The Master´s Diploma Thesis deals with the assessment of the recreational potential of the town of Jablonné v Podještědí. The area is divided into three types of landscape, each of which receives different protection treatment - Lužické hory Protected Landscape Area, Lembersko Landscape Conservation Area and an ordinary landscape without any protection. The theoretical part explains basic terms as well as summarises the knowledge concerning the recreation industry, recreational potential and landscape capacity and limits. The practical part defines natural, cultural-historical and perceptional features and values of the three mentioned types of landscape. One of the aims is to discover whether the public perceives these very features and values. Then the thesis assesses the recreational potential of the landscapes with different protection treatment. Lužické hory Protected Landscape Area has the highest recreational potential while an ordinary landscape without any protection features the lowest potential. The outcome is then a map concerning the recreational potential assessment. After the assessment an appropriate management for ensuring potential development without exceeding the landscape limits is recommended.

Neste trabalho investigamos a dinâmica de crescimento de filmes de diamante sintetizados por meio de deposição química a vapor ativada por plasma de microondas (CVD). A caracterização foi feita utilizando, fundamentalmente, microscopia de força atômica (AFM). Analisamos o comportamento da rugosidade dos filmes como função da escala de observação e do tempo de deposição. Dessa maneira verificamos a existência de leis de potência para o crescimento e determinamos os expoentes críticos associados a essas leis. Os resultados obtidos estão em bom acordo com o processo de crescimento descrito pela equação estocástica KPZ. Os mecanismos principais são a deposição aleatória de partículas na superfície, o crescimento lateral e a dessorção. / Diamond films have been grown by Microwave Plasma assisted Chemical Vapor Deposition (CVD). The characterization has been made mainly by Atomic Force Microscopy (AFM). We could analyze the roughness behavior with the scale of observation and with the deposition time. We could determine the critical exponents associated with these laws. The results suggest that the growth process is in good agreement with the stochastic growth equation known as KPZ. The most important mechanisms are the random deposition, the lateral growth and the desorption.

Neste trabalho investigamos a dinâmica de crescimento de filmes de diamante sintetizados por meio de deposição química a vapor ativada por plasma de microondas (CVD). A caracterização foi feita utilizando, fundamentalmente, microscopia de força atômica (AFM). Analisamos o comportamento da rugosidade dos filmes como função da escala de observação e do tempo de deposição. Dessa maneira verificamos a existência de leis de potência para o crescimento e determinamos os expoentes críticos associados a essas leis. Os resultados obtidos estão em bom acordo com o processo de crescimento descrito pela equação estocástica KPZ. Os mecanismos principais são a deposição aleatória de partículas na superfície, o crescimento lateral e a dessorção. / Diamond films have been grown by Microwave Plasma assisted Chemical Vapor Deposition (CVD). The characterization has been made mainly by Atomic Force Microscopy (AFM). We could analyze the roughness behavior with the scale of observation and with the deposition time. We could determine the critical exponents associated with these laws. The results suggest that the growth process is in good agreement with the stochastic growth equation known as KPZ. The most important mechanisms are the random deposition, the lateral growth and the desorption.

