ENERGETIC BIOCIDAL MATERIALS AND SPORE NEUTRALIZATION

The objective of this dissertation is to explore a more accurate and versatile approach to investigating the neutralization of spores suffered from ultrafast heating and biocide based stresses, and further to explore and understand novel methods to supply ultrafast heating and biocides through nanostructured energetic materials A surface heating method was developed to apply accurate (± 25 ˚C), high heating rate thermal energy (200 - 800 ˚C, ~103 - ~105 ˚C/s). Uniform attachment of bacterial spores was achieved electrophoretically onto fine wires in liquids, which could be quantitatively detached into suspension for spore enumeration. The spore inactivation increased with temperature and heating rate, and fit a sigmoid response. The neutralization mechanisms of peak temperature and heating rate were correlated to the DNA damage at ~104 ˚C/s, and to the coat rupture by ultrafast vapor pressurization inside spores at ~105 ˚C/s. Humidity was found to have a synergistic effect of rapid heating and chlorine gas to neutralization efficiency. The primary neutralization mechanism of Cl2 and rapid heat is proposed to be chlorine reacting with the spore surface. The stress-kill correlation above provides guidance to explore new biocidal thermites, and to probe mechanisms. Results show that nano-Al/K2S2O8 released more gas at a lower temperature and generated a higher maximum pressure than the other nano-Al/oxysalts. Given that this thermite formulation generates the similar amount of SO2 as O2, it can be considered as a potential candidate for use in energetic biocidal applications. The reaction mechanisms of persulfate and other oxysalts containing thermites can be divided into two groups, with the reactive thermites (e.g. Al/K2S2O8) that generate ~10× higher of pressure and ~10× shorter of burn time ignited via a solid-gas Al/O2 reaction, while the less reactive thermites (e.g. Al/K2SO4) following a condensed phase Al/O reaction mechanism. These different ignition mechanisms were further re-evaluated by investigating the roles of free and bound oxygen. A constant critical reaction rate for ignition was found which is independent to ignition temperature, heating rate and free vs. bound oxygen.

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.