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

2. Why Multiscale Models ?  Solid State Lighting Spatial Scale 1nm 1m1m 1mm 1cm Coupled Physical Phenomena Light Emission In h Clustering/ Diffusion Light Extraction Photonic Crystal Heat Transport Stress Solid State Bulb Band gap Lattice LED device

3. The Building Blocks Electronic Structure Calculations Solve Schrodinger’s equation for ground states of electrons: Affinities SensorsSolid state lighting LED Band gap calculations Band gap Scale ~ 0.1nm

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

5. The Building Blocks Discrete Mesoscale Simulations  Coarse grained polymer models Discrete dislocation dynamics (metals) Discrete dislocation dynamics Polymer models Continuum Atomistically informed constitutive equations Scale ~ 1  m Polycrystal plasticity AtomisticCoarse grained

6. The Building Blocks Continuum Simulations  Single scale models – Integrate the relevant system of PDEs. Multiscale models – Sequential methods: Variational multiscale Time/space assymptotic expansion – Embedded methods: Multigrid Domain decomposition Scale > 0.1  m (system specific)

7. Linking the Building Blocks Across Scales  Electronic structure Atomistics Mesoscale Continuum micro Discrete models Continuum models Coupled atomistic-continuum Interatomic potentials Calibration of higher order continuum based on atomistics and Continuum macro Calibration of continuum constitutive laws based on discrete models Continuum multiscale models

8. 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

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

10. 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. Control Optimization 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 Feed forward control Controller Reduced order model Physical system disturbance noise

11. Modeling Challenges  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. The time scale linking problem is much more difficult; consistent procedures with high degree of generality are lacking. The various physical phenomena are intimately coupled at the atomic scale. They are usually treated as being decoupled in continuum models. Temporal scale linking Spatial scale linking Multiple physical phenomena

12. 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.