O modelo estocástico Raise and Peel é estudado nesta tese. Para isto é utilizado o método de simulação por Monte Carlo junto com os métodos de diagonalização exata e numérica do operador de Liouville. Este modelo estocástico é um modelo de crescimento unidimensional com dois parâmetros livres. Um parâmetro de absorção local e um parâmetro de dessorção não local. Em função destes dois parâmetros se observa um rico diagrama de fase, apresentando regiões massivas, regiões criticamente auto-organizadas, estados quase-estacionários e transições a múltiplos estados absorventes. O principal resultado deste trabalho é ressaltar a existência de células de Jordan no operador de Liouville. Células de Jordan que crescem com o tamanho do sistema e portanto no limite termodinâmico a dinâmica assintótica pode ser mascarada. A nível numérico estas células de Jordan podem levar a errôneas interpretações de fases criticas quando são na realidade fases massivas ou vice-versa. Portanto dependendo da condição inicial observa-se que a presença de células de Jordan pode levar à determinação errônea de expoentes críticos e a observações de tempos de decaimentos excessivamente grandes. Tudo isto ressalta a necessidade de se determinar os expoentes críticos e os tempos de decaimento por diversos métodos, sempre que for possível, além de se controlar o comportamento destas quantidades considerando a evolução do modelo com diferentes condições inicias. Entre outros resultados que obtivemos observamos a existência de estados quase-estacionários com tempos de vida que crescem muito mais rápido que uma lei de potencia do tamanho do sistema. Encontramos o expoente critico dinâmico z=1, no caso da transição a estados multi-absorventes. Este resultado ocorreu tanto nos casos sem absorção como nos casos sem dessorção. O modelo exibe também uma fase rugosa com um expoente de rugosidade próximo de zero quando a taxa de absorção é maior que a taxa dessorção. E finalmente observamos que o modelo estudado em condições periódicas de contorno pode ser enxergado como um modelo KPZ em 1+1 dimensões, sujeito a dois tipos de perturbações. Uma das pertubações sendo relevante e a outra irrelevante. / The stochastic model Raise and Peel is studied in this thesis. we use the Monte Carlo simulation method together with the exact and numerical diagonalization methods of the Liouville operator. This stochastic model is a one-dimensional growth model with two free parameters. A local absorption parameter and a non-local desorption one. As a function of these two parameters, a rich phase diagram is observed, presenting massive regions, critically self-organized regions, quasi-stationary states and transitions to multiple absorbing states. The main result of this work is to emphasize the existence of Jordan cells in the Liouville operator. Jordan cells that grow with the size of the system and therefore in the thermodynamic limit the asymptotic dynamics can be masked. At the numerical level, these Jordan cells can lead to erroneous interpretations of massive phases as being massless critical ones or vice versa. Therefore depending on the initial condition, it is observed that the presence of Jordan cells can lead to the erroneous determination of critical exponents and produce excessively large lifetimes. Due to these effects, it is necessary to determine the critical exponents and the lifetimes by several distinct methods whenever possible, besides controlling the behavior of these quantities, by considering the evolution with different initial conditions. Among other results, we found the existence of quasi-stationary states with lifetimes that grow much faster than a power law of the systems size. We obtained a dynamic critical exponent z = 1 in the transition to multi-absorbent states in both cases without absorption or desorption. The model also shows a rough phase with a roughness exponent close to zero when the absorption rate is higher than the desorption rate. Finally, we observed that the model studied under periodic boundary conditions, can be seen as a KPZ model in 1 + 1 dimensions, under the effect of two perturbations. One of them being relevant and the other one irrelevant.

O modelo estocástico Raise and Peel é estudado nesta tese. Para isto é utilizado o método de simulação por Monte Carlo junto com os métodos de diagonalização exata e numérica do operador de Liouville. Este modelo estocástico é um modelo de crescimento unidimensional com dois parâmetros livres. Um parâmetro de absorção local e um parâmetro de dessorção não local. Em função destes dois parâmetros se observa um rico diagrama de fase, apresentando regiões massivas, regiões criticamente auto-organizadas, estados quase-estacionários e transições a múltiplos estados absorventes. O principal resultado deste trabalho é ressaltar a existência de células de Jordan no operador de Liouville. Células de Jordan que crescem com o tamanho do sistema e portanto no limite termodinâmico a dinâmica assintótica pode ser mascarada. A nível numérico estas células de Jordan podem levar a errôneas interpretações de fases criticas quando são na realidade fases massivas ou vice-versa. Portanto dependendo da condição inicial observa-se que a presença de células de Jordan pode levar à determinação errônea de expoentes críticos e a observações de tempos de decaimentos excessivamente grandes. Tudo isto ressalta a necessidade de se determinar os expoentes críticos e os tempos de decaimento por diversos métodos, sempre que for possível, além de se controlar o comportamento destas quantidades considerando a evolução do modelo com diferentes condições inicias. Entre outros resultados que obtivemos observamos a existência de estados quase-estacionários com tempos de vida que crescem muito mais rápido que uma lei de potencia do tamanho do sistema. Encontramos o expoente critico dinâmico z=1, no caso da transição a estados multi-absorventes. Este resultado ocorreu tanto nos casos sem absorção como nos casos sem dessorção. O modelo exibe também uma fase rugosa com um expoente de rugosidade próximo de zero quando a taxa de absorção é maior que a taxa dessorção. E finalmente observamos que o modelo estudado em condições periódicas de contorno pode ser enxergado como um modelo KPZ em 1+1 dimensões, sujeito a dois tipos de perturbações. Uma das pertubações sendo relevante e a outra irrelevante. / The stochastic model Raise and Peel is studied in this thesis. we use the Monte Carlo simulation method together with the exact and numerical diagonalization methods of the Liouville operator. This stochastic model is a one-dimensional growth model with two free parameters. A local absorption parameter and a non-local desorption one. As a function of these two parameters, a rich phase diagram is observed, presenting massive regions, critically self-organized regions, quasi-stationary states and transitions to multiple absorbing states. The main result of this work is to emphasize the existence of Jordan cells in the Liouville operator. Jordan cells that grow with the size of the system and therefore in the thermodynamic limit the asymptotic dynamics can be masked. At the numerical level, these Jordan cells can lead to erroneous interpretations of massive phases as being massless critical ones or vice versa. Therefore depending on the initial condition, it is observed that the presence of Jordan cells can lead to the erroneous determination of critical exponents and produce excessively large lifetimes. Due to these effects, it is necessary to determine the critical exponents and the lifetimes by several distinct methods whenever possible, besides controlling the behavior of these quantities, by considering the evolution with different initial conditions. Among other results, we found the existence of quasi-stationary states with lifetimes that grow much faster than a power law of the systems size. We obtained a dynamic critical exponent z = 1 in the transition to multi-absorbent states in both cases without absorption or desorption. The model also shows a rough phase with a roughness exponent close to zero when the absorption rate is higher than the desorption rate. Finally, we observed that the model studied under periodic boundary conditions, can be seen as a KPZ model in 1 + 1 dimensions, under the effect of two perturbations. One of them being relevant and the other one irrelevant.

