The debate over the origin of the ultrafast demagnetization has been intensively active for the past 16 years. Several microscopic mechanisms have been proposed but none has managed so far to provide direct and incontrovertible evidences of their validity. In this context I have proposed an approach based on spin dependent electron superdiffusion as the driver of the ultrafast demagnetization. Excited electrons and holes in the ferromagnetic metal start diffusing after the absorption of the laser photons. Being the material ferromagnetic, the majority and minority spin channels occupy very different bands. It is then not surprising that transport properties are strongly spin dependent. In most of the ferromagnetic metals, majority spin excited electrons have better transport properties than minority ones. The effect is that majority carriers are more efficient in leaving the area irradiated by the laser, triggering a net spin transport. Recent experimental findings are revolutionising the field by being incompatible with previously proposed models and showing uncontrovertibly the sign of spin superdiffusion. We have shown that spin diffusing away from a layer undergoing ultrafast demagnetization can be used to create an ultrafast increase of magnetization in a neighboring magnetic layer. We have also shown that optical excitation is not a prerequisite for the ultrafast demagnetization and that excited electrons superdiffusing from a non-magnetic substrate can trigger the demagnetization. Finally we have shown that it is possible to control the time shape of the spin currents created and developed a technique to detect directly spin currents in a contact-less way.  The impact of these new discoveries goes beyond the solution of the mystery of ultrafast demagnetization. It shows how spin information can be, not only manipulated, as shown 16 years ago, but most importantly transferred at unprecedented speeds. This new discovery lays the basis for a full femtosecond spintronics.

The phenomenon of dynamically induced anomalous diffusion is both the classical and quantum kicked rotor is investigated in this dissertation. We discuss the capability of the quantum mechanical version of the system to reproduce for extended periods the corresponding classical chaotic behavior.

Considere um meio desordenado formado por $N$ pontos cujas coordenadas são geradas aleatoriamente com probabilidade uniforme ao longo das arestas unitárias de um hipercubo de $d$ dimensões. Um caminhante, partindo de um ponto qualquer desse meio, se desloca seguindo a regra determinista de dirigir-se sempre ao ponto mais próximo que não tenha sido visitado nos últimos $\\mu$ passos. Esta dinâmica de movimentação, denominada caminhada determinista do turista, leva a trajetórias formadas por uma parte inicial transiente de $t$ pontos, e uma parte final cíclica de $p$ pontos. A exploração do meio se limita aos $t+p$ pontos percorridos na trajetória. O sucesso da exploração depende do valor da memória $\\mu$ do viajante. Para valores pequenos de $\\mu$ a exploração é altamente localizada e o sistema não é satisfatoriamente explorado. Já para $\\mu$ da ordem de $N$, aparecem ciclos longos, permitindo a exploração global do meio. O objetivo deste estudo é determinar o valor de memória $\\mu_1$ para o qual ocorre uma transição abrupta no comportamento exploratório do turista em meios unidimensionais. Procuramos também entender a distribuição da posição final do turista após atingir um estado estacionário que é atingido quando o turista fica aprisionado nos ciclos. Os resultados obtidos por simulações numéricas e por um tratamento analítico mostram que $\\mu_1 = \\log_2 N$. O estudo também mostrou a existência de uma região de transição com largura $\\varepsilon = e/ \\ln 2$ constante, caracterizando uma transição aguda de fase no comportamento exploratório do turista em uma dimensão. A análise do estado estacionário da caminhada em função da memória mostrou que, para $\\mu$ distante de $\\mu_1$, a dinâmica de exploração ocorre como um processo difusivo tradicional (distribuição gaussiana). Já para $\\mu$ próximo de $\\mu_1$ (região de transição), essa dinâmica segue um processo superdifusivo não-linear, caracterizado por distribuições $q$-gaussianas e distribuições $\\alpha$-estáveis de Lévy. Neste processo, o parâmetro $q$ funciona como parâmetro de ordem da transição. / Consider a disordered medium formed by $N$ point whose coordinates are randomly generated with uniform probability along the unitary edges of a $d$-dimensional hypercube. A walker, starting to walk from any point of that medium, moves following the deterministic rule of always going to the nearest point that has not been visited in the last $\\mu$ steps. This dynamic of moving, called deterministic tourist walk, leads to trajectories formed by a initial transient part of $t$ points and a final cycle of $p$ points. The exploration of the medium is limited to the $t+p$ points covered. The success of the exploration depends on the traveler\'s memory value $\\mu$. For small values of $\\mu$, the exploration is highly localized and the whole system remains unexplored. For values of $\\mu$ of the order of $N$, however, long cycles appear, allowing global exploration of the medium. The objective of this study is to determine the memory value $\\mu_1$ for which a sharp transition in the exploratory behavior of the tourist in one-dimensional media occurs. We also want to understand the distribution of the final position of the tourist after reaches a steady state in exploring the medium. That steady state is reached when the tourist is trapped in cycles. The results achieved by numerical simulations and analytical treatment has shown that $\\mu_1 = \\log_2 N$. The study has also shown the existence of a transition region, with a constant width of $\\varepsilon = e/ \\ln 2$, characterizing a phase transition in the exploratory behavior of the tourist in one dimension. The analysis of the walk steady state as a function of the memory has shown that for $\\mu$ far from $\\mu_1$, the exploratory dynamic follows a traditional diffusion process (with gaussian distribution). In the other hand, for $\\mu$ near $\\mu_1$ (transition region), the dynamic follows a non-linear superdiffusion process, characterized by $q$-gaussian distributions and Lèvy $\\alpha$-stable distributions. In this process, the parameter $q$ plays the role of a transition order parameter.

