A self-consistent nodal method in response matrix formalism for the multigroup diffusion equations

1996 ◽  
Vol 23 (2) ◽  
pp. 99-118 ◽  
Author(s):  
E.M. Malambu ◽  
E.H. Mund
Keyword(s):  
Diffusion Equations ◽  
Matrix Formalism ◽  
Response Matrix ◽  
Nodal Method ◽  
Self Consistent

Exponential Function Expansion Nodal Diffusion Method

2010 ◽  
Author(s):  
Yunzhao Li ◽  
Hongchun Wu ◽  
Liangzhi Cao ◽  
Qichang Chen
Keyword(s):  
Exponential Function ◽  
Flux Distribution ◽  
Diffusion Method ◽  
Response Matrix ◽  
Nodal Method ◽  
Function Expansion ◽  
Diffusion Calculation ◽  
Nodal Diffusion ◽  
Triangular Block ◽  
Neutron Diffusion Equation

An exponential function expansion nodal diffusion method is proposed to take care of diffusion calculation in unstructured geometry. Transverse integral technique is widely used in nodal method in regular geometry, such as rectangular and hexagonal, while improper in arbitrary triangular geometry because of the mathematical singularity. In this paper, nodal response matrix is derived by expanding detailed nodal flux distribution into a sum of exponential functions, and nodal balance equation can be obtained by strict integral in the polygonal node. Numerical results illustrate that the exponential function expansion nodal method in rectangular and triangular block can solve neutron diffusion equation in regular and irregular geometry.

ILLICO-HO: A Self-Consistent Higher Order Coarse-Mesh Nodal Method

1988 ◽  
Vol 100 (3) ◽  
pp. 332-341 ◽  
Author(s):  
Abderrafi M. Ougouag ◽  
Hrabri L. Rajic
Keyword(s):  
Higher Order ◽  
Coarse Mesh ◽  
Nodal Method ◽  
Self Consistent

A Three-Dimensional Flux Expansion Nodal Method for Hexagonal Geometry Application

2016 ◽  
Author(s):  
Yun Cai ◽  
Xingjie Peng ◽  
Qing Li ◽  
Kan Wang ◽  
Wei Sun ◽  
...  
Keyword(s):  
Power Distribution ◽  
Three Dimensional ◽  
Diffusion Equations ◽  
Benchmark Problems ◽  
Neutron Diffusion ◽  
Exponential Functions ◽  
First Order ◽  
Nodal Method ◽  
Nodal Surfaces ◽  
Flux Expansion

In this paper, a new flux expansion nodal method for hexagonal-z geometry is presented to solve multi-group neutron diffusion equations. In each three dimensional node and each group, the intra-nodal flux is approximated by the linear combination of exponential functions and orthogonal polynomials up to the second order. The coefficients are obtained by the weighted residual methods and the coupling conditions of the nodes, which satisfy the continuity of both the zero- and first-order moments of fluxes and currents across the nodal surfaces. A series of benchmark problems including the three dimensional cases are used to test this method. The numerical results verify that it is a rather accurate and efficient for the estimation of the eigenvalue and power distribution.

Application of the Density Matrix Formalism for Obtaining the Channel Density of a Dual Gate Nanoscale Ultra-Thin MOSFET and its Comparison with the Semi-Classical Approach

2020 ◽  
Vol 19 (06) ◽  
pp. 2050010
Author(s):  
Surender Pratap ◽  
Niladri Sarkar
Keyword(s):  
Density Matrix ◽  
Oxide Semiconductor ◽  
Hamiltonian Matrix ◽  
Matrix Formalism ◽  
Oxide Interface ◽  
Semiconductor Interface ◽  
Channel Density ◽  
Density Matrix Formalism ◽  
Self Consistent ◽  
Dual Gate

Density Matrix Formalism using quantum methods has been used for determining the channel density of dual gate ultra-thin MOSFETs. The results obtained from the quantum methods have been compared with the semi-classical methods. This paper discusses in detail the simulation methods using self-consistent schemes and the discretization procedures for constructing the Hamiltonian Matrix for a dual gate MOSFET consisting of oxide/semiconductor/oxide interface and the self-consistent procedure involving the discretization of Poisson’s equation for satisfying the charge neutrality condition in the channel of different thicknesses. Under quantum methods, the channel densities are determined from the diagonal elements of the density matrix. This successfully simulates the size quantization effect for thin channels. For semi-classical methods, the Fermi–Dirac Integral function is used for the determination of the channel density. For thin channels, the channel density strongly varies with the values of the effective masses. This variation is simulated when we use Quantum methods. The channel density also varies with the asymmetric gate bias and this variation is more for thicker channels where the electrons get accumulated near the oxide/semiconductor interface. All the calculations are performed at room temperature (300[Formula: see text]K).

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