Dissertations / Theses on the topic 'Dynamic heterogeneities'

The glass-transition traverses continuously from liquid to solid behaviour, yet the role of structure in this large and gradual dynamic transition is poorly understood. This thesis presents a theoretical study of the relationship between structure and dynamics in two-dimensional glass-forming alloys, and provides new tools and real-space insight into the relationship at a microscopic level. The work is divided into two parts. Part I is concerned with the role of structure in the appearance of spatially heterogeneous dynamics in a supercooled glass-forming liquid. The isoconfigurational ensemble method is introduced as a general tool for analysing the effect that a configuration has on the subsequent particle motion, and the dynamic propensity is presented as the aspect of structural relaxation that can be directly related to microscopic variations in the structure. As the temperature is reduced, the spatial distribution of dynamic propensity becomes increasingly heterogeneous. This provides the first direct evidence that the development of spatially heterogeneous dynamics in a fragile glass-former is related to spatial variations in the structure. The individual particle motion also changes from Gaussian to non- Gaussian as the temperature is reduced, i.e. the configuration expresses its character more and more intermittently. The ability of several common measures of structure and a measure of structural ‘looseness’ to predict the spatial distribution of dynamic propensity are then tested. While the local coordination environment, local potential energy, and local free volume show some correlation with propensity, they are unable to predict its spatial variation. Simple coarse-graining does not help either. These results cast doubt on the microscopic basis of theories of the glass transition that are based purely on concepts of free volume or local potential energy. In sharp contrast, a dynamic measure of structural ‘looseness’ - an isoconfigurational single-particle Debye-Waller (DW) factor - is able to predict the spatial distribution of propensity in the supercooled liquid. This provides the first microscopic evidence for previous correlations found between short- and long-time dynamics in supercooled liquids. The spatial distribution of the DW factor changes rapidly in the supercooled liquid and suggests a picture of structural relaxation that is inconsistent with simple defect diffusion. Overall, the work presented in Part I provides a real-space description of the transition from structure-independent to structure-dependent dynamics, that is complementary to the configuration-space description provided by the energy landscape picture of the glass transition. In Part II, an investigation is presented into the effect of varying the interparticle potential on the phase behaviour of the binary soft-disc model. This represents a different approach to studying the role of structure in glass-formation, and suggests many interesting directions for future work. The structural and dynamic properties of six different systems are characterised, and some comparisons are made between them. A wide range of alloy-like structures are formed, including substitutionally ordered crystals, amorphous solids, and multiphase materials. Approximate phase diagrams show that glass-formation generally occurs between competing higher symmetry structures. This work identifies two new glass-forming systems with effective chemical ordering and substantially different short- and medium-range structure compared to the glassformer studied in Part I. These represent ideal candidates for extending the study presented in Part I. There also appears to be a close connection between quasicrystal and glass-formation in 2D via random-tiling like structures. This may help explain the experimental observation that quasicrystals sometimes vitrify on heating. The alignment of asymmetric unit cells is found to be the rate-limiting step in the crystal nucleation and growth of a substitutionally ordered crystal, and another system shows amorphous-crystal coexistence and appears highly stable to complete phase separation. The generality of these results and their implications for theoretical descriptions of the glass transition are also discussed.

Doctor of Philosophy (PhD)
The glass-transition traverses continuously from liquid to solid behaviour, yet the role of structure in this large and gradual dynamic transition is poorly understood. This thesis presents a theoretical study of the relationship between structure and dynamics in two-dimensional glass-forming alloys, and provides new tools and real-space insight into the relationship at a microscopic level. The work is divided into two parts. Part I is concerned with the role of structure in the appearance of spatially heterogeneous dynamics in a supercooled glass-forming liquid. The isoconfigurational ensemble method is introduced as a general tool for analysing the effect that a configuration has on the subsequent particle motion, and the dynamic propensity is presented as the aspect of structural relaxation that can be directly related to microscopic variations in the structure. As the temperature is reduced, the spatial distribution of dynamic propensity becomes increasingly heterogeneous. This provides the first direct evidence that the development of spatially heterogeneous dynamics in a fragile glass-former is related to spatial variations in the structure. The individual particle motion also changes from Gaussian to non- Gaussian as the temperature is reduced, i.e. the configuration expresses its character more and more intermittently. The ability of several common measures of structure and a measure of structural ‘looseness’ to predict the spatial distribution of dynamic propensity are then tested. While the local coordination environment, local potential energy, and local free volume show some correlation with propensity, they are unable to predict its spatial variation. Simple coarse-graining does not help either. These results cast doubt on the microscopic basis of theories of the glass transition that are based purely on concepts of free volume or local potential energy. In sharp contrast, a dynamic measure of structural ‘looseness’ - an isoconfigurational single-particle Debye-Waller (DW) factor - is able to predict the spatial distribution of propensity in the supercooled liquid. This provides the first microscopic evidence for previous correlations found between short- and long-time dynamics in supercooled liquids. The spatial distribution of the DW factor changes rapidly in the supercooled liquid and suggests a picture of structural relaxation that is inconsistent with simple defect diffusion. Overall, the work presented in Part I provides a real-space description of the transition from structure-independent to structure-dependent dynamics, that is complementary to the configuration-space description provided by the energy landscape picture of the glass transition. In Part II, an investigation is presented into the effect of varying the interparticle potential on the phase behaviour of the binary soft-disc model. This represents a different approach to studying the role of structure in glass-formation, and suggests many interesting directions for future work. The structural and dynamic properties of six different systems are characterised, and some comparisons are made between them. A wide range of alloy-like structures are formed, including substitutionally ordered crystals, amorphous solids, and multiphase materials. Approximate phase diagrams show that glass-formation generally occurs between competing higher symmetry structures. This work identifies two new glass-forming systems with effective chemical ordering and substantially different short- and medium-range structure compared to the glassformer studied in Part I. These represent ideal candidates for extending the study presented in Part I. There also appears to be a close connection between quasicrystal and glass-formation in 2D via random-tiling like structures. This may help explain the experimental observation that quasicrystals sometimes vitrify on heating. The alignment of asymmetric unit cells is found to be the rate-limiting step in the crystal nucleation and growth of a substitutionally ordered crystal, and another system shows amorphous-crystal coexistence and appears highly stable to complete phase separation. The generality of these results and their implications for theoretical descriptions of the glass transition are also discussed.

