Marek Spěšný - abstract This thesis has the nature of a survey report of a specific area. The task was to localize with the help of microgravimetry anomalous places in an area of a by-pass road construction, where subsurface inhomogeneities may possibly exist due to subsurface and surface historical mining of ceramic clay. The gravimetrical measurements were carried out with a relative gravimeter Scintrex model CG-5 AUTOGRAV. After the first stage of the gravimetrical measurements and following two weeks of recultivation works our assignment was to verify the success of the first measurements by the means of repeated microgravimetric control measurements. The results from both stages of measurement were processed into a 4D gravimetrical form. The results of the 4D gravimetry displayed that contrary to the expectations, the measured gravity of most of the area of interest decreased as much as by 30 ?Gal. We conclude that this is due to the drainage of injected material beyond the recultivated mining area, which washed and carried away a portion of the existing material. Our proposition was also supported by results of repeated leveling, which discovered subsidence of the road at times by up to 3 centimeters.

Characterization of the dynamic behavior of defect-bearing ablator materials subjected to extreme conditions is essential in advancing fusion energy as an reliable and abundant energy source. By understanding how materials evolve spatially and temporally we can minimize hydrodynamic instabilities, which are major contributing factors to energy yield degradation in inertial confinement fusion (ICF) experiments. In this thesis we demonstrate the capabilities of an ultrafast x-ray imaging (UXI) detector, the Icarus V2, where we capture multiple frames of single void-bearing sample compressed by a high-intensity laser shockwave. Using the Matter in Extreme Conditions (MEC) instrument at the Linac Coherent Light Source (LCLS), we conducted two experiments with the x-ray free electron laser (XFEL) multi-pulse mode, delivering four nanosecond-separated pulses to a sample impacted by a laser shockwave, obtaining multiframe images of a single sample in the holographic and direct imaging regime with the UXI detector. In contrast to the low temporal resolution provided by current cameras, the Icarus V2 can capture images with high temporal resolution, which can be used to determine the mechanisms that prevent thermonuclear ignition in ICF experiments. For images captured in the holographic regime at our XFEL energy of 8.23 keV, we realized that the shock front was obscured by strong phase-contrast effects. We recognized that by increasing the XFEL energy while in the holographic regime, more distinguishable features could be revealed behind and along the shock front. Alternatively, in the direct-imaging configuration we discovered that the evolution of microstructural features were directly recognizable in comparison to the holographic regime at lower XFEL energies. Overall, the images captured by the UXI in both regimes demonstrated our ability to obtain multiframe images of processes that occur over several nanoseconds for single samples, which has never been done before. Moreover, the capabilities of the UXI enable extraction of quantitative information over multiple frames, which can help with uncovering the underlying physics involved in high energy density (HED) physics experiments and other experiments involving non-repeatable ultrafast phenomena. Specifically, insight into the behavior of the void can be gained by performing phase retrieval on the images and obtaining the areal density of the materials during laser-shock ablation. Generally, the UXI improves data acquisition speed and operational efficiency, which extends this camera's functionality to experiments that occur at various time scales or experiments that require multiple images to be captured.

Cell migration and invasion is a key driving factor for providing essential cellular functions under physiological conditions or the malignant progression of tumors following downward the metastatic cascade. Although there has been plentiful of molecules identified to support the migration and invasion of cells, the mechanical aspects have not yet been explored in a combined and systematic manner. In addition, the cellular environment has been classically and frequently assumed to be homogeneous for reasons of simplicity. However, motility assays have led to various models for migration covering only some aspects and supporting factors that in some cases also include mechanical factors. Instead of specific models, in this review, a more or less holistic model for cell motility in 3D is envisioned covering all these different aspects with a special emphasis on the mechanical cues from a biophysical perspective. After introducing the mechanical aspects of cell migration and invasion and presenting the heterogeneity of extracellular matrices, the three distinct directions of cell motility focusing on the mechanical aspects are presented. These three different directions are as follows: firstly, the commonly used invasion tests using structural and structure-based mechanical environmental signals; secondly, the mechano-invasion assay, in which cells are studied by mechanical forces to migrate and invade; and thirdly, cell mechanics, including cytoskeletal and nuclear mechanics, to influence cell migration and invasion. Since the interaction between the cell and the microenvironment is bi-directional in these assays, these should be accounted in migration and invasion approaches focusing on the mechanical aspects. Beyond this, there is also the interaction between the cytoskeleton of the cell and its other compartments, such as the cell nucleus. In specific, a three-element approach is presented for addressing the effect of mechanics on cell migration and invasion by including the effect of the mechano-phenotype of the cytoskeleton, nucleus and the cell’s microenvironment into the analysis. In precise terms, the combination of these three research approaches including experimental techniques seems to be promising for revealing bi-directional impacts of mechanical alterations of the cellular microenvironment on cells and internal mechanical fluctuations or changes of cells on the surroundings. Finally, different approaches are discussed and thereby a model for the broad impact of mechanics on cell migration and invasion is evolved.

