John Bell

Will Pazner, Andrew Nonaka, John Bell et al.

We present a fourth-order finite-volume algorithm in space and time for low Mach number reacting flow with detailed kinetics and transport. Our temporal integration scheme is based on a multi-implicit spectral deferred correction (MISDC) strategy that iteratively couples advection, diffusion, and reactions evolving subject to a constraint. Our new approach overcomes a stability limitation of our previous second-order method encountered when trying to incorporate higher-order polynomial representations of the solution in time to increase accuracy. We have developed a new iterative scheme that naturally fits within our MISDC framework that allows us to simultaneously conserve mass and energy while satisfying on the equation of state. We analyse the conditions for which the iterative schemes are guaranteed to converge to the fixed point solution. We present numerical examples illustrating the performance of the new method on premixed hydrogen, methane, and dimethyl ether flames.

John Bell, Marcus Day, Jonathan Goodman et al.

First-principles Markov Chain Monte Carlo sampling is used to investigate uncertainty quantification and uncertainty propagation in parameters describing hydrogen kinetics. Specifically, we sample the posterior distribution of thirty-one parameters focusing on the H2O2 and HO2 reactions resulting from conditioning on ninety-one experiments. Established literature values are used for the remaining parameters in the mechanism. The samples are computed using an affine invariant sampler starting with broad, noninformative priors. Autocorrelation analysis shows that O(1M) samples are sufficient to obtain a reasonable sampling of the posterior. The resulting distribution identifies strong positive and negative correlations and several non-Gaussian characteristics. Using samples drawn from the posterior, we investigate the impact of parameter uncertainty on the prediction of two more complex flames: a 2D premixed flame kernel and the ignition of a hydrogen jet issuing into a heated chamber. The former represents a combustion regime similar to the target experiments used to calibrate the mechanism and the latter represents a different combustion regime. For the premixed flame, the net amount of product after a given time interval has a standard deviation of less than 2% whereas the standard deviation of the ignition time for the jet is more than 10%. The samples used for these studies are posted online. These results indicate the degree to which parameters consistent with the target experiments constrain predicted behavior in different combustion regimes. This process provides a framework for both identifying reactions for further study from candidate mechanisms as well as combining uncertainty quantification and propagation to, ultimately, tie uncertainty in laboratory flame experiments to uncertainty in end-use numerical predictions of more complicated scenarios.

John Bell, Ana Djurdjevac, Nicolas Perkowski

We consider stochastic particle dynamics on hypersurfaces represented in Monge gauge parametrization. Starting from the underlying Langevin system, we derive the surface Dean-Kawasaki (DK) equation and formulate it in the martingale sense. The resulting SPDE explicitly reflects the geometry of the hypersurface through the induced metric and its differential operators. Our framework accommodates both pairwise interactions and environmental potentials, and we extend the analysis to evolving hypersurfaces driven by an SDE that interacts with the particles, yielding the corresponding surface DK equation for the coupled surface-particle system. We establish a weak uniqueness result in the non-interacting case, and we develop a finite-volume discretization preserving the fluctuation-dissipation relation. Numerical experiments illustrate equilibrium properties and dynamical behavior influenced by surface geometry and external potentials.

John Bell, H. Harry Asada

In providing physical assistance to elderly people, ensuring cooperative behavior from the elderly persons is a critical requirement. In sit-to-stand assistance, for example, an older adult must lean forward, so that the body mass can shift towards the feet before a caregiver starts lifting the body. An experienced caregiver guides the older adult through verbal communications and physical interactions, so that the older adult may be cooperative throughout the process. This guidance is of paramount importance and is a major challenge in introducing a robotic aid to the eldercare environment. The wide-scope goal of the current work is to develop an intelligent eldercare robot that can a) monitor the mental state of an older adult, and b) guide the older adult through an assisting procedure so that he/she can be cooperative in being assisted. The current work presents a basic modeling framework for describing a human's physical behaviors reflecting an internal mental state, and an algorithm for estimating the mental state through interactive observations. The sit-to-stand assistance problem is considered for the initial study. A simple Kalman Filter is constructed for estimating the level of cooperativeness in response to applied cues, with a thresholding scheme being used to make judgments on the cooperativeness state.