Cette étude est divisée en deux parties: l'analyse des propriétés optiques non linéaires (NLO) de nouveaux dérivés pi-conjugués d’Azobenzène Iminopyridine et les hétérogénéités dynamiques (DH) des mélanges eau/méthanol. La première partie a été réalisée en utilisant la technique Z-scan ainsi que les techniques de génération de deuxième et troisième harmoniques (SHG/THG). Communément, l'optique non linéaire est le domaine de l'optique qui étudie l'interaction de la lumière avec un système matériel et les changements induits dans les propriétés optiques des matériaux parun champ électromagnétique intense. La non-linéarité réside dans le fait que la réponse du matériau ne dépend pas linéairement de l'intensité du champ électrique. Les matériaux qui possèdent une forte réponse non linéaire sont très utiles pour la photonique et l'optoélectronique. Ils peuvent être utilisés comme limiteurs optiques pour protéger les détecteurs de faisceaux laser de haute intensité, également comme commutateurs optiques, portes optiques logiques, etc., avec un objectif ultime qui est le traitement de signal optique et la fabrication d'ordinateurs optiques. La deuxième partie a été réalisée au moyen de calculs informatiques et plus particulièrement de simulations de dynamiques moléculaires dans l'eau, dans le méthanol et dans des mélanges eau/méthanol à différentes températures. La simulation par ordinateur est un outil très approprié pour explorer les liquides, également dans la plage de régime en surfusion, sans les limitations du processus de nucléation qui a lieu dans l'expérience réelle. Lorsque la température diminue les liquides surfondus subissent a minima une augmentation exponentielle de leur viscosité (Arrhenius). Cette grande modification des propriétés detransport apparaît bien que la structure ne change que légèrement avec la température
This study is divided into two parts: the investigation of the nonlinear optical (NLO) properties of new (pi)- conjugated Azobenzene Iminopyridine derivatives and the Dynamic Heterogeneities (DH) of water/methanol mixtures. The first part was achieved employing Z-scan, Second and Third Harmonic Generation (SHG/THG) techniques. Generally, nonlinear optics is the domain of optics that studies the interaction of light with a material system and the changes resulted in the optical properties of the materials by an intense electromagnetic field. The nonlinearity lies in the fact that the material response does not depend linearly on the intensity of the electric field. Materials with significant nonlinear response are very useful for photonics and optoelectronics. They can be used as optical limiters to protect sensitive detectors of high-intensity laser beams, as well as optical switches, optical logic gates and etc., with an ultimate objective the processing of optical signal and manufacture of optical computers. The second part was done via computer calculationsand more specifically Molecular Dynamic Simulations in water, methanol and water/methanol mixtures at different temperatures. Computer simulation is a very suitable tool for exploring liquids, also in the range of the supercooled regime, without the limitations of the nucleation process, which takes place in the real experiment. Supercooled liquids undergo an exponential (Arrhenius) or even larger increase of their viscosity, when the temperature decreases. This large modification of the transport properties appear while the structure only slightly changes with temperature