Magistro baigiamajame darbe tiriamos nevienalyčių plačiajuosčių periodinių sistemų užtvarinės savybės. Aptariamos periodinės sistemos ir jų charakteristikų skaičiavimo metodai. Nevienalyčių periodinių savybių tyrimui panaudoti du modeliai. Pradžioje nagrinėjamos periodinės ilgosios linijos savybės, vėliau taikomas spiralinės sistemos modelis. Modelių analizė atliekama klasikiniu, matriciniu ir daugialaidžių linijų metodais. Taikomas kompiuterinis modeliavimas. Sudarytos įėjimo varžos, perdavimo ir lėtinimo koeficientų, vėlinimo laikų bei pereinamosios charakteristikos skaičiavimo programos. Parodyta, kad linijos su periodiniais netolygumais įgyja užtvarinio filtro savybes, kurios ryškėja, didėjant sistemos nevienalytiškumui. / In order to reveal general properties of the structures, containing periodical inhomogeneities, the inhomogeneous electromagnetic line and the inhomogeneous helical retard structure are considered. The overview of periodical systems and methods of their analysis are presented. The structures, containing periodical inhomogeneities, are analyzed using classical, matrix and multiconductor line methods. The programs for calculation of line input impedance, transfer coefficient, delay coefficient and width of the stop-band are developed. The results show that the stop–band appears due to periodical inhomogeneities and the width of the stop-band and the attenuation in it depend on intensities of periodical inhomogeneities.

A hybrid FEM/FDM algorithm for particle migration of quasi-steady flow in concentrated suspension materials is proposed in this study. This hybrid FEM/FDM algorithm in which the planar variables, such as pressure field, are described in terms of finite element method, and gapwise variables of temperature, density concentration and time derivatives are expressed by finite difference method. The particle concentration inhomogeneities can be predicted, which is ignored by the existing injection molding simulation packages. Simulation results indicated that powder concentration variation could be significant in practical processing in PIM. / Singapore-MIT Alliance (SMA)

