To understand how a solution's properties differ from those of the components, it is useful to have information on the local environment of the molecules in the solution. How does it differ from the average bulk environment? Here, "local" means within perhaps 2 intermolecular distances. It has long been known in a formal way how such information is encoded in the bulk thermodynamic properties (static) of the solution. In this talk I show how judicious approximations to the formal theory can often tease out this information in a more usable form. The theory contains a internal check on the validity of its approximations. Applications to experimental results will be presented.

Optical Metamaterials have shown great promise for cloaking and negative refractive subwavelength focusing. We ask what metamaterial parameters are necessary to coax electron-like behavior out of light. By using a quaternion formulation of Maxwell's equations that puts them in the form of the Dirac equation, we propose that a great many properties of electrons do have classical optical vector analogs, but in the class of metamaterials that have a near-zero permittivity or permeability. When we impose the condition that a Dirac metamaterial gives us Schrödinger's equation in a slowly varying limit, we obtain the same form and constants for other relativistic, spin-orbit, and Darwin term fine structure corrections with no further assumptions. We find that the angular momentum dependence of these optical corrections is different for light than for electrons. We briefly discuss the similarities and differences between classical optical hydrogen-like resonators, and the real hydrogen atom. We also discuss how a material with a tensor refractive index can give an optical analog of a constant magnetic field, and we suggest future experiments to verify these predictions.

I will discuss my work as Chief Architect of Wolfram|Alpha, a "computational knowledge engine" whose foremost face is the website, www.wolframalpha.com. I will talk about its vision, its history and current status, and hopes for the future. I will give examples of its capabilities, usage, limitations, and the technology behind it.

Coarse-graining of polymer systems facilitates the investigation of their dynamical and structural properties. Molecular-dynamics (MD) simulations of coarse-grained systems correctly reproduce the structural properties, but the dynamics becomes accelerated due to averaged out internal degrees of freedom. We take into account two corrections to compensate effects caused by coarse-graining: change in entropy and change in friction. We derive rescaling factors analytically from Generalized Langevin Equations for the coarse-grained at the monomer level representation and coarse-grained at the mesoscopic level representation. After applying our rescaling we compare the data of translational diffusion measured experimentally and from atomistic MD simulations.