Enhancement of shock-capturing methods via machine learning

In recent years, machine learning has been used to create data-driven solutions to problems for which an algorithmic solution is intractable, as well as fine-tuning existing algorithms. This research applies machine learning to the development of an improved finite-volume method for simulating PDEs with discontinuous solutions. Shock-capturing methods make use of nonlinear switching functions that are not guaranteed to be optimal. Because data can be used to learn nonlinear relationships, we train a neural network to improve the results of a fifth-order WENO method. We post-process the outputs of the neural network to guarantee that the method is consistent. The training data consist of the exact mapping between cell averages and interpolated values for a set of integrable functions that represent waveforms we would expect to see while simulating a PDE. We demonstrate our method on linear advection of a discontinuous function, the inviscid Burgers’ equation, and the 1-D Euler equations. For the latter, we examine the Shu–Osher model problem for turbulence–shock wave interactions. We find that our method outperforms WENO in simulations where the numerical solution becomes overly diffused due to numerical viscosity

COFFEE -- An MPI-parallelized Python package for the numerical evolution of differential equations

COFFEE (ConFormal Field Equation Evolver) is a Python package primarily developed to numerically evolve systems of partial differential equations over time using the method of lines. It includes a variety of time integrators and finite differencing stencils with the summation-by-parts property, as well as pseudo-spectral functionality for angular derivatives of spin-weighted functions. Some additional capabilities include being MPI-parallelisable on a variety of different geometries, HDF data output and post processing scripts to visualize data, and an actions class that allows users to create code for analysis after each timestep.Comment: 12 pages, 1 figure, accepted to be published in Software

Identity in the Anglo-Indian Novel: "The Passing Figure" and Performance

In the following thesis, two interrelated arguments are offered: firstly, a re-appropriation of the passing figure from an African-American context to the Anglo-Indian context is suggested, which it is argued, will allow new methods for the study of the hybrid figure in British literature to develop. Secondly, the thesis works to critique the relationship between poststructuralism and postcolonialism, suggesting a move away from a discourse concerned with anti-reality and its linguistic-theoretical focus to a framework with stronger roots in the study of postcoloniality as a real, lived condition experienced by a large number of people. The above arguments are realized through a reading of Anglo-Indian literature which closely aligns both the displaced postcolonial figure and the passing figure through a shared ability to perform multiple identities. In adopting the passing figure, Anglo-Indian literature illustrates the rejection of in culture forms of rigid and constraining essentialisms and the commitment to modernist and contemporary cultural discourses of identity construction in the hybrid figure of postcolonial works. Such cultural discourses of identity presuppose the intervention of performativity in the negotiation of multiple selves. Both the hybrid postcolonial figure and the passing figure display an adoption of performance in identity construction. In a theoretical reflection of the multiplicity offered by the passing figure, a number of diverse critical approaches to these Anglo-Indian texts are introduced. Specifically, the aim is to suggest alternative theoretical approaches to the hegemonic poststructuralist critical view. I will argue that the reliance upon poststructuralist theory can be detrimental to the full exploration of the postcolonial identity, due largely to the tendency to privilege textual fee-play over experiential analysis. I am proposing a modification to the relationship between deconstruction and postcolonialism, whereby certain selected deconstructive techniques are appropriated alongside more existentialist concerns that reflect the real, lived conditions of postcolonial environments. In relocating textual critique within an approach more concerned with the real-life experience of multiplicity, this study advocates a continuing relevance of a more existentialist mode of postcolonialism, as exemplified by Sartre and Fanon, and other adjacent theorists. An example of this is that popular and contemporary authors such as Naipaul, Rushdie, Kureishi and Malkani are read in light of “dialogical self theory”, R.D. Laing’s “false-self system”, Fish’s “interpretive communities” thesis and Goffman’s concept of “front”. Dialogical self theory and the false-self system ensure a firm underpinning of the internal psychological structure of the passing figure’s psyche, establishing a discourse of postcolonialism that is centred on the real experience of multiplicity. The following work on interpretive communities and front allow for the connection of the internal construction of self to the wider social environment through the relocation of the passing figure’s identity in relation to the interpretations of the audience

Enhancement of shock-capturing methods via machine learning

In recent years, machine learning has been used to create data-driven solutions to problems for which an algorithmic solution is intractable, as well as fine-tuning existing algorithms. This research applies machine learning to the development of an improved finite-volume method for simulating PDEs with discontinuous solutions. Shock-capturing methods make use of nonlinear switching functions that are not guaranteed to be optimal. Because data can be used to learn nonlinear relationships, we train a neural network to improve the results of a fifth-order WENO method. We post-process the outputs of the neural network to guarantee that the method is consistent. The training data consist of the exact mapping between cell averages and interpolated values for a set of integrable functions that represent waveforms we would expect to see while simulating a PDE. We demonstrate our method on linear advection of a discontinuous function, the inviscid Burgers’ equation, and the 1-D Euler equations. For the latter, we examine the Shu–Osher model problem for turbulence–shock wave interactions. We find that our method outperforms WENO in simulations where the numerical solution becomes overly diffused due to numerical viscosity

Changes in Intragastric Temperature Reflect Changes in Heat Stress Following Tepid Fluid Ingestion But Not Ice Slurry Ingestion

This study examined the effects of fluid and ice slurry ingestion on the relationship between intragastric temperature and rectal temperature in humans during physical activity. The purpose was to identify a technique to quantify changes in heat stress in situations when temperature probes are not feasible and when time constraints do not allow for a period long enough for an indigestible temperature capsule to reach the lower gastrointestinal tract. Eight moderately trained male runners inserted a rectal probe and ingested a telemetric capsule before randomized, crossover, pre-exercise ingestion of 7.5 mL x kg-1 x BM-1tepid fluid (22°C) or ice slurry (-1°C). Beverage ingestion was followed by a self-paced endurance running time trial. Average intragastric temperature was significantly lower than average rectal temperature across the run following both fluid (37.9 +/- 0.4°C vs. 38.4 +/- 0.2°C; p=0.003) and ice slurry ingestion (37.2 +/- 0.9 vs. 38.3 +/- 0.2; p=0.009). However, a strong relationship was observed between measurements following fluid (r=0.89) but not ice slurry (r=0.18). The average bias +/- limits of agreement during the run was 0.46 +/- 0.50 following fluid and 1.09 +/- 1.68 following ice slurry ingestion, which improved to 0.06 +/- 0.76 and 0.65 +/- 1.42, respectively when analyzed as delta scores. Intragastric temperature appears to not be a valid measure of absolute core body temperature at baseline or during exercise following either fluid or ice slurry ingestion. However, the relative changes in intragastric temperature during endurance exercise appears to be a strong indicator of systemic heat stress during exercise following ingestion of fluid at 22°C, but not ice slurry at -1°C