Relaxation-Time Limit in the Isothermal Hydrodynamic Model for Semiconductors

2009 ◽  
Vol 40 (5) ◽  
pp. 1979-1991 ◽  
Author(s):  
Jiang Xu
Keyword(s):  
Relaxation Time ◽  
Hydrodynamic Model ◽  
Time Limit

scholarly journals Relaxation-time limit of the multidimensional bipolar hydrodynamic model in Besov space

2011 ◽  
Vol 251 (11) ◽  
pp. 3143-3162 ◽  
Author(s):  
Yeping Li ◽  
Ting Zhang
Keyword(s):  
Relaxation Time ◽  
Besov Space ◽  
Hydrodynamic Model ◽  
Time Limit ◽  
Bipolar Hydrodynamic Model

Instability of a viscous coflowing jet in a radial electric field

2008 ◽  
Vol 596 ◽  
pp. 285-311 ◽  
Author(s):  
FANG LI ◽  
XIE-YUAN YIN ◽  
XIE-ZHEN YIN
Keyword(s):  
Relaxation Time ◽  
Electric Field ◽  
Thin Layer ◽  
Euler Number ◽  
Radial Electric Field ◽  
Dispersion Relations ◽  
Time Limit ◽  
Liquid Viscosity ◽  
Electrical Relaxation ◽  
Thin Layer Approximation

A temporal linear instability analysis of a charged coflowing jet with two immiscible viscous liquids in a radial electric field is carried out for axisymmetric disturbances. According to the magnitude of the liquid viscosity relative to the ambient air viscosity, two generic cases are considered. The analytical dimensionless dispersion relations are derived and solved numerically. Two unstable modes, namely the para-sinuous mode and the para-varicose mode, are identified in the Rayleigh regime. The para-sinuous mode is found to always be dominant in the jet instability. Liquid viscosity clearly stabilizes the growth rates of the unstable modes, but its effect on the cut-off wavenumber is negligible. The radial electric field has a dual effect on the modes, stabilizing them when the electrical Euler number is smaller than a critical value and destabilizing them when it exceeds that value. Moreover, the electrical Euler number and Weber number increase the dominant and cut-off wavenumbers significantly. Based on the Taylor–Melcher leaky dielectric theory, two limit cases, i.e. the small electrical relaxation time limit (SERT) and the large electrical relaxation time limit (LERT), are discussed. For coflowing jets having a highly conducting outer liquid, SERT may serve as a good approximation. In addition, the dispersion relations under the thin layer approximation are derived, and it is concluded that the accuracy of the thin layer approximation is closely related to the values of the dimensionless parameters.

The relaxation-time limit in the compressible Euler–Maxwell equations

2011 ◽  
Vol 74 (18) ◽  
pp. 7005-7011 ◽  
Author(s):  
Jianwei Yang ◽  
Shu Wang ◽  
Juan Zhao
Keyword(s):  
Relaxation Time ◽  
Maxwell Equations ◽  
Time Limit ◽  
Compressible Euler

scholarly journals The relaxation-time limit in the quantum hydrodynamic equations for semiconductors

2006 ◽  
Vol 225 (2) ◽  
pp. 440-464 ◽  
Author(s):  
Ansgar Jüngel ◽  
Hai-Liang Li ◽  
Akitaka Matsumura
Keyword(s):  
Relaxation Time ◽  
Time Limit ◽  
Hydrodynamic Equations ◽  
Quantum Hydrodynamic ◽  
Quantum Hydrodynamic Equations

scholarly journals Switching behavior of a Stoner particle beyond the relaxation time limit

2000 ◽  
Vol 61 (5) ◽  
pp. 3410-3416 ◽  
Author(s):  
M. Bauer ◽  
J. Fassbender ◽  
B. Hillebrands ◽  
R. L. Stamps
Keyword(s):  
Relaxation Time ◽  
Time Limit ◽  
Switching Behavior

STEADY-STATE SOLUTIONS AND ASYMPTOTIC LIMITS ON THE MULTI-DIMENSIONAL SEMICONDUCTOR QUANTUM HYDRODYNAMIC MODEL

2007 ◽  
Vol 17 (02) ◽  
pp. 253-275 ◽  
Author(s):  
BO LIANG ◽  
KAIJUN ZHANG
Keyword(s):  
Relaxation Time ◽  
Steady State ◽  
Hydrodynamic Model ◽  
Planck Constant ◽  
Quantum Hydrodynamic Model ◽  
Uniqueness Results ◽  
Qhd Model ◽  
Quantum Hydrodynamic ◽  
Dispersive Limit ◽  
Steady State Solutions

In this paper we study the steady-state quantum hydrodynamic model for semiconductors. The existence of solutions on the bipolar QHD model is obtained in the case of sufficiently small relaxation time. Uniqueness results are showed both in the thermal equilibrium states and the scaled Planck constant being large enough. The relaxation time and dispersive limit are performed on the bipolar and unipolar equations, respectively. In a sense, we have made a complete answer to the original unsolved problems of the steady-state QHD model.

scholarly journals A Note on the Relaxation-Time Limit of the Isothermal Euler Equations

2007 ◽  
Vol 2007 ◽  
pp. 1-10 ◽  
Author(s):  
Jiang Xu ◽  
Daoyuan Fang
Keyword(s):  
Relaxation Time ◽  
Euler Equations ◽  
Time Limit ◽  
Isothermal Euler Equations
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