Sinkkirikasteen liuotusprosessin kineettinen mallinnus

Työssä on tehty kineettinen simulointimalli sinkkirikasteen liuotusprosessista. Prosessi on pieni osa Kokkolan sinkinvalmistusprosessia, jonka muita osia ovat: pasutus, neutraaliliuotus, konversio, liuospuhdistus ja elektrolyysi. Rikasteen liuotukseen tulee konversioprosessin liuos ja liuotuksesta lähtevä neste menee takaisin neutraaliliuotukseen. Saostunut jarosiitti läjitetään. Kokkolan liuotusprosessi koostuu liettoreaktorista ja kahdesta neljän liuotusreaktorin sarjasta. Liuotukseen syötetään paluuhappoa liettoreaktoriin ja liuotuspiirien ensimmäisiin liuotusreaktoreihin. Happea syötetään kaikkiin liuotusreaktoreihin. Prosessin mallintamiseen käytettiin Aspen Plus-simulointiohjelmaa, johon pystyttiin syöttämään kineettisiä yhtälöitä. Reaktionopeusyhtälöitä käytettiin raudan hapetuksen, sulfidien liuotuksen ja jarosiitiin saostumisen mallintamiseen, eli kaikkiin liuotusreaktoreissa tapahtuviin reaktioihin. Kineettiset yhtälöt etsittiin kirjallisuudesta. Liettoreaktori puolestaan mallinnettiin syöttämällä ohjelmaan reaktioyhtälöt ja antamalla niille etenemisasteet. Jarosiitin liukenemisesta työssä on tehty laboratoriokokeita, koska aiheesta ei kirjallisuudesta löytynyt kineettistä tietoa. Liuotuskokeissa käytetyn kiintoaineen kuitenkin todettiin sisältävän liikaa götiittiä, että tuloksista olisi voitu laskea kinetiikkaa jarosiitin liukenemiselle. Simulointimallilla laskettiin yksi tapaus vertailukohdaksi, johon malliin tehtyjä muutoksia verrattiin. Mallilla tutkittiin konversiosta tulevan jarosiitin määrän vaikutusta, reaktorikoon merkitystä ja rikasteen liuotuksen sekä jarosiitin saostuksen reaktionopeuksien muutoksen vaikutuksia. Käytetyillä kineettisillä yhtälöillä reaktioiden todettiin tarvitsevan vain ¾ käytetystä reaktiotilavuudesta, rikasteen liuotusnopeuden kohtalaisen pienellä hidastamisen todettiin vähentävän sinkin saantoa ja jarosiitin saostuksen reaktionopeuden kasvulla todettiin myös olevan negatiivinen vaikutus sinkin saantoon. Simulointimallissa käytettyjen reaktionopeusyhtälöiden varmentaminen kokeilla todettiin tarpeelliseksi, sillä jo kohtalaisen pienillä muutoksilla havaittiin olevan merkitystä prosessin toimivuuteen. Lisäksi todettiin jarosiitin liukenemisen huomioimisen olevan tarpeen.

Diverse set of Turing nanopatterns coat corneae across insect lineages.

Nipple-like nanostructures covering the corneal surfaces of moths, butterflies, and Drosophila have been studied by electron and atomic force microscopy, and their antireflective properties have been described. In contrast, corneal nanostructures of the majority of other insect orders have either been unexamined or examined by methods that did not allow precise morphological characterization. Here we provide a comprehensive analysis of corneal surfaces in 23 insect orders, revealing a rich diversity of insect corneal nanocoatings. These nanocoatings are categorized into four major morphological patterns and various transitions between them, many, to our knowledge, never described before. Remarkably, this unexpectedly diverse range of the corneal nanostructures replicates the complete set of Turing patterns, thus likely being a result of processes similar to those modeled by Alan Turing in his famous reaction-diffusion system. These findings reveal a beautiful diversity of insect corneal nanostructures and shed light on their molecular origin and evolutionary diversification. They may also be the first-ever biological example of Turing nanopatterns.

Critical behavior in nonequilibrium phase transitions

The nonequilibrium phase transitions occurring in a fast-ionic-conductor model and in a reaction-diffusion Ising model are studied by Monte Carlo finite-size scaling to reveal nonclassical critical behavior; our results are compared with those in related models.

