Conoids and Hyperbolic Paraboloids in Le Corbusier’s Philips Pavilion

The Philips Pavilion at the Brussels World Fair is the first of Le Corbusier’s architectural works to connect the evolution of his mathematical thought on harmonic series and modular coordination with the idea of three-dimensional continuity. This propitious circumstance was the consequence of his collaboration with Iannis Xenakis, whose profound interest in mathematical structures was improved on his becaming acquainted with the Modulor, while at the same time Le Corbusier encountered double ruled quadric surfaces. For the Philips Pavilion—the Poème Électronic—Corbusier entrusted Xenakis with a “mathematical translation” of his sketches, which represented the volume of a rounded bottle with a stomach-shaped plan. The Pavilion was designed as if it were an orchestral work in which lights, loudspeakers, film projections on curved surfaces, spectators’ shadows and their expression of wonder, objects hanging from the ceiling and the containing space itself were all virtual instrument

Effect of Metal Element in Catalytic Growth of Carbon Nanotubes

Using first principles calculations, we model the chemical vapor deposition (CVD) growth of carbon nanotubes (CNT) on nanoparticles of late transition (Ni, Pd, Pt) and coinage (Cu, Ag, Au) metals. The process is analyzed in terms of the binding of mono- and diatomic carbon species, their diffusion pathways, and the stability of the growing CNT. We find that the diffusion pathways can be controlled by the choice of the catalyst and the carbon precursor. Binding of the CNT through armchair edges is more favorable than through zigzag ones, but the relative stability varies significantly among the metals. Coinage metals, in particular Cu, are found to favor CVD growth of CNTs at low temperatures and with narrow chirality distributions.Comment: Phys. Rev. Lett., accepte

Diameter-Selective Dispersion of Carbon Nanotubes via Polymers: A Competition between Adsorption and Bundling

The mechanism of the selective dispersion of single-walled carbon nanotubes (CNTs) by polyfluorene polymers is studied in this paper. Using extensive molecular dynamics simulations, it is demonstrated that diameter selectivity is the result of a competition between bundling of CNTs and adsorption of polymers on CNT surfaces. The preference for certain diameters corresponds to local minima of the binding energy difference between these two processes. Such minima in the diameter dependence occur due to abrupt changes in the CNT's coverage with polymers and their calculated positions are in quantitative agreement with preferred diameters, reported experimentally. The presented approach defines a theoretical framework for the further understanding and improvement of dispersion/extraction processes.Comment: 22 pages, 5 figures, ACS Nano (2015

Experimental Synthetic Aperture Radar with Dynamic Metasurfaces

We investigate the use of a dynamic metasurface as the transmitting antenna for a synthetic aperture radar (SAR) imaging system. The dynamic metasurface consists of a one-dimensional microstrip waveguide with complementary electric resonator (cELC) elements patterned into the upper conductor. Integrated into each of the cELCs are two diodes that can be used to shift each cELC resonance out of band with an applied voltage. The aperture is designed to operate at K band frequencies (17.5 to 20.3 GHz), with a bandwidth of 2.8 GHz. We experimentally demonstrate imaging with a fabricated metasurface aperture using existing SAR modalities, showing image quality comparable to traditional antennas. The agility of this aperture allows it to operate in spotlight and stripmap SAR modes, as well as in a third modality inspired by computational imaging strategies. We describe its operation in detail, demonstrate high-quality imaging in both 2D and 3D, and examine various trade-offs governing the integration of dynamic metasurfaces in future SAR imaging platforms