Multiscale Modeling Methods Product design optimization Product model

Multiscale Modeling Methods Product design optimization Product model Process optimization Physical system Process model Reduced experimentation Market need

Why Multiscale Models ? Solid State Lighting 1 nm Spatial Scale 1 m 1 mm 1 cm h In Band gap Lattice LED device Photonic Crystal Light Clustering/ Coupled Extraction Emission Diffusion Physical Phenomena Heat Transport Stress Solid State Bulb

The Building Blocks Electronic Structure Calculations Scale ~ 0. 1 nm Solve Schrodinger’s equation for ground states of electrons: Affinities Band gap calculations Band gap LED Sensors Solid state lighting

The Building Blocks Atomistic Simulations Scale ~ 10 nm Molecular dynamics Monte Carlo Enzyme in octane Discrete model of island nucleation Polymer nanocomposites Nanocrystalline materials Nanostructured materials Mapping to continuum Thin film growth

The Building Blocks Discrete Mesoscale Simulations Scale ~ 1 mm Coarse grained polymer models Discrete dislocation dynamics (metals) Discrete dislocation dynamics Atomistic Coarse grained Atomistically informed constitutive equations Polymer models Continuum Polycrystal plasticity

The Building Blocks Continuum Simulations Scale > 0. 1 mm Single scale models – Integrate the relevant system of PDEs. (system specific) Multiscale models – Sequential methods: Variational multiscale Time/space assymptotic expansion – Embedded methods: Multigrid Domain decomposition

Linking the Building Blocks Across Scales Continuum multiscale models Calibration of higher order continuum based on atomistics Calibration of continuum constitutive laws based on discrete models and Continuum macro Coupled atomistic-continuum Interatomic potentials Continuum micro um u n i t n o C Mesoscale Electronic structure s l e Atomistics d o m e t e r c s Di ls e d o m

Stochastic Nature of Physical Problems • Multiple sources of uncertainty on all scales. • Scale linking or system reduction must account for uncertainty. Discrete systems – Statistical Mechanics Methods Continuum systems – Stochastic Partial Differential Equations

Multiscale Modeling Methods Product design optimization Product model Process optimization Physical system Process model Reduced experimentation Market need

System Level Methods • Construct a reduced order model to be used in control and system/process optimization. The reduced order model is calibrated based on input from the full multiscale model and the physical system. Optimization Control noise disturbance Controller Feed forward control Reduced order model Physical system • System level modeling handled as a hierarchical multilevel optimization problem -Optimization methods provide compatibility in models at different scales - Desirable system level attributes communicated to bottom level

Modeling Challenges Spatial scale linking • Usually, no more than 2 scales are linked. Most models refer to a single spatial scale. • This requires assumptions to be made about the gross behavior (constitutive laws) of the smaller scale. Temporal scale linking • The time scale linking problem is much more difficult; consistent procedures with high degree of generality are lacking. Multiple physical phenomena • The various physical phenomena are intimately coupled at the atomic scale. They are usually treated as being decoupled in continuum models.

Summary of MSERC Modeling Requirements • Need hierarchies of physical models ranging from electronic structure to reduced order system models. • Modeling methods must include procedures to link models across spatial and temporal scales. • The model hierarchies must include models appropriate for answering the pertinent questions arising at the various stages of multiscale systems engineering design.