Showing papers by "Baskar Ganapathysubramanian published in 2009"

Using data to account for lack of data: Linking material informatics with stochastic analysis

Abstract: Many material systems of fundamental as well as industrial importance are significantly affected by underlying fluctuations and variations in boundary conditions, initial conditions, material property, as well as variabilities in operating and surrounding conditions. There has been increasing interest in analyzing, quantifying, and controlling the effects of such uncertain inputs on complex systems. This has resulted in the development of techniques in stochastic analysis and predictive modeling. A general application of stochastic techniques to many significant problems in engineering has been limited due to the lack of realistic, viable models of the input variability. Ideas of material informatics can be used to utilize available data about the input to construct a data-driven, computationally viable model of the input variability. This promising coupling of material informatics and stochastic analysis is investigated and some results are showcased using a simple example of analyzing diffusion in heterogeneous random media. Limited microstructural data is utilized to construct a realistic model of the thermal conductivity variability in a system. This reduced-order model then serves as the input to the stochastic partial differential equation describing thermal diffusion through random heterogeneous media.

Data Mining and Informatics for Quantitative Atom Probe Tomography

Abstract: Extended abstract of a paper presented at Microscopy and Microanalysis 2009 in Richmond, Virginia, USA, July 26 – July 30, 2009

Transfer operator method for control in fluid flows

Abstract: In this paper, we present a systematic approach inspired from the ergodic theory of dynamical system for the optimal control of complex fluid flows. The infinite dimensional Navier Stokes equation describing the complex fluid flow is first reduced to a finite set of coupled ordinary differential equations. We utilize Proper Orthogonal Decomposition techniques to obtain a reduced order model. The linear transfer, Perron Frobenius (P-F), operator-based Lyapunov measure framework is used for the nonlinear stability analysis and optimal control design of the reduced order system. Efficient numerical schemes that leverage the linearity of the framework have been developed for analysis and control design. The framework is utilized to analyze a benchmark problem in fluid dynamics: the control of recirculation in a two-dimensional channel flow with a backward facing step.