This paper illustrates the use of a general purpose differential equation （DE） solver called FlexPDE for the solution heat transfer problems in electric wire. FlexPDE uses the finite element method for the solution ...This paper illustrates the use of a general purpose differential equation （DE） solver called FlexPDE for the solution heat transfer problems in electric wire. FlexPDE uses the finite element method for the solution of boundary and initial value problems. A flexible input of the governing DE＇s and of material properties functions allows the simulation of non-linear variable behavior quickly and inexpensively. A modeling of temperature distribution in one-dimensional problem, a cross section of an electric wire was simulated. Comparison of those results obtained by FlexPDE with analytical and numerical solutions are done. The results compared well with those obtained from the analytical and numerical methods. The adaptability of the FlexPDE software for solving a variety of problem types was clearly demonstrated.展开更多
In this paper,we consider a localized problem with free boundary for the heat equation in higher space dimensions and heterogeneous environment.For simplicity,we assume that the environment and solution are radially s...In this paper,we consider a localized problem with free boundary for the heat equation in higher space dimensions and heterogeneous environment.For simplicity,we assume that the environment and solution are radially symmetric.First,by using the contraction mapping theorem,we prove that the local solution exists and is unique.Then,some sufficient conditions are given under which the solution will blow up in finite time.Our results indicate that the blowup occurs if the initial data are sufficiently large.Finally,the long time behavior of the global solution is discussed.It is shown that the global fast solution does exist if the initial data are sufficiently small,while the global slow solution is possible if the initial data are suitably large.展开更多
The piezoresistive behavior of carbon black (CB) filled poly(methyl vinyl siloxane) (PMVS) vulcanites under uniaxial compression was studied.At filler weight frac- tions φ slightly above the percolation threshold φc...The piezoresistive behavior of carbon black (CB) filled poly(methyl vinyl siloxane) (PMVS) vulcanites under uniaxial compression was studied.At filler weight frac- tions φ slightly above the percolation threshold φc,resistance first increased with pressure and then turned to decrease at a critical compressive stress,exhibiting a positive pressure co- efficient of resistance (PPCR) and a negative pressure coeffi- cient of resistance (NPCR) effects ,respectively.The NPCR effect became much more pronounced at φ>>φc,while com- pressive cycles facilitated the occurrence of the weak PPCR effect during compression.The PPCR-NPCR transition was a process related to true stress.It is believed that the changes of microstructure in the percolating network,i.e. the breakdown and the reformation of infinite conducting clusters,under pressure would be responsible for the uniaxial piezoresis- tance and the plastic deformation of the filled vulcanites.展开更多
文摘This paper illustrates the use of a general purpose differential equation （DE） solver called FlexPDE for the solution heat transfer problems in electric wire. FlexPDE uses the finite element method for the solution of boundary and initial value problems. A flexible input of the governing DE＇s and of material properties functions allows the simulation of non-linear variable behavior quickly and inexpensively. A modeling of temperature distribution in one-dimensional problem, a cross section of an electric wire was simulated. Comparison of those results obtained by FlexPDE with analytical and numerical solutions are done. The results compared well with those obtained from the analytical and numerical methods. The adaptability of the FlexPDE software for solving a variety of problem types was clearly demonstrated.
基金supported by National Natural Science Foundation of China (Grant Nos.11071209 and 10801115)the PhD Programs Foundation of Ministry of Education of China (Grant No.20113250110005)
文摘In this paper,we consider a localized problem with free boundary for the heat equation in higher space dimensions and heterogeneous environment.For simplicity,we assume that the environment and solution are radially symmetric.First,by using the contraction mapping theorem,we prove that the local solution exists and is unique.Then,some sufficient conditions are given under which the solution will blow up in finite time.Our results indicate that the blowup occurs if the initial data are sufficiently large.Finally,the long time behavior of the global solution is discussed.It is shown that the global fast solution does exist if the initial data are sufficiently small,while the global slow solution is possible if the initial data are suitably large.
基金This work was supported by the Key Program of the National Natural Science Foundation of China(Grant No.50133020)the National Science Foundation for Distinguished Young Scholars(Grant No.50125312).
文摘The piezoresistive behavior of carbon black (CB) filled poly(methyl vinyl siloxane) (PMVS) vulcanites under uniaxial compression was studied.At filler weight frac- tions φ slightly above the percolation threshold φc,resistance first increased with pressure and then turned to decrease at a critical compressive stress,exhibiting a positive pressure co- efficient of resistance (PPCR) and a negative pressure coeffi- cient of resistance (NPCR) effects ,respectively.The NPCR effect became much more pronounced at φ>>φc,while com- pressive cycles facilitated the occurrence of the weak PPCR effect during compression.The PPCR-NPCR transition was a process related to true stress.It is believed that the changes of microstructure in the percolating network,i.e. the breakdown and the reformation of infinite conducting clusters,under pressure would be responsible for the uniaxial piezoresis- tance and the plastic deformation of the filled vulcanites.
