Instabilities in threshold-diffusion equations with delay

The introduction of delays into ordinary or partial differential equation models is well known to facilitate the production of rich dynamics ranging from periodic solutions through to spatio-temporal chaos. In this paper we consider a class of scalar partial differential equations with a delayed threshold nonlinearity which admits exact solutions for equilibria, periodic orbits and travelling waves. Importantly we show how the spectra of periodic and travelling wave solutions can be determined in terms of the zeros of a complex analytic function. Using this as a computational tool to determine stability we show that delays can have very different effects on threshold systems with negative as opposed to positive feedback. Direct numerical simulations are used to confirm our bifurcation analysis, and to probe some of the rich behaviour possible for mixed feedback.

Frequency of elemental events of intracellular Ca²⁺ dynamics

The dynamics of intracellular Ca²⁺ is driven by random events called Ca²⁺ puffs, in which Ca²⁺ is liberated from intracellular stores. We show that the emergence of Ca²⁺ puffs can be mapped to an escape process. The mean first passage times that correspond to the stochastic fraction of puff periods are computed from a novel master equation and two Fokker-Planck equations. Our results demonstrate that the mathematical modeling of Ca²⁺ puffs has to account for the discrete character of the Ca²⁺ release sites and does not permit a continuous description of the number of open channels.

Error estimation and adaptive mesh refinement for aerodynamic flows

This lecture course covers the theory of so-called duality-based a posteriori error estimation of DG finite element methods. In particular, we formulate consistent and adjoint consistent DG methods for the numerical approximation of both the compressible Euler and Navier-Stokes equations; in the latter case, the viscous terms are discretized based on employing an interior penalty method. By exploiting a duality argument, adjoint-based a posteriori error indicators will be established. Moreover, application of these computable bounds within automatic adaptive finite element algorithms will be developed. Here, a variety of isotropic and anisotropic adaptive strategies, as well as $hp$-mesh refinement will be investigated.

Large-scale neural dynamics: simple and complex

We review the use of neural field models for modelling the brain at the large scales necessary for interpreting EEG, fMRI, MEG and optical imaging data. Albeit a framework that is limited to coarse-grained or mean-field activity, neural field models provide a framework for unifying data from different imaging modalities. Starting with a description of neural mass models we build to spatially extended cortical models of layered two-dimensional sheets with long range axonal connections mediating synaptic interactions. Reformulations of the fundamental non-local mathematical model in terms of more familiar local differential (brain wave) equations are described. Techniques for the analysis of such models, including how to determine the onset of spatio-temporal pattern forming instabilities, are reviewed. Extensions of the basic formalism to treat refractoriness, adaptive feedback and inhomogeneous connectivity are described along with open challenges for the development of multi-scale models that can integrate macroscopic models at large spatial scales with models at the microscopic scale.

THE STOCHASTIC NAVIER STOKES EQUATIONS FOR HEAT CONDUCTING, COMPRESSIBLE FLUIDS

This dissertation is devoted to the equations of motion governing the evolution of a fluid or gas at the macroscopic scale. The classical model is a PDE description known as the Navier-Stokes equations. The behavior of solutions is notoriously complex, leading many in the scientific community to describe fluid mechanics using a statistical language. In the physics literature, this is often done in an ad-hoc manner with limited precision about the sense in which the randomness enters the evolution equation. The stochastic PDE community has begun proposing precise models, where a random perturbation appears explicitly in the evolution equation. Although this has been an active area of study in recent years, the existing literature is almost entirely devoted to incompressible fluids. The purpose of this thesis is to take a step forward in addressing this statistical perspective in the setting of compressible fluids. In particular, we study the well posedness for the corresponding system of Stochastic Navier Stokes equations, satisfied by the density, velocity, and temperature. The evolution of the momentum involves a random forcing which is Brownian in time and colored in space. We allow for multiplicative noise, meaning that spatial correlations may depend locally on the fluid variables. Our main result is a proof of global existence of weak martingale solutions to the Cauchy problem set within a bounded domain, emanating from large initial datum. The proof involves a mix of deterministic and stochastic analysis tools. Fundamentally, the approach is based on weak compactness techniques from the deterministic theory combined with martingale methods. Four layers of approximate stochastic PDE's are built and analyzed. A careful study of the probability laws of our approximating sequences is required. We prove appropriate tightness results and appeal to a recent generalization of the Skorohod theorem. This ultimately allows us to deduce analogues of the weak compactness tools of Lions and Feireisl, appropriately interpreted in the stochastic setting.

