In this paper, a procedure for constructing discrete models of the high dimensional nonlinear evolution equanons is presented. In order to construct the difference model, with the aid of the potential system of the or...In this paper, a procedure for constructing discrete models of the high dimensional nonlinear evolution equanons is presented. In order to construct the difference model, with the aid of the potential system of the original equation and compatibility condition, the difference equations which preserve all Lie point symmetries can be obtained. As an example, invariant difference models of the （2＋1）-dimensional Burgers equation are presented.展开更多
Modern computer simulations of biological systems often involve an explicit treatment of the complex interactions among a large number of molecules. While it is straightforward to compute the short-ranged Van der Waal...Modern computer simulations of biological systems often involve an explicit treatment of the complex interactions among a large number of molecules. While it is straightforward to compute the short-ranged Van der Waals interaction in classical molecular dynamics simulations, it has been a long-lasting issue to develop accurate methods for the longranged Coulomb interaction. In this short review, we discuss three types of methodologies for the accurate treatment of electrostatics in simulations of explicit molecules： truncation-type methods, Ewald-type methods, and mean-field-type methods. Throughout the discussion, we brief the formulations and developments of these methods, emphasize the intrinsic connections among the three types of methods, and focus on the existing problems which are often associated with the boundary conditions of electrostatics. This brief survey is summarized with a short perspective on future trends along the method developments and applications in the field of biological simulations.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 11075055 and 11275072)the Innovative Research Team Program of the National Natural Science Foundation of China (Grant No. 61021004)+3 种基金National High Technology Research and Development Program of China (Grant No. 2011AA010101)the Leading Academic Discipline Project of Shanghai (Grant No. B412)the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120076110024)the Shanghai Knowledge Service Platform Project (Grant No. ZF1213)
文摘In this paper, a procedure for constructing discrete models of the high dimensional nonlinear evolution equanons is presented. In order to construct the difference model, with the aid of the potential system of the original equation and compatibility condition, the difference equations which preserve all Lie point symmetries can be obtained. As an example, invariant difference models of the （2＋1）-dimensional Burgers equation are presented.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.91127015 and 21522304)the Open Project from the State Key Laboratory of Theoretical Physicsthe Innovation Project from the State Key Laboratory of Supramolecular Structure and Materials
文摘Modern computer simulations of biological systems often involve an explicit treatment of the complex interactions among a large number of molecules. While it is straightforward to compute the short-ranged Van der Waals interaction in classical molecular dynamics simulations, it has been a long-lasting issue to develop accurate methods for the longranged Coulomb interaction. In this short review, we discuss three types of methodologies for the accurate treatment of electrostatics in simulations of explicit molecules： truncation-type methods, Ewald-type methods, and mean-field-type methods. Throughout the discussion, we brief the formulations and developments of these methods, emphasize the intrinsic connections among the three types of methods, and focus on the existing problems which are often associated with the boundary conditions of electrostatics. This brief survey is summarized with a short perspective on future trends along the method developments and applications in the field of biological simulations.