Le travail réalisé dans cette thèse porte sur l’étude du mouvement Brownien d’une suspension colloïdale sous champ de force optique faible et l’étude fondamentale des effets convectifs et de diffusion anormale. Nous avons construit un microscope à fond noir afin de suivre les particules et de reconstruire leurs trajectoires avec une résolution spatiale de 20 nm et une résolution temporelle de 8 ms. Ces trajectoires sont analysées statistiquement afin d’en extraire la contribution balistique induite par la force de pression de radiation appliquée par le laser d’illumination. En plus de l’effet mécanique du laser sur les particules, le fluide absorbe les radiations ce qui le chauffe et crée ainsi une différence de température entre la partie illuminée et la partie non illuminée de l’échantillon.Nous validons aussi les hypothèses de stationnarité et d’érgodicité qui sont fondamentales pour notre stratégie de mesure de force faible. L’analyse statistique fine de notre système nous permet de mettre en évidence et de caractériser des effets de diffusion anormale brownienne. Nos expériences révèlent en effet la présence de trajectoires anormales dont l’origine se comprend comme un effet d’interaction entre la particule suivie et le reste de l’ensemble colloïdal. / The work presented in this thesis deals with the study of the Brownian motion of a colloidal suspension under an external weak optical force, the study of convective effects and anomalous diffusion. We have built a dark field microscope in order to track the particles and reconstruct the Brownian trajectories with a spatial resolution of 20 nm and a temporal resolution of 8 ms.Statistical analysis of the trajectories has allowed us to extract the ballistic contribution induced by the radiation pressure force exerted by irradiating a laser on the particles. In addition to the mechanical effect of the laser on the particles, the fluid absorbs the radiation. Consequently, the temperature of the fluid rises and results in a thermal difference between the illuminated and the non-illuminated areas of the sample. In order to validate our weak force measurement, we have investigated two fundamental hypotheses in statistical physics: ergodicity and stationary aspect. A closer statistical analysis enables us to demonstrate and characterize the effect of anomalous Brownian diffusion. Our experiments have revealed the existence of anomalous trajectories, which can be understood as an effect of the interactions between the particles.