Chemical Reaction Dynamics of the Liquid/Vapor Interface Studied by Mass Spectrometry

This thesis presents investigations of chemical reactions occurring at the liquid/vapor interface studied using novel sampling methodologies coupled with detection by mass spectrometry. Chapters 2 and 3 utilize the recently developed technique of field-induced droplet ionization mass spectrometry (FIDI-MS), in which the application of a strong electric field to a pendant microliter droplet results in the ejection of highly charged progeny droplets from the liquid surface. In Chapter 2, this method is employed to study the base-catalyzed dissociation of a surfactant molecule at the liquid/vapor interface upon uptake of ammonia from the gas phase. This process is observed to occur without significant modulation of the bulk solution pH, suggesting a transient increase in surface pH following the uptake of gaseous ammonia. Chapter 3 presents real-time studies of the oxidation of the model tropospheric organic compound glycolaldehyde by photodissociation of iron (III) oxalate complexes. The oxidation products of glycolaldehyde formed in this process are identified, and experiments in a deoxygenated environment identify the role of oxygen in the oxidation pathway and in the regeneration of iron (III) following photo-initiated reduction. Chapter 4 explores alternative methods for the study of heterogeneous reaction processes by mass spectrometric sampling from liquid surfaces. Bursting bubble ionization (BBI) and interfacial sampling with an acoustic transducer (ISAT) generate nanoliter droplets from a liquid surface that can be sampled via the atmospheric pressure interface of a mass spectrometer. Experiments on the oxidation of oleic acid by ozone using ISAT are also presented. Chapters 5 and 6 detail mechanistic studies and applications of free-radical-initiated peptide sequencing (FRIPS), a technique employing gas-phase free radical chemistry to the sequencing of peptides and proteins by mass spectrometry. Chapter 5 presents experimental and theoretical studies on the anomalous mechanism of dissociation observed in the presence of serine and threonine residues in peptides. Chapter 6 demonstrates the combination of FRIPS with ion mobility-mass spectrometry (IM-MS) for the separation of isomeric peptides.

An enforced cooperation : understanding scientific assessments in adversarial polities through Quebec shale gas policymaking, 2010-2014

Les biotechnologies, le réchauffement climatique, les ressources naturelles et la gestion des écosystèmes sont tous représentatifs de la “nouvelle politique de la nature” (Hajer 2003), un terme englobant les enjeux marqués par une grande incertitude scientifique et un encadrement réglementaire inadapté aux nouvelles réalités, suscitant de fait un conflit politique hors du commun. Dans l'espoir de diminuer ces tensions et de générer un savoir consensuel, de nombreux gouvernements se tournent vers des institutions scientifiques ad hoc pour documenter l'élaboration des politiques et répondre aux préoccupations des partie-prenantes. Mais ces évaluations scientifiques permettent-elles réellement de créer une compréhension commune partagée par ces acteurs politiques polarisés? Alors que l'on pourrait croire que celles-ci génèrent un climat d'apprentissage collectif rassembleur, un environnement politique conflictuel rend l'apprentissage entre opposant extrêmement improbable. Ainsi, cette recherche documente le potentiel conciliateur des évaluation scientifique en utilisant le cas des gaz de schiste québécois (2010-2014). Ce faisant, elle mobilise la littérature sur les dimensions politiques du savoir et de la science afin de conceptualiser le rôle des évaluations scientifiques au sein d'une théorie de la médiation scientifique (scientific brokerage). Une analyse de réseau (SNA) des 5751 références contenues dans les documents déposés par 268 organisations participant aux consultations publiques de 2010 et 2014 constitue le corps de la démonstration empirique. Précisément, il y est démontré comment un médiateur scientifique peut rediriger le flux d'information afin de contrer l'incompatibilité entre apprentissage collectif et conflit politique. L'argument mobilise les mécanismes cognitifs traditionnellement présents dans la théorie des médiateurs de politique (policy broker), mais introduit aussi les jeux de pouvoir fondamentaux à la circulation de la connaissance entre acteurs politiques.

