Neuronal (Bi)Polarity as a Self-Organized Process Enhanced by Growing Membrane

Early in vitro and recent in vivo studies demonstrated that neuronal polarization occurs by the sequential formation of two oppositely located neurites. This early bipolar phenotype is of crucial relevance in brain organization, determining neuronal migration and brain layering. It is currently considered that the place of formation of the first neurite is dictated by extrinsic cues, through the induction of localized changes in membrane and cytoskeleton dynamics leading to deformation of the cells' curvature followed by the growth of a cylindrical extension (neurite). It is unknown if the appearance of the second neurite at the opposite pole, thus the formation of a bipolar cell axis and capacity to undergo migration, is defined by the growth at the first place, therefore intrinsic, or requires external determinants. We addressed this question by using a mathematical model based on the induction of dynamic changes in one pole of a round cell. The model anticipates that a second area of growth can spontaneously form at the opposite pole. Hence, through mathematical modeling we prove that neuronal bipolar axis of growth can be due to an intrinsic mechanism

Comparing plasma fluid models of different order for 1D streamer ionization fronts

We evaluate the performance of three plasma fluid models: the first order reaction-drift-diffusion model based on the local field approximation; the second order reaction-drift-diffusion model based on the local energy approximation and a recently developed high order fluid model by Dujko et al (2013 J. Phys. D 46 475202) We first review the fluid models: we briefly discuss their derivation, their underlying assumptions and the type of transport data they require. Then we compare these models to a particle-in-cell/Monte Carlo (PIC/MC) code, using a 1D test problem. The tests are performed in neon and nitrogen at standard temperature and pressure, over a wide range of reduced electric fields. For the fluid models, transport data generated by a multi-term Boltzmann solver are used. We analyze the observed differences in the model predictions and address some of the practical aspects when using these plasma fluid models

A Lagrangian Transport Eulerian Reaction Spatial (LATERS) Markov Model for Prediction of Effective Bimolecular Reactive Transport

Prediction of effective transport for mixing-driven reactive systems at larger scales, requires accurate representation of mixing at small scales, which poses a significant upscaling challenge. Depending on the problem at hand, there can be benefits to using a Lagrangian framework, while in others an Eulerian might have advantages. Here we propose and test a novel hybrid model which attempts to leverage benefits of each. Specifically, our framework provides a Lagrangian closure required for a volume-averaging procedure of the advection diffusion reaction equation. This hybrid model is a LAgrangian Transport Eulerian Reaction Spatial Markov model (LATERS Markov model), which extends previous implementations of the Lagrangian Spatial Markov model and maps concentrations to an Eulerian grid to quantify closure terms required to calculate the volume-averaged reaction terms. The advantage of this approach is that the Spatial Markov model is known to provide accurate predictions of transport, particularly at preasymptotic early times, when assumptions required by traditional volume-averaging closures are least likely to hold; likewise, the Eulerian reaction method is efficient, because it does not require calculation of distances between particles. This manuscript introduces the LATERS Markov model and demonstrates by example its ability to accurately predict bimolecular reactive transport in a simple benchmark 2-D porous medium

Simulation of non-conservative transport using particle tracking methods with an application to soils contaminated with heavy metals.

This thesis focuses on the development and application of a discrete time random walk particle tracking model to the simulation of non-conservative transport in porous media. The model includes the simulation of solute transport, reversible bimolecular reactions, and sorption. The functionality of the discrete time random walk method is expanded to allow for the simulation of more complicated chemical systems than previously achieved. The bimolecular reaction simulation is based on a colocation probability function method. This reaction simulation method is analysed to investigate the effects of the controlling parameters on its behaviour. This knowledge is then used to inform a discussion of its application to the simulation of mixing limited reactive transport and comparison with other approaches. The reaction simulation method developed in the thesis possesses a greater flexibility than previously developed methods for the simulation of reactions using particle tracking. The developed model is also applied, in combination with a chemical speciation model, to enable the production of a reduced complexity model to simulate effects of an amendment scheme on soils contaminated with heavy metals. The effect of the soil amendment scheme on the partitioning of Pb between solution, soil surfaces, and dissolved organic matter is approximated by rules fitted as functions of concentrations of single components within the soil amendment. This allows for the simulation of complicated chemical systems using particle tracking methods. As well as expanding the functionality of particle tracking methods the issue of the computational expense is also addressed. A scheme for the optimization of the reaction simulation is presented and its effectiveness investigated. Together with the use of graphics processing units for code acceleration, the computational and temporal expense of the solution is reduced. The combination of the expansion in functionality and reduction in run time makes particle tracking a more attractive simulation method

Characterizing the transport of hydrocarbon contaminants in peat soils and peatlands

