Hydrodynamic correlation functions of a driven granular fluid in steady state

We study a homogeneously driven granular fluid of hard spheres at intermediate volume fractions and focus on time-delayed correlation functions in the stationary state. Inelastic collisions are modeled by incomplete normal restitution, allowing for efficient simulations with an event-driven algorithm. The incoherent scattering function Fincoh(q,t ) is seen to follow time-density superposition with a relaxation time that increases significantly as the volume fraction increases. The statistics of particle displacements is approximately Gaussian. For the coherent scattering function S(q,ω), we compare our results to the predictions of generalized fluctuating hydrodynamics, which takes into account that temperature fluctuations decay either diffusively or with a finite relaxation rate, depending on wave number and inelasticity. For sufficiently small wave number q we observe sound waves in the coherent scattering function S(q,ω) and the longitudinal current correlation function Cl(q,ω). We determine the speed of sound and the transport coefficients and compare them to the results of kinetic theory.

Development of Dynamic Constraint Models for a Model Based Transient Calibration Process

Model based calibration has gained popularity in recent years as a method to optimize increasingly complex engine systems. However virtually all model based techniques are applied to steady state calibration. Transient calibration is by and large an emerging technology. An important piece of any transient calibration process is the ability to constrain the optimizer to treat the problem as a dynamic one and not as a quasi-static process. The optimized air-handling parameters corresponding to any instant of time must be achievable in a transient sense; this in turn depends on the trajectory of the same parameters over previous time instances. In this work dynamic constraint models have been proposed to translate commanded to actually achieved air-handling parameters. These models enable the optimization to be realistic in a transient sense. The air handling system has been treated as a linear second order system with PD control. Parameters for this second order system have been extracted from real transient data. The model has been shown to be the best choice relative to a list of appropriate candidates such as neural networks and first order models. The selected second order model was used in conjunction with transient emission models to predict emissions over the FTP cycle. It has been shown that emission predictions based on air-handing parameters predicted by the dynamic constraint model do not differ significantly from corresponding emissions based on measured air-handling parameters.

Development of a model-based transient calibration process for diesel engine electronic control module tables – Part 1: data requirements, processing, and analysis

This is the first part of a study investigating a model-based transient calibration process for diesel engines. The motivation is to populate hundreds of parameters (which can be calibrated) in a methodical and optimum manner by using model-based optimization in conjunction with the manual process so that, relative to the manual process used by itself, a significant improvement in transient emissions and fuel consumption and a sizable reduction in calibration time and test cell requirements is achieved. Empirical transient modelling and optimization has been addressed in the second part of this work, while the required data for model training and generalization are the focus of the current work. Transient and steady-state data from a turbocharged multicylinder diesel engine have been examined from a model training perspective. A single-cylinder engine with external air-handling has been used to expand the steady-state data to encompass transient parameter space. Based on comparative model performance and differences in the non-parametric space, primarily driven by a high engine difference between exhaust and intake manifold pressures (ΔP) during transients, it has been recommended that transient emission models should be trained with transient training data. It has been shown that electronic control module (ECM) estimates of transient charge flow and the exhaust gas recirculation (EGR) fraction cannot be accurate at the high engine ΔP frequently encountered during transient operation, and that such estimates do not account for cylinder-to-cylinder variation. The effects of high engine ΔP must therefore be incorporated empirically by using transient data generated from a spectrum of transient calibrations. Specific recommendations on how to choose such calibrations, how many data to acquire, and how to specify transient segments for data acquisition have been made. Methods to process transient data to account for transport delays and sensor lags have been developed. The processed data have then been visualized using statistical means to understand transient emission formation. Two modes of transient opacity formation have been observed and described. The first mode is driven by high engine ΔP and low fresh air flowrates, while the second mode is driven by high engine ΔP and high EGR flowrates. The EGR fraction is inaccurately estimated at both modes, while EGR distribution has been shown to be present but unaccounted for by the ECM. The two modes and associated phenomena are essential to understanding why transient emission models are calibration dependent and furthermore how to choose training data that will result in good model generalization.

