It is conceptually proposed that the total entropy of polymer solution is contributed from two distinct parts: the positional and the oomformational. The former can be represented analytically, while the latter can be...It is conceptually proposed that the total entropy of polymer solution is contributed from two distinct parts: the positional and the oomformational. The former can be represented analytically, while the latter can be simulated with the random self-avoiding walk model on the simple cubic lattice for multichain systems. The obtained results indicated that both the conformational entropy and the mixing heat are consistent with the scaling laws wry well.展开更多
The statistical counting method for the computer simulation of the thermodynamic quantities of polymer solution has been reviewed. The calculating results for a single athermal chain confirm the theory of the renorma...The statistical counting method for the computer simulation of the thermodynamic quantities of polymer solution has been reviewed. The calculating results for a single athermal chain confirm the theory of the renormalization group. The results for the athermal solution are consistent with the scaling law of the osmotic pressure with the exponent 2.25. The results for a single chain with the segmental interaction are in a good agreement with the exact results obtained by the direct counting method. The results for the polymer solution show us that the Flory-Huggins parameter is strongly dependent on both the polymer concentration and the interaction energy between segments. (Author abstract) 15 Refs.展开更多
In this paper,a conformal energy-conserved scheme is proposed for solving the Maxwell’s equations with the perfectly matched layer.The equations are split as a Hamiltonian system and a dissipative system,respectively...In this paper,a conformal energy-conserved scheme is proposed for solving the Maxwell’s equations with the perfectly matched layer.The equations are split as a Hamiltonian system and a dissipative system,respectively.The Hamiltonian system is solved by an energy-conserved method and the dissipative system is integrated exactly.With the aid of the Strang splitting,a fully-discretized scheme is obtained.The resulting scheme can preserve the five discrete conformal energy conservation laws and the discrete conformal symplectic conservation law.Based on the energy method,an optimal error estimate of the scheme is established in discrete L2-norm.Some numerical experiments are addressed to verify our theoretical analysis.展开更多
Scattering of the shear waves by a nano-sized cylindrical hole embedded the inhomogeneous is investigated in this study. The Helmholtz equation with a variable coefficient is transformed the standard Helmholtz equatio...Scattering of the shear waves by a nano-sized cylindrical hole embedded the inhomogeneous is investigated in this study. The Helmholtz equation with a variable coefficient is transformed the standard Helmholtz equation by the complex function method and the conformal mapping method. By wave function expanding method, the analytical expressions of the displacement field and stress field in the inhomogeneous medium are obtained. Considering the surface effect and using the generalized Young-Laplace equation, we obtain the boundary conditions at nano arbitrary-shaped hole, then the field equations satisfying boundary conditions are attributed to solving a set of infinite algebraic equations. Numerical results show that when the radius of the cylindrical cavity shrinks to nanometers, surface energy becomes a dominant factor that affects the dynamic stress concentration factor (DSCF) around the cylindrical cavity. The influence the density variation of the inhomogeneity on the DSCF is discussed at the same time.展开更多
Abstract Considering the generalized Davey-Stewartson equation $i\mathop u\limits^. - \Delta u + \lambda \left| u \right|^p u + \mu E\left( {\left| u \right|^q } \right)\left| u \right|^{q - 2} u = 0$ where $\lambda &...Abstract Considering the generalized Davey-Stewartson equation $i\mathop u\limits^. - \Delta u + \lambda \left| u \right|^p u + \mu E\left( {\left| u \right|^q } \right)\left| u \right|^{q - 2} u = 0$ where $\lambda > 0,\mu \ge 0,E = F^{ - 1} \left( {\xi _1^2 /\left| \xi \right|^2 } \right)F$ we obtain the existence of scattering operator in ^(A↑^n) := { u ] H1(A↑^n) : |x|u ] L2(A↑^n)}.展开更多
基金Project supported by the National Key Project for Fundamental Research 'Macromolecular Condensed State', the State ScienceTechnology Commission of China.
文摘It is conceptually proposed that the total entropy of polymer solution is contributed from two distinct parts: the positional and the oomformational. The former can be represented analytically, while the latter can be simulated with the random self-avoiding walk model on the simple cubic lattice for multichain systems. The obtained results indicated that both the conformational entropy and the mixing heat are consistent with the scaling laws wry well.
基金This work was supported by the National Key Project for Fundamental Research"Macromolecular Condensed State",The State Science and Technology Commission of China
文摘The statistical counting method for the computer simulation of the thermodynamic quantities of polymer solution has been reviewed. The calculating results for a single athermal chain confirm the theory of the renormalization group. The results for the athermal solution are consistent with the scaling law of the osmotic pressure with the exponent 2.25. The results for a single chain with the segmental interaction are in a good agreement with the exact results obtained by the direct counting method. The results for the polymer solution show us that the Flory-Huggins parameter is strongly dependent on both the polymer concentration and the interaction energy between segments. (Author abstract) 15 Refs.
基金supported by the National Natural Science Foundation of China(Grant Nos.11771213,41504078)the National Key Research and Development Project of China(Grant No.2016YFC0600310)+2 种基金supported by National Key R&D Program of the Ministry of Science and Technology of China with the Project"Integration Platform Construction for Joint Inversion and Interpretation of Integrated Geophysics"(Grant No.2018YFC0603500)the Major Projects of Natural Sciences of University in Jiangsu Province of China(Grant No.15KJA110002)the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘In this paper,a conformal energy-conserved scheme is proposed for solving the Maxwell’s equations with the perfectly matched layer.The equations are split as a Hamiltonian system and a dissipative system,respectively.The Hamiltonian system is solved by an energy-conserved method and the dissipative system is integrated exactly.With the aid of the Strang splitting,a fully-discretized scheme is obtained.The resulting scheme can preserve the five discrete conformal energy conservation laws and the discrete conformal symplectic conservation law.Based on the energy method,an optimal error estimate of the scheme is established in discrete L2-norm.Some numerical experiments are addressed to verify our theoretical analysis.
文摘Scattering of the shear waves by a nano-sized cylindrical hole embedded the inhomogeneous is investigated in this study. The Helmholtz equation with a variable coefficient is transformed the standard Helmholtz equation by the complex function method and the conformal mapping method. By wave function expanding method, the analytical expressions of the displacement field and stress field in the inhomogeneous medium are obtained. Considering the surface effect and using the generalized Young-Laplace equation, we obtain the boundary conditions at nano arbitrary-shaped hole, then the field equations satisfying boundary conditions are attributed to solving a set of infinite algebraic equations. Numerical results show that when the radius of the cylindrical cavity shrinks to nanometers, surface energy becomes a dominant factor that affects the dynamic stress concentration factor (DSCF) around the cylindrical cavity. The influence the density variation of the inhomogeneity on the DSCF is discussed at the same time.
文摘Abstract Considering the generalized Davey-Stewartson equation $i\mathop u\limits^. - \Delta u + \lambda \left| u \right|^p u + \mu E\left( {\left| u \right|^q } \right)\left| u \right|^{q - 2} u = 0$ where $\lambda > 0,\mu \ge 0,E = F^{ - 1} \left( {\xi _1^2 /\left| \xi \right|^2 } \right)F$ we obtain the existence of scattering operator in ^(A↑^n) := { u ] H1(A↑^n) : |x|u ] L2(A↑^n)}.
