Making use of a new and more general ansatz, we present the generalized algebraic method to uniformlyconstruct a series of new and general travelling wave solution for nonlinear partial differential equations. As an a...Making use of a new and more general ansatz, we present the generalized algebraic method to uniformlyconstruct a series of new and general travelling wave solution for nonlinear partial differential equations. As an applicationof the method, we choose a (1+1)-dimensional dispersive long wave equation to illustrate the method. As a result, wecan successfully obtain the solutions found by the method proposed by Fan [E. Fan, Comput. Phys. Commun. 153 (2003)17] and find other new and more general solutions at the same time, which include polynomial solutions, exponentialsolutions, rational solutions, triangular periodic wave solutions, hyperbolic and soliton solutions, Jacobi and Weierstrassdoubly periodic wave solutions.展开更多
The structure of fractures in nature rock appears irregular and induces complicated seepage flow behavior.The mechanism and quantitative description of fluid flow through rock fractures is a difficult subject that has...The structure of fractures in nature rock appears irregular and induces complicated seepage flow behavior.The mechanism and quantitative description of fluid flow through rock fractures is a difficult subject that has been greatly concerned in the fields of geotechnical,mining,geological,and petroleum engineering.In order to probe the mechanism of fluid flow and the effects of rough structures,we conducted a few laboratory tests of fluid flow through single rough fractures,in which the Weierstrass-Mandelbrot fractal function and PMMA material were employed to produce the fracture models with various fractal roughnesses.A high-speed video camera was employed to record the fluid flow through the entire single rough fracture with a constant hydraulic pressure.The properties of fluid flow varying with the fracture roughness and the influences of the rough structure were analyzed.The components of flow resistance of a single rough fracture were discussed.A fractal model was proposed to relate the fluid resistance to the fracture roughness.A fractal equivalent permeability coefficient of a single rough fracture was formulated.This study aims to provide an experimental basis and reference for better understanding and quantitatively relating the fluid flow properties to the structures of rock fractures.展开更多
文摘Making use of a new and more general ansatz, we present the generalized algebraic method to uniformlyconstruct a series of new and general travelling wave solution for nonlinear partial differential equations. As an applicationof the method, we choose a (1+1)-dimensional dispersive long wave equation to illustrate the method. As a result, wecan successfully obtain the solutions found by the method proposed by Fan [E. Fan, Comput. Phys. Commun. 153 (2003)17] and find other new and more general solutions at the same time, which include polynomial solutions, exponentialsolutions, rational solutions, triangular periodic wave solutions, hyperbolic and soliton solutions, Jacobi and Weierstrassdoubly periodic wave solutions.
基金supported by the National Science Funds for Distinguished Young Scholar of China (Grant No. 51125017)the National Basic Research Program of China (Grant Nos. 2010CB226804,2011CB201201)+2 种基金the National Natural Science Foundation of China (Grant No. 50974125)the International Cooperation Project of Ministry of Science & Technology of China (Grant No. 2012DFA60760-2)NSFC International Cooperation and Exchange Program (Grant No. 51120145001)
文摘The structure of fractures in nature rock appears irregular and induces complicated seepage flow behavior.The mechanism and quantitative description of fluid flow through rock fractures is a difficult subject that has been greatly concerned in the fields of geotechnical,mining,geological,and petroleum engineering.In order to probe the mechanism of fluid flow and the effects of rough structures,we conducted a few laboratory tests of fluid flow through single rough fractures,in which the Weierstrass-Mandelbrot fractal function and PMMA material were employed to produce the fracture models with various fractal roughnesses.A high-speed video camera was employed to record the fluid flow through the entire single rough fracture with a constant hydraulic pressure.The properties of fluid flow varying with the fracture roughness and the influences of the rough structure were analyzed.The components of flow resistance of a single rough fracture were discussed.A fractal model was proposed to relate the fluid resistance to the fracture roughness.A fractal equivalent permeability coefficient of a single rough fracture was formulated.This study aims to provide an experimental basis and reference for better understanding and quantitatively relating the fluid flow properties to the structures of rock fractures.