Il est bien établi que les propriétés mécaniques et rhéologiques d'une large classe de matériaux vitreux amorphes met en jeu - contrairement aux dislocations dans les cristaux - des rearrangements structuraux localisés formant par un processus de cascade des bandes de cisaillements. Cette localisation de la déformation est observée dans divers systèmes vitreux ainsi que dans des simulations numériques. Cette réponse mécanique complexe reste mal comprise à une échelle microscopique et il n'est pas clair si l'écoulement plastique peut être associé à une origine structurale locale ou à des processus purement dynamiques.Dans cette thèse nous envisageons ces problématiques à l'aide de simulations atomiques athermales sur un système Lennard-Jones modèle. Nous calculons le tenseur élastique moyenné localement sur une échelle nanométrique. A cette échelle, le verre est assimilable à un matériau composite comprenant un échafaudage rigide et des zones fragiles. L'étude détaillée de la déformation plastique à différents taux de cisaillement met en évidence divers régimes d'écoulement. En dessous d'un taux de cisaillement critique dépendant de la taille du système, la réponse mécanique atteind une limite quasistatique (effets de taille fini, cascades d'événements plastiques, contrainte seuil) alors que pour des taux de cisaillement plus importants les propriétés rhéologiques sont fixées par le taux de cisaillement imposé. Dans ce régime nous mettons en évidence la croissance d'une longueur de coopérativité dynamique et discutons de sa dépendance avec le taux de cisaillements.

L'eau est un liquide omniprésent, son omniprésence n'a d'équivalence que la multitude de ses secrets. En effet, dans le cas de l'eau, le comportement de nombreuses grandeurs thermodynamiques et dynamiques se différencie de celui des liquides « standard ». Cette différence est d'autant plus importante dans l'état dit surfondue. Dans cette thèse, on s'intéresse à la viscosité de l'eau légère et lourde dans l'état surfondue à pression atmosphérique. Pour ce faire, nous avons utilisé la méthode de microscopie dynamique différentielle. Nous avons ainsi pu mesurer la viscosité jusqu'à -34°C pour l'eau légère et -25°C pour l'eau lourde. Ces mesures de viscosité corrélées à des mesures de coefficient d'auto-diffusion nous ont permis de confirmer l'existence d'une anomalie dite violation de Stokes-Einstein
Water is an omnipresent liquid, indeed secrets of water are uncountable. In the water case, the behaviour of many thermodynamical and dynamicalquantities is very different from other standard liquids. This difference is more important in the supercooled state. In this thesis we focus on the viscosity of the heavy and light water into the supercooled state at atmospheric pressure. To do this we use the differential dynamic microscopy method. We were able to measure the viscosity to -34 C for light water and -25°C for heavy water. These viscosity measurements correlated to measurements of self-diffusion coefficient allowed us to confirm the existence of a so-called anomaly violation Stokes-Einstein

This thesis is concerned with exploring how cell heterogeneity and drug resistance can cause long term persistence of HIV. We examine models of multiple viral strains to assess the impact of drug resistance on viral persistence and extend our cell heterogeneity models to include multiple strains. Chapter 1 summarises the nature of HIV infection within host. The key barriers to HIV eradication within host and the role of mathematical models to help understand these issues are discussed. In Chapter 2 we analyse models that include cell heterogeneity. We find robust long term viral persistence is possible on therapy and differences in viral load between body compartments explained by cell heterogeneity. The inclusion of a drug sanctuary also allows low level viral load on treatment. Competition and evolutionary models of wildtype and drug resistant strains of virus are described in Chapter 3. We analyse two models containing three strains of virus with different mutation mechanisms. We find that the proportion of the minority strains of virus is determined by the number of mutations away from the dominant strain. In Chapter 4 we extend our cell heterogeneity models from Chapter 2 to include a drug resistant strain of virus. We find that when a drug sanctuary is present coexistence is possible in the absence of an evolutionary mechanism. The two compartment model also shows differential dominance whereby a different strain is dominant in each compartment. within the host. We find the latent cell reservoir acts as an archive for previously dominant viral strains when there is a mechanism for latent cell maintenance and that the balance between ongoing viral and latent cell replication determines the longevity of the archive.

Lorsqu'un liquide est refroidit suffisamment vite, la cristallisation peut être évitée. On a alors un liquide surfondu dont le temps de relaxation augmente fortement quand la température diminue vers la température de transition vitreuse Tg. En-dessous de Tg, le systèmeest dans l'état vitreux. Il vieillit : son temps de relaxation augmente au cours du temps. L'existence d'une longueur de corrélation croissante associée au ralentissement de la dynamique des liquides surfondus (ou des verres) est une des grandes questions toujours ouvertes dans la physique de la transition vitreuse. Des arguments théoriques très généraux ont montré que la mesure de la susceptibilité alternative non linéaire d'ordre trois des liquides surfondus (ou des verres) donnait directement accès à la longueur de corrélation dynamique. Nous avons mis au point une expérience à haute sensibilité permettant d'accéder à deux susceptibilités diélectriques non linéaires d'ordre trois près de Tg. Nos résultats obtenus sur du glycrol surfondu sont quantitativement en très bon accord avec les prédictions théoriques. Ils montrent que la longueur de corrélation dynamique augmente lorsque T diminue vers Tg. En dessous de Tg, l'étude du vieillissement d'une des susceptibilités non linéaires nous a permis de mettre en évidence que la longueur de corrélation dynamique augmente au cours du temps. Ces résultats renforcent le scénario selon lequel la transition vitreuse serait liée à un point critique sous-jacent, ce qui expliquerait l'ubiquité du comportement vitreux dans la nature.

