APPLICATION OF WEAK EQUIVALENCE TRANSFORMATIONS TO A GROUP ANALYSIS OF A DRIFT-DIFFUSION MODEL
@article{Romano1999APPLICATIONOW, title={APPLICATION OF WEAK EQUIVALENCE TRANSFORMATIONS TO A GROUP ANALYSIS OF A DRIFT-DIFFUSION MODEL}, author={Vittorio Romano and Mariano Torrisi}, journal={Journal of Physics A}, year={1999}, volume={32}, pages={7953-7963} }
A group analysis of a class of drift-diffusion systems is performed. In account of the presence of arbitrary constitutive functions, we look for Lie symmetries starting from the weak equivalence transformations. Applications to the transport of charges in semiconductors are presented and a special class of solutions is given for particular doping profiles.
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References
SHOWING 1-10 OF 21 REFERENCES
A group analysis approach for a nonlinear differential system arising in diffusion phenomena
- Mathematics
- 1996
We consider a class of second‐order partial differential equations which arises in diffusion phenomena and, following a new approach, we look for a Lie invariance classification via equivalence…
Nonlocal symmetries. Heuristic approach
- Mathematics
- 1991
A constructive method for constructing nonlocal symmetries of differential equations based on the Lie—Bäcklund theory of groups is developed. The concept of quasilocal symmetries is introduced. With…
Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics
- Mathematics
- 1993
Some remarks on a class of ordinary differential equations: the Riccati property, differential-algebraic and differential-geometric approach to the study of involutive symbols, and the bihamiltonian approach to integrable systems.
Preliminary group classification of equations vtt=f(x,vx)vxx+g(x,vx)
- Mathematics, Computer Science
- 1991
The paper is one of few applications of a new algebraic approach to the problem of group classification: the method of preliminary group classification.
Applications of lie groups to differential equations
- Mathematics
- 1986
1 Introduction to Lie Groups.- 1.1. Manifolds.- Change of Coordinates.- Maps Between Manifolds.- The Maximal Rank Condition.- Submanifolds.- Regular Submanifolds.- Implicit Submanifolds.- Curves and…
The drift diffusion equation and its applications in MOSFET modeling
- Engineering
- 1991
1 Boltzmann's Equation.- 1.1 Introduction.- 1.2 Many-Body System in Equilibrium.- 1.2.1 Quantum Mechanics of Many-Body Systems.- 1.2.2 Green's Functions for Electrons.- 1.2.3 Self-Energy.- 1.2.4…
Analysis and simulation of semiconductor devices
- Engineering
- 1984
1. Introduction.- 1.1 The Goal of Modeling.- 1.2 The History of Numerical Device Modeling.- 1.3 References.- 2. Some Fundamental Properties.- 2.1 Poisson's Equation.- 2.2 Continuity Equations.- 2.3…