RUI: Vortex Arrays in Superconducting Multilayers - in the current context, a vortex is a tube of magnetic field which penetrates the bulk of a superconducting material. The structure, distribution, and elastic properties of vortices in superconducting multilayer materials is of fundamental importance to both their physical characterization and to their potential for technological applications. Vortex arrays play a role in determining the upper and lower critical magnetic fields for multilayer superconductors. Intrinsic and extrinsic pinning of vortices due to layering or to defects at interfaces is likely to be of great importance for understanding of superconducting multilayers. Similar issues, such as the flow and creep of vortices in the presence of a transport current and the melting of a flux lattice, currently limit the application of high-Tc superconductors. The proposal is to study the effects vortices have on Josephson-coupled multilayers consisting of alternating layers of superconducting sheets and insulating layers. Using Ginzburg-Landau theory, the properties listed above will be studied for real materials in realistic environments. The results are expected to be relevent to high-Tc materials. %%% Superconductors are of particular interest to materials science because they represent both a splendid example of a quantum mechanical phase transition and a unique class of materials having many potential applications. Under conditions of high magnetic field (or high current density), some superconductors become threaded by small tubular regions of normal material, called vortices. One class of superconducting materials which admits vortices consists of thin layers of superconductor separated by thin layers of normal material. This is a common configuration for superconducting materials intended for real-world applications. Understanding the properties of such materials well enough to predict and utilize their special nature is crucial to developing applications for both typical and the high-Tc superconductors. This is the goal of the current study.