Canonical stratifications along bisheaves

A theory of bisheaves has been recently introduced to measure the homological stability of fibers of maps to manifolds. A bisheaf over a topological space is a triple consisting of a sheaf, a cosheaf, and compatible maps from the stalks of the sheaf to the stalks of the cosheaf. In this note we describe how, given a bisheaf constructible (i.e., locally constant) with respect to a triangulation of its underlying space, one can explicitly determine the coarsest stratification of that space for which the bisheaf remains constructible.Comment: 10 pages; this is the Final Version which appeared in the Proceedings of the 2018 Abel Symposium on Topological Data Analysi

Quantifying Transversality by Measuring the Robustness of Intersections

By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbations, we assign to each homology class of the intersection its robustness, the magnitude of a perturbations in this space necessary to kill it, and prove that robustness is stable. Among the applications of this result is a stable notion of robustness for fixed points of continuous mappings and a statement of stability for contours of smooth mappings

Summers with My Bapuji: Opening Up a World of What-Ifs

Graduate Winner: 2nd Place, 2010. 23rd Annual Carl Neureuther Student Book Collection Competitio

External Reforming SOFC Coupled with Biomass-to-Syngas Reactor

This thesis introduces a thermodynamic model of an external reforming SOFC coupled with a biomass-to-syngas reactor in order to calculate energy and power that can be extracted from the fuel. Some of this energy will be used for electrical work and some of this energy will be used to provide heat to the reactor to drive the endothermic reactions occurring throughout the process. We analyzed four different feedstocks for their fuel cell heat dissipation and fuel cell power characteristic: pure syngas, pure carbon-derived syngas, coal-derived syngas, and biomass-derived syngas. Pure syngas consists of only CO and H2 while the other three cases of syngas consist of CO, H2, H2O, CO2, and CH4. Pure syngas did not take the reactor into account. The results of the analysis had shown that the absolute value of the Gibbs free energy of the fuel cell for pure syngas increased as the hydrogen concentration increased for temperatures above 1100 K. Opposite behavior occured for temperatures below 1100 K due to entropy change being less significant at lower temperatures. The results had also shown pure carbon-derived syngas to have the highest hydrogen concentration coming out of the reactor, which led to a higher Gibbs free energy of the fuel cell. This consequently led to a much higher maximum power density for any given temperature, followed by coal-derived syngas and biomass-derived syngas. Pure carbon-derived syngas also allowed the fuel cell to dissipate more heat than coal-derived syngas and biomass-derived syngas. Pure carbon was oxygen-free before the reactor and hydrogenrich after the reactor, thus allowing for high overall performance. High oxygen content hindered the performance of biomass-derived syngas, thus requiring the incorporation of de-oxygenation in the reactor. Coal gives higher overall performance compared to biomass at the expense of excess burning of air in the reactor and excess ash emission

Studio Bench: the DIY Nomad and Noise Selector

This thesis asks questions about developing a holistic practice that could be termed ‘Studio Bench’ from what have been previously seen as three separate activities: DIY electronic instrument making, sound studio practice, and live electronics. These activities also take place in three very specific spaces. Firstly, the workshop with its workbench provides a way of making and exploring sound(-making) objects, and this workbench is considered more transient and expedient in relation to finding sounds, and the term DIY Nomad is used to describe this new practitioner. Secondly, the recording studio provides a way to carefully analyse sound(-making) objects that have been self-built and record music to play back in different contexts. Finally, live practice is used to bridge the gap between the workbench and studio, by offering another place for making and an opportunity to observe and listen to the sound(-making) object in another environment in front of a live audience. The DIY Nomad’s transient nature allows for free movement between these three spaces, finding sounds and making in a holistic fashion. Spaces are subverted. Instruments are built in the studio and recordings made on the workbench. From the nomadity of the musician, sounds are found and made quickly and intuitively, and it is through this recontextualisation that the DIY Nomad embraces appropriation, remixing, hacking and expediency. The DIY Nomad also appropriates cultures and the research is shaped through DJ practice - remixing and record selecting - noise music, and improvisation