This thesis provides a study of different aspects of the mechanical and vibrational properties of disordered and amorphous solids. Resorting to the theoretical framework of non-affine lattice dynamics the attention is focused on the analysis of disordered networks and lattices which serve as tractable model systems for real materials. Firstly, we discuss the static elastic response and the vibrational spectra of defective fcc crystals. The connection to different types of microstructural disorder in the form of bond-depletion and vacancies is described within the context of the inversion symmetry breaking of the local particle configurations. We identify the fluctuations of the local inversion symmetry breaking, which is directly linked to the non-affinity of the disordered solid, as the source of different scalings behaviours of the position of the boson peak. Furthermore, we describe the elastic heterogeneities occurring in a bond-depleted two- dimensional lattice with long-range interactions. The dependence of the concomitant correlations of the local elastic moduli are studied in detail in terms of the interaction range and the degree of disorder. An analytical scaling relation is derived for the radial part of the elastic correlations in the affine limit. Subsequently, we provide an argument for the change of the angular symmetry of the elastic correlation function which was observed in simulations and experiments on glasses and colloids, respectively. Moving to the dynamical behaviour of disordered solids, a framework is developed based on the kernel polynomial method for the approximate computation of the non- affine correlator of displacement fields which is the key requirement to describe the linear viscoelastic response of the system within the quasi-static non-affine formalism. This approach is then extended to the case of multicomponent polymer melts and validated against molecular dynamics simulations at low non-zero temperatures. We also consider the dynamical behaviour of metallic glasses in terms of its shear elasticity and viscosity. A theoretical scheme is suggested which links the repulsive strength of the interatomic potential to the viscoelasticity and fragility in metallic glasses in the quasi-affine limit.

This thesis examines the parasite dynamics and the mechanisms affecting parasite load and transmission focalising on the role played by host and habitat heterogeneities. This study is based on the gastrointestinal nematode Heligmosomoides polygyrus and the small mammal yellow necked mouse and uses data gathered from experimental field manipulations of parasites intensities and data gathered from trapping monitoring. Initially the parasite community of yellow-necked mouse (Apodemus flavicollis) was explored in North-Eastern Italian Alps with the aim to describe the major patterns and identify the factors affecting parasite community structure. Despite the observed spatial variability it has been found that differences within the host population such age and secondly sex and breeding conditions, were the major factors acting on parasite occurrence and intensity. Habitat differences had a less apparent effect on parasite community structure. The consequences of H. polygyrus infection on other parasite species infections have been analysed, in specific the infestation of the tick Ixodes ricinus in populations of A. flavicollis. H. polygyrus load and tick infestation were monitored as well as were carried out field manipulations of H. polygyrus intensity and were monitored changes in tick infestation. It has been found that H. polygyrus load was negatively related to I. ricinus infestations. Host factors mediated the H. polygyrus-I. ricinus interaction such that young and non-breeding mice exhibited higher I. ricinus to H. polygyrus intensity respect breeding adults. The role of host sex on parasite abundance was then investigated carrying out a field experiment where the H. polygyrus intensity were manipulated in relation to mice gender. In specific, H. polygyrus was removed alternately from either sexes and the parasite load was analysed in the untreated sex. It was found that males mice were responsible to drive parasite transmission in the host population and this was observed in absence of sex-bias in parasite infection, suggesting that this pattern was not a mere consequence of quantitative differences in parasite loads between sexes. To disentangle the possible mechanism causing this sex bias in parasite transmission mathematical simulations based on parameters obtained for the field experiment were used. Two non mutually exclusive hypotheses causing sex bias in parasite transmission were tested: a- males immune response is less efficient and this causes the development of more successful parasite infective stages or b-males behaviours allow them to be more efficient is spreading in more exposed areas parasite infective stages. Multi-host models were developed and simulations were compared with field results. While it was not disentangled the most dominant mechanism causing sex bias in parasite transmission this study underlined the importance of host sexes in affecting parasite dynamics and host-parasite interaction. In conclusion this thesis highlighted the importance of considering host and environmental differences when investigating host parasite interactions. This finding could be extremely important when planning measured of disease control or to avoid disease outbreak. Controlling target group of individuals host could avoid economical losses and a more effective measure of intervention.