Widespread transportation corridors crossing Canadian peatlands make these landscapes vulnerable to hydrocarbon spills. After a spill happens, free hydrocarbon spreads in the peat layer forming a free-phase plume. Water soluble compounds of the free-phase plume then partition into the pore water and the flowing aqueous phase forming a dissolved-phase plume. These plumes threaten peatland ecosystem health and impose risk to aquatic systems located nearby the contaminated area. For this reason, environmental scientists should be able to predict the behavior of hydrocarbon contaminants and the temporal evolution of the hydrocarbon plumes. Properties of peat soils control the fate and transport of the spilled non-aqueous phase liquids (NAPL) and dissolved-phase hydrocarbon solutes in contaminated peatlands. Since the fate and transport of these contaminants in peat has received little attention, there is insufficient knowledge of parameters governing their mobility. The cumulative effect of processes including dissolution, advection, and dispersion, diffusion into immobile water, adsorption onto soil matrix, volatilization, biodegradation, and other transformation processes determines the temporal evolution of contaminants in aquifers. The physical, hydraulic, and chemical properties of the aquifer soil and the hydrological, thermal, biological, and geochemical characteristics of the aquifer determine the rates and the relative dominance of abovementioned processes. It is well established that peat physical and hydraulic properties including its porosity, hydraulic conductivity, and average pore radius size vary systematically with peat depth. Also, peat decomposition and humification modifies the chemical composition of the peat matrix. However, the effect such systematic variations in peat has on the redistribution of hydrocarbon contaminants has not been investigated. Multiphase flow characteristics of peat including capillary pressure-saturation-relative permeability (Pc-S-kr) relations control the redistribution of free-phase hydrocarbon in a peatland. These relations will be functions of peat type and its physical properties. The functionality of Pc-S-kr relations and residual NAPL (diesel) saturation (SNr) with peat type were examined in two types of peat in which SNr ranged between 0.3-17% and increased with peat bulk density. In a given peat, SNr was a function of saturation history and increased with increasing maximum diesel saturation. Irreducible water saturation, which is the saturation at which aqueous phase stops moving, and the curvature of water kr-S curves both were a function of peat type, and increased with peat bulk density. The results suggested that the kr-S relations of water derived from unsaturated hydraulic conductivity of peat (in the presence of air) might be a good estimate of the water kr-S relation in presence of NAPL. Although the functionality Pc-S-kr relations to peat depth was not determined in this study, conceptually, it is expected that the reduction of pore radius typically taking place down the peat profile leads to 1) reduction of peat hydraulic conductivity with depth, 2) increase in NAPL-entry capillary pressure and water retention with depth, which cumulatively could cause a preferential migration of NAPL in shallower peat layers after a pressurized release of NAPL. In this condition, the exchange of gases between the source zone and the atmosphere happening due to wind or water table fluctuations may efficiently 1) drain contaminated soil-gas, and 2) promote aerobic conditions in the contaminated area. The water table fluctuation, however, might enhance the lateral redistribution of the free-phase plume. The retardation of dissolved hydrocarbons is dominantly controlled by their adsorption onto the soil. The adsorption of benzene and toluene, as two of the most toxic and mobile dissolved organic compounds present in petroleum liquids, and their dependency on peat depth were explored. The linear adsorption isotherms for benzene and toluene were obtained with adsorption coefficients ranging from 16.2-48.7 L/kg and 31.6-48.7 L/kg, respectively. In the experiments, the benzene and toluene adsorption coefficients were not constant along the peat profile and varied with peat depth. The variations of toluene adsorption correlated with typical variations of cellulose and humic acid characteristic of a peat matrix. The organic carbon adsorption coefficient (KOC) obtained for benzene in peat was equal and higher than the average benzene KOC reported in literature for soils with low organic carbon content (fOC). However, toluene KOC was 10-50% less than the average value which suggests that using the average value might overestimate toluene retardation and underestimate its mobility down-gradient of the spill zone. The competition between benzene and toluene adsorption was insignificant, suggesting that individual adsorption coefficients could be used to study the adsorption of individual contaminants in a multi-solute problem. The adsorption studies showed adsorption of benzene and toluene at the equilibrium condition. However, the adsorption model parameters that control the chemical equilibrium during contaminant transport remained unknown. Besides, the effect of mobile-immobile mass transfer, which takes place due to the dual-porosity pore structure of peat, on the retardation of dissolved hydrocarbons in the inactive pores, were not known. To address these, miscible (solute) transport experiments were conducted showing that the mass transfer rate between mobile and immobile zones of peat could be sufficiently high to establish physical-equilibrium between mobile and immobile zones of peat pore space. The results also showed that the relatively slow kinetics of adsorption could cause chemical non-equilibrium between the aqueous phase and adsorbed phase, leading to decreased adsorptive retardation in high discharge conditions. The retardation factor of benzene increased with depth and degree of peat decomposition. This coupled with the typical reduction of hydraulic conductivity with depth could cause a preferential redistribution of dissolved-contaminants in shallow peat layers in a contaminated peatland. This study is the first study that characterizes the fate and transport of hydrocarbon contaminants in peat at the laboratory-scale and with specific focus on peat properties. Although scale-dependent phenomena such as field-scale heterogeneities might impose additional complexities to the fate and transport processes, the scale-independent parameters obtained in this study including adsorption partitioning coefficients and adsorption kinetics parameters, as well as residual NAPL saturation, irreducible water saturation, and water relative permeability relations have increased our understanding on the transport of free-phase and dissolved-phase hydrocarbons in in peat. The results can help predict the temporal evolution of the hydrocarbon plumes after a spill. The results also can help in assessing the risk after an oil spill accident and for evaluating the appropriateness of potential remediation plans