COMPREENSÃO MATEMÁTICA DA DIFUSÃO NO CONTEXTO ELETROQUÍMICO

The aim of this study was to explain in detail the mathematical methods used to deal with diffusion equations, mainly for students and researchers interested in electrochemistry and related areas. Emphasis was placed on the deduction and resolution of diffusion equations, as well as addressing cartesian, spherical and cylindrical coordinates. Different aspects of mass transfer processes were discussed including the importance of the resolution of Fick's laws equations to understand and derive parameters of the electroactive species (e.g., diffusion coefficients, formal electrode potentials) from the electrochemical techniques. As an example, the resolution of diffusion equations for a reversible reduction process of soluble oxidized species was presented for the chronopotentiometry technique. This study is envisaged to broaden the understanding of these frequently used methods, in which mathematical deductions are not always completely understood.

The bifurcational behaviour of the spatially distributed Rayleigh equation

At the present work the bifurcational behaviour of the solutions of Rayleigh equation and corresponding spatially distributed system is being analysed. The conditions of oscillatory and monotonic loss of stability are obtained. In the case of oscillatory loss of stability, the analysis of linear spectral problem is being performed. For nonlinear problem, recurrent formulas for the general term of the asymptotic approximation of the self-oscillations are found, the stability of the periodic mode is analysed. Lyapunov-Schmidt method is being used for asymptotic approximation. The correlation between periodic solutions of ODE and PDE is being investigated. The influence of the diffusion on the frequency of self-oscillations is being analysed. Several numerical experiments are being performed in order to support theoretical findings.

Modélisation d'arythmies auriculaires modulées par le système nerveux autonome

La fibrillation auriculaire (FA) est la forme d’arythmie la plus fréquente et représente environ un tiers des hospitalisations attribuables aux troubles du rythme cardiaque. Les mécanismes d’initiation et de maintenance de la FA sont complexes et multiples. Parmi ceux-ci, une contribution du système nerveux autonome a été identifiée mais son rôle exact demeure mal compris. Ce travail cible l’étude de la modulation induite par l’acétylcholine (ACh) sur l’initiation et le maintien de la FA, en utilisant un modèle de tissu bidimensionnel. La propagation de l’influx électrique sur ce tissu est décrite par une équation réaction-diffusion non-linéaire résolue sur un maillage rectangulaire avec une méthode de différences finies, et la cinétique d'ACh suit une évolution temporelle prédéfinie qui correspond à l’activation du système parasympathique. Plus de 4400 simulations ont été réalisées sur la base de 4 épisodes d’arythmies, 5 tailles différentes de région modulée par l’ACh, 10 concentrations d’ACh et 22 constantes de temps de libération et de dégradation d’ACh. La complexité de la dynamique des réentrées est décrite en fonction de la constante de temps qui représente le taux de variation d’ACh. Les résultats obtenus suggèrent que la stimulation vagale peut mener soit à une dynamique plus complexe des réentrées soit à l’arrêt de la FA en fonction des quatre paramètres étudiés. Ils démontrent qu’une décharge vagale rapide, représentée par des constantes de temps faibles combinées à une quantité suffisamment grande d’ACh, a une forte probabilité de briser la réentrée primaire provoquant une activité fibrillatoire. Cette activité est caractérisée par la création de plusieurs ondelettes à partir d’un rotor primaire sous l’effet de l’hétérogénéité du gradient de repolarisation causé par l’activité autonomique.

Critical behavior in nonequilibrium phase transitions

The nonequilibrium phase transitions occurring in a fast-ionic-conductor model and in a reaction-diffusion Ising model are studied by Monte Carlo finite-size scaling to reveal nonclassical critical behavior; our results are compared with those in related models.

Front spreading in population dynamic models. Theory and application to the Neolithic transition

This thesis presents population dynamics models that can be applied to predict the rate of spread of the Neolithic transition (change from hunter-gathering to farming economics) across the European continent, which took place about 9000 to 5000 years ago. The first models in this thesis provide predictions at a continental scale. We develop population dynamics models with explicit kernels and apply realistic data. We also derive a new time-delayed reaction-diffusion equation which yields speeds about a 10% slower than previous models. We also deal with a regional variability: the slowdown of the Neolithic front when reaching the North of Europe. We develop simple reaction-diffusion models that can predict the measured speeds in terms of the non-homogeneous distribution of pre-Neolithic (Mesolithic) population in Europe, which were present in higher densities at the North of the continent. Such models can explain the observed speeds.

Self-consistent field theory for diblock copolymers grafted to a sphere

An efficient numerical self-consistent field theory (SCFT) algorithm is developed for treating structured polymers on spherical surfaces. The method solves the diffusion equations of SCFT with a pseudospectral approach that combines a spherical-harmonics expansion for the angular coordinates with a modified real-space Crank–Nicolson method for the radial direction. The self-consistent field equations are solved with Anderson-mixing iterations using dynamical parameters and an alignment procedure to prevent angular drift of the solution. A demonstration of the algorithm is provided for thin films of diblock copolymer grafted to the surface of a spherical core, in which the sequence of equilibrium morphologies is predicted as a function of diblock composition. The study reveals an array of interesting behaviors as the block copolymer pattern is forced to adapt to the finite surface area of the sphere.

Efficiency of pseudo-spectral algorithms with Anderson mixing for the SCFT of periodic block-copolymer phases

This study examines the numerical accuracy, computational cost, and memory requirements of self-consistent field theory (SCFT) calculations when the diffusion equations are solved with various pseudo-spectral methods and the mean field equations are iterated with Anderson mixing. The different methods are tested on the triply-periodic gyroid and spherical phases of a diblock-copolymer melt over a range of intermediate segregations. Anderson mixing is found to be somewhat less effective than when combined with the full-spectral method, but it nevertheless functions admirably well provided that a large number of histories is used. Of the different pseudo-spectral algorithms, the 4th-order one of Ranjan, Qin and Morse performs best, although not quite as efficiently as the full-spectral method.

Travelling waves in a model of species migration

A model of species migration is presented which takes the form of a reaction-diffusion system. We consider special limits of this model in which we demonstrate the existence of travelling wave solutions. These solutions can be used to describe the migration of cells, bacteria, and some organisms. © 2000 Elsevier Science Ltd. All rights reserved.

Cortical hot spots and labyrinths: why cortical neuromodulation for episodic migraine with aura should be personalized

Stimulation protocols for medical devices should be rationally designed. For episodic migraine with aura we outline model-based design strategies toward preventive and acute therapies using stereotactic cortical neuromodulation. To this end, we regard a localized spreading depression (SD) wave segment as a central element in migraine pathophysiology. To describe nucleation and propagation features of the SD wave segment, we define the new concepts of cortical hot spots and labyrinths, respectively. In particular, we firstly focus exclusively on curvature-induced dynamical properties by studying a generic reaction-diffusion model of SD on the folded cortical surface. This surface is described with increasing level of details, including finally personalized simulations using patient's magnetic resonance imaging (MRI) scanner readings. At this stage, the only relevant factor that can modulate nucleation and propagation paths is the Gaussian curvature, which has the advantage of being rather readily accessible by MRI. We conclude with discussing further anatomical factors, such as areal, laminar, and cellular heterogeneity, that in addition to and in relation to Gaussian curvature determine the generalized concept of cortical hot spots and labyrinths as target structures for neuromodulation. Our numerical simulations suggest that these target structures are like fingerprints, they are individual features of each migraine sufferer. The goal in the future will be to provide individualized neural tissue simulations. These simulations should predict the clinical data and therefore can also serve as a test bed for exploring stereotactic cortical neuromodulation.

Processos difusivos generalizados

We investigate several diffusion equations which extend the usual one by considering the presence of nonlinear terms or a memory effect on the diffusive term. We also considered a spatial time dependent diffusion coefficient. For these equations we have obtained a new classes of solutions and studied the connection of them with the anomalous diffusion process. We start by considering a nonlinear diffusion equation with a spatial time dependent diffusion coefficient. The solutions obtained for this case generalize the usual one and can be expressed in terms of the q-exponential and q-logarithm functions present in the generalized thermostatistics context (Tsallis formalism). After, a nonlinear external force is considered. For this case the solutions can be also expressed in terms of the q-exponential and q-logarithm functions. However, by a suitable choice of the nonlinear external force, we may have an exponential behavior, suggesting a connection with standard thermostatistics. This fact reveals that these solutions may present an anomalous relaxation process and then, reach an equilibrium state of the kind Boltzmann- Gibbs. Next, we investigate a nonmarkovian linear diffusion equation that presents a kernel leading to the anomalous diffusive process. Particularly, our first choice leads to both a the usual behavior and anomalous behavior obtained through a fractionalderivative equation. The results obtained, within this context, correspond to a change in the waiting-time distribution for jumps in the formalism of random walks. These modifications had direct influence in the solutions, that turned out to be expressed in terms of the Mittag-Leffler or H of Fox functions. In this way, the second moment associated to these distributions led to an anomalous spread of the distribution, in contrast to the usual situation where one finds a linear increase with time

Stochastic Skellam model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Lap number properties for p-Laplacian problems investigated by Lyapunov methods

In this work we consider a one-dimensional quasilinear parabolic equation and we prove that the lap number of any solution cannot increase through orbits as the time passes if the initial data is a continuous function. We deal with the lap number functional as a Lyapunov function, and apply lap number properties to reach an understanding on the asymptotic behavior of a particular problem. (c) 2006 Published by Elsevier Ltd.