Mathematical Techniques in the Modeling of Computational Nanotechnology

Abstract

Computational nanotechnology integrates nanoscale science and engineering with high-performance mathematical modeling to simulate and predict material behaviors and device performance. Mathematical techniques including differential equations, stochastic models, multiscale analysis, and quantum mechanics are at the forefront of this field. This paper surveys the essential mathematical frameworks used in computational nanotechnology to capture phenomena like electron transport, molecular dynamics, and material deformation at the nanoscale. The study also highlights the role of numerical methods and machine learning in refining nano system simulations, enhancing their scalability and predictive accuracy.