Les polymères amorphes présentent des hétérogénéités dynamiques à l'échelle de 3 à 5nm proche de la température de transition vitreuse. Leur contribution aux propriétés mécaniques est encore mal connue. Pour ce faire, nous considérons un modèle simple dans lequel chaque hétérogénéité dynamique possède un unique temps de relaxation distribué aléatoirement selon une loi log-normale. Un modèle coarse-grained à l’échelle d’une hétérogénéité dynamique est alors développé dans le cadre de l'approximation des milieux continus. Ainsi, des simulations par éléments finis nous permettent de calculer les propriétés mécaniques macroscopiques des polymères en tenant compte des effets de couplage mécaniques en hétérogénéités. Nous montrons que la transition vitreuse est pilotée par un réseau de percolation des domaines lents. Nous mettons également en évidence les couplages mécaniques intervenant entre hétérogénéités dynamiques. Dans le cas des films minces de polymères confinés à l’échelle de quelques dizaines de nanomètres, nous montrons que les hétérogénéités dynamiques permettent de rendre compte d’un ralentissement de la dynamique macroscopique du film. En considérant que pour de fortes contraintes, la dynamique locale des polymères massifs est accélérée, nous démontrons que les hétérogénéités dynamiques permettent de rendre compte d’un phénomène de contrainte interne à un système, celle-ci étant la cause d’une partie non récupérable de l’énergie élastique stockée un système lors d’une déformation plastique
Amorphous polymers present dynamical heterogeneities at the scale of 3 to 5nm near Tg. Their contributions to mechanical properties are still not well known. We thus consider a simple model where each dynamical heterogeneities has its own relaxation time randomly drawn is a log-normal time distribution. A coarse –grained model at the dynamical heterogeneity is then developed in the continuous medium approximation. Finite element simulations are performed to calculate macroscopic mechanical properties of amorphous polymers taking account of mechanical couplings between heterogeneities. We show that the glass transition is controlled by a percolation of slow domains. Mechanical couplings result in viscoelastic spectrum highly narrowed as compared to the microscopic one. In thin films of polymers, we evidence a slowdown of the dynamics of relaxation as compared to the bulk one. Considering that a high applied stress increase the dynamics of polymers, we show that dynamical heterogeneities result in an internal stress network. The latter is a consequence a plastic deformation and result in an internal energy which is not released after an unloading

La prédiction de la géométrie d'une pièce mise en forme par déformation plastique grâce à un logiciel de calcul par éléments finis (EF) s'effectue en suivant séquentiellement différentes étapes : la caractérisation thermo-mécanique du matériau, la modélisation de son comportement et son intégration dans un logiciel EF, puis la mise en données et la simulation de l'opération de formage. La phase de modélisation consiste entre autre à identifier quel type de modèle de comportement est le plus approprié pour prédire les réactions du matériau lors de l'opération de formage. Ces modèles sont essentiellement développés dans le cadre de la mécanique des milieux continus (MMC). L'hypothèse forte, si ce n'est centrale, de la MMC consiste à considérer que les variables qui servent à déterminer le comportement du matériau sont continues et dérivables. Cependant, les connaissances les plus élémentaires de métallurgie indiquent que les grandeurs locales dans les matériaux métalliques sont discontinues. La majorité des modèles de comportement mécanique des matériaux métalliques repose sur la définition d'un volume élémentaire représentatif dont la taille est assez grande pour permettre une homogénéisation de la description du comportement en gommant l'influence des hétérogénéités localesL'objet de ces travaux est de montrer que la prise en compte des hétérogénéités locales dans la modélisation du comportement des matériaux métalliques est pertinente et contribue à l'amélioration de la prédiction des simulations d'opérations de mise en forme en élargissant le potentiel prédictif des modèles ainsi construits. Un modèle élasto-plastique prenant en compte les hétérogénéités locales est alors proposé
To obtain a relevant shape of a formed part during its finite element simulation, several steps are needed: thermo-mechanical caracterization of the material, definition of the most relevant model and integration of this model in the FE software and finally after data converting and computing processes. The modelling step include, among other things, the identification of the most appropriate model to fit the experimental material behaviour. Those models are essentially developped within the framework of continuum mechanics (CM). A strong, if not the main assumption of the CM consists in considering that mechanical description variables are continuous and differentiable. However, the basic knowledge of metallurgy indicates that local data in metallic materials are discontinuous. For metallic materials, the majority of constitutive models are based on the definition of a representative elementary volume (REV). This REV is supposed to be large enough to erase the incidence of local heterogeneities. Then those constitutive models are assumed to be homogeneous.The aim of this work is to show that introducing local heterogeneities in the description of constitutive models is relevant and contribute to improve the simulation accuracy. Those models also provide an enlargement of the simulation predictive potential. Then an elasto-plastic model, based on local heterogeneities description, is proposed