Dinâmica espacial e temporal do metabolismo aquático em sistemas subtropicais

A tese investigou o uso de uma ferramenta computacional para avaliar a dinâmica espaço-temporal do metabolismo em ecossistemas aquáticos onde a hidrodinâmica possui papel de destaque na estruturação das comunidades planctônicas. A modelagem matemática foi realizada utilizando o modelo IPH-ECO, uma ferramenta computacional complexa capaz de integrar processos físicos, químicos e biológicos em três dimensões. O trabalho foi dividido em quatro capítulos principais, tendo como base os processos físicos e biológicos que influenciam as estimativas de metabolismo (Capítulos #02 e #03) e melhorias nos métodos numéricos utilizados no modelo IPH-ECO (Capítulos #04 e #05). Os primeiros dois capítulos apresentam o desenvolvimento e aplicação de um algoritmo computacional capaz de quantificar as estimativas de metabolismo aquático baseado (em termos de Produção Primária Bruta - GPP, Respiração do ecossistema - R e Produção Líquida do Ecossistema - NEP = GPP - R) em processos biológicos individuais que influenciam o balanço de oxigênio dissolvido em ecossistemas aquáticos (e.g., respiração de zooplâncton, produção primária de macrófitas aquáticas). A implementação deste algoritmo no modelo IPH-ECO permitiu quantificar as estimativas de metabolismo aquático na Lagoa Mangueira, sul do Brasil, avaliando a importância relativa de diferentes processos individuais e o efeito da hidrodinâmica sobre os processos que compõem o metabolismo da lagoa. O metabolismo aquático da Lagoa Mangueira apresentou um gradiente espacial com maiores valores na região Litorânea e menores na região Pelágica. Além da heterogeneidade espacial, foi possível observar uma heterogeneidade temporal, com valores de produção primária mais elevados durante o verão e primavera e menores durante o inverno e outono. Esta heterogeneidade espacial e temporal acarreta em alterações no estado trófico (autotrófico - NEP positivo ou heterotrófico - NEP negativo) da lagoa, dependendo do local sendo avaliado (zona litorânea ou zona pelágica) e da época do ano. A simulação de diferentes cenários de vento (cinco no total) demonstraram que os padrões de circulação da água podem alterar a dinâmica das estimativas de metabolismo na Lagoa Mangueira, alterando a forma como o sistema é classificado (autotrofia vs. heterotrofia) e influenciando os diferentes processos biológicos que compõem estas estimativas. Os Capítulos #04 e #05 apresentam o desenvolvimento de um novo esquema numérico visando auxiliar na simulação de problemas de qualidade de água. O novo esquema é baseado no método dos Volumes Finitos e permite a integração numérica de equações de transporte utilizando um passo de tempo localizado, calculado a partir da condição de estabilidade de Courant-Friedrich-Lewy (condição CFL). A nova solução numérica é diretamente acoplada a um modelo hidrodinâmico tridimensional em grades triangulares não-estruturadas (e.g, modelo UnTRIM), que utiliza uma solução numérica semi-implícita (Crank-Nicholson) baseada em diferenças finitas e volumes finitos. Diferentes testes clássicos e idealizados são simulados e é realizada uma comparação entre o método com esquema numérico localizado (LTS - Local Time Stepping) e o método tradicional (GTS - Global Time Stepping). Ambos os métodos se mostraram conservativos considerando uma, duas e três dimensões, e ainda foi respeitada uma condição de estabilidade baseada nos valores máximos e mínimos sendo transportados (i.e., não são criados novos valores máximos nem mínimos). Os métodos também foram avaliados de forma acoplada com escoamentos a superfície livre, levando em conta substâncias conservativas e não-conservativas (e.g., balanço de temperatura na água), assim como situações onde a hidrodinâmica é controlada por vento (forte mistura vertical e horizontal) e onde a hidrodinâmica é controlada por um gradiente de pressão (e.g., maré). Além disso, situações onde a secagem e inundação de células computacionais ocorrem foram testadas e os métodos se mostraram estáveis e conservativos. O esquema numérico LTS se mostrou mais rápido do ponto de vista computacional, exigindo menos tempo de simulação em praticamente todos os testes realizados. Além disso, o esquema mostrou resultados similares ao obtidos utilizando o esquema GTS tradicional. Os testes mostraram que a eficiência do esquema LTS é maior quando ocorre a combinação de altas velocidades e pequenos elementos (alta restrição dada pela condição CFL), como a simulação da interface entre rios e lagos, entradas de água rápida (e.g., tromba d’água, Dam-Break) e