Multiscale Systems (with Application to Nanocomposites)

Macroscopic material transport properties such as viscosity, diffusivity, conductivity, etc., may be computed by using molecular level simulation such as molecular dynamics or Monte Carlo methods.  This computation is time consuming since simulations over sufficiently long times are needed to ensure that the assumed statistical properties are satisfied.  As a result, such tools are useful in gaining insight and understanding of the underlying mechanisms behind observed physical phenomena, but are not amenable to material property design or material process control. In this project, we take a systems approach by regarding the transport property (our currently focus on shear viscosity) as a input/output map from an external stimulus to a material response (e.g., shear stress to shear strain rate).  Linearizing this map about an equilibrated trajectory results in a linear time varying system.  By freezing the time along the equilibrated trajectory, we obtain a set of linear time invariant systems.  These systems are usually unstable, but may be transformed to stable systems by weighing all signals with sufficiently fast decaying exponential functions.  Viscosity is then estimated directly from the frequency responses of these systems. Model reduction such as approximate balanced truncation may be applied to further reduce model complexity and computation load.  This approach has a potential computation advantage since extensive simulation runs using high order molecular dynamics model are not required.  Our long term objective is to develop efficient computation methods to facilitate rapid material and process design iterations.  We have applied the approach initially to a simple Leonard-Jones fluid.  We are currently focusing on the computation (and then design) of complex modulus of untangled polymers (with FENE potential).

Reports and Papers:

 

Talk on October 13,2004

 

Acknowledgment
This work is supported in part by the National Science Foundation under grant No. 031056, Multiscale Systems Engineering for Nanocomposites.

Contact Information:

John T. Wen
Office: CII 8213
Voice: (518)-276-8744
Fax: (518)-276-4897
Email: wen@cat.rpi.edu