# Multiscale and multiphysical computer simulaton methods

Continuum field
models

Continuum field models based simulation techniques based on differential equations have shown the power to solve real-world problems since the development of digital computers. The viability of the model relies on corresponding approximation for physical fields. With great and solid successes among industrial applications including engineering mechanics, heat transfer and chemical reaction, the continuum models, as we believe, can reach much further by integrating multiphysical models. Two simple examples related to the energetic issues are fluid-structure interaction in biological systems and electromechanical coupling in nanoscale devices.

Atomistic
simulations I

classical
mechanics

Giving the Newton's second law, a large set of phenomena can be investigated using the Monte-Carlo or molecular dynamics methods, from mechanical stiffness, fracture toughness, phase transformation, transport phenomena to protein folding problems. The key is the interatomic interaction form, where all other informations are implicitly integrated. We thus have the ability to perform in-silico experiments for complex systems, with the help from basic statistical physics principles.

Atomistic
simulations II

quantum mechanics methods for electronic structures

Speaking of first-principles simulations of material properies, to solving the Schoedinger equations in quantum mechanics with the minimum approximation and empirical parameter inputs are the only affordable approach we can employ nowadays. Quantum Monte-Carlo simulations, Hartree-Fock and density functional theory with different description for the many-body picture of the electronic system give accurate prediction for materials properties. By including the electrons, we are much beyond the atomic and phononic point of view, electronic, magnetic and optical properties become also treatable.

Mesoscale
simulations - coarse-graining and multiscale modeling

To bridge the scales in these models, hierarchically or concurrently, coarse-graining at different levels are implemented: mapping atomic structure to continuum models, bead-spring models for biological networks, dielectric correction of interatomic interaciton in implicit solvent model, elastic network model are constructed for protein. These are the key to extend highly accurate atomistic simulation methods to the real-world engineering problems that are across multiple temporal and spatial scales.