Pressure Induced Structural Changes and Gas Diffusion Pathways in Monomeric Fluorescent Proteins

Fluorescent proteins (FPs) are extremely valuable biochemical markers which have found a wide range of applications in cellular and molecular biology research. The monomeric variants of red fluorescent proteins (RFPs), known as mFruits, have been especially valuable for in vivo applications in mammalian cell imaging. Fluorescent proteins consist of a chromophore caged in the beta-barrel protein scaffold. The photophysical properties of an FP is determined by its chromophore structure and its interactions with the protein barrel. Application of hydrostatic pressure on FPs results in the modification of the chromophore environment which allows a systematic study of the role of the protein-chromophore interactions on photophysical properties of FPs. Using Molecular Dynamics (MD) computer simulations, I investigated the pressure induced structural changes in the monomeric variants mCherry, mStrawberry, and Citrine. The results explain the molecular basis for experimentally observed pressure responses among FP variants. It is found that the barrel flexibility, hydrogen bonding interactions and chromophore planarity of the FPs can be correlated to their contrasting photophysical properties at vaious pressures. I also investigated the oxygen diffusion pathways in mOrange and mOrange2 which exhibit marked differences in oxygen sensitivities as well as photostability. Such computational identifications of structural changes and oxygen diffusion pathways are important in guiding mutagenesis efforts to design fluorescent proteins with improved photophysical properties.

Tubular and Sector Heat Pipes with Interconnected Branches for Gas Turbine and/or Compressor Cooling

Designing turbines for either aerospace or power production is a daunting task for any heat transfer scientist or engineer. Turbine designers are continuously pursuing better ways to convert the stored chemical energy in the fuel into useful work with maximum efficiency. Based on thermodynamic principles, one way to improve thermal efficiency is to increase the turbine inlet pressure and temperature. Generally, the inlet temperature may exceed the capabilities of standard materials for safe and long-life operation of the turbine. Next generation propulsion systems, whether for new supersonic transport or for improving existing aviation transport, will require more aggressive cooling system for many hot-gas-path components of the turbine. Heat pipe technology offers a possible cooling technique for the structures exposed to the high heat fluxes. Hence, the objective of this dissertation is to develop new radially rotating heat pipe systems that integrate multiple rotating miniature heat pipes with a common reservoir for a more effective and practical solution to turbine or compressor cooling. In this dissertation, two radially rotating miniature heat pipes and two sector heat pipes are analyzed and studied by utilizing suitable fluid flow and heat transfer modeling along with experimental tests. Analytical solutions for the film thickness and the lengthwise vapor temperature distribution for a single heat pipe are derived. Experimental tests on single radially rotating miniature heat pipes and sector heat pipes are undertaken with different important parameters and the manner in which these parameters affect heat pipe operation. Analytical and experimental studies have proven that the radially rotating miniature heat pipes have an incredibly high effective thermal conductance and an enormous heat transfer capability. Concurrently, the heat pipe has an uncomplicated structure and relatively low manufacturing costs. The heat pipe can also resist strong vibrations and is well suited for a high temperature environment. Hence, the heat pipes with a common reservoir make incorporation of heat pipes into turbo-machinery much more feasible and cost effective.