We describe a set of single molecule fluorescence experiments that directly demonstrate the existence of spatial and temporal heterogeneity in two different small molecule glass former, glycerol and ortho-terphenyl (OTP) as well as the polymeric glass former polystyrene near their glass transition temperatures. The rotational dynamics of a set of perylene diimide probes are investigated in each small molecule glass former in a temperature range near their glass transition temperature. For all probes, the temperature dependence of their median rotational relaxation times (τc) reflect that of the structural relaxation of glycerol and OTP. The distribution of relaxation times for each probe at each temperature span around one decade and remain constant across all temperatures probed. In both glass formers, a trend as a function of probe rate of rotation occurs, where the fastest rotating probes exhibit the broadest τc distributions. Unexpectedly, a correlation between the rotational dynamics and the strength of the probe's intermolecular interactions with the host is seen. In OTP, the fastest rotating probe is the smallest probe, with the lowest molecular weight, as expected. But in glycerol, the largest probe exhibits the fastest rotational dynamics. This counterintuitive result arises from the apparent inhibition of hydrogen bonding between the probe and host due to bulky non-polar groups sterically hindering the polar carbonyl groups on the probe. Analysis of dynamic exchange of probes on long time scales in glycerol (102 - 106 times the structural relaxation) does not reveal the presence of temporal heterogeneity on this time scale. Another technique employed to assess exchange on a shorter time scale reveals that ~30 % of molecules exhibit temporally heterogeneous behavior. Single molecule experiments on polystyrene (PS) near its glass transition temperature are also presented. Here, the rotational and translational dynamics of perlyene diimide probes in 100 nm PS films near its glass transition are studied. As in glycerol and OTP, average rotational relaxation times are found to mimic the temperature dependence of the host structural relaxation. These studies, intended as control experiments for confined film SM studies, reveal spatial and temporal heterogeneity in PS dynamics. The measured distribution of rotational relaxation times spans 1.5 decades and remains constant across all temperature probed. These distributions fall between the expected distribution width for the purely spatially and temporally heterogeneous cases, suggesting the distributions are comprised of combination of spatial and temporal components. The median stretching exponent (β) from fitting SM trajectories results in β = 0.63 and a "quasi-ensemble" result of β = 0.58 found from combining SM linear dichroism autocorrelation functions. These represent the smallest stretching exponents reported for single molecule studies in supercooled liquids to date, indicating that the probe employed truly mirrors the dynamic heterogeneity of the host. The SM rotational relaxation rates are found to be correlated to their stretching exponents i.e. the lowest relaxation rates also have, on average, the lowest β values. Additionally, small stretching exponents are correlated with long trajectories, suggesting that the rate of rotation together with the length of the trajectory dictate the degree of heterogeneity the probe is able to sample. Surprisingly, a mobile layer is observed in the films at temperatures near the glass transition. Translating molecules in this region are tracked and represent ~10% of the total molecules evaluated in this film. Molecules in the mobile region appear to be diffusing at rates that are magnitudes greater than the molecules rotating in the bulk region of the film.

Waveform and differential travel-time (DTT) of various PKP phases have been utilized to study the velocity variations at the core-mantle boundary (CMB) and the inner-core boundary (ICB). The spatial concentration of events and stations, and the significant variations in PKPab-PKPdf DTT and waveform of PKPab, indicate localized sharp lateral variation of velocity at the CMB as supported by simulations. Modeling of DTT's among PKiKP, PKIKP and PKP-B-diffracted (B_diff) phases, and waveform of B_diff supports that the ratio of relative velocity variations of S- and P-wave at the CMB is larger than 2, and that hemispheric P-wave velocity variations exist at the top of the inner core, and that D' structure is related to the ICB via core dynamics.

The equation of state of stishovite is obtained by direct shock wave loading up to 235 GPa as K_0T=306 ± 5 GPa and K_0T' = 5.0 ± 0.2 where K_0T is ambient bulk modulus and K_0T' its pressure derivative. Phase diagram of silica (including melting curve) up to megabar pressure regime is established based on molecular dynamics (MD) simulations and dynamic and static experiments. Calculations show that perovskite is thermodynamically stable relative to the stishovite and periclase assemblage at lower mantle conditions. A detailed and quantitative examination is conducted on the thermodynamics and phase change mechanisms (including amorphization) that occur upon shock wave loading and unloading of silica. The systematics of maximum undercooling and superheating, are established by incorporating normalized energy barrier for nucleation and heating (cooling) rate, and validated at the atomic level with systematic MD simulations. By considering superheating in shock wave experiments, high-pressure melting curves for silica, alkali halides and transition metals are constructed based on the Lindemann law and the $ln2$ rule for the entropy of melting.

Livestock grazing is the most important type of land-use in arid and semi-arid regions. In these regions, uncertain and highly variable climate conditions cause scarce and spatio-temporally variable resource availability. The major challenge to livestock grazing is the efficient utilisation of these resources without running the risk of degradation. Therefore, well adapted grazing strategies that consider both local environmental characteristics and the farmers' individual needs and perceptions are crucial for sustaining human livelihoods. Particularly, rotational grazing is presumed to render adaptation to spatio-temporal heterogeneities possible. A systematic investigation, however, that analyses the interrelations between the major components of rotational grazing systems on appropriate spatial and temporal scales was missing so far. This doctoral thesis investigates different management strategies for sustainable livestock grazing in semi-arid rangelands. Using an integrated modelling approach, it enters into the question: how to adapt grazing systems to spatio-temporal heterogeneous rangeland conditions, variable and changing climate conditions, and different individual needs and goals of livestock farmers? In order to address these issues, the taken approach tackles both methodical challenges and applied concerns. In the first part of this study, a generic modelling framework is developed that incorporates important components of grazing systems on appropriate spatial and temporal scales. To parameterise the model, a pattern-oriented approach is developed that uses qualitative patterns to derive a broad range of plausible parameter sets supporting a general model analysis. In the second part, a variety of management strategies is explored under different climatic, ecological, and economic conditions. The research focuses in particular on combined effects between and relative importance of different management components. The question how the results of different management strategies depend on the type of vegetation is investigated. Furthermore, the performance of rotational grazing strategies is analysed under different economic requirements and rainfall conditions. The study also identifies management strategies that are suitable to adapt a grazing system to spatio-temporally variable rangeland conditions. Overall, this thesis contributes to a general understanding of basic principles for adaptation to spatio-temporal heterogeneities as well as the interplay of different management components. The results allow an evaluation of management strategies for specific situations and the identification of strategies that are robust to a broad range of situations including different aspects of global change.

