Analysis of pattern dynamics for a nonlinear model of the human cortex via bifurcation theories

This thesis examines the bifurcations, i.e., the emergent behaviours, for the Waikato cortical model under the influence of the gap-junction inhibitory diffusion D₂ (identified as the Turing bifurcation parameter) and the time-to-peak for hyperpolarising GABA response γi (i.e., inhibitory rate-constant, identified as the Hopf bifurcation parameter). The cortical model simplifies the entire cortex to a cylindrical macrocolumn (∼ 1 mm³) containing ∼ 10⁵ neurons (85% excitatory, 15% inhibitory) communicating via both chemical and electrical (gap-junction) synapses. The linear stability analysis of the model equations predict the emergence of a Turing instability (in which separated areas of the cortex become activated) when gap-junction diffusivity is increased above a critical level. In addition, a Hopf bifurcation (oscillation) occurs when the inhibitory rate-constant is sufficiently small. Nonlinear interaction between these instabilities leads to spontaneous cortical patterns of neuronal activities evolving in space and time. Such model dynamics of delicately balanced interplay between Turing and Hopf instabilities may be of direct relevance to clinically observed brain dynamics such as epileptic seizure EEG spikes, deep-sleep slow-wave oscillations and cognitive gamma-waves. The relationship between the modelled brain patterns and model equations can normally be inferred from the eigenvalue dispersion curve, i.e., linear stability analysis. Sometimes we experienced mismatches between the linear stability analysis and the formed cortical patterns, which hampers us in identifying the type of instability corresponding to the emergent patterns. In this thesis, I investigate the pattern-forming mechanism of the Waikato cortical model to better understand the model nonlinearities. I first study the pattern dynamics via analysis of a simple pattern-forming system, the Brusselator model, which has a similar model structure and bifurcation phenomena as the cortical model. I apply both linear and nonlinear perturbation methods to analyse the near-bifurcation behaviour of the Brusselator in order to precisely capture the dominant mode that contributes the most to the final formed-patterns. My nonlinear analysis of the Brusselator model yields Ginzburg-Landau type amplitude equations that describe the dynamics of the most unstable mode, i.e., the dominant mode, in the vicinity of a bifurcation point. The amplitude equations at a Turing point unfold three characteristic spatial structures: honeycomb Hπ, stripes, and reentrant honeycomb H₀. A codimension-2 Turing–Hopf point (CTHP) predicts three mixed instabilities: stable Turing–Hopf (TH), chaotic TH, and bistable TH. The amplitude equations precisely determine the bifurcation conditions for these instabilities and explain the pattern-competition mechanism once the bifurcation parameters cross the thresholds, whilst driving the system into a nonlinear region where the linear stability analysis may not be applicable. Then, I apply the bifurcation theories to the cortical model for its pattern predictions. Analogous to the Brusselator model, I find cortical Turing pattens in Hπ, stripes and H₀ spatial structures. Moreover, I develop the amplitude equations for the cortical model, with which I derive the envelope frequency for the beating-waves of a stable TH mode; and propose ideas regarding emergence of the cortical chaotic mode. Apart from these pattern dynamics that the cortical model shares with the Brusselator system, the cortical model also exhibits “eye-blinking” TH patterns latticed in hexagons with localised oscillations. Although we have not found biological significance of these model pattens, the developed bifurcation theories and investigated pattern-forming mechanism may enrich our modelling strategies and help us to further improve model performance. In the last chapter of this thesis, I introduce a Turing–Hopf mechanism for the anaesthetic slow-waves, and predict a coherence drop of such slow-waves with the induction of propofol anaesthesia. To test this hypothesis, I developed an EEG coherence analysing algorithm, EEG coherence, to automatically examine the clinical EEG recordings across multiple subjects. The result shows significantly decreased coherence along the fronto-occipital axis, and increased coherence along the left- and right-temporal axis. As the Waikato cortical model is spatially homogenous, i.e., there are no explicit front-to-back or right-to-left directions, it is unable to produce different coherence changes for different regions. It appears that the Waikato cortical model best represents the cortical dynamics in the frontal region. The theory of pattern dynamics suggests that a mode transition from wave–Turing–wave to Turing–wave–Turing introduces pattern coherence changes in both positive and negative directions. Thus, a further modelling improvement may be the introduction of a cortical bistable mode where Turing and wave coexist

Turing instability and pattern formation of a fractional Hopfield reaction–diffusion neural network with transmission delay

It is well known that integer-order neural networks with diffusion have rich spatial and temporal dynamical behaviors, including Turing pattern and Hopf bifurcation. Recently, some studies indicate that fractional calculus can depict the memory and hereditary attributes of neural networks more accurately. In this paper, we mainly investigate the Turing pattern in a delayed reaction–diffusion neural network with Caputo-type fractional derivative. In particular, we find that this fractional neural network can form steadily spatial patterns even if its first-derivative counterpart cannot develop any steady pattern, which implies that temporal fractional derivative contributes to pattern formation. Numerical simulations show that both fractional derivative and time delay have influence on the shape of Turing patterns

