Modeling the Network of Dutch and Flemish Print Production, 1550-1750

The production of artistic prints in the sixteenth- and seventeenth-century Netherlands was an inherently social process. Turning out prints at any reasonable scale depended on the fluid coordination between designers, platecutters, and publishers; roles that, by the sixteenth century, were considered distinguished enough to merit distinct credits engraved on the plates themselves: invenit, fecit/sculpsit, and excudit. While any one designer, plate cutter, and publisher could potentially exercise a great deal of influence over the production of a single print, their individual decisions (Whom to select as an engraver? What subjects to create for a print design? What market to sell to?) would have been variously constrained or encouraged by their position in this larger network (Who do they already know? And who, in turn, do their contacts know?) This dissertation addresses the impact of these constraints and affordances through the novel application of computational social network analysis to major databases of surviving prints from this period. This approach is used to evaluate several questions about trends in early modern print production practices that have not been satisfactorily addressed by traditional literature based on case studies alone: Did the social capital demanded by print production result in centralized, or distributed production of prints? When, and to what extent, did printmakers and publishers in the Low countries favor international versus domestic collaborators? And were printmakers under the same pressure as painters to specialize in particular artistic genres? This dissertation ultimately suggests how simple professional incentives endemic to the practice of printmaking may, at large scales, have resulted in quite complex patterns of collaboration and production. The framework of network analysis surfaces the role of certain printmakers who tend to be neglected in aesthetically-focused histories of art. This approach also highlights important issues concerning art historians’ balancing of individual influence versus the impact of longue durée trends. Finally, this dissertation also raises questions about the current limitations and future possibilities of combining computational methods with cultural heritage datasets in the pursuit of historical research.

Multiscale Modeling and Simulation of Stepped Crystal Surfaces

A primary goal of this dissertation is to understand the links between mathematical models that describe crystal surfaces at three fundamental length scales: The scale of individual atoms, the scale of collections of atoms forming crystal defects, and macroscopic scale. Characterizing connections between different classes of models is a critical task for gaining insight into the physics they describe, a long-standing objective in applied analysis, and also highly relevant in engineering applications. The key concept I use in each problem addressed in this thesis is coarse graining, which is a strategy for connecting fine representations or models with coarser representations. Often this idea is invoked to reduce a large discrete system to an appropriate continuum description, e.g. individual particles are represented by a continuous density. While there is no general theory of coarse graining, one closely related mathematical approach is asymptotic analysis, i.e. the description of limiting behavior as some parameter becomes very large or very small. In the case of crystalline solids, it is natural to consider cases where the number of particles is large or where the lattice spacing is small. Limits such as these often make explicit the nature of links between models capturing different scales, and, once established, provide a means of improving our understanding, or the models themselves. Finding appropriate variables whose limits illustrate the important connections between models is no easy task, however. This is one area where computer simulation is extremely helpful, as it allows us to see the results of complex dynamics and gather clues regarding the roles of different physical quantities. On the other hand, connections between models enable the development of novel multiscale computational schemes, so understanding can assist computation and vice versa. Some of these ideas are demonstrated in this thesis. The important outcomes of this thesis include: (1) a systematic derivation of the step-flow model of Burton, Cabrera, and Frank, with corrections, from an atomistic solid-on-solid-type models in 1+1 dimensions; (2) the inclusion of an atomistically motivated transport mechanism in an island dynamics model allowing for a more detailed account of mound evolution; and (3) the development of a hybrid discrete-continuum scheme for simulating the relaxation of a faceted crystal mound. Central to all of these modeling and simulation efforts is the presence of steps composed of individual layers of atoms on vicinal crystal surfaces. Consequently, a recurring theme in this research is the observation that mesoscale defects play a crucial role in crystal morphological evolution.