Cette thèse présente plusieurs aspects de la physique des systèmes élastiques désordonnés et des méthodes analytiques utilisées pour les étudier. On s’intéressera d’une part aux propriétés universelles des processus d’avalanches statiques et dynamiques (à la transition de dépiégeage) d’interfaces élastiques de dimension arbitraire en milieu aléatoire à température nulle. Pour étudier ces questions nous utiliserons le groupe de renormalisation fonctionnel. Après une revue de ces aspects,nous présenterons plus particulièrement les résultats obtenus pendant la thèse sur (i) la structure spatiale des avalanches et (ii) les corrélations entre avalanches.On s’intéressera d’autre part aux propriétés statiques à température finie de polymères dirigés en dimension 1+1, et en particulier aux observables liées à la classe d’universalité KPZ. Dans ce contexte l’étude de modèles exactement solubles a récemment permis de grands progrès. Après une revue de ces aspects, nous nous intéresserons plus particulièrement aux modèles exactement solubles de polymère dirigé sur le réseau carré, et présenterons les résultats obtenus pendantla thèse dans cette voie: (i) classification des modèles à température finie sur le réseau carré exactement solubles par ansatz de Bethe; (ii) universalité KPZ pour les modèles Log-Gamma et Inverse-Beta; (iii) universalité et nonuniversalitéKPZ pour le modèle Beta; (iv) mesures stationnaires du modèle Inverse-Beta et des modèles à température nulle associés. / This thesis presents several aspects of the physics of disordered elastic systems and of the analytical methods used for their study.On one hand we will be interested in universal properties of avalanche processes in the statics and dynamics (at the depinning transition) of elastic interfaces of arbitrary dimension in disordered media at zero temperature. To study these questions we will use the functional renormalization group. After a review of these aspects we will more particularly present the results obtained during the thesis on (i) the spatial structure of avalanches and (ii) the correlations between avalanches.On the other hand we will be interested in static properties of directed polymers in 1+1 dimension, and in particular in observables related to the KPZ universality class. In this context the study of exactly solvable models has recently led to important progress. After a review of these aspects we will be more particularly interested in exactly solvable models of directed polymer on the square lattice and present the results obtained during the thesis in this direction: (i) classification ofBethe ansatz exactly solvable models of directed polymer at finite temperature on the square lattice; (ii) KPZ universality for the Log-Gamma and Inverse-Beta models; (iii) KPZ universality and non-universality for the Beta model; (iv) stationary measures of the Inverse- Beta model and of related zero temperature models.

Dans cette thèse, on s'intéresse à l'existence et à l'unicité d'une solution pour l'équation KPZ généralisée. On utilise la théorie récente des structures de régularité inspirée des chemins rugueux et introduite par Martin Hairer afin de donner sens à ce type d'équations singulières. La procédure de résolution comporte une partie algébrique à travers la définition du groupe de renormalisation et une partie stochastique avec la convergence de processus stochastiques renormalisés. Une des améliorations notoire de ce travail apportée aux structures de régularité est la définition du groupe de renormalisation par le biais d'une algèbre de Hopf sur des arbres labellés. Cette nouvelle construction permet d'obtenir des formules simples pour les processus stochastiques renormalisés. Ensuite, la convergence est obtenue par un traitement efficace de diagrammes de Feynman. / In this thesis, we investigate the existence and the uniqueness of the solution of the generalised KPZ equation. We use the recent theory of regularity structures inspired from the rough path and introduced by Martin Hairer in order to give a meaning to this singular equation. The procedure contains an algebraic part through the renormalisation group and a stochastic part with the computation of renormalised stochastic processes. One major improvement in the theory of the regularity structures is the definition of the renormalisation group using a Hopf algebra on some labelled trees. This new construction paves the way to simple formulas very useful for the renormalised stochastic processes. Then the convergence is obtained by an efficient treatment of some Feynman diagrams.