Doctor of Philosophy / Department of Chemistry / Daniel A. Higgins / This dissertation describes single-molecule tracking (SMT) studies for the quantitative characterization of one-dimensional (1D) solvent-filled surfactant-templated mesoporous silica (STMS) materials and other nanostructured materials, such as double-stranded DNA. SMT permits the simultaneous and quantitative assessment of the nanoscale and microscale morphologies and mass-transport properties of the materials with nanometer-scale spatial resolution. The efficiency and selectivity of catalytic reactions and chemical separations occurring in liquid-filled mesoporous materials are governed by the translational and orientational mobilities and surface interactions of the incorporated reagents and analytes. Polarization dependent SMT results demonstrate that the dye molecules used as probes of materials nanostructure are tightly confined within the one-dimensional (1D) pores of surfactant-templated mesoporous silica films. Spectroscopic single molecule tracking (sSMT) data reveal that the hydrophobic probe dyes are confined within nonpolar regions of the nanomaterials For this dissertation, surfactant templated mesoporous silica films were prepared by the spin coating of acid catalyzed tetramethoxysilane (TMOS)-based silica sols on glass substrates in the presence of Cetyltrimethylammonium bromide (CTAB). Cylindrical CTAB micelles formed during evaporation of the solvent acted as a structure directing template, forming nanometer-sized one-dimensional pores within the silica films. SMT experiments were performed using a wide-field fluorescence microscope that was sufficiently sensitive to allow detection of the fluorescence from individual dye molecules. A series of perylene diimide (PDI) dyes was employed for basic structural characterization of the silica materials. Single molecule fluorescence was recorded in the form of fluorescence videos. These videos revealed the presence of immobile dye molecules, along with those diffusing in one and two dimensions (1D and 2D). The 1D diffusing molecules provided basic evidence for the confinement mass transport of the dye molecules within the silica mesopores. Spectroscopic single molecule tracking (sSMT) studies served as an extension of basic SMT experiments and were employed to determine the location of the molecules. The polarity sensitive dye Nile Red (NR) was employed in these studies. It exhibits 1D diffusion, consistent with its confinement to the cylindrical pores, as was also the case for the PDI dyes. The sSMT data revealed that the majority of NR molecules were found in nonpolar environments having polarities similar to that of n-hexane. Single molecule emission polarization (SMEP) measurements were employed to explore the orientational confinement of the dyes. The results of these experiments demonstrated that the PDI and NR molecules diffuse with their long axes aligned parallel to the long axis of the pores. All of the dyes employed were found to be orientationally confined to ∼1 nm diameter pathways within the pores. The diffusion coefficient for the dyes was also shown to be ∼10^3 -fold smaller than in bulk solution. The results of the NR studies demonstrate that the dye molecules were confined to the hydrophobic cores of the micelles, and provide support for the conclusion that the PDI dyes are similarly confined. These studies afford an enhanced understanding of how nanostructuring of the pore-filling medium in solvent- and surfactant-filled mesoporous materials governs the mass transport and surface interactions of incorporated reagents and analytes. The dependence of molecular confinement on dye charge and structure was also explored in this dissertation. The confined translational and orientational motions of a series of four different PDI dyes diffusing along one dimension (1D) within individual cylindrical silica mesopores were investigated in these studies. Specifically, the motions of cationic and anionic PDI dyes were compared to those of two uncharged PDIs having different alkane tail lengths. All four dyes exhibited populations that were immobile, along with separate populations that diffused in either 1D or 2D. The anionic and cationic PDI dyes exhibited the largest and smallest populations, respectively, of immobile molecules, suggesting that electrostatic interactions between the charged dyes and the cationic surfactant head groups play a significant role in limiting molecular motion. The cationic and anionic PDI dyes also exhibit the largest populations of 2D diffusing molecules, suggesting they may more readily pass between the cylindrical micelles and through the silica pore walls. All four dyes also emit strongly polarized fluorescence as they move in 1D, indicating they are orientationally confined within the nanochannels. Nile Red dye was used to determine the dielectric constant, ε, of nonpolar microenvironments in double-stranded DNA (ds-DNA) single molecules both in aqueous buffer solution and when adsorbed on amine-modified chemical gradient surfaces. The value of ε within the DNA decreased with increasing buffer concentration. Values of ε ∼ 6.75 and ∼3.00 were obtained in 0.1 mM phosphate buffered saline (PBS) and in 10 mM PBS, respectively. Similar effects were observed upon adsorption to chemically graded amine-modified silica surfaces. Under 1 mM buffer, ε was measured to be ∼2.84 and ∼1.90 at the low amine (high silica), and high amine (low silica) ends of the gradient, respectively. An increase in the buffer concentration again led to a decrease in ε, but only at the low amine end. It is concluded that high buffer concentrations and binding to an amine surface cause condensation of the ds-DNA, forming less polar microenvironments within its structure. These results provide important knowledge of the factors governing the polarity of DNA microenvironments to which intercalators bind.

