Baskar Ganapathysubramanian

Sparse grid collocation schemes for stochastic natural convection problems

In recent years, there has been an interest in analyzing and quantifying the effects of random inputs in the solution of partial differential equations that describe thermal and fluid flow problems. Spectral stochastic methods and Monte-Carlo based sampling methods are two approaches that have been used to analyze these problems. As the complexity of the problem or the number of random variables involved in describing the input uncertainties increases, these approaches become highly impractical from implementation and convergence points-of-view. This is especially true in the context of realistic thermal flow problems, where uncertainties in the topology of the boundary domain, boundary flux conditions and heterogeneous physical properties usually require high-dimensional random descriptors. The sparse grid collocation method based on the Smolyak algorithm offers a viable alternate method for solving high-dimensional stochastic partial differential equations. An extension of the collocation approach to include adaptive refinement in important stochastic dimensions is utilized to further reduce the numerical effort necessary for simulation. We show case the collocation based approach to efficiently solve natural convection problems involving large stochastic dimensions. Equilibrium jumps occurring due to surface roughness and heterogeneous porosity are captured. Comparison of the present method with the generalized polynomial chaos expansion and Monte-Carlo methods are made.

Engineering fluid flow using sequenced microstructures

Controlling the shape of fluid streams is important across scales: from industrial processing to control of biomolecular interactions. Previous approaches to control fluid streams have focused mainly on creating chaotic flows to enhance mixing. Here we develop an approach to apply order using sequences of fluid transformations rather than enhancing chaos. We investigate the inertial flow deformations around a library of single cylindrical pillars within a microfluidic channel and assemble these net fluid transformations to engineer fluid streams. As these transformations provide a deterministic mapping of fluid elements from upstream to downstream of a pillar, we can sequentially arrange pillars to apply the associated nested maps and, therefore, create complex fluid structures without additional numerical simulation. To show the range of capabilities, we present sequences that sculpt the cross-sectional shape of a stream into complex geometries, move and split a fluid stream, perform solution exchange and achieve particle separation. A general strategy to engineer fluid streams into a broad class of defined configurations in which the complexity of the nonlinear equations of fluid motion are abstracted from the user is a first step to programming streams of any desired shape, which would be useful for biological, chemical and materials automation.

Machine Learning for High-Throughput Stress Phenotyping in Plants

Advances in automated and high-throughput imaging technologies have resulted in a deluge of high-resolution images and sensor data of plants. However, extracting patterns and features from this large corpus of data requires the use of machine learning (ML) tools to enable data assimilation and feature identification for stress phenotyping. Four stages of the decision cycle in plant stress phenotyping and plant breeding activities where different ML approaches can be deployed are (i) identification, (ii) classification, (iii) quantification, and (iv) prediction (ICQP). We provide here a comprehensive overview and user-friendly taxonomy of ML tools to enable the plant community to correctly and easily apply the appropriate ML tools and best-practice guidelines for various biotic and abiotic stress traits.

Modeling diffusion in random heterogeneous media: Data-driven models, stochastic collocation and the variational multiscale method

In recent years, there has been intense interest in understanding various physical phenomena in random heterogeneous media. Any accurate description/simulation of a process in such media has to satisfactorily account for the twin issues of randomness as well as the multilength scale variations in the material properties. An accurate model of the material property variation in the system is an important prerequisite towards complete characterization of the system response. We propose a general methodology to construct a data-driven, reduced-order model to describe property variations in realistic heterogeneous media. This reduced-order model then serves as the input to the stochastic partial differential equation describing thermal diffusion through random heterogeneous media. A decoupled scheme is used to tackle the problems of stochasticity and multilength scale variations in properties. A sparse-grid collocation strategy is utilized to reduce the solution of the stochastic partial differential equation to a set of deterministic problems. A variational multiscale method with explicit subgrid modeling is used to solve these deterministic problems. An illustrative example using experimental data is provided to showcase the effectiveness of the proposed methodology.

Computationally efficient solution to the Cahn-Hilliard equation: Adaptive implicit time schemes, mesh sensitivity analysis and the 3D isoperimetric problem

We present an efficient numerical framework for analyzing spinodal decomposition described by the Cahn-Hilliard equation. We focus on the analysis of various implicit time schemes for two and three dimensional problems. We demonstrate that significant computational gains can be obtained by applying embedded, higher order Runge-Kutta methods in a time adaptive setting. This allows accessing time-scales that vary by five orders of magnitude. In addition, we also formulate a set of test problems that isolate each of the sub-processes involved in spinodal decomposition: interface creation and bulky phase coarsening. We analyze the error fluctuations using these test problems on the split form of the Cahn-Hilliard equation solved using the finite element method with basis functions of different orders. Any scheme that ensures at least four elements per interface satisfactorily captures both sub-processes. Our findings show that linear basis functions have superior error-to-cost properties. This strategy - coupled with a domain decomposition based parallel implementation - let us notably augment the efficiency of a numerical Cahn-Hillard solver, and open new venues for its practical applications, especially when three dimensional problems are considered. We use this framework to address the isoperimetric problem of identifying local solutions in the periodic cube in three dimensions. The framework is able to generate all five hypothesized candidates for the local solution of periodic isoperimetric problem in 3D - sphere, cylinder, lamella, doubly periodic surface with genus two (Lawson surface) and triply periodic minimal surface (P Schwarz surface).