Using an infra-red sensor to measure the dynamic behaviour of N2O gas escaping through different sized holes

An anastomosis is a surgical procedure that consists of the re-connection of two parts of an organ and is commonly required in cases of colorectal cancer. Approximately 80% of the patients diagnosed with this problem require surgery. The malignant tissue located on the gastrointestinal track must be resected and the most common procedure adopted is the anastomosis. Studies made with 2,980 patients that had this procedure, show that the leakage through the anastomosis was 5.1%. This paper discusses the dynamic behavior of N2O gas through different sized leakages as detected by an Infra-Red gas sensor and how the sensors response time changes depending on the leakage size. Different sized holes were made in the rigid tube to simulate an anastomostic leakage. N2O gas was injected into the tube through a pipe and the leakage rate measured by the infra-red gas sensor. Tests were also made experimentally also using a CFD (Computational Fluid Dynamics) package called FloWorks. The results will be compared and discussed in this paper.

An enforced cooperation : understanding scientific assessments in adversarial polities through Quebec shale gas policymaking, 2010-2014

Les biotechnologies, le réchauffement climatique, les ressources naturelles et la gestion des écosystèmes sont tous représentatifs de la “nouvelle politique de la nature” (Hajer 2003), un terme englobant les enjeux marqués par une grande incertitude scientifique et un encadrement réglementaire inadapté aux nouvelles réalités, suscitant de fait un conflit politique hors du commun. Dans l'espoir de diminuer ces tensions et de générer un savoir consensuel, de nombreux gouvernements se tournent vers des institutions scientifiques ad hoc pour documenter l'élaboration des politiques et répondre aux préoccupations des partie-prenantes. Mais ces évaluations scientifiques permettent-elles réellement de créer une compréhension commune partagée par ces acteurs politiques polarisés? Alors que l'on pourrait croire que celles-ci génèrent un climat d'apprentissage collectif rassembleur, un environnement politique conflictuel rend l'apprentissage entre opposant extrêmement improbable. Ainsi, cette recherche documente le potentiel conciliateur des évaluation scientifique en utilisant le cas des gaz de schiste québécois (2010-2014). Ce faisant, elle mobilise la littérature sur les dimensions politiques du savoir et de la science afin de conceptualiser le rôle des évaluations scientifiques au sein d'une théorie de la médiation scientifique (scientific brokerage). Une analyse de réseau (SNA) des 5751 références contenues dans les documents déposés par 268 organisations participant aux consultations publiques de 2010 et 2014 constitue le corps de la démonstration empirique. Précisément, il y est démontré comment un médiateur scientifique peut rediriger le flux d'information afin de contrer l'incompatibilité entre apprentissage collectif et conflit politique. L'argument mobilise les mécanismes cognitifs traditionnellement présents dans la théorie des médiateurs de politique (policy broker), mais introduit aussi les jeux de pouvoir fondamentaux à la circulation de la connaissance entre acteurs politiques.

Measure-valued mass evolution problems with flux boundary conditions and solution-dependent velocities

In this paper we prove well-posedness for a measure-valued continuity equation with solution-dependent velocity and flux boundary conditions, posed on a bounded one-dimensional domain. We generalize the results of an earlier paper [J. Differential Equations, 259 (2015), pp. 10681097] to settings where the dynamics are driven by interactions. In a forward-Euler-like approach, we construct a time-discretized version of the original problem and employ those results as a building block within each subinterval. A limit solution is obtained as the mesh size of the time discretization goes to zero. Moreover, the limit is independent of the specific way of partitioning the time interval [0, T]. This paper is partially based on results presented in Chapter 5 of [Evolution Equations for Systems Governed by Social Interactions, Ph.D. thesis, Eindhoven University of Technology, 2015], while a number of issues that were still open there are now resolved.