This thesis is devoted to the study of the dynamics of spiral and scroll waves in a mathematical model for cardiac tissue. We study the effects of the presence of heterogeneities on electrical-wave dynamics. The heterogeneities in the medium occur because of the variation in the electrophysiological properties of the constituent myocytes in the tissue, or because of the presence of cells like fibroblasts and pathological myocytes that can trigger early afterdepolarizations (EADs). We study how these heterogeneities can lead to the formation of spiral and scroll waves and how they can affect the stability of the spiral and scroll waves in cardiac tissue. We also investigate the role of abnormal cells, which can trigger pathological excitations like EADs, on the formation of spiral and scroll waves, and how such cells can trigger premature electrical pulses like premature-ventricular-complexes (PVCs) in cardiac tissue. Earlier studies have examined the role of ionic heterogeneities on spiral-wave initiation and their effects on spiral-wave stability. However, none of these studies has calculated, in a controlled way, the effects of individual ion-channel conductances on spiral- and scroll-wave properties, such as the frequency of these waves, and the effects of the spatial gradients, in each ion-channel conductance, on their stability; we present these results in Chapter 2. Although many studies in the past have studied the effects of fibroblast coupling on wave-dynamics in cardiac tissue, a detailed study of spiral-wave dynamics in a medium with a well-defined, heterogeneous distribution of fibroblasts (e.g., with a gradient in the fibroblast density (GFD)) has not been performed; therefore, in Chapter 3 we present the effects of such GFD on spiral- and scroll-wave dynamics. Then, in Chapter 4, we present a systematic study of how a clump of fibroblasts can lead to spiral waves via high-frequency pacing. Some studies in the past have studied the role of early afterdepolarizations (EADs) in the formation of arrhythmias in cardiac tissue; we build on such studies and present a detailed study of the effects of EADs on the formation of spiral waves and their dynamics, in Chapter 5. Finally, in Chapter 6 we provide the results of our detailed investigation of the factors that assist the triggering of abnormal electrical pulses like premature ventricular complexes by a cluster of EAD-capable cells. A brief summary of the chapters is provided below: Chapter 2: In this chapter we investigate the effects of spatial gradients in the ion-channel conductances of various ionic currents on spiral-and scroll-wave dynamics. Ionic heterogeneities in cardiac tissue arise from spatial variations in the electrophysiological properties of cells in the tissue. Such variations, which are known to be arrhythmogenic, can be induced by diseases like ischemia. It is important, therefore, to understand the effects of such ionic heterogeneities on electrical-wave dynamics in cardiac tissue. To investigate such effects systematically, of changing the ion-channel properties by modifying the conductances of each ionic currents, on the action-potential duration (APD) of a myocyte cell. We then study how these changes in the APD affect the spiral-wave frequency ω in two-dimensional tissue. We also show that changing the ion-channel conductance not only changes ω but also the meandering pattern of the spiral wave. We then study how spatial gradients in the ion-channel conductances affect the spiral-wave stability. We find that the presence of this ionic gradient induces a spatial variation of the local ω, which leads to an anisotropic reduction of the spiral wavelength in the low-ω region and, thereby, leads to a breakup of the spiral wave. We find that the degree of the spiral-wave stability depends on the magnitude of the spatial variation in ω, induced by the gradient in the ion-channel conductances. We observe that ω varies most drastically with the ion-channel conductance of rapid delayed rectifier K+ current GKr, and, hence, a spiral wave is most unstable in the presence of a gradient in GKr (as compared to other ion-channel conductances). By contrast, we find that ω varies least prominently with the conductances of the transient outward K+ current Gto and the fast inward Na+ current (GNa); hence, gradients in these conduc-tances are least likely to lead to spiral-wave breaks. We also investigate scroll-wave instability in an anatomically-realistic human-ventricular heart model with an ionic gradient along the apico-basal direction. Finally, we show that gradients in the ion-channel densities can also lead to spontaneous initiation of spiral waves when we pace the medium at high frequency. Chapter 3: In this chapter we study the effects of gradients in the density of fibroblasts on wave-dynamics in cardiac tissue. The existence of fibroblast-myocyte coupling can modulate electrical-wave dynamics in cardiac tissue. In diseased hearts, the distribution of fibroblasts is heterogeneous, so there can be gradients in the fibroblast density (henceforth we call this GFD) especially from highly injured regions, like infarcted or ischemic zones, to less-wounded regions of the tissue. Fibrotic hearts are known to be prone to arrhythmias, so it is important to understand the effects of GFD in the formation and sustenance of arrhythmic re-entrant waves, like spiral or scroll waves. Therefore, we investigate the effects of GFD on the stability of spiral and scroll waves of electrical activation in a state-of-the-art mathematical model