Cette thèse est principalement consacrée à l'étude des inhomogénéités de taille nanométrique dans les systèmes magnétiques désordonnés ou dilués. La présence d'inhomogénéités, souvent mise en évidence dans de nombreux matériaux, donne lieu à des propriétés physiques intéressantes et inattendues. La possibilité de ferromagnétisme à l'ambiante dans certains matéraux a généré un grand enthousiasme en vue d'application dans la spintronique. Cependant, d'un point de vue fondamental la physique de ces systèmes reste peu explorée et mal comprise. Dans ce manuscrit, on se propose de fournir une étude théorique complète et détaillée des effets des inhomogenéités de tailles nanométriques sur les propriétés magnétiques dans les systèmes dilués. Tout d'abord, on montre que l'approche RPA locale autocohérente est l'outil le plus adapté et fiable pour un traitement approprié du désordre et de la percolation. Nous avons implémenté cet outil et étudié dans un premier temps, les propriétés magnétiques dynamiques d'un modèle Heisenberg dilué (couplages premiers voisins) sur un reseau cubique simple. Nous avons reproduit précisémment la disparition de l'ordre à longue portée au seuil de percolation et comparé ce travail à des études précédentes. Dans le cadre d'un Hamiltonien minimal (modèle $V$-$J$) nous avons ensuite étudié en détails les propriétés magnétiques de (Ga,Mn)As (température critique, excitations magnétiques, stiffness,..). Nous avons obtenu de très bon accords avec les calculs textit{ab initio} et les résulats expérimentaux. Finalement, nous avons étudié les effets des inhomogénéités dans les sytèmes dilués. Nous avons montré, qu'inclure des inhomogenéités pourrait s'averer être une voie très efficace et prometteuse pour dépasser l'ambiante dans de nombreux matériaux. Nous avons pu obtenir une augmentation colossale de la température critique dans certains cas comparée à celle des systèmes dilués homogènes. Nous avons atteint une augmentation de 1600% dans certains cas. Nous avons également analysé les effets des inhomogénéités sur les courbes d'aimantations, elles sont inhabituelles et peu conventionelles dans ces systèmes. Les spectres d'excitations magnétiques sont très complexes, avec des structures très riches, et présentent de nombreux modes discrets à haute energie. De plus, nos calculs ont montré que la ``spin-stiffness" est fortement supprimé par l'introduction d'inhomogénéités. Il reste encore de nombreuses voies à explorer, ce travail devrait servir de base à de futures études théoriques et expérimentales des systèmes inhomogènes. / This thesis is mainly devoted to the study of nanoscale inhomogeneities in diluted and disordered magnetic systems. The presence of inhomogeneities was detected experimentally in several disordered systems which in turn gave rise to various interesting and unexpected properties. In particular, the possibility of room-temperature ferromagnetism generated a huge thrust in these inhomogeneous materials for potential spintronics applications. However, a proper theoretical understanding of the underlying physics was a longstanding debate. In this manuscript we provide a detailed theoretical account of the effects of these nanoscale inhomogeneities on the magnetic properties of diluted systems. First we show the importance of disorder effects in these systems, and the need to treat them in an appropriate manner. The self-consistent local RPA (SC-LRPA) theory, based on finite temperature Green's function, is found to be the most reliable and accurate tool for this. We have successfully implemented the SC-LRPA to study the dynamical magnetic properties of the 3D nearest-neighbor diluted Heisenberg model. The percolation threshold is found to be reproduced exactly in comparison with previous existing studies. Following this, we discuss the essential role of a minimal model approach to study diluted magnetic systems. The one-band $V$-$J$ model, has been used to calculate the Curie temperature and the spin excitation spectrum in (Ga,Mn)As. An excellent agreement is obtained with first principles based calculations as well as experiments. Finally we propose an innovative path to room-temperature ferromagnetism in these materials, by nanoscale cluster inclusion. We find a colossal increase in $T_C$ of up to 1600% compared to the homogeneous case in certain cases. Also the spontaneous magnetization is found to exhibit anomalous non-mean-field like behavior in the presence of inhomogeneities. In addition we observe a complex nature of the magnon excitation spectrum with prominent features appearing at high energies, which is drastically different from the homogeneous case. Our study interestingly reveals a strong suppression of the spin-stiffness in these inhomogeneous systems. The results indicate toward the strong complexities associated with the interplay/competition between several typical length scales. We believe this work would strongly motivate detailed experimental as well as theoretical studies in this direction in the near future.

Des techniques statistiques de détection d'objet ponctuel dans le ciel ou résolu dans la mer dans des images infrarouges de veille panoramique sont développées. Ces techniques sont adaptées aux inhomogénéités présentes dans ce type d'image. Elles ne sont fondées que sur l'analyse de l'information spatiale et ont pour objectif de maîtriser le taux de fausse alarme sur chaque image. Pour les zones de ciel, une technique conjointe de segmentation et détection adaptée aux variations spatiales de la luminosité moyenne est mise en œuvre et l'amélioration des performances auxquelles elle conduit est analysée. Pour les zones de mer, un détecteur de bord à taux de fausse alarme constant en présence d'inhomogénéités et de corrélations spatiales des niveaux de gris est développé et caractérisé. Dans chaque cas, la prise en compte des inhomogénéités dans les algorithmes statistiques s'avère essentielle pour maîtriser le taux de fausse alarme et améliorer les performances de détection. / Statistical detection techniques of point target in the sky or resolved target in the sea in infrared surveillance system images are developed. These techniques are adapted to inhomogeneities present in this kind of images. They are based on the spatial information analysis and allow the control of the false alarm rate in each image.For sky areas, a joint segmentation detection technique adapted to spatial variations of the mean luminosity is developed and its performance improvement is analyzed. For sea areas, an edge detector with constant false alarm rate when inhomogeneities and grey level spatial correlations are present is developed and characterized. In each case, taking into account the inhomogeneities in these statistical algorithms is essential to control the false alarm rate and to improve the detection performance.

