Reflection and Transmission Coefficients for Two- and Three-Dimensional Quantum Wires

1997 ◽  
Vol 11 (23) ◽  
pp. 2777-2790 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Reflection Coefficient ◽  
Quantum Wires ◽  
Three Dimensional ◽  
Variable Cross Section ◽  
Wave Number ◽  
Variable Cross ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Matrix Differential Equations ◽  
Matrix Differential

The problem of a quantum wire connected smoothly on both sides to leads of variable cross section is studied. A method for solving this problem in terms of a set of nonlinear first order matrix differential equations for the variable reflection amplitude is discussed. The reflection coefficient obtained in this way is directly related to the conductivity, and is calculated as a function of the energy of the ballistic electrons. This formulation can be applied to three-dimensional as well as two dimensional quantum wires. For two specific cases the reflection coefficient is obtained as a function of the wave number of the incident electron, and the contribution of quantum tunneling to the transmission in each case is demonstrated. Also a model with a dissipative force is introduced and its effect on the transmission of the electrons is investigated.

Boundary element method in numerical study of three-dimensional Stokes flows in channels of arbitrary shape

2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Periodic Flows ◽  
Element Method

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.

scholarly journals Homogenization of very rough three-dimensional interfaces for the poroelasticity theory with Biot's model

2019 ◽  
Author(s):  
Nguyen Thi Kieu ◽  
Pham Chi Vinh ◽  
Do Xuan Tung
Keyword(s):  
Incident Angle ◽  
Three Dimensional ◽  
Homogenization Method ◽  
Reflection And Transmission Coefficients ◽  
Biot Theory ◽  
Rough Interface ◽  
Matrix Formulation ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
The Matrix

In this paper, we carry out the homogenization of a very rough three-dimensional interface separating  two dissimilar generally anisotropic poroelastic solids modeled by the Biot theory. The very rough interface is assumed to be a cylindrical surface that rapidly oscillates between two parallel planes, and the motion is time-harmonic. Using the homogenization method with the matrix formulation of the poroelasicity theory, the explicit  homogenized equations have been derived. Since the obtained  homogenized equations are totally explicit, they are very convenient for solving various practical problems. As an example proving this, the reflection and transmission of SH waves at a very rough interface of tooth-comb type is considered. The closed-form analytical expressions of the reflection and transmission coefficients have been  derived. Based on them, the effect of the incident angle and some material parameters  on the reflection and transmission coefficients are examined numerically.

Three-Dimensional Force and Deflection Analysis of a Variable Cross Section Drill String

1977 ◽  
Vol 99 (2) ◽  
pp. 367-373 ◽  
Author(s):  
B. H. Walker ◽  
M. B. Friedman
Keyword(s):  
Mechanical Properties ◽  
Mathematical Model ◽  
Cross Section ◽  
Three Dimensional ◽  
Variable Cross Section ◽  
Drill String ◽  
Oil Field ◽  
Variable Cross ◽  
Deflection Curve ◽  
Deflection Analysis

A mathematical model of an oil field drill string which includes the effect of torque has been developed. The drill string can include arbitrary members with known mechanical properties. The solution gives the three-dimensional deflection curve, forces on the borehole wall, the magnitude and direction of the resultant force and slope of the deflection curve at the bit.

Scattering of surface waves obliquely incident on a fixed half immersed circular cylinder

1984 ◽  
Vol 96 (2) ◽  
pp. 359-369 ◽  
Author(s):  
B. N. Mandal ◽  
S. K. Goswami
Keyword(s):  
Integral Equation ◽  
Surface Water ◽  
Circular Cylinder ◽  
Water Waves ◽  
Wave Number ◽  
Angle Of Incidence ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Obliquely Incident ◽  
Surface Water Waves

AbstractThe problem of scattering of surface water waves obliquely incident on a fixed half immersed circular cylinder is solved approximately by reducing it to the solution of an integral equation and also by the method of multipoles. For different values of the angle of incidence and the wave number the reflection and transmission coefficients obtained by both methods are evaluated numerically and represented graphically to compare the results obtained by the respective methods.

Elastic-Plastic Finite Element Simulation of Bulge Forming Process Using a Variable Cross-Section Solid Bulging Mold

2011 ◽  
Vol 189-193 ◽  
pp. 4405-4408
Author(s):  
Ke Wang ◽  
Zhe Ying Wang ◽  
Xing Wei Sun
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Metal Flow ◽  
Three Dimensional ◽  
Variable Cross Section ◽  
Flow Mode ◽  
Variable Cross ◽  
Forming Process ◽  
Element Analysis ◽  
Screw Rotor

Bulge forming is a novel process aimed at common products including T-branches, cross branches and angle branches. But bulging forming has not applied for two-head abnormity-shaped hollow screw rotor reported in literature. Simulation of the bulging forming of two-head abnormity-shaped hollow screw rotor has not been reported. This paper presents a simulation of the bulge forming process of two-head abnormity-shaped hollow screw rotor using a variable cross-section solid bulging mold. Some conditions including the effect of friction, boundary conditions, contact conditions and the space motion, etc are presented. The mathematical model of three-dimensional finite element analysis has been established. The distribution of generalized plastic strain and general metal flow mode in cross section of two abnormity-shaped hollow screw rotor has been analyzed. It is an effective method for the analysis of other defects and the optimization of process parameters further.

NEW ANALYTICAL METHOD OF DISPERSION CURVES IN PLANE LAYERED STRUCTURES

2012 ◽  
Vol 20 (03) ◽  
pp. 1250010 ◽  
Author(s):  
C. PACHIU ◽  
H. FRANKLIN ◽  
J.-L. IZBICKI
Keyword(s):  
Computation Time ◽  
Layered Structures ◽  
Dispersion Curves ◽  
Wave Number ◽  
Dual Representation ◽  
Reflection And Transmission ◽  
The Real ◽  
Transmission Coefficients ◽  
Layer Structures ◽  
Raphson Method

The propagation of sound through plane layered structures is considered, with emphasis on three-layers made up of thick isotropic plates coupled with a thin anisotropic one. Modes are obtained by means of the transition terms method (TTM) based upon the use of the reflection and transmission coefficients. This method differs from the root searching methods (RSM) of dispersion equations such as, for instance, the Newton–Raphson method. The TTM provides dispersion curves with very little computation time. It unifies the dual representation of the dispersion curves: either complex wave numbers versus the real frequency, or complex frequencies versus the real wave number. The application to various cases of three-layer structures allows us to check the validity of the method and to discuss the connection between the TTM and Cremer's correspondence principle.

Three-dimensional numerical simulation of viscous liquid flow in channel of variable cross-section using boundary element method

2011 ◽  
Vol 8 (1) ◽  
pp. 155-162
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Viscous Liquid ◽  
Cross Section ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Element Method

In the present work the three-dimensional flow of a viscous liquid described by Stokes equations is studied in a cylindrical tube and a channel of variable cross-section. A qualitative triangulation of the surface of a channel variable cross-section is constructed. The problem is solved numerically using the boundary element method in two modifications. A comparison of the method modifications for a channel of different radius of a neck, as well as for the Poiseuille flow with an analytical solution. It is found out the critical radius of the channel neck at which the vortices arise.

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