A few years ago, Tzeng settled a remarkable conjecture of Goettsche on counting nodal curves on smooth surfaces, proving that the formulas are given by certain universal polynomials. At the same time, Ardila and Block used the tropical approach of Brugalle, Mihalkin and Fomin to count nodal curves on a certain class of (not necessarily smooth) toric surfaces, and obtained similar polynomiality ...

Understanding the behavior of ionic liquids (ILs) either confined between rough surfaces or in rough nanoscale pores is of great relevance to extend studies performed on ideally flat surfaces to real applications. In this work we have performed an extensive investigation of the structural forces between two surfaces with well-defined roughness (<9 nm RMS) in 1-hexyl-3-methylimidazolium bis(trif...

Coherent anti-Stokes Raman spectroscopy (CARS) is a well-known tool in multiphoton imaging and nonlinear spectroscopy. In this work we combine CARS with plasmonic surface enhancement on reproducible nanostructured surfaces. We demonstrate strong correlation between plasmon resonances and surface-enhanced CARS (SECARS) intensities on our nanostructured surfaces and show that an enhancement of ∼1...

Implicit surfaces are one technique for surface modeling in computer graphics. In this report, we survey some implicit surface papers, present some projects using implicit surfaces, and give our evaluation of this work.

Space and spatial arrangements play an important role in our everyday social interactions. The way we use and manage our surrounding space is not coincidental, on the contrary, it reflects the way we think, plan and act. Within collaborative contexts, its ability to support social activities makes space an important component of human cognition in the post-cognitive era. As technology designers...

Understanding the mechanisms that are involved in determining bacterial growth rates is fundamental to infection biology, yet the factors that influence bacterial growth variation on surfaces are largely unknown. In this issue of ACS Nano, Lee et al. track individual bacteria on surfaces for several generations to discover systematic differences in growth rate variation between cells that dispe...

This work concerns the approximation of the shape operator of smooth surfaces in R from polyhedral surfaces. We introduce two generalized shape operators that are vector-valued linear functionals on a Sobolev space of vector fields and can be rigorously defined on smooth and on polyhedral surfaces. We consider polyhedral surfaces that approximate smooth surfaces and prove two types of approxima...