Publications

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This paper presents recent progress on the use of Computational Singular Perturbation (CSP) techniques for time integration of stiff chemical systems. The CSP integration approach removes fast time scales from the reaction system, thereby enabling integration with explicit time stepping algorithms. For further efficiency improvements, a tabulation strategy was developed to allow reuse of the relevant CSP quantities. This paper outlines the method and demonstrates its use on the simulation of hydrogen-air ignition.

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We present a rapid method for the identification of viruses using microfluidic chip gel electrophoresis (CGE) of high-copy number proteins to generate unique protein profiles. Viral proteins are solubilized by heating at 95°C in borate buffer containing detergent (5 min), then labeled with fluorescamine dye (10 s), and analyzed using the μChemLab CGE system (5 min). Analyses of closely related T2 and T4 bacteriophage demonstrate sufficient assay sensitivity and peak resolution to distinguish the two phage. CGE analyses of four additional viruses - MS2 bacteriophage, Epstein - Barr, respiratory syncytial, and vaccinia viruses - demonstrate reproducible and visually distinct protein profiles. To evaluate the suitability of the method for unique identification of viruses, we employed a Bayesian classification approach. Using a subset of 126 replicate electropherograms of the six viruses and phage for training purposes, successful classification with non-training data was 66/69 or 95% with no false positives. The classification method is based on a single attribute (elution time), although other attributes such as peak width, peak amplitude, or peak shape could be incorporated and may improve performance further. The encouraging results suggest a rapid and simple way to identify viruses without requiring specialty reagents such as PCR probes and antibodies. © 2008 American Chemical Society.

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Fundamentals of ion transport in nanopores were studied through a joint experimental and computational effort. The study evaluated both nanoporous polymer membranes and track-etched nanoporous polycarbonate membranes. The track-etched membranes provide a geometrically well characterized platform, while the polymer membranes are more closely related to ion exchange systems currently deployed in RO and ED applications. The experimental effort explored transport properties of the different membrane materials. Poly(aniline) membranes showed that flux could be controlled by templating with molecules of defined size. Track-etched polycarbonate membranes were modified using oxygen plasma treatments, UV-ozone exposure, and UV-ozone with thermal grafting, providing an avenue to functionalized membranes, increased wettability, and improved surface characteristic lifetimes. The modeling effort resulted in a novel multiphysics multiscale simulation model for field-driven transport in nanopores. This model was applied to a parametric study of the effects of pore charge and field strength on ion transport and charge exclusion in a nanopore representative of a track-etched polycarbonate membrane. The goal of this research was to uncover the factors that control the flux of ions through a nanoporous material and to develop tools and capabilities for further studies. Continuation studies will build toward more specific applications, such as polymers with attached sulfonate groups, and complex modeling methods and geometries.

Many systems involving chemical reactions between small numbers of molecules exhibit inherent stochastic variability. Such stochastic reaction networks are at the heart of processes such as gene transcription, cell signaling or surface catalytic reactions, which are critical to bioenergy, biomedical, and electrical storage applications. The underlying molecular reactions are commonly modeled with chemical master equations (CMEs), representing jump Markov processes, or stochastic differential equations (SDEs), rather than ordinary differential equations (ODEs). As such reaction networks are often inferred from noisy experimental data, it is not uncommon to encounter large parametric uncertainties in these systems. Further, a wide range of time scales introduces the need for reduced order representations. Despite the availability of mature tools for uncertainty/sensitivity analysis and reduced order modeling in deterministic systems, there is a lack of robust algorithms for such analyses in stochastic systems. In this talk, we present advances in algorithms for predictability and reduced order representations for stochastic reaction networks and apply them to bistable systems of biochemical interest. To study the predictability of a stochastic reaction network in the presence of both parametric uncertainty and intrinsic variability, an algorithm was developed to represent the system state with a spectral polynomial chaos (PC) expansion in the stochastic space representing parametric uncertainty and intrinsic variability. Rather than relying on a non-intrusive collocation-based Galerkin projection [1], this PC expansion is obtained using Bayesian inference, which is ideally suited to handle noisy systems through its probabilistic formulation. To accommodate state variables with multimodal distributions, an adaptive multiresolution representation is used [2]. As the PC expansion directly relates the state variables to the uncertain parameters, the formulation lends itself readily to sensitivity analysis. Reduced order modeling in the time dimension is accomplished using a Karhunen-Loeve (KL) decomposition of the stochastic process in terms of the eigenmodes of its covariance matrix. Subsequently, a Rosenblatt transformation relates the random variables in the KL decomposition to a set of independent random variables, allowing the representation of the system state with a PC expansion in those independent random variables. An adaptive clustering method is used to handle multimodal distributions efficiently, and is well suited for high-dimensional spaces. The spectral representation of the stochastic reaction networks makes these systems more amenable to analysis, enabling a detailed understanding of their functionality, and robustness under experimental data uncertainty and inherent variability.

While models of combustion processes have been successful in developing engines with improved fuel economy, more costly simulations are required to accurately model pollution chemistry. These simulations will also involve significant parametric uncertainties. Computational singular perturbation (CSP) and polynomial chaos-uncertainty quantification (PC-UQ) can be used to mitigate the additional computational cost of modeling combustion with uncertain parameters. PC-UQ was used to interrogate and analyze the Davis-Skodje model, where the deterministic parameter in the model was replaced with an uncertain parameter. In addition, PC-UQ was combined with CSP to explore how model reduction could be combined with uncertainty quantification to understand how reduced models are affected by parametric uncertainty.

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