Development of a model-based transient calibration process for diesel engine electronic control module tables – Part 2: modelling and optimization

This is the second part of a study investigating a model-based transient calibration process for diesel engines. The first part addressed the data requirements and data processing required for empirical transient emission and torque models. The current work focuses on modelling and optimization. The unexpected result of this investigation is that when trained on transient data, simple regression models perform better than more powerful methods such as neural networks or localized regression. This result has been attributed to extrapolation over data that have estimated rather than measured transient air-handling parameters. The challenges of detecting and preventing extrapolation using statistical methods that work well with steady-state data have been explained. The concept of constraining the distribution of statistical leverage relative to the distribution of the starting solution to prevent extrapolation during the optimization process has been proposed and demonstrated. Separate from the issue of extrapolation is preventing the search from being quasi-static. Second-order linear dynamic constraint models have been proposed to prevent the search from returning solutions that are feasible if each point were run at steady state, but which are unrealistic in a transient sense. Dynamic constraint models translate commanded parameters to actually achieved parameters that then feed into the transient emission and torque models. Combined model inaccuracies have been used to adjust the optimized solutions. To frame the optimization problem within reasonable dimensionality, the coefficients of commanded surfaces that approximate engine tables are adjusted during search iterations, each of which involves simulating the entire transient cycle. The resulting strategy, different from the corresponding manual calibration strategy and resulting in lower emissions and efficiency, is intended to improve rather than replace the manual calibration process.

Entrainment and Unit Velocity: Surprises in an Accelerated Exclusion Process

We introduce a class of distance-dependent interactions in an accelerated exclusion process inspired by the observation of transcribing RNA polymerase speeding up when “pushed” by a trailing one. On a ring, the accelerated exclusion process steady state displays a discontinuous transition, from being homogeneous (with augmented currents) to phase segregated. In the latter state, the holes appear loosely bound and move together, much like a train. Surprisingly, the current-density relation is simply J=1-ρ, signifying that the “hole train” travels with unit velocity.

Entrainment and Unit Velocity: Surprises in an Accelerated Exclusion Process

We introduce a class of distance-dependent interactions in an accelerated exclusion process inspired by the observation of transcribing RNA polymerase speeding up when “pushed” by a trailing one. On a ring, the accelerated exclusion process steady state displays a discontinuous transition, from being homogeneous (with augmented currents) to phase segregated. In the latter state, the holes appear loosely bound and move together, much like a train. Surprisingly, the current-density relation is simply J=1-ρ, signifying that the “hole train” travels with unit velocity.

Interplay Between Finite Resources and a Local Defect in an Asymmetric Simple Exclusion Process

When particle flux is regulated by multiple factors such as particle supply and varying transport rate, it is important to identify the respective dominant regimes. We extend the well-studied totally asymmetric simple exclusion model to investigate the interplay between a controlled entrance and a local defect site. The model mimics cellular transport phenomena where there is typically a finite particle pool and nonuniform moving rates due to biochemical kinetics. Our simulations reveal regions where, despite an increasing particle supply, the current remains constant while particles redistribute in the system. Exploiting a domain wall approach with mean-field approximation, we provide a theoretical ground for our findings. The results in steady-state current and density profiles provide quantitative insights into the regulation of the transcription and translation process in bacterial protein synthesis.

Mass Transport Perspective on an Accelerated Exclusion Process: Analysis of Augmented Current and Unit-Velocity Phases

In an accelerated exclusion process (AEP), each particle can "hop" to its adjacent site if empty as well as "kick" the frontmost particle when joining a cluster of size ℓ⩽ℓ_{max}. With various choices of the interaction range, ℓ_{max}, we find that the steady state of AEP can be found in a homogeneous phase with augmented currents (AC) or a segregated phase with holes moving at unit velocity (UV). Here we present a detailed study on the emergence of the novel phases, from two perspectives: the AEP and a mass transport process (MTP). In the latter picture, the system in the UV phase is composed of a condensate in coexistence with a fluid, while the transition from AC to UV can be regarded as condensation. Using Monte Carlo simulations, exact results for special cases, and analytic methods in a mean field approach (within the MTP), we focus on steady state currents and cluster sizes. Excellent agreement between data and theory is found, providing an insightful picture for understanding this model system.

