capture） some important physical properties of the biological systems. Considerable efforts have been made to improve the con- tinuum model to account for discrete particle interactions and to make progress in numerical methods to provide accurate and efficient simulations. This review will summarize recent main improvements in continuum modeling for biomolecu- lar systems, with focus on the size-modified models, the coupling of the classical density functional theory and the PNP equations, the coupling of polar and nonpolar interactions, and numerical progress.
基金supported by the Natural Science Foundation of Fujian Province(2015J01012,2015J01019)
文摘In this paper, the almost periodic predator-prey-mutualist model with Holling type II functional response is discussed. A set of sufficient condi- tions which guarantee the uniform persistence and the global attractivity of the system are obtained. For the almost periodic case, by constructing a suit- able Lyapunov function, sufficient conditions which guarantee the existence of a unique globally attractive positive almost periodic solution of the system are obtained. An example together with its numerical simulations shows the feasibility of the main results.
基金supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry of China,National Center for Mathematics and Interdisciplinary Sciences in China
文摘Starting with the many-body SchrSdinger Hamiltonian in R2, we prove that the ground state energy of a two-dimensional interacting Bose gas with the pairwise attractive interaction approaches to the minimum of the Gross-Pitaevskii energy functional in the mean- field regime, as the particle number N → ∞ and however the scattering length → 0. By fixing N｜k｜, this leads to the mean-field approximation of Bose-Einstein condensates with attractive interactions in R^2.
