This work builds an isobaric steady-state fluid analytical-physical model of the plasma conduction region in a conical target. The hydrodynamic instability in the double-cone ignition scheme^([21]) for inertial confin...This work builds an isobaric steady-state fluid analytical-physical model of the plasma conduction region in a conical target. The hydrodynamic instability in the double-cone ignition scheme^([21]) for inertial confinement fusion(ICF) proposed by Zhang is studied with the built model. With this idealized model, the relevant parameters, such as density, temperature,and length of the plasma in the conduction region of the conical target under long-pulse conditions are given. The solution of the proposed analytical model dovetails with the trend of the numerical simulation. The model and results in this paper are beneficial for discussing how to attenuate Rayleigh-Taylor instability in ICF processes with conical and spherical targets.展开更多
The mathematical model of the three-dimensional semiconductor devices of heat conduction is described by a system of four quasilinear partial differential equations for initial boundary value problem. One equation in ...The mathematical model of the three-dimensional semiconductor devices of heat conduction is described by a system of four quasilinear partial differential equations for initial boundary value problem. One equation in elliptic form is for the electric potential; two equations of convection-dominated diffusion type are for the electron and hole concentration; and one heat conduction equation is for temperature. Characteristic finite difference schemes for two kinds of boundary value problems are put forward. By using the thick and thin grids to form a complete set and treating the product threefold-quadratic interpolation, variable time step method with the boundary condition, calculus of variations and the theory of prior estimates and techniques, the optimal error estimates in L2 norm are derived in the approximate solutions.展开更多
Characteristic finite difference fractional step schemes are put forward. The electric potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are t...Characteristic finite difference fractional step schemes are put forward. The electric potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are treated by a kind of characteristic finite difference fractional step methods. The temperature equation is described by a fractional step method. Thick and thin grids are made use of to form a complete set. Piecewise threefold quadratic interpolation, symmetrical extension, calculus of variations, commutativity of operator product, decomposition of high order difference operators and prior estimates are also made use of. Optimal order estimates in l2 norm are derived to determine the error of the approximate solution. The well-known problem is thorongley and completely solred.展开更多
The effective conductivity of graphene-based nanocomposites is suggested by the characteristics of polymer-filler interfacial areas as well as the contact resistance between the neighboring nanosheets.The interfacial ...The effective conductivity of graphene-based nanocomposites is suggested by the characteristics of polymer-filler interfacial areas as well as the contact resistance between the neighboring nanosheets.The interfacial properties are expressed by the effective levels of the inverse aspect ratio and the filler volume fraction.Moreover,the resistances of components in the contact regions are used to define the contact resistance,which inversely affects the effective conductivity.The obtained model is utilized to predict the effective conductivity for some examples.The discrepancy of the effective conductivity at various ranks of all factors is clarified.The interfacial conductivity directly controls the effective conductivity,while the filler conductivity plays a dissimilar role in the effective conductivity,due to the incomplete interfacial adhesion.A high operative conductivity is also achieved by small contact distances and high interfacial properties.Additionally,big contact diameters and little tunnel resistivity decrease the contact resistance,thus enhancing the effective conductivity.展开更多
基金Project supported by the Strategic Priority Research Program of Chinese Academy of Sciences (Grant Nos. XDA 25051000 and XDA 25010100)。
文摘This work builds an isobaric steady-state fluid analytical-physical model of the plasma conduction region in a conical target. The hydrodynamic instability in the double-cone ignition scheme^([21]) for inertial confinement fusion(ICF) proposed by Zhang is studied with the built model. With this idealized model, the relevant parameters, such as density, temperature,and length of the plasma in the conduction region of the conical target under long-pulse conditions are given. The solution of the proposed analytical model dovetails with the trend of the numerical simulation. The model and results in this paper are beneficial for discussing how to attenuate Rayleigh-Taylor instability in ICF processes with conical and spherical targets.
基金Project supported by the National Scaling Program,the National Eighth-Five Year Tackling Key Problems Program and the Doctoral Found of the National Education Commission.
文摘The mathematical model of the three-dimensional semiconductor devices of heat conduction is described by a system of four quasilinear partial differential equations for initial boundary value problem. One equation in elliptic form is for the electric potential; two equations of convection-dominated diffusion type are for the electron and hole concentration; and one heat conduction equation is for temperature. Characteristic finite difference schemes for two kinds of boundary value problems are put forward. By using the thick and thin grids to form a complete set and treating the product threefold-quadratic interpolation, variable time step method with the boundary condition, calculus of variations and the theory of prior estimates and techniques, the optimal error estimates in L2 norm are derived in the approximate solutions.
基金This work is supported by the Major State Basic Research Program of China (19990328), the National Tackling Key Problem Program, the National Science Foundation of China (10271066 and 0372052), and the Doctorate Foundation of the Ministry of Education of China (20030422047).
文摘Characteristic finite difference fractional step schemes are put forward. The electric potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are treated by a kind of characteristic finite difference fractional step methods. The temperature equation is described by a fractional step method. Thick and thin grids are made use of to form a complete set. Piecewise threefold quadratic interpolation, symmetrical extension, calculus of variations, commutativity of operator product, decomposition of high order difference operators and prior estimates are also made use of. Optimal order estimates in l2 norm are derived to determine the error of the approximate solution. The well-known problem is thorongley and completely solred.
基金Project supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education,Science and Technology(No.2022R1A2C1004437)。
文摘The effective conductivity of graphene-based nanocomposites is suggested by the characteristics of polymer-filler interfacial areas as well as the contact resistance between the neighboring nanosheets.The interfacial properties are expressed by the effective levels of the inverse aspect ratio and the filler volume fraction.Moreover,the resistances of components in the contact regions are used to define the contact resistance,which inversely affects the effective conductivity.The obtained model is utilized to predict the effective conductivity for some examples.The discrepancy of the effective conductivity at various ranks of all factors is clarified.The interfacial conductivity directly controls the effective conductivity,while the filler conductivity plays a dissimilar role in the effective conductivity,due to the incomplete interfacial adhesion.A high operative conductivity is also achieved by small contact distances and high interfacial properties.Additionally,big contact diameters and little tunnel resistivity decrease the contact resistance,thus enhancing the effective conductivity.