Assessing the Validity of Brain Glucose Concentration Measurement Using Microdialysis

Brain functions, such as learning, orchestrating locomotion, memory recall, and processing information, all require glucose as a source of energy. During these functions, the glucose concentration decreases as the glucose is being consumed by brain cells. By measuring this drop in concentration, it is possible to determine which parts of the brain are used during specific functions and consequently, how much energy the brain requires to complete the function. One way to measure in vivo brain glucose levels is with a microdialysis probe. The drawback of this analytical procedure, as with many steadystate fluid flow systems, is that the probe fluid will not reach equilibrium with the brain fluid. Therefore, brain concentration is inferred by taking samples at multiple inlet glucose concentrations and finding a point of convergence. The goal of this thesis is to create a three-dimensional, time-dependent, finite element representation of the brainprobe system in COMSOL 4.2 that describes the diffusion and convection of glucose. Once validated with experimental results, this model can then be used to test parameters that experiments cannot access. When simulations were run using published values for physical constants (i.e. diffusivities, density and viscosity), the resulting glucose model concentrations were within the error of the experimental data. This verifies that the model is an accurate representation of the physical system. In addition to accurately describing the experimental brain-probe system, the model I created is able to show the validity of zero-net-flux for a given experiment. A useful discovery is that the slope of the zero-net-flux line is dependent on perfusate flow rate and diffusion coefficients, but it is independent of brain glucose concentrations. The model was simplified with the realization that the perfusate is at thermal equilibrium with the brain throughout the active region of the probe. This allowed for the assumption that all model parameters are temperature independent. The time to steady-state for the probe is approximately one minute. However, the signal degrades in the exit tubing due to Taylor dispersion, on the order of two minutes for two meters of tubing. Given an analytical instrument requiring a five μL aliquot, the smallest brain process measurable for this system is 13 minutes.

Testing the TICT State Hypothesis: an Investigation into the Solvatochromic Behavior of 2-Naphthalenylmethylene Malononitrile

Towards the goal of investigating the possible Twisted Intramolecular Charge Transfer (TICT) state mechanism of fluorescence emission, two aromatic dicyanovinyl compounds, 2-(naphthalene-2-ylmethylene) malononitrile (DCN) and a rigidified analogue, 3,4-dihydrophenanthren-1(2H)-ylidene)malononitrile (RDCN) were synthesized and their absorption and steady-state fluorescence emission spectra characterized. The spectral characterization was divided into two studies: first, DCN and RDCN were characterized in liquid solvents of increasing polarity; second, DCN and RDCN were characterized in viscous solvents and rigid glass media. The absorption spectra for both DCN and RDCN in all solvents demonstrated little to no solvatochromism. Emission results for DCN and RDCN in liquid solvents of increasing polarity showed DCN possessing strong solvatochromism while RDCN showed much less solvatochromism. Using the Lippert-Mataga equation, the difference between the ground and excited state dipole moment for DCN was estimated to be 8.4 + 0.4 Debye and between ~3.0 to 5.0 Debye for RDCN. Quantum yield measurements for DCN and RDCN in hexane, diethyl ether and acetonitrile were less than 0.01 and independent of polarity for both both solvents, with DCN generally possessing a quantum yield 3-4 times greater than RDCN. Experiments in glass media for DCN and RDCN showed a lessening of their solvatochromic character in both polar and non-polar glasses. These data provide strong evidence for a link between molecular flexibility and solvatochromism. However, while these data are consistent with a TICT state hypothesis for the emission mechanism, an alternative mechanism proposed by Maroncelli et al.10 involving rotation about the dicyanovinyl double bond in the excited state remains a possibility as well.