Nonthermal atmospheric rf plasma in one-dimensional spherical coordinates: Asymmetric sheath structure and the discharge mechanism

2007 ◽  
Vol 101 (7) ◽  
pp. 073306 ◽  
Author(s):  
Yukinori Sakiyama ◽  
David B. Graves
Keyword(s):  
Rf Plasma ◽  
Spherical Coordinates ◽  
One Dimensional ◽  
Discharge Mechanism ◽  
Sheath Structure

One-Dimensional PbS/Polymer Nanocomposite of Core/Sheath Structure Fabricated by Hydrothermal Polymerization and Simultaneous Sulfidation

2001 ◽  
Vol 30 (10) ◽  
pp. 1000-1001 ◽  
Author(s):  
Jing-hui Zeng ◽  
Yu Zhu ◽  
Jian Yang ◽  
Yuan-fang Liu ◽  
Yi-Tai Qian
Keyword(s):  
Polymer Nanocomposite ◽  
One Dimensional ◽  
Sheath Structure

Parity inversion property of the double ring-shaped oscillator in cylindrical coordinates

2015 ◽  
Vol 30 (39) ◽  
pp. 1550200 ◽  
Author(s):  
Dong-Sheng Sun ◽  
Fa-Lin Lu ◽  
Yuan You ◽  
Chang-Yuan Chen ◽  
Shi-Hai Dong
Keyword(s):  
Functional Analysis ◽  
Singular Point ◽  
Harmonic Oscillator ◽  
Two Dimensional ◽  
Spherical Coordinates ◽  
Analysis Method ◽  
Cylindrical Coordinates ◽  
One Dimensional ◽  
Double Ring ◽  
The One

Using the functional analysis method, we present the exact solutions of the double ring-shaped oscillator (DRSO) potential with certain parity in the cylindrical coordinates. Such a quantum system is separated to two differential equations, i.e. a one-dimensional harmonic oscillator plus an inverse square term and a two-dimensional harmonic oscillator plus an inverse square term. The key point is how to find the adapted symmetrical solutions of the one-dimensional harmonic oscillator plus an inverse square term at the singular point [Formula: see text]. The obtained results are compared with those in the spherical coordinates. We also explore intimate connections [Formula: see text] and [Formula: see text] by substituting [Formula: see text] and [Formula: see text].

One-dimensional modelling of a capacitively coupled rf plasma in silane/helium, including small concentrations of O2and N2

2003 ◽  
Vol 36 (15) ◽  
pp. 1826-1833 ◽  
Author(s):  
K De Bleecker ◽  
D Herrebout ◽  
A Bogaerts ◽  
R Gijbels ◽  
P Descamps
Keyword(s):  
Rf Plasma ◽  
Capacitively Coupled ◽  
One Dimensional

Heat conduction in one-dimensional functionally graded media based on the dual-phase-lag theory

2012 ◽  
Vol 227 (4) ◽  
pp. 744-759 ◽  
Author(s):  
AH Akbarzadeh ◽  
ZT Chen
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Functionally Graded ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Dual Phase ◽  
Spherical Coordinates ◽  
One Dimensional ◽  
Phase Lags ◽  
Functionally Graded Media

In this article, heat conduction in one-dimensional functionally graded media is investigated based on the dual-phase-lag theory to consider the microstructural interactions in the fast transient process of heat conduction. All material properties of the media are assumed to vary continuously according to a power-law formulation with arbitrary non-homogeneity indices except the phase lags which are taken constant for simplicity. The one-dimensional heat conduction equations based on the dual-phase-lag theory are derived in a unified form which can be used for Cartesian, cylindrical, and spherical coordinates. A semi-analytical solution for temperature and heat flux is presented using the Laplace transform to eliminate the time dependency of the problem. The results in the time domain are then given by employing a numerical Laplace inversion technique. The semi-analytical solution procedure leads to exact expressions for the thermal wave speed in one-dimensional functionally graded media with different geometries based on the dual-phase-lag and hyperbolic heat conduction theories. The transient temperature distributions have been found for various types of dynamic thermal loading. The numerical results are shown to reveal the effects of phase lags, non-homogeneity indices, and thermal boundary conditions on the thermal responses for different temporal disturbances. The results are verified with those reported in the literature for hyperbolic heat conduction in cylindrical and spherical coordinates.

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