The bombardment of surfaces by ions can lead to the spontaneous formation of nano-structures. Depending on the irradiation conditions, smoothening or roughening mechanisms can be the leading order in pattern formation which can result in the creation of dots, ripples or ultra-smoothening effects. Because ion bombardment is already ubiquitous in industrial settings, and is relatively inexpensive compared to other surface processing techniques, self-organized patterning by ion bombardment could enable a simple, economical means of inducing well-defined nanoscale structures in a variety of settings. Understanding the fundamental behavior of surfaces during ion bombardment is therefore a vital goal; however, a complete understanding of physical processes governing surface pattern formation has not been reached yet. In order to address this issue, my thesis research has utilized three primary approaches. First, I have done real-time non-coherent X-ray scattering experiments at Cornell High Energy Synchrotron Source (CHESS) for studying kinetics of structure formation of Silicon undergoing Ar⁺ bombardment over a range of wavenumbers 4-5 times larger than has previously been obtained. From our data, we were able to extract values of the angle-dependent thickness of the amorphous layer that forms under ion bombardment, the ion-enhanced fluidity within that film, the magnitude of the stress being generated by the ion beam, and the strength of prompt atomic displacement mechanisms. Second, to further deepen our knowledge of surface dynamics, I have performed coherent X-ray studies of Ar⁺ bombardment of SiO₂ at the Advanced Photon Source (APS) for investigating the dynamics more profoundly than can be done with traditional time-resolved experiments. When using a focused ion beam, an inhomogeneous ripple motion was generated, this phenomenon reflected as an oscillatory behavior in the two-time and corresponding g₂(t) correlation functions. By fitting the oscillations in the g₂(t) correlation function, we have determined the surface ripple velocity on SiO₂ driven by Ar⁺ sputter erosion. Finally, to support the results of coherent X-ray experiments, simulations of growth models such as linear Kuramoto-Sivashinsky (KS) and Kardar-Parisi-Zhang (KPZ) have been carried out in order to compare the simulated temporal correlation functions of the scattered intensity with those obtained from the coherent x-ray scattering experiments.

Submitted by Marco Antônio de Ramos Chagas (mchagas@ufv.br) on 2015-11-11T07:40:21Z No. of bitstreams: 1 texto completo.pdf: 3139560 bytes, checksum: 8091366b90c6c5b8590b10f9c10eeec6 (MD5) / Made available in DSpace on 2015-11-11T07:40:21Z (GMT). No. of bitstreams: 1 texto completo.pdf: 3139560 bytes, checksum: 8091366b90c6c5b8590b10f9c10eeec6 (MD5) Previous issue date: 2014-02-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Isto tem motivado trabalhos considerando modelos típicos de crescimento plano em substratos que crescem lateralmente ao longo do tempo como uma primeira abordagem para analisar interfaces verdadeiramente cur- vas. Entretanto, todos estes estudos basearam-se em cálculos de expoentes de escala da rugosidade e, portanto, não demonstram conclusivamente se esta simplificação leva a uma dinâmica similar a das superfícies curvas. Para esclarecer este ponto, nós es- tudamos modelos onde a deposição de partículas e o crescimento lateral do substrato são realizados estocasticamente de acordo com suas respectivas probabilidades. Este método permite-nos estudar qualquer modelo discreto de crescimento em substratos que aumentam lateralmente. Entretanto, aqui nós nos restringimos a modelos na classe Kardar-Parisi-Zhang (KPZ), onde as distribuições de alturas das superfícies são diferentes para interfaces curvas e planas. Nós obtivemos que assintoticamente estas distribuições são dadas pelas distribuições das interfaces curvas, tanto em substratos unidimensionais quanto bidimensionais. No último caso, onde a forma analítica da distribuição de altura não é conhecida exatamente, nós obtivemos estimativas precisas dos seus primeiros cumulantes e confirmamos sua universalidade. Surpreendentemente, correções logarítmicas foram encontradas no KPZ “ansatz” para as distribuições de al- turas, que não existem nos mesmos modelos em substratos estaticos. A origem destas correções foi eXplicada como um efeito das duplicações de colunas no crescimento lat- era] do substrato. Iniciando o crescimento em substratos grandes, um crossover foi encontrado nas distribuições de alturas de plano para curvo. / This has motivated some works considering typical flat growth models on substrates which grow laterally in time, as a first approach for analyze truly curved interfaces. However, all these studies were based on the calculation of scaling exponents, from the roughness dynamic scaling, and, thus, they do not show conclusively if this simplification leads to a dynamic similar to the one of curved surfaces. In order to clarify this point, we study models where particle deposition and lateral growth of the substrate are stochasticaly performed ac- cordingly to their respective probabilities. This method allows us to study any discrete growth model on growing substrates. However, here we restrict ourselves to models in Kardar-Parisi-Zhang (KPZ) class, where surface height distributions are different for curved and flat interfaces. We found that asymptotically these distributions are given by the ones of curved interfaces, in one- as well as in two-dimensional substrates. In the last case, where the analytical form of the height distributions are not known exactly, we obtain accurate estimates of their first cumulants and confirm their universality. Surprisingly, logarithmic corrections were found in the KPZ ansatz for the height dis- tributions, which do not exist for the same models on static substrates. The origin of these corrections was explained as an effect of the duplication of columns in the lateral growth of the substrate. Starting the growth on large substrates, a crossover was found in the height distributions from flat to curved ones.

