American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Existence and uniqueness of solutions of a system of nonlinear PDE for phase transitions with vector order parameter
  • PROC Home
  • This Issue
  • Next Article
    Exponential attractors for 2d magneto-micropolor fluid flow in bounded domain
2005, 2005(Special): 642-651. doi: 10.3934/proc.2005.2005.642

Accounting for nonlinearities in mathematical modelling of quantum dot molecules

Roderick Melnik 1, , B. Lassen 2, , L. C Lew Yan Voon 3, , M. Willatzen 2, and  C. Galeriu 4,

1. 

Mathematical Modelling and Computational Sciences, Wilfrid Laurier University, Waterloo, 75 University Avenue West, Waterloo, ON, Canada
2. 

Mads Clausen Institute, Syddansk University, Grundtvigs Alle 150, DK-6400 Sonderborg, Denmark, Denmark
3. 

Department of Physics, Wright State University, 3640 Colonel Glenn Highway, Dayton, OH 45305, United States
4. 

Department of Physics, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, United States

Received  September 2004 Revised  May 2005 Published  September 2005

Nonlinear mathematical models are becoming increasingly important for new applications of low-dimensional semiconductor structures. Examples of such structures include quasi-zero-dimensional quantum dots that have potential applications ranging from quantum computing to nano-biological devices. In this contribution, we analyze presently dominating linear models for bandstructure calculations and demonstrate why nonlinear models are required for characterizing adequately optoelectronic properties of self-assembled quantum dots.
Keywords: quantum dots, coupled PDEs, strain, modeling, bandstructures..
Mathematics Subject Classification: Primary: 35, 65, 8.
Citation: Roderick Melnik, B. Lassen, L. C Lew Yan Voon, M. Willatzen, C. Galeriu. Accounting for nonlinearities in mathematical modelling of quantum dot molecules. Conference Publications, 2005, 2005 (Special) : 642-651. doi: 10.3934/proc.2005.2005.642
[1]

Doron Levy, Tiago Requeijo. Modeling group dynamics of phototaxis: From particle systems to PDEs. Discrete & Continuous Dynamical Systems - B, 2008, 9 (1) : 103-128. doi: 10.3934/dcdsb.2008.9.103
[2]

Marco Cicalese, Antonio DeSimone, Caterina Ida Zeppieri. Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers. Networks & Heterogeneous Media, 2009, 4 (4) : 667-708. doi: 10.3934/nhm.2009.4.667
[3]

Juan Li, Wenqiang Li. Controlled reflected mean-field backward stochastic differential equations coupled with value function and related PDEs. Mathematical Control & Related Fields, 2015, 5 (3) : 501-516. doi: 10.3934/mcrf.2015.5.501
[4]

Ronald E. Mickens. Positivity preserving discrete model for the coupled ODE's modeling glycolysis. Conference Publications, 2003, 2003 (Special) : 623-629. doi: 10.3934/proc.2003.2003.623
[5]

Maria Francesca Carfora, Enrica Pirozzi. Stochastic modeling of the firing activity of coupled neurons periodically driven. Conference Publications, 2015, 2015 (special) : 195-203. doi: 10.3934/proc.2015.0195
[6]

Joseph R. Zipkin, Martin B. Short, Andrea L. Bertozzi. Cops on the dots in a mathematical model of urban crime and police response. Discrete & Continuous Dynamical Systems - B, 2014, 19 (5) : 1479-1506. doi: 10.3934/dcdsb.2014.19.1479
[7]

Olaf Hansen. A global existence theorem for two coupled semilinear diffusion equations from climate modeling. Discrete & Continuous Dynamical Systems - A, 1997, 3 (4) : 541-564. doi: 10.3934/dcds.1997.3.541
[8]

Sandesh Athni Hiremath, Christina Surulescu, Anna Zhigun, Stefanie Sonner. On a coupled SDE-PDE system modeling acid-mediated tumor invasion. Discrete & Continuous Dynamical Systems - B, 2018, 23 (6) : 2339-2369. doi: 10.3934/dcdsb.2018071
[9]

Helmut Kröger. From quantum action to quantum chaos. Conference Publications, 2003, 2003 (Special) : 492-500. doi: 10.3934/proc.2003.2003.492
[10]

Alexander Komech. Attractors of Hamilton nonlinear PDEs. Discrete & Continuous Dynamical Systems - A, 2016, 36 (11) : 6201-6256. doi: 10.3934/dcds.2016071
[11]

Gilles A. Francfort, Alessandro Giacomini, Alessandro Musesti. On the Fleck and Willis homogenization procedure in strain gradient plasticity. Discrete & Continuous Dynamical Systems - S, 2013, 6 (1) : 43-62. doi: 10.3934/dcdss.2013.6.43
[12]

Enrico Valdinoci. Contemporary PDEs between theory and applications. Discrete & Continuous Dynamical Systems - A, 2015, 35 (12) : i-i. doi: 10.3934/dcds.2015.35.12i
[13]

Paolo Antonelli, Pierangelo Marcati. Quantum hydrodynamics with nonlinear interactions. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 1-13. doi: 10.3934/dcdss.2016.9.1
[14]

Gabriel Rivière. Remarks on quantum ergodicity. Journal of Modern Dynamics, 2013, 7 (1) : 119-133. doi: 10.3934/jmd.2013.7.119
[15]

Sergei Avdonin, Pavel Kurasov. Inverse problems for quantum trees. Inverse Problems & Imaging, 2008, 2 (1) : 1-21. doi: 10.3934/ipi.2008.2.1
[16]

Dmitry Jakobson. On quantum limits on flat tori. Electronic Research Announcements, 1995, 1: 80-86.

[17]

Frédéric Sur, Michel Grédiac. Towards deconvolution to enhance the grid method for in-plane strain measurement. Inverse Problems & Imaging, 2014, 8 (1) : 259-291. doi: 10.3934/ipi.2014.8.259
[18]

Alessandro Giacomini. On the energetic formulation of the Gurtin and Anand model in strain gradient plasticity. Discrete & Continuous Dynamical Systems - B, 2012, 17 (2) : 527-552. doi: 10.3934/dcdsb.2012.17.527
[19]

Raz Kupferman, Asaf Shachar. On strain measures and the geodesic distance to $SO_n$ in the general linear group. Journal of Geometric Mechanics, 2016, 8 (4) : 437-460. doi: 10.3934/jgm.2016015
[20]

Junyuan Yang, Yuming Chen, Jiming Liu. Stability analysis of a two-strain epidemic model on complex networks with latency. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2851-2866. doi: 10.3934/dcdsb.2016076

 Impact Factor: 

Tools

Metrics

  • PDF downloads (4)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences