A teoria de pearson para a disciplina de química orgânica: um exercício prático e teórico aplicado em sala de aula

We report a didactic experience in teaching Pearson's theory (HSAB) to graduate students in organic chemistry. This approach was based on teaching students how to use computer programs to calculate frontier orbitals (HOMO-LUMO). The suggested level of calculation was a semi-empiric PM3, proving to be efficient for obtaining robust and fast numerical results that can be performed easily in the classroom. We described a practical computational exercise and asked students to compare these numerical data with qualitative analysis using valence bond theory. A comprehensive solution of this exercise is presented, aiming to support teachers in their lessons.

Dinâmica não-linear e reagente limitante: um exemplo de bifurcação transcrítica

The nonlinear analysis of a general mixed second order reaction was performed, aiming to explore some basic tools concerning the mathematics of nonlinear differential equations. Concepts of stability around fixed points based on linear stability analysis are introduced, together with phase plane and integral curves. The main focus is the chemical relationship between changes of limiting reagent and transcritical bifurcation, and the investigation underlying the conclusion.

Parallella, dynamiska representationer i gymnasiefysiken : implementering av ett interaktivt datorverktyg i didaktiska situationer och uppfattning av effektivt lärande

The computer is a useful tool in the teaching of upper secondary school physics, and should not have a subordinate role in students' learning process. However, computers and computer-based tools are often not available when they could serve their purpose best in the ongoing teaching. Another problem is the fact that commercially available tools are not usable in the way the teacher wants. The aim of this thesis was to try out a novel teaching scenario in a complicated subject in physics, electrodynamics. The didactic engineering of the thesis consisted of developing a computer-based simulation and training material, implementing the tool in physics teaching and investigating its effectiveness in the learning process. The design-based research method, didactic engineering (Artigue, 1994), which is based on the theoryof didactical situations (Brousseau, 1997), was used as a frame of reference for the design of this type of teaching product. In designing the simulation tool a general spreadsheet program was used. The design was based on parallel, dynamic representations of the physics behind the function of an AC series circuit in both graphical and numerical form. The tool, which was furnished with possibilities to control the representations in an interactive way, was hypothesized to activate the students and promote the effectiveness of their learning. An effect variable was constructed in order to measure the students' and teachers' conceptions of learning effectiveness. The empirical study was twofold. Twelve physics students, who attended a course in electrodynamics in an upper secondary school, participated in a class experiment with the computer-based tool implemented in three modes of didactical situations: practice, concept introduction and assessment. The main goal of the didactical situations was to have students solve problems and study the function of AC series circuits, taking responsibility for theirown learning process. In the teacher study eighteen Swedish speaking physics teachers evaluated the didactic potential of the computer-based tool and the accompanying paper-based material without using them in their physics teaching. Quantitative and qualitative data were collected using questionnaires, observations and interviews. The result of the studies showed that both the group of students and the teachers had generally positive conceptions of learning effectiveness. The students' conceptions were more positive in the practice situation than in the concept introduction situation, a setting that was more explorative. However, it turned out that the students' conceptions were also positive in the more complex assessment situation. This had not been hypothesized. A deeper analysis of data from observations and interviews showed that one of the students in each pair was more active than the other, taking more initiative and more responsibilityfor the student-student and student-computer interaction. These active studentshad strong, positive conceptions of learning effectiveness in each of the threedidactical situations. The group of less active students had a weak but positive conception in the first iv two situations, but a negative conception in the assessment situation, thus corroborating the hypothesis ad hoc. The teacher study revealed that computers were seldom used in physics teaching and that computer programs were in short supply. The use of a computer was considered time-consuming. As long as physics teaching with computer-based tools has to take place in special computer rooms, the use of such tools will remain limited. The affordance is enhanced when the physical dimensions as well as the performance of the computer are optimised. As a consequence, the computer then becomes a real learning tool for each pair of students, smoothly integrated into the ongoing teaching in the same space where teaching normally takes place. With more interactive support from the teacher, the computer-based parallel, dynamic representations will be efficient in promoting the learning process of the students with focus on qualitative reasoning - an often neglected part of the learning process of the students in upper secondary school physics.

Algorithm to determine the intersection curves between bezier surfaces by the solution of multivariable polynomial system and the differential marching method

The determination of the intersection curve between Bézier Surfaces may be seen as the composition of two separated problems: determining initial points and tracing the intersection curve from these points. The Bézier Surface is represented by a parametric function (polynomial with two variables) that maps a point in the tridimensional space from the bidimensional parametric space. In this article, it is proposed an algorithm to determine the initial points of the intersection curve of Bézier Surfaces, based on the solution of polynomial systems with the Projected Polyhedral Method, followed by a method for tracing the intersection curves (Marching Method with differential equations). In order to allow the use of the Projected Polyhedral Method, the equations of the system must be represented in terms of the Bernstein basis, and towards this goal it is proposed a robust and reliable algorithm to exactly transform a multivariable polynomial in terms of power basis to a polynomial written in terms of Bernstein basis .

On state and parameter estimation in chaotic systems

State-of-the-art predictions of atmospheric states rely on large-scale numerical models of chaotic systems. This dissertation studies numerical methods for state and parameter estimation in such systems. The motivation comes from weather and climate models and a methodological perspective is adopted. The dissertation comprises three sections: state estimation, parameter estimation and chemical data assimilation with real atmospheric satellite data. In the state estimation part of this dissertation, a new filtering technique based on a combination of ensemble and variational Kalman filtering approaches, is presented, experimented and discussed. This new filter is developed for large-scale Kalman filtering applications. In the parameter estimation part, three different techniques for parameter estimation in chaotic systems are considered. The methods are studied using the parameterized Lorenz 95 system, which is a benchmark model for data assimilation. In addition, a dilemma related to the uniqueness of weather and climate model closure parameters is discussed. In the data-oriented part of this dissertation, data from the Global Ozone Monitoring by Occultation of Stars (GOMOS) satellite instrument are considered and an alternative algorithm to retrieve atmospheric parameters from the measurements is presented. The validation study presents first global comparisons between two unique satellite-borne datasets of vertical profiles of nitrogen trioxide (NO3), retrieved using GOMOS and Stratospheric Aerosol and Gas Experiment III (SAGE III) satellite instruments. The GOMOS NO3 observations are also considered in a chemical state estimation study in order to retrieve stratospheric temperature profiles. The main result of this dissertation is the consideration of likelihood calculations via Kalman filtering outputs. The concept has previously been used together with stochastic differential equations and in time series analysis. In this work, the concept is applied to chaotic dynamical systems and used together with Markov chain Monte Carlo (MCMC) methods for statistical analysis. In particular, this methodology is advocated for use in numerical weather prediction (NWP) and climate model applications. In addition, the concept is shown to be useful in estimating the filter-specific parameters related, e.g., to model error covariance matrix parameters.

Lujasta teräksestä valmistetun palkin poikkileikkauksen optimointi

Parin viime vuosikymmenen aikana on kehitetty huomattavasti entistä lujempia teräslaatuja, joiden käyttö ei kuitenkaan ole yleistynyt läheskään samaan tahtiin. Korkeamman hinnan lisäksi yksi merkittävä syy tähän on, että suunnittelijoilla ei usein ole riittäviä tietoja siitä, millaisissa tilanteissa lujemman teräslaadun käytöstä on merkittävää hyötyä. Tilannetta ei myöskään helpota se, että käytössä olevat standardit eivät tarjoa lainkaan ohjeistusta kaikkein lujimpien, myötörajaltaan yli 700MPa terästen käyttöön ja mitoitukseen. Tässä työssä pyritään tarjoamaan suunnittelijalle ohjeita ja nyrkkisääntöjä sopivan lujuusluokan ja profiilin valintaan sekä yleisesti lujempien teräslaatujen käyttöön. Lujemman teräslaadun käytöllä voidaan keventää suunniteltavaa rakennetta ja saada aikaan huomattavia painonsäästöjä. Usein ongelmaksi nousevat kuitenkin stabiiliuskriteerit, sillä teräksen lommahduskestävyys määräytyy suuresti sen lujuusluokasta siten, että mitä lujempaa teräs on, sitä helpommin se lommahtaa. Kun tämä yhdistetään siihen, että lujempaa terästä käytettäessä rakenteesta tulee optimoituna muutenkin pienempi ja kevyempi, kasvaa näiden kahden asian yhteisvaikutuksena kantokyvyn mukaan mitoitetun rakenteen taipuma korkeampiin lujuusluokkiin edetessä hyvin nopeasti sallittujen rajojen yli. Työssä etsitään siksi keinoja sopivan kompromissin löytämiseksi lujuuden ja jäykkyyden välille. Koska muotoilulla ja poikkileikkauksella on suuri merkitys sekä taipuman että stabiliteetin kannalta, tutkitaan erilaisia poikkileikkausvaihtoehtoja ja etsitään optimaalista poikkileikkausta taivutuspalkille matemaattisen optimointimallin avulla. Kun eri poikkileikkausvaihtoehdot on käsitelty ja optimoitu taivutuksen suhteen, tutkitaan poikkileikkauksia myös muissa kuormitustapauksissa. Huomattavan raskaan laskentatyön takia apuna käytetään Matlab-ohjelmistoa itse optimointiin ja Femap-ohjelmaa muiden kuormitustapausten tutkimiseen ja tulosten verifioitiin.

Bayesian analysis of SEIR epidemic models

This thesis concerns the analysis of epidemic models. We adopt the Bayesian paradigm and develop suitable Markov Chain Monte Carlo (MCMC) algorithms. This is done by considering an Ebola outbreak in the Democratic Republic of Congo, former Zaïre, 1995 as a case of SEIR epidemic models. We model the Ebola epidemic deterministically using ODEs and stochastically through SDEs to take into account a possible bias in each compartment. Since the model has unknown parameters, we use different methods to estimate them such as least squares, maximum likelihood and MCMC. The motivation behind choosing MCMC over other existing methods in this thesis is that it has the ability to tackle complicated nonlinear problems with large number of parameters. First, in a deterministic Ebola model, we compute the likelihood function by sum of square of residuals method and estimate parameters using the LSQ and MCMC methods. We sample parameters and then use them to calculate the basic reproduction number and to study the disease-free equilibrium. From the sampled chain from the posterior, we test the convergence diagnostic and confirm the viability of the model. The results show that the Ebola model fits the observed onset data with high precision, and all the unknown model parameters are well identified. Second, we convert the ODE model into a SDE Ebola model. We compute the likelihood function using extended Kalman filter (EKF) and estimate parameters again. The motivation of using the SDE formulation here is to consider the impact of modelling errors. Moreover, the EKF approach allows us to formulate a filtered likelihood for the parameters of such a stochastic model. We use the MCMC procedure to attain the posterior distributions of the parameters of the SDE Ebola model drift and diffusion parts. In this thesis, we analyse two cases: (1) the model error covariance matrix of the dynamic noise is close to zero , i.e. only small stochasticity added into the model. The results are then similar to the ones got from deterministic Ebola model, even if methods of computing the likelihood function are different (2) the model error covariance matrix is different from zero, i.e. a considerable stochasticity is introduced into the Ebola model. This accounts for the situation where we would know that the model is not exact. As a results, we obtain parameter posteriors with larger variances. Consequently, the model predictions then show larger uncertainties, in accordance with the assumption of an incomplete model.

Stochastic particle models: mean reversion and burgers dynamics. An application to commodity markets

The aim of this study is to propose a stochastic model for commodity markets linked with the Burgers equation from fluid dynamics. We construct a stochastic particles method for commodity markets, in which particles represent market participants. A discontinuity in the model is included through an interacting kernel equal to the Heaviside function and its link with the Burgers equation is given. The Burgers equation and the connection of this model with stochastic differential equations are also studied. Further, based on the law of large numbers, we prove the convergence, for large N, of a system of stochastic differential equations describing the evolution of the prices of N traders to a deterministic partial differential equation of Burgers type. Numerical experiments highlight the success of the new proposal in modeling some commodity markets, and this is confirmed by the ability of the model to reproduce price spikes when their effects occur in a sufficiently long period of time.

The effectiveness of a computer program on career planning for university students

This study investigated the effectiveness of a computer program, PERSONAL CAREER DIRECTIONS (PC DIRECTIONS) (Anderson, Welborn, & Wright, 1983) on career planning and exploration for twenty-four Brock University students (18 women and 6 men) who requested career planning assistance at the Career/Placement Services of the Counselling Centre. A one-group pretest/posttest design was used in the study_ Progress in career planning and exploration was measured by Career Planning (CP) and Career Exploration (CE) scales of the Career Development Inventory (College and University Form) (Super, Thompson, Lindeman, Jordaan, & Myers, 1981). A paired samples 2-tailed t test for Career Development Attitudes (CDA) , the combined CP and CE scales, revealed the posttest scores were significantly higher than the pretest scores, t(23) = 3.74, 2 < .001. Student progress was also assessed by self-report lists of job titles which reflected positive changes after students used PC DIRECTIONS. In response to several questions, students' attitudes were more positive than negative toward the program. Implications are that PC DIRECTIONS is an effective component in promoting career planning for university students. Further studies may reveal that different types of students may benefit from different interventions in the career planning process.

Simulation de la nage anguilliforme

Ce document traite premièrement des diverses tentatives de modélisation et de simulation de la nage anguilliforme puis élabore une nouvelle technique, basée sur la méthode de la frontière immergée généralisée et la théorie des poutres de Reissner-Simo. Cette dernière, comme les équations des fluides polaires, est dérivée de la mécanique des milieux continus puis les équations obtenues sont discrétisées afin de les amener à une résolution numérique. Pour la première fois, la théorie des schémas de Runge-Kutta additifs est combinée à celle des schémas de Runge-Kutta-Munthe-Kaas pour engendrer une méthode d’ordre de convergence formel arbitraire. De plus, les opérations d’interpolation et d’étalement sont traitées d’un nouveau point de vue qui suggère l’usage des splines interpolatoires nodales en lieu et place des fonctions d’étalement traditionnelles. Enfin, de nombreuses vérifications numériques sont faites avant de considérer les simulations de la nage.

Sur un modèle d'érythropoïèse comportant un taux de mortalité dynamique

Ce mémoire concerne la modélisation mathématique de l’érythropoïèse, à savoir le processus de production des érythrocytes (ou globules rouges) et sa régulation par l’érythropoïétine, une hormone de contrôle. Nous proposons une extension d’un modèle d’érythropoïèse tenant compte du vieillissement des cellules matures. D’abord, nous considérons un modèle structuré en maturité avec condition limite mouvante, dont la dynamique est capturée par des équations d’advection. Biologiquement, la condition limite mouvante signifie que la durée de vie maximale varie afin qu’il y ait toujours un flux constant de cellules éliminées. Par la suite, des hypothèses sur la biologie sont introduites pour simplifier ce modèle et le ramener à un système de trois équations différentielles à retard pour la population totale, la concentration d’hormones ainsi que la durée de vie maximale. Un système alternatif composé de deux équations avec deux retards constants est obtenu en supposant que la durée de vie maximale soit fixe. Enfin, un nouveau modèle est introduit, lequel comporte un taux de mortalité augmentant exponentiellement en fonction du niveau de maturité des érythrocytes. Une analyse de stabilité linéaire permet de détecter des bifurcations de Hopf simple et double émergeant des variations du gain dans la boucle de feedback et de paramètres associés à la fonction de survie. Des simulations numériques suggèrent aussi une perte de stabilité causée par des interactions entre deux modes linéaires et l’existence d’un tore de dimension deux dans l’espace de phase autour de la solution stationnaire.

Caractère intrinsèque des matrices de Stokes

Il est connu qu’une équation différentielle linéaire, x^(k+1)Y' = A(x)Y, au voisinage d’un point singulier irrégulier non-résonant est uniquement déterminée (à isomorphisme analytique près) par : (1) sa forme normale formelle, (2) sa collection de matrices de Stokes. La définition des matrices de Stokes fait appel à un ordre sur les parties réelles des valeurs propres du système, ordre qui peut être perturbé par une rotation en x. Dans ce mémoire, nous avons établi le caractère intrinsèque de cette relation : nous avons donc établi comment la nouvelle collection de matrices de Stokes obtenue après une rotation en x qui change l’ordre des parties réelles des valeurs propres dépend de la collection initiale. Pour ce faire, nous donnons un chapitre de préliminaires généraux sur la forme normale des équations différentielles ordinaires puis un chapitre sur le phénomène de Stokes pour les équations différentielles linéaires. Le troisième chapitre contient nos résultats.

Ultrasonic Study Of The Elastic Properties And Phase Transitions In Selected Mixed Sulphate Crystals

The thesis investigated the elastic properties and phase transitions in selected mixed sulphate crystals – Lithium Hydrazinium Sulphate [LiN2H2SO4], Lithium Ammonium Sulphate [LiNH4SO4] and Lithium Potassium Sulphate [LiKSO4] – using ultrasonic technique. The pulse echo overlap technique has been used for measuring ultrasonic velocity and its dependence on temperature along different directions with waves of longitudinal and transverse polarizations. Two major numerical techniques and the corresponding computer programs developed as part of present work are presented in this thesis. All the 9 elastic constants of LHS are determined accurately from ultrasonic measurements and applying misorientation correction refines the constants. Ultrasonic measurements are performed in LAS to determine the elastic constants and to study the low temperature phase transitions. Temperature variation studies of elastic constant of LAS are performed for 6 different modes of propagation for heating and cooling at low temperatures. All the 5 independent elastic constants of LPS is determined using ultrasonic measurements. It is concluded that LPS crystal does not undergo a phase transition near this temperature. A comparison of the three crystals studied shows that LPS has maximum number of phase transitions and LHS has the least number. It is interesting to note that LPS has the simplest formula unit among the three. There is considerable scope for the future work on these crystals and others belonging to the sulphate family.

Studies on the dynamics and rheology of dilute suspensions of Brownian particles in simple shear flow under the action of an external force

We present a novel approach to computing the orientation moments and rheological properties of a dilute suspension of spheroids in a simple shear flow at arbitrary Peclct number based on a generalised Langevin equation method. This method differs from the diffusion equation method which is commonly used to model similar systems in that the actual equations of motion for the orientations of the individual particles are used in the computations, instead of a solution of the diffusion equation of the system. It also differs from the method of 'Brownian dynamics simulations' in that the equations used for the simulations are deterministic differential equations even in the presence of noise, and not stochastic differential equations as in Brownian dynamics simulations. One advantage of the present approach over the Fokker-Planck equation formalism is that it employs a common strategy that can be applied across a wide range of shear and diffusion parameters. Also, since deterministic differential equations are easier to simulate than stochastic differential equations, the Langevin equation method presented in this work is more efficient and less computationally intensive than Brownian dynamics simulations.We derive the Langevin equations governing the orientations of the particles in the suspension and evolve a procedure for obtaining the equation of motion for any orientation moment. A computational technique is described for simulating the orientation moments dynamically from a set of time-averaged Langevin equations, which can be used to obtain the moments when the governing equations are harder to solve analytically. The results obtained using this method are in good agreement with those available in the literature.The above computational method is also used to investigate the effect of rotational Brownian motion on the rheology of the suspension under the action of an external force field. The force field is assumed to be either constant or periodic. In the case of con- I stant external fields earlier results in the literature are reproduced, while for the case of periodic forcing certain parametric regimes corresponding to weak Brownian diffusion are identified where the rheological parameters evolve chaotically and settle onto a low dimensional attractor. The response of the system to variations in the magnitude and orientation of the force field and strength of diffusion is also analyzed through numerical experiments. It is also demonstrated that the aperiodic behaviour exhibited by the system could not have been picked up by the diffusion equation approach as presently used in the literature.The main contributions of this work include the preparation of the basic framework for applying the Langevin method to standard flow problems, quantification of rotary Brownian effects by using the new method, the paired-moment scheme for computing the moments and its use in solving an otherwise intractable problem especially in the limit of small Brownian motion where the problem becomes singular, and a demonstration of how systems governed by a Fokker-Planck equation can be explored for possible chaotic behaviour.

Some non- linear problems in theoretical physics

An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.