Development of Hybrid Fuel Cell / Li-ion Battery Systems

Electrochemical power systems are needed to de-carbonise the transport industry. Fuel cells and battery systems alone may not be able to meet the diverse set of requirements, but when hybridised, their applicability to this sector is vastly increased. This raises questions around the specific nature of hybridisation. This thesis aims to expand our understanding of fuel cell and lithium-ion battery hybridisation for automotive applications, through a combined experimental and computational approach. Prior to undertaking such research, an understanding of each individual system is required. This is perused along the themes of current heterogeneity, and applied to parallel battery cells in two common electrical configurations and across the active area of a 100 cm2 polymer exchange fuel cell. First, it is shown the electrical configuration of the parallel string has significant impact on the current distribution, impacting the charge throughput of each cell and the usable capacity of the module. Degradation modelling showed the lifetime of the module is reduced by 4.5% in the less optimal configuration. Secondly, the current and thermal distribution within a fuel cell is investigated for a range of operating conditions such as flooding, drying and cold start. Electrochemical impedance spectroscopy is used to understand the conditions of the membrane and reactant time constants in-situ. Results indicate how the design of fuel cells can be refined to improve performance in challenging operating conditions. Finally, the investigation of electrical and thermal hybridisation is conducted on a passenger sized vehicle. A common modelling framework is developed, using the models developed in the fuel cell and battery chapters, to assess electrical energy management systems. A novel fuzzy logic controller is developed which mutates the output membership functions based on the ‘state-of-degradation’, a parameter derived from an interconnected electrochemical surface area loss and system state model. The controller is able to extend the lifetime of the fuel cell by 32.8% in its presented configuration. The common framework is then developed to include dynamic thermal models of the fuel cell, battery pack, radiator and auxiliaries to investigate whether combining the battery pack and fuel cell stack onto a single coolant loop is feasible. The system is tested against a range of operating conditions and its performance is discussed. These findings are expected to aid the transport industry in the transition to a zero emission future

Control and operation of a spinning disc reactor

PhD ThesisThe aim of the present research is to assess the control and operation of a Spinning Disc Reactor (SDR), carried out via four separate investigations. Firstly, the effect of equipment size reduction on control is studied by comparing the performance of a PID controller applied to simulated intensified and conventional processes. It was found that superior control performance in terms of Integral of Absolute Error (IAE) is achieved for the simulated intensified system. However, the results showed that intensified systems are more susceptible to disturbances and the controlled variable exhibits larger overshoots. Furthermore, the frequency response analysis of the two systems showed that the simulated intensified system has reduced stability margins. The second part of the research investigates the task of pH control in a SDR using a PID controller by means of simulation and experimental studies. The effectiveness of a disturbance observer (DO) and a pH characteriser to compensate for the severe pH system nonlinearity is also explored in detail. The experimental studies showed that a PID controller provides adequate setpoint tracking and disturbance rejection performances. However, sluggish transient responses prevailed and the effluent pH limit cycled around the setpoint. There were indications of unstable behaviour at lower flowrates, which implied more advanced control schemas may be required to adapt to various operating regions dictated by the complex thin film hydrodynamics. The addition of the DO scheme improved the control performance by reducing the limit cycles. In the third segment of the investigations, the potential of exploiting the disc rotational speed as a manipulated variable is assessed for the process of barium sulphate precipitation. A PI controller is successfully used to regulate the conductivity of the effluent stream by adjusting the disc rotational speed. The results are immensely encouraging and show that the disc speed may be used as an extra degree of freedom in control system design. Finally, the flow regimes and wave characteristics of thin liquid films produced in a SDR are investigated by means of a thermal imaging camera. The film hydrodynamics strongly affect the heat and mass transfer processes within the processing films, and thus the intensification aspects of SDRs. Therefore, effective control and operation of such units is significantly dependent on the knowledge of film hydrodynamics and the underlying impact of the operating parameters and the manipulated variables on a given process. The results provided an interesting insight and unveiled promising potentials for characterisation of thin liquid film flow and temperature profiles across the disc by means of thermographic techniques. The present study reveals both challenges and opportunities regarding the control aspects of SDRs. It is recommended that equipment design and process control need to be considered simultaneously during the early stages of the future developments. Furthermore, intensified sensors and advanced controllers may be required to achieve an optimum control capability. Currently, the control performance is inhibited by the lack of sufficient considerations during the SDR design and manufacturing stages, and also by the characteristics of the commercially available instrumentation.EPSRC Doctoral Training Awar

The production, properties and applications of the zinc imidazolate, ZIF-8.

