Computationally efficient representation of statistically described material microstructure for tractable forming simulations

The purpose of this project is to reduce a large statistical distribution of metal microstructure orientations to a manageable distribution to be used in metal forming simulations. Microstructure sensitive simulations at the macro-scale are impractical, because with so many state variables associated with material microstructure data, these simulations are extremely computationally expensive. The goal was to develop a framework to accurately model plastic material response while repre- senting the material microstructure in a more compact form, reducing 106 or more microstructure orientations to a significantly smaller statistical distribution of representative orientations. This will significantly increase the computational efficiency and make the design process known as mi- crostructure sensitive design (MSD) feasible for industry applications. This framework is applied to metals with both cubic and hexagonal structure to validate this approach for slip and twinning deformation mechanisms. Performing microstructure sensitive metal-forming simulations is widely recognized as a computational challenge because of the need to store large sets of state variables related to microstructure data. This makes the investigation of the accuracy of smaller, representative data sets in these simulations profitable. The project accomplished two main goals; the development of an effective fitting algorithm to generate compacted data sets and validation of the framework for data compaction on metals with cubic structure, and hexagonal symmetry, with and without twinning. The research was applied to oxygen-free high-conductivity copper (OFHC Cu) and 6016 aluminum (Al-6016) for application of the framework to cubic metals. An anisotropic (clock-rolled) zirconium (Zr) texture was used to develop the framework for hexagonal metals. The minimum accurate data set for cubic was determined to be 825 orientations and for hexagonal metals, considering twinning and absence of twinning, the minimum number was 1600 orientations. This compaction method will increase the computational speed of microstructure sensitive forming simulations by several orders of magnitude, contributing to the computational feasibility of microstructure informed design

Computationally efficient representation of statistically described material microstructure for tractable forming simulations

The purpose of this project is to reduce a large statistical distribution of metal microstructure orientations to a manageable distribution to be used in metal forming simulations. Microstructure sensitive simulations at the macro-scale are impractical, because with so many state variables associated with material microstructure data, these simulations are extremely computationally expensive. The goal was to develop a framework to accurately model plastic material response while representing the material microstructure in a more compact form, reducing 106 or more microstructure orientations to a significantly smaller statistical distribution of representative orientations. This will significantly increase the computational efficiency and make the design process known as microstructure sensitive design (MSD) feasible for industry applications. This framework is applied to metals with both cubic and hexagonal structure to validate this approach for slip and twinning deformation mechanisms. Performing microstructure sensitive metal-forming simulations is widely recognized as a computational challenge because of the need to store large sets of state variables related to microstructure data. This makes the investigation of the accuracy of smaller, representative data sets in these simulations profitable. The project accomplished two main goals; the development of an effective fitting algorithm to generate compacted data sets and validation of the framework for data compaction on metals with cubic structure, and hexagonal symmetry, with and without twinning. The research was applied to oxygen-free high-conductivity copper (OFHC Cu) and 6016 aluminum (Al-6016) for application of the framework to cubic metals. An anisotropic (clock-rolled) zirconium (Zr) texture was used to develop the framework for hexagonal metals. The minimum accurate data set for cubic was determined to be 825 orientations and for hexagonal metals, considering twinning and absence of twinning, the minimum number was 1600 orientations. This compaction method will increase the computational speed of microstructure sensitive forming simulations by several orders of magnitude, contributing to the computational feasibility of microstructure informed design

Opinion disparity in hypergraphs with community structure

The division of a social group into subgroups with opposing opinions, which we refer to as opinion disparity, is a prevalent phenomenon in society. This phenomenon has been modeled by including mechanisms such as opinion homophily, bounded confidence interactions, and social reinforcement mechanisms. In this paper we study a complementary mechanism for the formation of opinion disparity based on higher-order interactions, i.e., simultaneous interactions between multiple agents. We present an extension of the planted partition model for uniform hypergraphs as a simple model of community structure and consider the hypergraph SIS model on a hypergraph with two communities where the binary ideology can spread via links (pairwise interactions) and triangles (three-way interactions). We approximate this contagion process with a mean-field model and find that for strong enough community structure, the two communities can hold very different average opinions. We determine the regimes of structural and infectious parameters for which this opinion disparity can exist and find that the existence of these disparities is much more sensitive to the triangle community structure than to the link community structure. We show that the existence and type of opinion disparities are extremely sensitive to differences in the sizes of the two communities.Comment: 14 pages, 8 figure