Die Struktur von Netzwerken wird durch die Wahl der Netzwerkaufbaureaktion, der Ausgangsmoleküle und der Reaktionsbedingungen bestimmt. Es ist schwierig, wenn nicht gar unmöglich, geeignete Reaktionsparameter zu finden, die zum Aufbau homogener Netzwerkstrukturen führen. Die unterschiedliche Reaktivität der Ausgangsmoleküle resultiert in Unregelmäßigkeiten innerhalb der Netzwerkstruktur, z. B. durch inhomogene Verteilung der Vernetzungspunkte. Als Maß für die Heterogenität eines Netzwerkes kann die Streuintensität herangezogen werden. Diese besteht bei Netzwerken aus einem dynamischen und einem statischen Teil. In stark heterogenen Netzwerken überwiegt die statische Komponente der Streuintensität, die dynamischen Beiträge sind gering. Bei homogeneren Strukturen überwiegt die dynamische Komponente. Deshalb kann der Beitrag dynamischer Konzentrationsfluktuationen zur Gesamtstreuintensität als Maß für den Grad der Heterogenität dienen. Die meisten Netzwerke werden durch radikalische Copolymerisation von Monomeren und Vernetzern synthetisiert. Aufgrund der unterschiedlichen Reaktivitäten sind die entstehenden Strukturen stark heterogen. Die Verwendung anderer Mechanismen zum Netzwerkaufbau bietet eine Möglichkeit, homogenere Netzwerke zu erhalten. Vor allem die Vernetzung polymerer Ketten, ausgehend von einer homogenen halbverdünnten Lösung, ist eine strategisch interessante Variante. Ziel dieser Arbeit war die systematische Untersuchung des Einflusses der chemischen Zusammensetzung, der Netzwerkaufbaureaktion, der Polymerkonzentration und der Netzwerkdichte auf die thermodynamischen Eigenschaften (kooperative Diffusionskoeffizienten Dcoop) und die Netzwerkstruktur (Heterogenität) unterschiedlicher Netzwerksysteme. Am Beispiel von Polyacrylsäure (PAS) Netzwerken (radikalische Vernetzung) und Poly(styrol-co-maleinsäureanhydrid) (PScoMSA) Netzwerken (Vernetzung polymerer Lösungen) wurden zwei Netzwerksysteme untersucht, die sich hinsichtlich ihrer Aufbaureaktion unterscheiden. Mittels klassischer Netzwerkanalyse können diese Systeme sehr gut charakterisiert werden. Die kooperativen Diffusionskoeffizienten sowie die Netzwerkheterogenität wurden durch dynamische Lichtstreuung bestimmt.

A in uência do caráter inomogêneo da região-fonte na ampli cação da Radiação Quilom étrica das Auroras é investigada. Inicialmente é feita uma revisão de trabalhos relevantes publicados a respeito do mesmo tema geral, tanto os que concernem aos dados observacionais como os que concernem aos modelos teóricos e simulações numéricas. Esta revisão é precedida pelo estabelecimento de conceitos e de nições pertinentes ao tema. São consideradas duas abordagens distintas na determinação da ampli cação da radiação na região-fonte. A primeira considera o plasma localmente homogêneo, enquanto a segunda toma em conta, explicitamente, a contribuição dos gradientes dos parâmetros do plasma. A ampli cação da radiação é determinada pela avaliação do tensor dielétrico do plasma e pela evolução da radia ção através do estudo de traçado de raios. Os parâmetros do plasma são obtidos através de uma formulação autoconsistente que toma em conta uma queda de potencial elétrico ao longo das linhas de campo geomagnético. Utiliza-se um modelo de lâmina auroral em que o campo magnético ambiente é considerado localmente homogêneo. O modelo teórico subjacente adotado é o do maser de elétron-cíclotron. O principal resultado obtido revela uma diminuição na ampli cação nal por um fator em torno de três, quando os gradientes dos parâmetros do plasma são considerados explicitamente. Este resultado pode ter implicações na capacidade do maser de elétron-cíclotron em explicar os níveis de radiação mais elevados observados. / The in uence from source region inhomogeneous character on ampli cation of Auroral Kilometric Radiation is investigated. Firstly, a review over relevant works published about the same general theme is made, concerning about observational data as well theoretical models and numerical simulations. This review is preceded by the establishment of de nitions and concepts related to the theme. Two distinct approaches are considered in determining the ampli cation of radiation across the source region. First approach takes the plasma as locally homogeneous, while second approach account, explicitly, for gradients on plasma parameters. The ampli cation is obtained through evaluation of the dielectric tensor and the evolution of radiation through ray tracing. Plasma parameters are obtained using a self-consistent formulation which account for an electric potential drop along geomagnetic eld lines. An auroral slab model is used where the ambient magnetic eld is taken as locally homogeneous. The subjacent theoretical model adopted is the electron-cyclotron maser. The main result obtained reveals a reduction on nal ampli cation by a factor about three, when plasma parameters gradients are explicitly accounted. This nding may have implications on capability of electron-cyclotron maser for explanation the most intense levels of radiation observed.