Métodos de suavização através de processos de difusão é frequentemente utilizado como etapa prévia em diferentes procedimentos em imagens. Apesar da difusão anômala ser um processo físico conhecido, ainda não é aplicada à suavização de imagens como a difusão clássica. Esta dissertação propõe e relata a implementação e avaliação de filtros de difusão anômala, tanto isotrópico quanto anisotrópico, como um método de melhoramento em imagens ponderadas em difusão (DWI) e imagens de tensor de difusão (DTI) dentro do imageamento por ressonãncia magnética (MRI). Aqui propõe-se generalizar a difusão anisotrópica e isotrópica com o conceito de difusão anômala em processamento de imagens. Como metodologia implementou-se computacionalmente as equações de difusão bidimensional e aplicou às imagens MRI para avaliar o seu potencial como filtro de melhoramento. Foram utilizadas imagens de ressonância magnética de aquisição DTI em voluntários saudáveis. Os resultados obtidos neste estudo foram a verificação que métodos baseados em difusão anômala melhoram a qualidade em processamento das imagens DTI e DWI quando observadas medidas de qualidade como a relação sinal ruído (SNR) e índice de similaridade estrutural (SSIM), e assim determinou-se parâmetros ótimos para as diferentes imagens e situações que foram avaliadas em função dos seus parâmetros de controle, em especial o parâmetro anômalo, chamado de q. Os resultados apresentados aqui permitem prever não apenas uma melhora na qualidade das imagens DTI e DWI resultantes do processamento proposto, como também possível redução de repetições na sequência de aquisição de MRI para um SNR predeterminado. / Smoothing methods through diffusion processes is often used as a preliminary step in different procedures in images. Although the anomalous diffusion is a known physical process, it is not applied to image smoothing as the classical diffusion. This paper proposes and describes implementation and evaluation of anomalous diffusion filters, both isotropic and anisotropic, as a method of improving on diffusion-weighted images (DWI) and diffusion tensor images (DTI) within the magnetic resonance imaging (MRI). Hereby is proposed to generalize the isotropic and anisotropic diffusion with the concept of anomalous diffusion in image processing. The methodology is implemented computationally as bidimensional diffusion equations and applied to MRI images to evaluate its potential as a filter for quality improvement. We used DTI and DWI imaging to acquire from healthy volunteers as image set. The results of this study verified that methods based on anomalous diffusion improved DWI and DTI image processing when observed quality measures such as signal to noise ratio (SNR) and structural similarity index (SSIM), and determined filter optimal parameters for different images and situations evaluated in terms of their control parameters, particularly the anomalous parameter, called q. The results presented here can predict not only an improvement in the quality of DWI and DTI images resulting from the proposed method, and additionally the possible reduction of repetitions following acquisition of MRI for a predetermined SNR.

The purpose of this research is to investigate properties of diffusion processes in porous media. Porous media are modelled by random Sierpinski carpets, each carpet is constructed by mixing two different generators with the same linear size. Diffusion on porous media is studied by performing random walks on random Sierpinski carpets and is characterized by the random walk dimension $d_w$. In the first part of this work we study $d_w$ as a function of the ratio of constituents in a mixture. The simulation results show that the resulting $d_w$ can be the same as, higher or lower than $d_w$ of carpets made by a single constituent generator. In the second part, we discuss the influence of static external fields on the behavior of diffusion. The biased random walk is used to model these phenomena and we report on many simulations with different field strengths and field directions. The results show that one structural feature of Sierpinski carpets called traps can have a strong influence on the observed diffusion properties. In the third part, we investigate the effect of diffusion under the influence of external fields which change direction back and forth after a certain duration. The results show a strong dependence on the period of oscillation, the field strength and structural properties of the carpet.

