Rensselaer Polytechnic Institute

About: Rensselaer Polytechnic Institute is a education organization based out in Troy, New York, United States. It is known for research contribution in the topics: Terahertz radiation & Finite element method. The organization has 19024 authors who have published 39922 publications receiving 1414699 citations. The organization is also known as: RPI & Rensselaer Institute.

Diffusion in Zircon

Abstract: Despite its low abundance in most rocks, zircon is extraordinarily useful in interpreting crustal histories. The importance of U-Th-Pb isotopic dating of zircon is well and long established (Davis et al., this volume; Parrish et al., this volume). Zircon also tends to incorporate trace elements useful as geochemical tracers, such as the REE, Y, and Hf. A number of characteristics of zircon encourage the preservation of internal isotopic and chemical variations, often on extremely fine scale, which provide valuable insight into thermal histories and past geochemical environments. The relative insolubility of zircon in crustal melts and fluids, as well as its general resistance to chemical and physical breakdown, often result in the existence of several generations of geochemical information in a single zircon grain. The fact that this information is so frequently retained (as evidenced through backscattered electron or cathodoluminescence imaging that often reveal fine-scale zoning down to the sub-micron scale) has long suggested that diffusion of most elements is quite sluggish in zircon. In this chapter, we present an overview of the findings to date from laboratory measurements of diffusion of cations and oxygen in zircon. Because of its importance as a geochronometer, attempts have been made to measure diffusion (especially of Pb) for over 30 years. But only in the last decade or so have profiling techniques with adequate depth resolution been employed in these studies, resulting in a plethora of new diffusion data. These findings have important implications for isotopic dating, interpretation of stable-isotope ratios, closure temperatures, and formation and preservation of primary chemical composition and zoning in zircon. Efforts have been made for some time to quantify and characterize diffusion in zircon, most notably of Pb, in deference to its significance in interpreting Pb isotopic signatures and refining understanding of thermal histories. As is evident from …

Nanograssed Micropyramidal Architectures for Continuous Dropwise Condensation

Abstract: Engineering the dropwise condensation of water on surfaces is critical in a wide range of applications from thermal management (e.g. heat pipes, chip cooling etc.) to water harvesting technologies. Surfaces that enable both effi cient droplet nucleation and droplet self-removal (i.e. droplet departure) are essential to accomplish successful dropwise condensation. However it is extremely challenging to design such surfaces. This is because droplet nucleation requires a wettable surface while droplet departure necessitates a super-hydrophobic surface. Here we report that these confl icting requirements can be satisfi ed using a hierarchical (multiscale) nanograssed micropyramid architecture that yield a gobal superhydrophobicity as well as locally wettable nucleation sites, allowing for ˜65% increase in the drop number density and ˜450% increase in the drop self-removal volume as compared to a superhydrophobic surface with nanostructures alone. Further we fi that synergistic co-operation between the hierarchical structures contributes directly to a continuous process of nucleation, coalescence, departure, and re-nucleation enabling sustained dropwise condensation over prolonged periods. Exploiting such multiscale coupling effects can open up novel and exciting vistas in surface engineering leading to optimal condensation surfaces for high performance electronics cooling and water condenser systems.

Faster least squares approximation

Abstract: Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets n be the number of constraints and d be the number of variables, with $${n \gg d}$$. Then, existing exact methods find a solution vector in O(nd 2) time. We present two randomized algorithms that provide accurate relative-error approximations to the optimal value and the solution vector of a least squares approximation problem more rapidly than existing exact algorithms. Both of our algorithms preprocess the data with the Randomized Hadamard transform. One then uniformly randomly samples constraints and solves the smaller problem on those constraints, and the other performs a sparse random projection and solves the smaller problem on those projected coordinates. In both cases, solving the smaller problem provides relative-error approximations, and, if n is sufficiently larger than d, the approximate solution can be computed in O(nd ln d) time.