Venna, Carreon, and Jasinski produced and characterized the first samples of the zinc imidazolate framework ZIF-8 at the University of Louisville in 2010. In this dissertation the production, properties, and applications of this unique metal-organic framework are explored. Previously, only minute laboratory amounts (1/4 gram), of ZIF-8 were produced via time-consuming and expensive processes. Production quantities have been synthesized via both a continuous and a batch process using a spray drying operation to effect separation of the solid product (ZIF-8) from the mother liquor. Approximately 85% of the mother liquor (methanol), can be recovered from the spray dryer resulting in magnitude-of-order savings in time and money. Before any engineering applications could be suggested it was necessary to quantify important physical properties of ZIF-8 not currently available. The density, thermal conductivity, specific heat, and BET surface area were measured via strict ASTM procedures and reported. It was hoped that the massive surface area of ZIF-8 (~ 1300 m2/g), would effect enhanced heat transfer in engineering applications. The Heat Transfer Laboratories at the University of Louisville, served as the testing site for the use of the microparticle ZIF-8 as an agent for enhanced heat transfer when mixed in small vol% in synthetic oil. Unfortunately ZIF-8 delivered no such enhancement

Modeling of Instabilities and Self-Organization at the Frictional Interface

The field of friction-induced self-organization and its practical importance remains unknown territory to many tribologists. Friction is usually thought of as irreversible dissipation of energy and deterioration; however, under certain conditions, friction can lead to the formation of new structures at the interface, including in-situ tribofilms and various patterns at the interface. This thesis studies self-organization and instabilities at the frictional interface, including the instability due to the temperature-dependency of the coefficient of friction, the transient process of frictional running-in, frictional Turing systems, the stick-and-slip phenomenon, and, finally, contact angle (CA) hysteresis as an example of solid-liquid friction and dissipation. All these problems are chosen to bridge the gap between fundamental interest in understanding the conditions leading to self-organization and practical motivation. We study the relationship between friction-induced instabilities and friction-induced self-organization. Friction is usually thought of as a stabilizing factor; however, sometimes it leads to the instability of sliding, in particular when friction is coupled with another process. Instabilities constitute the main mechanism for pattern formation. At first, a stationary structure loses its stability; after that, vibrations with increasing amplitude occur, leading to a limit cycle corresponding to a periodic pattern. The self-organization is usually beneficial for friction and wear reduction because the tribological systems tend to enter a state with the lowest energy dissipation. The introductory chapter starts with basic definitions related to self-organization, instabilities and friction, literature review, and objectives. We discuss fundamental concepts that provide a methodological tool to investigate, understand and enhance beneficial processes in tribosystems which might lead to self-organization. These processes could result in the ability of a frictional surface to exhibit self-protection and self-healing properties. Hence, this research is dealing with the fundamental concepts that allow the possibility of the development of a new generation of tribosystem and materials that reinforce such properties. In chapter 2, we investigate instabilities due to the temperature-dependency of the coefficient of friction. The temperature-dependency of the coefficient of friction can have a significant effect on the frictional sliding stability, by leading to the formation of hot and cold spots on the contacting surfaces. We formulate a stability criterion and perform a case study of a brake disk. We show that the mechanism of instability can contribute to poor reproducibility of aircraft disk brake tests reported in the literature. Furthermore, a method to increase the reproducibility by dividing the disk into several sectors with decreased thermal conductivity between the sectors is proposed. In chapter 3, we study frictional running-in. Running-in is a transient period on the onset of the frictional sliding, in which friction and wear decrease to their stationary values. In this research, running-in is interpreted as friction-induced self-organization process. We introduce a theoretical model of running-in and investigate rough profile evolution assuming that its kinetics is driven by two opposite processes or events, i.e., smoothening which is typical for the deformation-driven friction and wear, and roughening which is typical for the adhesion-driven friction and wear. To validate our modeling results, we examine experimentally running-in in ultrahigh vacuum friction tests for WC pin versus Cu substrate. We propose to calculate the Shannon entropy of a rough profile and to use it as a simple test for self-organization. We observe, theoretically and experimentally, how Shannon entropy as a characteristic of a rough surface profile changes during running-in, and quantifies the degree of orderliness of the self-organized system. In chapter 4, we investigate the possibility of the so-called Turing-type pattern formation during friction. Turing or reaction-diffusion systems describe variations of spatial concentrations of chemical components with time due to local chemical reactions coupled with diffusion. During friction, the patterns can form at the sliding interface due to the mass transfer (diffusion), heat transfer, various tribochemical reactions, and wear. We present a mathematical model, and solve the governing equations by using a finite-difference method. The results demonstrate a possibility of such pattern-formation. We also discuss existing experimental data that suggest that tribofilms can form in-situ at the frictional interface due to a variety of friction-induced chemical reactions (oxidation, the selective transfer of Cu ions, etc.). In chapter 5, we investigate how interfacial patterns including propagating trains of stick and slip zones form due to dynamic sliding instabilities. These can be categorized as self-organized patterns. We treat stick and slip as two phases at the interface, and study the effects related to phase transitions. Our results show how interfacial patterns form, how the transition between stick and slip zones occurs, and which parameters affect them. In chapter 6, we use Cellular Potts Model to study contact angle (CA) hysteresis as a measure of solid-liquid energy dissipation. We simulate CA hysteresis for a droplet over the tilted patterned surface, and a bubble placed under the surface immersed in liquid. We discuss the dependency of CA hysteresis on the surface structure and other parameters. This analysis allows decoupling of the 1D (pinning of the triple line) and 2D effects (adhesion hysteresis in the contact area) and obtain new insights on the nature of CA hysteresis. To summarize, we examine different cases in frictional interface and observe similar trends. We investigate and discus how these trends could be beneficial in design, synthesis and characterization of different materials and tribosystems. Furthermore, we describe how to utilize fundamental concepts for specific engineering applications. Finally, the main theme of this research is to find new applications of concept of self-organization to tribology and the role played by different physical and chemical interactions in modifying and controlling friction and wear

