## Simulation System Level Modeling

MEMS devices contain varied components including electronics. We can model mini- and micro-scale MEMS using classical mechanical, electromagnetic and thermodynamic theory. Most studies concentrate on designing, modeling, and fabricating these systems. Comprehensive analysis precedes prototyping and fabrication. A common representation that encompasses multiple energy domains becomes useful in modeling the whole system. The bond-graph notation, based on energy transport (or power flow) may represent an entire system at the highest level. Ultimately, one seeks to know the dynamical behavior of the entire system.

But most transducers are nonlinear; they involve at least two energy domains, and they operate in the large signal regime. Direct numerical simulation of the dynamics of the fully meshed distributed model of such a system is computationally difficult and expensive. Therefore, one needs to reduce the degrees of freedom from hundreds or thousands in the meshed 3-D model to as few degrees as possible. We can then use such reduced order models to simulate and approximate the dynamics of the whole system. Such macro-models, however, should agree with our 3-D numerical simulations and our experimental results when describing the macro behavior of the system. Macro-models can also represent the behavior of a subsystem in one energy domain as well as the interactions from other domains. Hence, we need to automatically generate macro-models, and then we must insert these smaller models into some system-level dynamic simulator.

We also need to develop procedures to make quantum models of nano-scaled systems. Such models should avoid the complexities posed by the many-electron wave functions of classical quantum mechanical formulations. The complexity of the Schrodinger equation describing even a six-electron carbon atom requires visualizing a six-dimensional space. Each added electron requires adding an additional dimension.

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