Die Diffusion durch Polyelektrolytschichten ist bei vielen biotechnologisch-pharmazeutischen Anwendungen im Nanometerbereich von Bedeutung. Bei Experimenten wurde gefunden, dass bei der Diffusion eines Quenchers in mit Fluoreszenzfarbstoff markierten Polyelektrolytmultischichten die Kinetik des Diffusionsprozesses Charakteristika einer anormalen Diffusion aufweist. In dieser Arbeit wird qualitativ und quantitativ gezeigt, dass die Diffusion des Quenchers mit Subdiffusion beschrieben werden kann. Der gemessene Diffusionsprozess kann durch eine Superposition von Markov‘schen Diffusionsprozessen dargestellt werden. Das wird mit einer Monte-Carlo-Simulation nachgewiesen, die auf der analytischen Lösung des vorliegenden Reaktions-Diffusionsgleichungssystems basiert. Die experimentellen Daten werden im Zusammenhang mit der strukturellen Basis der parallel ablaufenden Diffusionsprozesse diskutiert.

The purpose of this research is to investigate properties of diffusion processes in porous media. Porous media are modelled by random Sierpinski carpets, each carpet is constructed by mixing two different generators with the same linear size. Diffusion on porous media is studied by performing random walks on random Sierpinski carpets and is characterized by the random walk dimension $d_w$. In the first part of this work we study $d_w$ as a function of the ratio of constituents in a mixture. The simulation results show that the resulting $d_w$ can be the same as, higher or lower than $d_w$ of carpets made by a single constituent generator. In the second part, we discuss the influence of static external fields on the behavior of diffusion. The biased random walk is used to model these phenomena and we report on many simulations with different field strengths and field directions. The results show that one structural feature of Sierpinski carpets called traps can have a strong influence on the observed diffusion properties. In the third part, we investigate the effect of diffusion under the influence of external fields which change direction back and forth after a certain duration. The results show a strong dependence on the period of oscillation, the field strength and structural properties of the carpet.

Métodos de suavização através de processos de difusão é frequentemente utilizado como etapa prévia em diferentes procedimentos em imagens. Apesar da difusão anômala ser um processo físico conhecido, ainda não é aplicada à suavização de imagens como a difusão clássica. Esta dissertação propõe e relata a implementação e avaliação de filtros de difusão anômala, tanto isotrópico quanto anisotrópico, como um método de melhoramento em imagens ponderadas em difusão (DWI) e imagens de tensor de difusão (DTI) dentro do imageamento por ressonãncia magnética (MRI). Aqui propõe-se generalizar a difusão anisotrópica e isotrópica com o conceito de difusão anômala em processamento de imagens. Como metodologia implementou-se computacionalmente as equações de difusão bidimensional e aplicou às imagens MRI para avaliar o seu potencial como filtro de melhoramento. Foram utilizadas imagens de ressonância magnética de aquisição DTI em voluntários saudáveis. Os resultados obtidos neste estudo foram a verificação que métodos baseados em difusão anômala melhoram a qualidade em processamento das imagens DTI e DWI quando observadas medidas de qualidade como a relação sinal ruído (SNR) e índice de similaridade estrutural (SSIM), e assim determinou-se parâmetros ótimos para as diferentes imagens e situações que foram avaliadas em função dos seus parâmetros de controle, em especial o parâmetro anômalo, chamado de q. Os resultados apresentados aqui permitem prever não apenas uma melhora na qualidade das imagens DTI e DWI resultantes do processamento proposto, como também possível redução de repetições na sequência de aquisição de MRI para um SNR predeterminado. / Smoothing methods through diffusion processes is often used as a preliminary step in different procedures in images. Although the anomalous diffusion is a known physical process, it is not applied to image smoothing as the classical diffusion. This paper proposes and describes implementation and evaluation of anomalous diffusion filters, both isotropic and anisotropic, as a method of improving on diffusion-weighted images (DWI) and diffusion tensor images (DTI) within the magnetic resonance imaging (MRI). Hereby is proposed to generalize the isotropic and anisotropic diffusion with the concept of anomalous diffusion in image processing. The methodology is implemented computationally as bidimensional diffusion equations and applied to MRI images to evaluate its potential as a filter for quality improvement. We used DTI and DWI imaging to acquire from healthy volunteers as image set. The results of this study verified that methods based on anomalous diffusion improved DWI and DTI image processing when observed quality measures such as signal to noise ratio (SNR) and structural similarity index (SSIM), and determined filter optimal parameters for different images and situations evaluated in terms of their control parameters, particularly the anomalous parameter, called q. The results presented here can predict not only an improvement in the quality of DWI and DTI images resulting from the proposed method, and additionally the possible reduction of repetitions following acquisition of MRI for a predetermined SNR.