Contagion on Complex Systems: Structure and Dynamics

Complex systems are important when representing empirical systems in that they can model the underlying structure of interactions. Accounting for this structure can offer important insights for empirical systems such as social networks, biological processes, social phenomena, opinion formation, and many other examples. Pairwise networks are a representation of complex systems comprising a collection of entities (nodes) and pairwise interactions between entities (edges). Hypergraphs are a generalization of pairwise networks where interactions are no longer constrained to be between two nodes, but rather can be of arbitrary size. Modeling dynamics on hypergraphs can uncover rich behavior that one might not see if the dynamics simply occurred on a pairwise network. We focus on the interplay between the structure of a complex system, a particular dynamical process, and the resulting dynamical behavior. In the context of hypergraphs, we explain the effects that degree heterogeneity, assortative mixing, and community structure have on a simple hypergraph contagion model. Likewise, for pairwise networks, we explore both types of structure; structure in the underlying contact network and varying heterogeneity in the infection model. We examine the effect that representing inherently multiplex data (relationships of different types) with uniplex networks (relationships of a single type) has on the resulting dynamical behavior. We present two open source software libraries: (1) XGI, a package for representing complex systems with group interactions and (2) HyperContagion, a package for simulating hypergraph contagion, both of which can be used by the growing community of researchers studying higher-order interactions

Toward an Understanding of the Economics of Charity: Evidence from a Field Experiment

This study develops theory and uses a door-to-door fundraising field experiment to explore the economics of charity. We approached nearly 5000 households, randomly divided into four experimental treatments, to shed light on key issues on the demand side of charitable fundraising. Empirical results are in line with our theory: in gross terms, our lottery treatments raised considerably more money than our voluntary contributions treatments. Interestingly, we find that a one standard deviation increase in female solicitor physical attractiveness is similar to that of the lottery incentive¡ªthe magnitude of the estimated difference in gifts is roughly equivalent to the treatment effect of moving from our theoretically most attractive approach (lotteries) to our least attractive approach (voluntary contributions).

The Hidden Benefits of Control: Evidence from a Natural Field Experiment

An important dialogue between theorists and experimentalists over the past few decades has raised the study of the interaction of psychological and economic incentives from academic curiosity to a bona fide academic field. One recent area of study within this genre that has sparked interest and debate revolves around the “hidden costs” of conditional incentives. This study overlays randomization on a naturally-occurring environment in a series of temporally-linked field experiments to advance our understanding of the economics of charity and test if such “costs” exist in the field. This approach permits us to examine why people initially give to charities, and what factors keep them committed to the cause. Several key findings emerge. First, there are hidden benefits of conditional incentives that would have gone undetected had we maintained a static theory and an experimental design that focused on short run substitution effects rather than dynamic interactions. Second, we can reject the pure altruism model of giving. Third, we find that public good provision is maximized in both the short and long run by using conditional, rather than unconditional, incentives.

Is There a 'Hidden Cost of Control' in Naturally-Occurring Markets? Evidence from a Natural Field Experiment

Several recent laboratory experiments have shown that the use of explicit incentives—such as conditional rewards and punishment—entail considerable “hidden” costs. The costs are hidden in the sense that they escape our attention if our reasoning is based on the assumption that people are exclusively self-interested. This study represents a first attempt to explore whether, and to what extent, such considerations affect equilibrium outcomes in the field. Using data gathered from nearly 3000 households, we find little support for the negative consequences of control in naturally-occurring labor markets. In fact, even though we find evidence that workers are reciprocal, we find that worker effort is maximized when we use conditional—not unconditional—rewards to incent workers.