Supervisory Control Optimization for a Series Hybrid Electric Vehicle with Consideration of Battery Thermal Management and Aging

This dissertation integrates battery thermal management and aging into the supervisory control optimization for a heavy-duty series hybrid electric vehicle (HEV). The framework for multi-objective optimization relies on novel implementation of the Dynamic Programing algorithm, and predictive models of critical phenomena. Electrochemistry based battery aging model is integrated into the framework to assesses the battery aging rate by considering instantaneous lithium ion (Li+) surface concentration rather than average concentration. This creates a large state-action space. Therefore, the computational effort required to solve a Deterministic or Stochastic Dynamic Programming becomes prohibitively intense, and a neuro-dynamic programming approach is proposed to remove the ‘curse of dimensionality’ in classical dynamic programming. First, unified simulation framework is developed for in-depth studies of series HEV system. The integration of a refrigerant system model enables prediction of energy use for cooling the battery pack. Side reaction, electrolyte decomposition, is considered as the main aging mechanism of LiFePO4/Graphite battery, and an electrochemical model is integrated to predict side reaction rate and the resulting fading of capacity and power. An approximate analytical solution is used to solve the partial difference equations (PDEs) for Li+ diffusion. Comparing with finite difference method, it largely reduces the number of states with only a slight penalty on prediction accuracy. This improves computational efficiency, and enables inclusion of the electrochemistry based aging model in the power management optimization framework. Next, a stochastic dynamic programming (SDP) approach is applied to the optimization of supervisory control. Auxiliary cooling power is included in addition to vehicle propulsion. Two objectives, fuel economy and battery life, are optimized by weighted sum method. To reduce the computation load, a simplified battery aging model coupled with equivalent circuit model is used in SDP optimization; Li+ diffusion dynamics are disregarded, and surface concentration is represented by the average concentration. This reduces the system state number to four with two control inputs. A real-time implementable strategy is generated and embedded into the supervisory controller. The result shows that SDP strategy can improve fuel economy and battery life simultaneously, comparing with Thermostatic SOC strategy. Further, the tradeoff between fuel consumption and active Li+ loss is studied under different battery temperature. Finally, the accuracy of battery aging model for optimization is improved by adding Li+ diffusion dynamics. This increases the number of states and brings challenges to classical dynamic programming algorithms. Hence, a neuro-dynamic programming (NDP) approach is proposed for the problem with large state-action space. It combines the idea of functional approximation and temporal difference learning with dynamic programming; in that case the computation load increases linearly with the number of parameters in the approximate function, rather than exponentially with state space. The result shows that ability of NDP to solve the complex control optimization problem reliably and efficiently. The battery-aging conscientious strategy generated by NDP optimization framework further improves battery life by 3.8% without penalty on fuel economy, compared to SDP strategy. Improvements of battery life compared to the heuristic strategy are much larger, on the order of 65%. This leads to progressively larger fuel economy gains over time

Engineering Education and Research Using MATLAB

MATLAB is a software package used primarily in the field of engineering for signal processing, numerical data analysis, modeling, programming, simulation, and computer graphic visualization. In the last few years, it has become widely accepted as an efficient tool, and, therefore, its use has significantly increased in scientific communities and academic institutions. This book consists of 20 chapters presenting research works using MATLAB tools. Chapters include techniques for programming and developing Graphical User Interfaces (GUIs), dynamic systems, electric machines, signal and image processing, power electronics, mixed signal circuits, genetic programming, digital watermarking, control systems, time-series regression modeling, and artificial neural networks