Identificación de redes nacionales y mundiales de distribución de petróleo y gas natural y su relación con la conformación de comunidades

El presente proyecto investiga la relación entre las organizaciones con el medio y marketing, para lo cual se debe mencionar el conflicto de intereses de la comunidad y de la organización, y como se intenta percibir a la organización como un buen vecino dentro de la comunidad. A su vez éste estudio cuenta con objetivos basados en la identificación de redes de distribución de petróleo y gas natural, tanto nacionales como internacionales, para así abarcar un sector estratégico más preciso, y mostrar las relación entre las organizaciones y la conformación de comunidades. Se tienen en cuenta factores elementales en el estudio de este sector energético, como son sus principales componentes, así como un marco teórico específico que permita desarrollar el concepto de conformación de comunidades para lograr una exitosa aplicación del mismo. Del mismo modo se incluirán temas relacionados con marketing, pero desde un punto de vista más cercano a la comunidad, tomando los medios y el marketing como un concepto más importante en el impacto de las organizaciones en la comunidad, es decir tomando el concepto de marketing como aquellas comunidades que rodean las organizaciones, como éstas dos interactúan, y que impactos tienen una sobre la otra. De la misma manera se tienen resultados en cuanto a planteamientos más profundos sobre conceptos de marketing que no son desarrollados muy a menudo, los cuales conservan su esencia fundamental y siguen impactando en silencio a las organizaciones, pero que si lo estudiamos y aprovechamos de algún modo lograremos beneficios para nuestra organización y para los intereses colectivos.

Gyrokinetic modelling of plasma transport and investigation on test particle dynamics

Turbulent plasmas inside tokamaks are modeled and studied using guiding center theory, applied to charged test particles, in a Hamiltonian framework. The equations of motion for the guiding center dynamics, under the conditions of a constant and uniform magnetic field and turbulent electrostatic field are derived by averaging over the fast gyroangle, for the first and second order in the guiding center potential, using invertible changes of coordinates such as Lie transforms. The equations of motion are then made dimensionless, exploiting temporal and spatial periodicities of the model chosen for the electrostatic potential. They are implemented numerically in Python. Fast Fourier Transform and its inverse are used. Improvements to the original Python scripts are made, notably the introduction of a power-law curve fitting to account for anomalous diffusion, the possibility to integrate the equations in two steps to save computational time by removing trapped trajectories, and the implementation of multicolored stroboscopic plots to distinguish between trapped and untrapped guiding centers. The post-processing of the results is made in MATLAB. The values and ranges of the parameters chosen for the simulations are selected based on numerous simulations used as feedback tools. In particular, a recurring value for the threshold to detect trapped trajectories is evidenced. Effects of the Larmor radius, the amplitude of the guiding center potential and the intensity of its second order term are studied by analyzing their diffusive regimes, their stroboscopic plots and the shape of guiding center potentials. The main result is the identification of cases anomalous diffusion depending on the values of the parameters (mostly the Larmor radius). The transitions between diffusive regimes are identified. The presence of highways for the super-diffusive trajectories are unveiled. The influence of the charge on these transitions from diffusive to ballistic behaviors is analyzed.

Numerical Analysis and Redesign of a High Speed Linear Cascade Wind Tunnel for Aircraft Gas Turbine Engines Testing

Linear cascade testing serves a fundamental role in the research, development, and design of turbomachines as it is a simple yet very effective way to compute the performance of a generic blade geometry. These kinds of experiments are usually carried out in specialized wind tunnel facilities. This thesis deals with the numerical characterization and subsequent partial redesign of the S-1/C Continuous High Speed Wind Tunnel of the Von Karman Institute for Fluid Dynamics. The current facility is powered by a 13-stage axial compressor that is not powerful enough to balance the energy loss experienced when testing low turning airfoils. In order to address this issue a performance assessment of the wind tunnel was performed under several flow regimes via numerical simulations. After that, a redesign proposal aimed at reducing the pressure loss was investigated. This consists of a linear cascade of turning blades to be placed downstream of the test section and designed specifically for the type of linear cascade being tested. An automatic design procedure was created taking as input parameters those measured at the outlet of the cascade. The parametrization method employed Bézier curves to produce an airfoil geometry that could be imported into a CAD software so that a cascade could be designed. The proposal was simulated via CFD analysis and proved to be effective in reducing pressure losses up to 41%. The same tool developed in this thesis could be adopted to design similar apparatuses and could also be optimized and specialized for the design of turbomachines components.