There is a growing consensus that life-threatening cardiac arrhythmias like ventricular tachycardia (VT) or ventricular fibrillation (VF) arise because of the formation of spiral waves of electrical activation in cardiac tissue; unbroken spiral waves are associated with VT and broken ones with VF. Several experimental studies have shown that inhomogeneities in cardiac tissue can have dramatic effects on such spiral waves. In this thesis we try to understand these experimental results by carrying out detailed and systematic studies of the interaction of spiral waves with different types of inhomogeneities in mathematical models for cardiac tissue. In Chapter 1 we begin with a general introduction to cardiac arrhythmias, the cardiac conduction system, and the connection between electrical activation waves in cardiac tissue and cardiac arrhythmias. As we have noted above, VT and VF are believed to be associated with spiral waves of electrical activation on cardiac tissue; such spiral waves form because cardiac tissue is an excitable medium. Thus we give an overview of excitable media, in which sub-threshold perturbations decay but super-threshold perturbations lead to an action potential that consists of a rapid stage of depolarization of cardiac cells followed by a slow phase of repolarization. During this repolarization phase the cells are refractory. We then give an overview of earlier studies of the effects of inhomogeneities in cardiac tissue; and we end with a brief description of the principal problems we study here. Chapter 2 describes the models we use in our work. We start with a general introduction to the cable equation and then discuss the Hodgkin-Huxley-formalism for the transport of ions across a cell membrane through voltage-gated ion channels. We then describe in detail the three models that we use for cardiac tissue, which are, in order of increasing complexity, the Panfilov model, the Luo Rudy Phase I (LRI) model, and the reduced Priebe Beuckelmann (RPB)model. We then give the numerical schemes we use for solving these model equations and the initial conditions that lead to the formation of spiral waves. For all these models we give representative results from our simulations and compare the states with spiral turbulence. In Chapter 3 we investigate the effects of conduction inhomogeneities (obstacles) in the three models introduced in Chapter 2. We outline first the experimental results that have provided the motivation for our study. We then discuss how we introduce obstacles in our simulations of the Panffilov, LRI, and RPB models for cardiac tissue. Next we present the results of our numerical studies of the effects, on spiral-wave dynamics, of the sizes, shapes, and positions of the obstacles. Our Principal result is that spiral-wave dynamics in these models depends sensitively on the position of the obstacle. We find, in particular, that, merely by changing the position of a conduction inhomogeneity, we may convert spiral turbulence (the analogue in our models of VF) to a single rotating spiral (the analogue of VT) anchored to the obstacle or vice versa; even more exciting is the possibility that, at the boundary between these two types of behaviour, we find a quiescent state Q with no spiral waves. Thus our study obtains all the possible qualitative behaviours found in experiments, namely, (1) VF might persist even in the presence of an obstacle, (2) it might be suppressed partially and become VT, or (3) it might be eliminated completely. In Chapter 4 we extend our work on conduction inhomogeneities (Chapter 3) to ionic inhomogeneities. Unlike conduction inhomogeneities, ionic inhomogeneities allow the conduction of activation waves. We find, nevertheless, that they too can lead to the anchoring of spiral waves or even the complete elimination of spiral-wave turbulence. Since spiral waves can enter the region in which there is an ionic inhomogeneity, their behaviours in the presence of such an inhomogeneity are richer than those with conduction inhomogeneities. We find, in particular, that a single spiral wave anchored at an ionic inhomogeneity can show temporal evolution that may be periodic, quasiperiodic, or even chaotic. In the last case the spiral wave shows a chaotic pattern inside the ionic inhomogeneity and a regular one outside it. Defibrillation is the control of arrhythmias such as VF. Most often defibrillation is effected electrically by administering a shock, either externally or via an internally implanted defibrillator. The development of low-amplitude defibrillation schemes, which minimise the deleterious effects of the applied shock, is a major challenge in the treatment of cardiac arrhythmias. Numerical studies of models for cardiac tissue provide us with convenient means of studying the elimination of spiral-wave turbulence by the application of external electrical stimuli; this is the numerical analogue of defibrillation. Over the years some low-amplitude defibrillation schemes have been suggested on the basis of such numerical studies. In Chapter 5 we discuss two such schemes that have been shown to suppress spiral-wave turbulence in two-dimensional models for cardiac tissue and also scroll-wave turbulence in three-dimensional models. One of these schemes uses local electrical pacing, typically in the centre of the simulation domain; the other applies the external electrical stimuli over a mesh. We study the efficacy of these schemes in the presence of conduction inhomogeneities. We find, in particular, that the local-pacing scheme, though effective in a homogeneous simulation domain, fails to control spiral turbulence in the presence of an obstacle and, indeed, might even facilitate spiral-wave break up. By contrast, the second scheme, which uses a mesh, succeeds in eliminating spiral-wave turbulence even in the presence of an obstacle. We end with some concluding remarks about the possible experimental implications of our study in Chapter 6.