Understanding the Reaction Mechanism of Nanocomposite Thermites

Nanocomposite energetics are a relatively new class of materials that combine nanoscale fuels and oxidizers to allow for the rapid release of large amounts of energy. In thermite systems (metal fuel with metal oxide oxidizer), the use of nanomaterials has been illustrated to increase reactivity by multiple orders of magnitude as a result of the higher specific surface area and smaller diffusion length scales. However, the highly dynamic and nanoscale processes intrinsic to these materials, as well as heating rate dependencies, have limited our understanding of the underlying processes that control reaction and propagation. For my dissertation, I have employed a variety of experimental approaches that have allowed me to probe these processes at heating rates representative of free combustion with the goal of understanding the fundamental mechanisms. Dynamic transmission electron microscopy (DTEM) was used to study the in situ morphological change that occurs in nanocomposite thermite materials subjected to rapid (10^11 K/s) heating. Aluminum nanoparticle (Al-NP) aggregates were found to lose their nanostructure through coalescence in as little as 10 ns, which is much faster than any other timescale of combustion. Further study of nanoscale reaction with CuO determined that a condensed phase interfacial reaction could occur within 0.5-5 µs in a manner consistent with bulk reaction, which supports that this mechanism plays a dominant role in the overall reaction process. Ta nanocomposites were also studied to determine if a high melting point (3280 K) affects the loss of nanostructure and rate of reaction. The condensed phase reaction pathway was further explored using reactive multilayers sputter deposited onto thin Pt wires to allow for temperature jump (T-Jump) heating at rates of ~5x10^5 K/s. High speed video and a time of flight mass spectrometry (TOFMS) were used to observe ignition temperature and speciation as a function of bilayer thickness. The ignition process was modeled and a low activation energy for effective diffusivity was determined. T-Jump TOFMS along with constant volume combustion cell studies were also used to determine the effect of gas release in nanoparticle systems by comparing the reaction properties of CuO and Cu2O.

A Generalized Methodology to Characterize Composite Materials for Pyrolysis Models

The predictive capabilities of computational fire models have improved in recent years such that models have become an integral part of many research efforts. Models improve the understanding of the fire risk of materials and may decrease the number of expensive experiments required to assess the fire hazard of a specific material or designed space. A critical component of a predictive fire model is the pyrolysis sub-model that provides a mathematical representation of the rate of gaseous fuel production from condensed phase fuels given a heat flux incident to the material surface. The modern, comprehensive pyrolysis sub-models that are common today require the definition of many model parameters to accurately represent the physical description of materials that are ubiquitous in the built environment. Coupled with the increase in the number of parameters required to accurately represent the pyrolysis of materials is the increasing prevalence in the built environment of engineered composite materials that have never been measured or modeled. The motivation behind this project is to develop a systematic, generalized methodology to determine the requisite parameters to generate pyrolysis models with predictive capabilities for layered composite materials that are common in industrial and commercial applications. This methodology has been applied to four common composites in this work that exhibit a range of material structures and component materials. The methodology utilizes a multi-scale experimental approach in which each test is designed to isolate and determine a specific subset of the parameters required to define a material in the model. Data collected in simultaneous thermogravimetry and differential scanning calorimetry experiments were analyzed to determine the reaction kinetics, thermodynamic properties, and energetics of decomposition for each component of the composite. Data collected in microscale combustion calorimetry experiments were analyzed to determine the heats of complete combustion of the volatiles produced in each reaction. Inverse analyses were conducted on sample temperature data collected in bench-scale tests to determine the thermal transport parameters of each component through degradation. Simulations of quasi-one-dimensional bench-scale gasification tests generated from the resultant models using the ThermaKin modeling environment were compared to experimental data to independently validate the models.

Mathematical Programming Models for Influence Maximization on Social Networks

In this dissertation, we apply mathematical programming techniques (i.e., integer programming and polyhedral combinatorics) to develop exact approaches for influence maximization on social networks. We study four combinatorial optimization problems that deal with maximizing influence at minimum cost over a social network. To our knowl- edge, all previous work to date involving influence maximization problems has focused on heuristics and approximation. We start with the following viral marketing problem that has attracted a significant amount of interest from the computer science literature. Given a social network, find a target set of customers to seed with a product. Then, a cascade will be caused by these initial adopters and other people start to adopt this product due to the influence they re- ceive from earlier adopters. The idea is to find the minimum cost that results in the entire network adopting the product. We first study a problem called the Weighted Target Set Selection (WTSS) Prob- lem. In the WTSS problem, the diffusion can take place over as many time periods as needed and a free product is given out to the individuals in the target set. Restricting the number of time periods that the diffusion takes place over to be one, we obtain a problem called the Positive Influence Dominating Set (PIDS) problem. Next, incorporating partial incentives, we consider a problem called the Least Cost Influence Problem (LCIP). The fourth problem studied is the One Time Period Least Cost Influence Problem (1TPLCIP) which is identical to the LCIP except that we restrict the number of time periods that the diffusion takes place over to be one. We apply a common research paradigm to each of these four problems. First, we work on special graphs: trees and cycles. Based on the insights we obtain from special graphs, we develop efficient methods for general graphs. On trees, first, we propose a polynomial time algorithm. More importantly, we present a tight and compact extended formulation. We also project the extended formulation onto the space of the natural vari- ables that gives the polytope on trees. Next, building upon the result for trees---we derive the polytope on cycles for the WTSS problem; as well as a polynomial time algorithm on cycles. This leads to our contribution on general graphs. For the WTSS problem and the LCIP, using the observation that the influence propagation network must be a directed acyclic graph (DAG), the strong formulation for trees can be embedded into a formulation on general graphs. We use this to design and implement a branch-and-cut approach for the WTSS problem and the LCIP. In our computational study, we are able to obtain high quality solutions for random graph instances with up to 10,000 nodes and 20,000 edges (40,000 arcs) within a reasonable amount of time.