Dans le cadre de cette thèse, nous nous intéressons à ”l’exposant de Lyapu-nov” pour deux modèles en milieu aléatoire : la marche aléatoire en potentiel aléatoire, le mouvement brownien en potentiel poissonnien.Dans la première partie de la thèse (chapitre II), on étudie une marche aléatoire dans un potentiel aléatoire donné par une famille de variables aléa¬toires i.i.d. non-négatives. La continuité des exposants de Lyapunov par rap¬port à la loi du potentiel est démontrée dans le cas transient, c’est-à-dire en dimension d ≥ 3 ou en dimension 2 pour un potentiel borné inférieurement. On poursuit avec l’étude des exposants critiques : l’exposant de volume ξ et l’exposant de fluctuation X. On obtient l’une des inégalités suggérée par la conjecture de KPZ sous une condition de courbure de la forme asymptotique. Les exposants de Lyapunov jouent un rôle important dans cette étude.La deuxième partie de la thèse (chapitre III) est surtout consacrée à l’étude du brownien dans un potentiel aléatoire de longue portée. On débute cependant par un potentiel classique à portée finie. Sznitman (1987-1998) a étudié plusieurs aspects de ce modèle. Un premier résultat de cette partie est la continuité des exposants de Lyapunov par rapport au paramètre du pro¬cessus de Poisson. On étudie ensuite le modèle proposé par Lacoin (2012) qui est un modèle avec un potentiel à longue portée. Il a obtenu des estimations des exposants critiques sensiblement différentes de celles de Wüthrich (1998) pour le modèle de Sznitman. Dans cette thèse, on poursuit l’étude du modèle de Lacoin. On montre l’existence des exposants de Lyapunov, le théorème de la forme limite et une estimation de grandes déviations. / In this thesis, we are interested in Lyapunov exponent for two models in random media : random walk in random potential, Brownian motion in Poisson potential.In the first part (chapter II), we study a random walk in a random potential given by a family of i.i.d random non-negative variables. The continuity of Lyapunov exponents with respect to the law of potential is shown in the case transient, that is, in the dimension d ≥ 3 or in the dimension d = 2 for a lower bounded potential. Next, we consider the critical exponents : the exponent of volume ξ and the exponent of fluctuation X. We give an inequality suggested by the KPZ conjecture under a condition of asymptotic form. Lyapunov exponents play an important role in this work.The second part (chapter III) is mainly devoted to the study Brownian motion in a long-range random potential. However, we begin with a classical finite-range potential. Sznitman (1987-1998) investigated several aspects of this model. The first result of this part is the continuity of the Lyapunov exponents with respect to the parameter of the Poisson process. Then, we study the model proposed by Lacoin (2012) which is a long-range potential model. He obtained some estimations of critical exponents that are significantly different from those of Wüthrich (1998) for the model of Sznitman.In this thesis, we pursue the study of Lacoin model. We show the existence of Lyapunov exponents, the shape limit theorem and an estimation of large deviations