estuários (efeito de maré).This thesis investigated the use of a mathematical model to evaluate the space-time dynamics of aquatic metabolism in ecossystems where hydrodynamics plays a key role in structuring the planktonic community. The mathematical model used was the IPH-ECO model, a complex tridimensional model capable of integrating physical, chemical, and biological processes in aquatic environments. The thesis was divided into four main chapters with focus in studying the biological processes and aquatic metabolism estimates (Chapters #2 and #3), and also the improvement of numerical methods used in the IPH-ECO model (Chapters #4 and #5). The first two chapters show the development and application of a computational algorithm capable of quantifying the aquatic metabolism estimates (in terms of Gross Primary Production - GPP, Ecosystem Respiration - R, and Net Ecosystem Production - NEP = GPP-R) based on individual biological processes affecting the dissolved oxygen budget in aquatic ecosystems (e.g., zooplankton respiration, aquatic macrophyte primary production). The numerical algorithm implemented on the IPH-ECO model allowed the quantification of aquatic metabolism estimates (GPP, R, and NEP) at Lake Mangueira, South of Brazil, and the evaluation of the relative importance of different individual processes and how the lake hydrodynamic can change the complex dynamics of the biological processes comprising the lake metabolism estimates. Lake Mangueira’s metabolism estimations showed a well-marked spatial gradient with higher values observed in the littoral zone and lower values observed in the pelagic zone. Besides the spatial heterogeneity, it was also possible to notice a strong seasonal heterogeneity, with increased values of GPP and R during summer and spring and lower values during winter and autumn. This space-time heterogeneity leads to a switching in the trophic state of the lake (autotrophic - Positive NEP or heteotrophic - Negative NEP), depending on the site being evaluated (littoral or pelagic) and also the time of the year being assessed. The simulation of different wind scenarios (a total of five) showed that the water circulation patterns can change the metabolism estimates dynamics in Lake Mangueira, changing the system trophic status (net autotrophy v.s. net heterotrophy) e also affecting the dynamics of individual biological processes composing the metabolism estimates. Chapters #4 and #5 show the development of a new numerical scheme capable of accelerate water quality simulations. The new numerical method is based on a Finite Volume framework and allows for numerical integration of scalar transport equations using a local time step, chosen based on the Courant-Friedrich-Lewy stability criteria (the CFL condition). This new solution is directly linked to a tridimensional hydrodynamic model on triangular unstructured mesh (e.g., UnTRIm model), using a semi-implicit solution based on finite differences and finite volume. Different classical and idealized test-cases were simulated and the results from using the new Local Time Stepping (LTS) numerical method is compared against the usage of a traditional Global Time Stepping method (GTS). Both implemented methods showed precise mass conservation in one, two, and three dimensions, moreover, a discrete max-min property was observed in all simulations (i.e., no new maximum nor minimum was created). The methods were also tested when the coupling with hydrodynamic models of free-surface flows is simulated, accounting both conservative (e.g., Salt) and non-conservative substances (e.g., water temperature). The idealized coupled test-cases accounted for situations where hydrodynamics is controled by the wind (strong vertical and horizontal mixing), and situations where hydrodynamics is driven by pressure gradients (e.g., tidal currents). Furthermore, situations where an intense wet- and dry-ing of computational cells is observed was tested and the methods showed stability and precise mass conservation. In a general manner, the new LTS scheme was faster from a computational point-of-view, requiring less simulation time in praticaly all tests. In addition, the new scheme presented concentration fields similar to the ones computed by a traditional GLS algorithm. Our findings suggested that the efficiency of the LTS algorithm is increased when a combination of high velocities and small polygons is observed (elevated CFL stability restriction), such as the simulation of the interface between rivers and lakes, fast water inflow (e.g., Dam-Break), and estuaries (Tidal effect)