for cardiac tissue in which we also include fibroblasts. By introducing GFD in controlled ways, we show that spiral and scroll waves can be unstable in the presence of GFDs because of regions with varying spiral or scroll-wave frequency ω, induced by the GFD. We examine the effects of the resting membrane potential of the fibroblast and the number of fibroblasts attached to the myocytes on the stability of these waves. Finally, we show that the presence of GFDs can lead to the formation of spiral waves at high-frequency pacing. Chapter 4: In this chapter we study the arrhythmogenic effects of lo-calized fibrobblast clumps. Localized heterogeneities, caused by the regional proliferation of fibroblasts, occur in mammalian hearts because of diseases like myocardial infarction. Such fibroblast clumps can become sources of pathological reentrant activities, e.g., spiral or scroll waves of electrical activation in cardiac tissue. The occurrence of reentry in cardiac tissue with heterogeneities, such as fibroblast clumps, can depend on the frequency at which the medium is paced. Therefore, it is important to study the reentry-initiating potential of such fibroblast clumps at different frequencies of pacing. We investigate the arrhythmogenic effects of fibroblast clumps at high- and low-frequency pacing. We find that reentrant waves are induced in the medium more prominently at high-frequency pacing than with low-frequency pacing. We also study the other factors that affect the potential of fibroblast clumps to induce reentry in cardiac tissue. In particular, we show that the ability of a fibroblast clump to induce reentry depends on the size of the clump, the distribution and percentage of fibroblasts in the clump, and the excitability of the medium. We study the process of reentry in two-dimensional and a three-dimensional mathematical models for cardiac tissue. Chapter 5: In this chapter we investigate the role of early afterdepolarizations (EADs) on the formation of spiral and scroll waves. Early after depolarizations, which are abnormal oscillations of the membrane poten-tial at the plateau phase of an action potential, are implicated in the de-velopment of cardiac arrhythmias like Torsade de Pointes. We carry out extensive numerical simulations of the TP06 and ORd mathematical models for human ventricular cells with EADs. We investigate the different regimes in both these models, namely, the parameter regimes where they exhibit (1) a normal action potential (AP) with no EADs, (2) an AP with EADs, and (3) an AP with EADs that does not go back to the resting potential. We also study the dependence of EADs on the rate of at which we pace a cell, with the specific goal of elucidating EADs that are induced by slow or fast rate pacing. In our simulations in two- and three-dimensional domains, in the presence of EADs, we find the following wave types: (A) waves driven by the fast sodium current and the L-type calcium current (Na-Ca-mediated waves); (B) waves driven only by the L-type calcium current (Ca-mediated waves); (C) phase waves, which are pseudo-travelling waves. Furthermore, we compare the wave patterns of the various wave-types (Na-Ca-mediated, Ca-mediated, and phase waves) in both these models. We find that the two models produce qualitatively similar results in terms of exhibiting Na-Ca- mediated wave patterns that are more chaotic than those for the Ca-mediated and phase waves. However, there are quantitative differences in the wave patterns of each wave type. The Na-Ca-mediated waves in the ORd model show short-lived spirals but the TP06 model does not. The TP06 model supports more Ca-mediated spirals than those in the ORd model, and the TP06 model exhibits more phase-wave patterns than does the ORd model. Chapter 6: In this chapter we study the role of EAD-capable cells, and fibroblasts on the trigerring of abnormal electrical pulses called premature ventricular complexes (PVCs). Premature ventricular complexes, which are abnormal impulse propagations in cardiac tissue, can develop because of various reasons including early afterdepolarizations (EADs). We show how a cluster of EAD-generating cells (EAD clump) can lead to PVCs in a model of cardiac tissue, and also investigate the factors that assist such clumps in triggering PVCs. In particular, we study, through computer simulations, the effects of the following factors on the PVC-triggering ability of an EAD clump: (1) the repolarization reserve (RR) of the EAD cells; (2) the size of the EAD clump; (3) the coupling strength between the EAD cells in the clump; and (4) the presence of fibroblasts in the EAD clump. We find that, although a low value of RR is necessary to generate EADs and hence PVCs, a very low value of RR leads to low-amplitude EAD oscillations that decay with time and do not lead to PVCs. We demonstrate that a certain threshold size of the EAD clump, or a reduction in the coupling strength between the EAD cells, in the clump, is required to trigger PVCs. We illustrate how randomly distributed inexcitable obstacles, which we use to model collagen deposits, affect PVC-triggering by an EAD clump. We show that the gap-junctional coupling of fibroblasts with myocytes can either assist or impede the PVC-triggering ability of an EAD clump, depending on the resting membrane potential of the fibroblasts and the coupling strength between the myocyte and fibroblasts. We also find that the triggering of PVCs by an EAD clump depends sensitively on factors like the pacing cycle length and the distribution pattern of the fibroblasts.