https://doi.org/10.65770/KFFB9968
ABSTRACT
Nano-bio-technologies are a new interdisciplinary scientific sector, with revolutionary perspectives due to the fact that, at nano-size, the behavior and characteristics of matter radically change with respect to macroscopic dimensions. The paper provides an overview of the mathematical analytical modeling for transport (nano-)processes, through which the phenomena of charge transport (at nanometer level) are considered (also with reference to the most used numerical methods); it considers also recent advances in analytical (nano-)modeling. Plasmonics and related applications are also described. Examples of application are collected in the Appendix.
References
- [1] Di Sia P (2011). An Analytical Transport Model for Nanomaterials. Journal of Computational and Theoretical Nanoscience 8, 84-89. https://doi.org/10.1166/jctn.2011.1663.
- [2] Hughes TJR (2000). The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Dover Publications, Mineola, NY.
- [3] Bucalem ML, Bathe K-J (2011). The Mechanics of Solids and Structures – Hierarchical Modeling and the Finite Element Solution. Springer, Berlin, Heidelberg.
- [4] Di Sia P (2014). Overview of Drude-Lorentz type models and their applications. Nanoscale Systems: Mathematical Modeling, Theory and Applications 3(1), 1-13. https://eudml.org/doc/267041.
- [5] Cleland AN (2003). Foundations of Nanomechanics: From Solid-State Theory to Device Applications. Springer, Berlin, Heidelberg.
- [6] Àlvarez FX, Cimmelli VA, Jou D, Sellitto A (2012). Mesoscopic description of boundary effects in nanoscale heat transport. Nanoscale Systems: Mathematical Modeling, Theory and Applications 1, 112-142. https://eudml.org/doc/266781.
- [7] Panasenko G (2005). Multi-scale Modelling for Structures and Composites. Springer, Berlin, Heidelberg.
- [8] Attinger S, Koumoutsakos PD (2004). Multiscale Modelling And Simulation. Springer, Berlin, Heidelberg.
- [9] Binder K, Heermann DW (2010). Monte Carlo Simulation in Statistical Physics: An Introduction. Springer, Berlin, Heidelberg.
- Abdi A, Schulz D (2024). Application of the tight-binding method onto the Von Neumann equation. Journal of Computational Electronics 23, 707-717. https://doi.org/10.1007/s10825-024-02173-6.
- Jones RO (2015). Density functional theory: Its origins, rise to prominence, and future. Reviews of Modern Physics 87, 897. https://doi.org/10.1103/RevModPhys.87.897.
- Parr RG, Gadre SR, Bartolotti LJ (1979). Local density functional theory of atoms and molecules. Proceedings of the National Academy of Sciences of the USA 76(6), 2522-2526. https://doi.org/10.1073/pnas.76.6.2522.
- Engel E, Dreizler RM (2011). Density Functional Theory. An Advanced Course. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14090-7.
- Car R, Parrinello M (1985). Unified Approach for Molecular Dynamics and Density-Functional Theory. Physical Review Letters 55(22), 2471. https://doi.org/10.1103/PhysRevLett.55.2471.
- Avriel M (2003). Nonlinear Programming: Analysis and Methods. Courier Dover Publications, Garden City, NY.
- Thijssen J (2007). Computational Physics. Cambridge University Press, Cambridge.
- Mizutani U (2001). Introduction to the Electron Theory of Metals. Cambridge University Press, Cambridge.
- Bland JAC, Bretislav H (2005). Ultrathin Magnetic Structures I: An Introduction to the Electronic, Magnetic and Structural Properties. Springer, Berlin, Heidelberg.
- Wandelt K (2012). Surface and Interface Science. John Wiley & Sons, Hoboken, NJ, vols 1-2.
- Wang J (2010). Key Issues of Classical Molecular Dynamics Simulation. Lambert Academic Publishing, Saarbrücken, Germany.
- Vinogradov SS, Smith PD, Vinogradova ED (2010). Canonical Problems in Scattering and Potential Theory Part II: Acoustic and Electromagnetic Diffraction by Canonical Structures. CRC Press, Boca Raton, FL.
- Fong CY, Shaughnessy M, Damewood L, Yang LH (2012). Theory, Experiment and Computation of Half Metals for Spintronics: Recent Progress in Si-based Materials. Nanoscale Systems: Mathematical Modeling, Theory and Applications 1, 1-22. https://eudml.org/doc/266869.
- Burkhardt CE, Leventhal JJ (2008). Foundations of Quantum Physics. Springer, Berlin, Heidelberg.
- Musa SM (2012). Computational Finite Element Methods in Nanotechnology. CRC Press, Boca Raton, FL.
- de Borst R, Ramm E (2011). Multiscale Methods in Computational Mechanics: Progress and Accomplishments. Springer, Berlin, Heidelberg.
- Mielke L, Belytschko T, Schatz GC (2007). Nanoscale Fracture Mechanics. Annual Review of Physical Chemistry 58, 185-209. doi: 10.1146/annurev.physchem.58.032806.104502.
- Gates TS, Odegard GM, Frankland SJV, Clancy TC (2005). Computational materials: Multi-scale modeling and simulation of nanostructured materials. Composites Science and Technology 65(15-16), 2416-2434. https://doi.org/10.1016/j.compscitech.2005.06.009.
Download all article in PDF
![]()



