Complex oscillations in the delayed Fitzhugh-Nagumo equation

Motivated by the dynamics of neuronal responses, we analyze the dynamics of the Fitzhugh-Nagumo slow-fast system with delayed self-coupling. This system provides a canonical example of a canard explosion for sufficiently small delays. Beyond this regime, delays significantly enrich the dynamics, leading to mixed-mode oscillations, bursting and chaos. These behaviors emerge from a delay-induced subcritical Bogdanov-Takens instability arising at the fold points of the S-shaped critical manifold. Underlying the transition from canard-induced to delay-induced dynamics is an abrupt switch in the nature of the Hopf bifurcation

Fluid transport through porous media: A novel application of kinetic Monte Carlo simulations

With increasing global energy demands, unconventional formations, such as shale rocks, are becoming an important source of natural gas. Current efforts are focused on understanding fluid dynamics to maximise natural gas yields. Although shale gas is playing an increasingly important role in the global energy industry, our knowledge of the fundamentals of fluid transport through multiscale and heterogeneous porous media is incomplete, as both static and dynamic properties of confined fluids differ tremendously from those at the macroscopic scale. Transport models, derived from atomistic studies, are frequently used to bridge this gap. However, capturing and upscaling the interactions between the pore surface and fluids remains challenging. In this thesis, a computationally efficient stochastic approach is implemented to simulate fluid transport through complex porous media. One-, two-, and three-dimensional kinetic Monte Carlo models were developed to predict methane transport in heterogeneous pore networks consisting of hydrated and water-free micro-, meso-, and macropores, representative of shale rock minerals. Molecular dynamics (MD) simulations, experimental imaging and adsorption data, which describe the surface – fluid interaction and the pore network features respectively were utilised to inform the KMC models. The stochastic approach was used to (1) quantify the effect of the pore network characteristics (pore size, chemistry, connectivity, porosity, and anisotropy) on the transport of supercritical methane, (2) estimate the permeability of an Eagle Ford shale sample and evaluate the effect of proppants on permeability, and (3) to upscale atomistic insights and predict fluid diffusivity through different size pores. The results obtained were consistent with the analytical solutions of the diffusion equation, experimental data, and MD simulations, respectively, demonstrating the effectiveness of the stochastic approach. In addition, the applicability of less computationally intensive deterministic approaches was examined using multiple case studies; recommendations are provided on the optimal conditions under which each method can be used

Statistical State Dynamics: a new perspective on turbulence in shear flow

Traditionally, single realizations of the turbulent state have been the object of study in shear flow turbulence. When a statistical quantity was needed it was obtained from a spatial, temporal or ensemble average of sample realizations of the turbulence. However, there are important advantages to studying the dynamics of the statistical state (the SSD) directly. In highly chaotic systems statistical quantities are often the most useful and the advantage of obtaining these statistics directly from a state variable is obvious. Moreover, quantities such as the probability density function (pdf) are often difficult to obtain accurately by sampling state trajectories even if the pdf is stationary. In the event that the pdf is time dependent, solving directly for the pdf as a state variable is the only alternative. However, perhaps the greatest advantage of the SSD approach is conceptual: adopting this perspective reveals directly the essential cooperative mechanisms among the disparate spatial and temporal scales that underly the turbulent state. While these cooperative mechanisms have distinct manifestation in the dynamics of realizations of turbulence both these cooperative mechanisms and the phenomena associated with them are not amenable to analysis directly through study of realizations as they are through the study of the associated SSD. In this review a selection of example problems in the turbulence of planetary and laboratory flows is examined using recently developed SSD analysis methods in order to illustrate the utility of this approach to the study of turbulence in shear flow.Comment: 27 pages, 18 figures. To appear in the book "Zonal jets: Phenomenology, genesis, physics", Cambridge University Press, edited by B. Galperin and P. L. Rea

Projections of epidemic transmission and estimation of vaccination impact during an ongoing Ebola virus disease outbreak in Northeastern Democratic Republic of Congo, as of Feb. 25, 2019.

BackgroundAs of February 25, 2019, 875 cases of Ebola virus disease (EVD) were reported in North Kivu and Ituri Provinces, Democratic Republic of Congo. Since the beginning of October 2018, the outbreak has largely shifted into regions in which active armed conflict has occurred, and in which EVD cases and their contacts have been difficult for health workers to reach. We used available data on the current outbreak, with case-count time series from prior outbreaks, to project the short-term and long-term course of the outbreak.MethodsFor short- and long-term projections, we modeled Ebola virus transmission using a stochastic branching process that assumes gradually quenching transmission rates estimated from past EVD outbreaks, with outbreak trajectories conditioned on agreement with the course of the current outbreak, and with multiple levels of vaccination coverage. We used two regression models to estimate similar projection periods. Short- and long-term projections were estimated using negative binomial autoregression and Theil-Sen regression, respectively. We also used Gott's rule to estimate a baseline minimum-information projection. We then constructed an ensemble of forecasts to be compared and recorded for future evaluation against final outcomes. From August 20, 2018 to February 25, 2019, short-term model projections were validated against known case counts.ResultsDuring validation of short-term projections, from one week to four weeks, we found models consistently scored higher on shorter-term forecasts. Based on case counts as of February 25, the stochastic model projected a median case count of 933 cases by February 18 (95% prediction interval: 872-1054) and 955 cases by March 4 (95% prediction interval: 874-1105), while the auto-regression model projects median case counts of 889 (95% prediction interval: 876-933) and 898 (95% prediction interval: 877-983) cases for those dates, respectively. Projected median final counts range from 953 to 1,749. Although the outbreak is already larger than all past Ebola outbreaks other than the 2013-2016 outbreak of over 26,000 cases, our models do not project that it is likely to grow to that scale. The stochastic model estimates that vaccination coverage in this outbreak is lower than reported in its trial setting in Sierra Leone.ConclusionsOur projections are concentrated in a range up to about 300 cases beyond those already reported. While a catastrophic outbreak is not projected, it is not ruled out, and prevention and vigilance are warranted. Prospective validation of our models in real time allowed us to generate more accurate short-term forecasts, and this process may prove useful for future real-time short-term forecasting. We estimate that transmission rates are higher than would be seen under target levels of 62% coverage due to contact tracing and vaccination, and this model estimate may offer a surrogate indicator for the outbreak response challenges

Distributed model predictive control of steam/water loop in large scale ships

In modern steam power plants, the ever-increasing complexity requires great reliability and flexibility of the control system. Hence, in this paper, the feasibility of a distributed model predictive control (DiMPC) strategy with an extended prediction self-adaptive control (EPSAC) framework is studied, in which the multiple controllers allow each sub-loop to have its own requirement flexibility. Meanwhile, the model predictive control can guarantee a good performance for the system with constraints. The performance is compared against a decentralized model predictive control (DeMPC) and a centralized model predictive control (CMPC). In order to improve the computing speed, a multiple objective model predictive control (MOMPC) is proposed. For the stability of the control system, the convergence of the DiMPC is discussed. Simulation tests are performed on the five different sub-loops of steam/water loop. The results indicate that the DiMPC may achieve similar performance as CMPC while outperforming the DeMPC method