scholarly journals Asymptotic expansion of solutions to the drift–diffusion equation with fractional dissipation

2016 ◽  
Vol 141 ◽  
pp. 57-87 ◽  
Author(s):  
Masakazu Yamamoto ◽  
Yuusuke Sugiyama
Keyword(s):  
Asymptotic Expansion ◽  
Diffusion Equation ◽  
Drift Diffusion ◽  
Asymptotic Expansion Of Solutions

scholarly journals Asymptotic Expansion of the Solutions to Time-Space Fractional Kuramoto-Sivashinsky Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Weishi Yin ◽  
Fei Xu ◽  
Weipeng Zhang ◽  
Yixian Gao
Keyword(s):  
Asymptotic Expansion ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Initial Conditions ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Power Series Method ◽  
Time Space ◽  
Residual Power Series ◽  
Asymptotic Expansion Of Solutions

This paper is devoted to finding the asymptotic expansion of solutions to fractional partial differential equations with initial conditions. A new method, the residual power series method, is proposed for time-space fractional partial differential equations, where the fractional integral and derivative are described in the sense of Riemann-Liouville integral and Caputo derivative. We apply the method to the linear and nonlinear time-space fractional Kuramoto-Sivashinsky equation with initial value and obtain asymptotic expansion of the solutions, which demonstrates the accuracy and efficiency of the method.

scholarly journals Formulation of the Boltzmann Equation as a Multi-Mode Drift-Diffusion Equation

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 539-544
Author(s):  
K. Banoo ◽  
F. Assad ◽  
M. S. Lundstrom
Keyword(s):  
Diffusion Coefficient ◽  
Boltzmann Equation ◽  
Diffusion Equation ◽  
Momentum Space ◽  
Bulk Silicon ◽  
Rigorous Solution ◽  
Drift Diffusion ◽  
The Boltzmann Equation ◽  
And Diffusion ◽  
Multi Mode

We present a multi-mode drift-diffusion equation as reformulation of the Boltzmann equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.

Numerical Modeling of Heat Transfer and Phase Transition in Programming the Ovonic Unified Memory Cells

2005 ◽  
Author(s):  
Evan Small ◽  
Sadegh M. Sadeghipour ◽  
Mehdi Asheghi
Keyword(s):  
Heat Transfer ◽  
Phase Transition ◽  
Diffusion Equation ◽  
Dynamic Range ◽  
Semiconductor Device ◽  
Computer Code ◽  
Drift Diffusion ◽  
Thermally Induced ◽  
Design And Optimization ◽  
Phase Prediction

An Ovonic Unified Memory (OUM) cell is a semiconductor device that stores data by a thermally induced phase transition between polycrystalline (set) and amorphous (reset) states in a thin film of chalcogenide alloy. The small volume of active media acts as a programmable resistor switching between a high (amorphous) and low (crystalline) resistance state. The change in the film resistivity (>40X dynamic range) caused by this rapid, reversible structural change is measured to detect the state of the cell (set or reset) for read out. OUM can benefit from a simulator capable of predicting the electrical, thermal, and crystallization behavior for design and optimization, particularly at the present stage of the development. This paper reports on the efforts being made to prepare such a numerical simulator, using an existing finite element computer code as the source for thermal and electrical modeling, and a custom crystallization code for phase prediction. Heat generation in the device is by Joule heating and is achieved by passage of the electric current, which is obtained from the electrical simulation. This result appears in the heat source term of the heat transfer equation that is solved for thermal modeling. As the first attempt the Ohmic current-voltage relation was implemented successfully to simulate set and reset in a two dimensional model of OUM. Solution of the drift-diffusion equation is now underway to capture the semiconductor behavior of the I-V curve. A good progress is made however, still more works needs to be done to fully implement the drift diffusion equation.

AN INEQUALITY BY GIANAZZA, SAVARÉ AND TOSCANI AND ITS APPLICATIONS TO THE VISCOUS QUANTUM EULER MODEL

2013 ◽  
Vol 15 (05) ◽  
pp. 1250067 ◽  
Author(s):  
XIANGSHENG XU
Keyword(s):  
Weak Solution ◽  
Diffusion Equation ◽  
Boundary Value Problem ◽  
Fisher Information ◽  
Gradient Flow ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Drift Diffusion ◽  
Euler Model ◽  
Initial Boundary Value

In this paper we present a simplified version of a coercivity inequality due to Gianazza, Savaré, and Toscani [The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation, Arch. Ration. Mech. Anal.194 (2009) 133–220]. Then we use the inequality to construct a weak solution to the initial-boundary value problem for the viscous quantum Euler model.

Sign in / Sign up

Export Citation Format

Share Document