A scalable framework for the solution of stochastic inverse problems using a sparse grid collocation approach

Experimental evidence suggests that the dynamics of many physical phenomena are significantly affected by the underlying uncertainties associated with variations in properties and fluctuations in operating conditions. Recent developments in stochastic analysis have opened the possibility of realistic modeling of such systems in the presence of multiple sources of uncertainties. These advances raise the possibility of solving the corresponding stochastic inverse problem: the problem of designing/estimating the evolution of a system in the presence of multiple sources of uncertainty given limited information.A scalable, parallel methodology for stochastic inverse/design problems is developed in this article. The representation of the underlying uncertainties and the resultant stochastic dependant variables is performed using a sparse grid collocation methodology. A novel stochastic sensitivity method is introduced based on multiple solutions to deterministic sensitivity problems. The stochastic inverse/design problem is transformed to a deterministic optimization problem in a larger-dimensional space that is subsequently solved using deterministic optimization algorithms. The design framework relies entirely on deterministic direct and sensitivity analysis of the continuum systems, thereby significantly enhancing the range of applicability of the framework for the design in the presence of uncertainty of many other systems usually analyzed with legacy codes. Various illustrative examples with multiple sources of uncertainty including inverse heat conduction problems in random heterogeneous media are provided to showcase the developed framework.

Enhanced charge separation in organic photovoltaic films doped with ferroelectric dipoles

A key requirement for realizing efficient organic photovoltaic (OPV) cells is the dissociation of photogenerated electron-hole pairs (singlet-excitons) in the donor polymer, and charge-transfer-excitons at the donor–acceptor interface. However, in modern OPVs, these excitons are typically not sufficiently harnessed due to their high binding energy. Here, we show that doping the OPV active-layers with a ferroelectric polymer leads to localized enhancements of electric field, which in turn leads to more efficient dissociation of singlet-excitons and charge-transfer-excitons. Bulk-heterojunction OPVs based on poly(3-hexylthiophene):[6,6]-phenyl-C61-butyric acid methyl ester are fabricated. Upon incorporating a ferroelectric polymer as additive in the active-layer, power conversion efficiencies increase by nearly 50%, and internal quantum efficiencies approach 100% – indicating complete exciton dissociation at certain photon energies. Similar enhancements in bilayer-heterojunctions, and direct influence of ferroelectric poling on device behavior show that improved dissociation is due to ferroelectric dipoles rather than any morphological change. Enhanced singlet-exciton dissociation is also revealed by photoluminescence lifetime measurements, and predicted by simulations using a numerical device model.

Modelling dendritic solidification with melt convection using the extended finite element method

Dendritic solidification of pure materials from an undercooled melt is studied using the extended finite element method/ level set method for modelling the thermal problem and a volume-averaged stabilized finite element formulation for modelling fluid flow. The extended finite element method using evolving enrichment functions allows accurate modelling of the discontinuous thermal conditions at the moving sharp freezing front thus capturing its motion precisely. The solution of the velocity field in the melt is obtained assuming that the sharp-interface is diffused over the length of two finite elements. The methodology presented is shown to be an effective tool for capturing the interface phenomena and freezing interface growth using a single uniform finite element grid. The whole formulation is packaged into a flexible, modular and parallel library with the ability to incorporate new physics. Comparisons with other numerical methods as well as analytical results emphasize the fidelity of the method in modelling the underlying physical phenomena and growth mechanisms. Various examples of dendritic growth in two- and three-dimensions are presented.

Analysis of Maize (Zea mays L.) Seedling Roots with the High-Throughput Image Analysis Tool ARIA (Automatic Root Image Analysis)

The maize root system is crucial for plant establishment as well as water and nutrient uptake. There is substantial genetic and phenotypic variation for root architecture, which gives opportunity for selection. Root traits, however, have not been used as selection criterion mainly due to the difficulty in measuring them, as well as their quantitative mode of inheritance. Seedling root traits offer an opportunity to study multiple individuals and to enable repeated measurements per year as compared to adult root phenotyping. We developed a new software framework to capture various traits from a single image of seedling roots. This framework is based on the mathematical notion of converting images of roots into an equivalent graph. This allows automated querying of multiple traits simply as graph operations. This framework is furthermore extendable to 3D tomography image data. In order to evaluate this tool, a subset of the 384 inbred lines from the Ames panel, for which extensive genotype by sequencing data are available, was investigated. A genome wide association study was applied to this panel for two traits, Total Root Length and Total Surface Area, captured from seedling root images from WinRhizo Pro 9.0 and the current framework (called ARIA) for comparison using 135,311 single nucleotide polymorphism markers. The trait Total Root Length was found to have significant SNPs in similar regions of the genome when analyzed by both programs. This high-throughput trait capture software system allows for large phenotyping experiments and can help to establish relationships between developmental stages between seedling and adult traits in the future.

Computer simulation of heterogeneous polymer photovoltaic devices

Polymer-based photovoltaic devices have the potential for widespread usage due to their low cost per watt and mechanical flexibility. Efficiencies close to 9.0% have been achieved recently in conjugated polymer based organic solar cells (OSCs). These devices were fabricated using solvent-based processing of electron-donating and electron-accepting materials into the so-called bulk heterojunction (BHJ) architecture. Experimental evidence suggests that a key property determining the power-conversion efficiency of such devices is the final morphological distribution of the donor and acceptor constituents. In order to understand the role of morphology on device performance, we develop a scalable computational framework that efficiently interrogates OSCs to investigate relationships between the morphology at the nano-scale with the device performance.In this work, we extend the Buxton and Clarke model (2007 Modelling Simul. Mater. Sci. Eng. 15 13–26) to simulate realistic devices with complex active layer morphologies using a dimensionally independent, scalable, finite-element method. We incorporate all stages involved in current generation, namely (1) exciton generation and diffusion, (2) charge generation and (3) charge transport in a modular fashion. The numerical challenges encountered during interrogation of realistic microstructures are detailed. We compare each stage of the photovoltaic process for two microstructures: a BHJ morphology and an idealized sawtooth morphology. The results are presented for both two- and three-dimensional structures.