Dissertationen zum Thema „Phase isotrope“

Une étude des interactions particule/particule est présentée suivant une simulation lagrangienne de plusieurs trajectoires simultanées et la simulation réelle des collisions entre les particules dans un écoulement turbulent donne. Un cas test en turbulence homogène isotrope, sans gravite, a ensuite été étudié et comparé à une simulation directe LES. On montre l'importance de conserver la corrélation V#PU#F globalement constante par une modification de la vitesse des particules fluides lors d'une collision. Cette modification a permis d'observer que pour un nuage distribué aléatoirement dans une turbulence isotrope ou aucune direction n'est privilégiée, les résultats ne montrent pas de variations sensibles des fluctuations de vitesses sous l'effet des collisions, mais la dispersion des particules est réduite. Un second cas test a été étudié suivant la même démarche, à savoir une turbulence de cisaillement donnée par des résultats les, afin de déterminer l'influence des collisions sur l'anisotropie du mouvement fluctuant des particules. Les résultats entre les différentes approches sont tout à fait similaires et montrent un retour vers l'isotropie des fluctuations de vitesses des particules. Enfin le couplage entre la phase dispersée et la turbulence est étudiée dans le cas d'un écoulement de tuyau. Les résultats sont en accord avec des résultats expérimentaux et montrent la diminution de l'anisotropie des deux phases sous l'effet des collisions.

La régulation des polluants a mené à la création de nouveaux systèmes de combustion. Le carburant étant stocké sous forme liquide, sa transformation jusqu’à sa combustion est complexe. La capacité de la Simulation aux grandes échelles à simuler des écoulements turbulents réactifs a été montrée sur des cas académiques comme sur des configurations industrielles, tout en prenant en compte les phénomènes multiphysiques intervenant dans ces configurations, mais les études sur la structure de flamme diphasique sont encore trop peu nombreuses. La présence de deux solveurs pour la simulation d’une phase liquide étant disponible dans le code AVBP, leur utilisation permet une comparaison et une compréhension des phénomènes en jeu combinant dispersion, évaporation, et combustion. La première partie de l’étude relate la validation du modèle d’injection FIM-UR. Ce modèle est capable de reconstruire les profils de vitesses et de granulométrie à l’injecteur sans avoir à simuler les phénomènes d’atomisation primaire et secondaire. Une validation en régime turbulent avait déjà été réalisée, et on propose ici de valider le modèle dans un cas laminaire. Des comparaisons entre simulations monodisperses et polydisperse et des expériences sont effectuées. La simulation monodisperse Lagrangienne donne une bonne structure globale mais la simulation polydisperse Lagrangienne permet de retrouver le comportement au centre du cône avec la présence des petites gouttes et à la périphérie du cône par la présence des grosses gouttes. De plus, des améliorations sont apportées au modèle pour le formalisme Eulérien et montrent de bons résultats. La partie suivante s’intéresse à caractériser un spray polydisperse par une distribution monodisperse. En effet, au cas où une approche polydisperse n’est pas possible, le choix du diamètre moyen à prendre pour une simulation monodisperse est délicat. On propose donc d’analyser le comportement d’un spray polydisperse en le comparant à ceux de sprays monodisperses. Deux configurations académiques sont choisies : des cas de Turbulence Homogène Isotrope chargée en particules pour étudier la dynamique, et des calculs d’évaporation 0D. Trois paramètres sont étudiés pour la dynamique : la concentration préférentielle (ou ségrégation), la traînée moyenne et la traînée réduite moyenne. Cette dernière et la ségrégation de la distribution polydisperse semblent affectées par les tailles de goutte les plus faibles, et la concentration préférentielle apparait alors comme la moyenne des ségrégations des classes qui la composent pondérées par l’inverse du nombre de Stokes associé à chacune de ces classes. La traînée moyenne de la simulation polydisperse possède un comportement proche des diamètres moyens D10 et D20. Ces analyses nous poussent donc à choisir le D10 pour caractériser la dynamique d’un spray polydisperse. Les calculs d’évaporation 0D ne permettent pas dans un premier temps de caractériser efficacement la masse évaporée d’un spray polydisperse par celle d’un spray monodisperse équivalent, mais la définition de nouveaux diamètres issus de la littérature des lits fluidisés comme le D50% le permet, ce qui le place autour du D32. On propose donc de caractériser l’évaporation d’un spray polydisperse par ce diamètre. Enfin, la dernière partie étudie la structure de flamme diphasique dans la chambre MERCATO, à l’aide du formalisme Lagrangien, monodisperse et polydisperse, mais aussi en utilisant le formalisme Eulérien. La validation du modèle FIM-UR du premier chapitre et ses améliorations sont utilisées pour représenter les conditions d’injection liquide. En plus d’un calcul polydisperse, deux simulations monodisperses Lagrangiennes sont réalisées en prenant les diamètres moyens D10 et D32, suite à la partie précédente. Des comparaisons qualitatives et des validations sont réalisées, en comparant des profils de vitesses gazeuses axiale et fluctuante et vitesse axiale liquide issus de l’expérience
Regulations on pollutants have led to the creation of new combustion systems. Giving that fuel is stored in a liquid form, its evolution until combustion is complex. The ability of Large Eddy Simulation has been demonstrated on academic cases, as well as on industrial configurations, by taking into account the multi-physics phenomena, but there is a lack of studies about two-phase flow flame structures. Two solvers for the simulation of two-phase flows are available in the AVBP code, hence both simulations are performed to compare and increase understanding of the phenomena involved such as dispersion, evaporation and combustion. The first part of the study focuses on the validation of the FIM-UR injection model. This model is able to build velocity and droplet profiles at the injector, without simulating primary and secondary break up. A validation in a turbulent case has already been done, and this study validates the model in a laminar case. Comparisons between monodisperse and polydisperse simulations, and experiments are performed. The monodisperse Lagrangian simulation shows good results but the polydisperse simulation is able to represent profiles in the center of the cone by small droplets and at the peripheral part of the cone, by big ones. Moreover, improvements in the Eulerian model exhibit good results. The next section tries to evaluate the impact of polydispersion. Indeed, when a polydisperse approach is not available, choosing the mean diameter can be tricky. A comparison between the behavior of polydisperse spray and monodisperse sprays ones is realised. Two academic cases are studied: Homogeneous Isotropic Turbulence with particles to analyze the dynamics, and 0D evaporation cases. For the dynamics, preferential concentration, mean drag and reduced mean drag are studied. The latter and preferential concentration are affected by small droplets, and the preferential concentration of a polydisperse spray is equivalent to the average of preferential concentration of classes, extracted from the polydisperse distribution, weighted by the inverse of the Stokes number of each class. The mean drag behaves like the D10 and D20 mean drags. This analysis allows us to choose the D10 to characterize a polydisperse distribution for the dynamics. Zero-D evaporation simulations cannot characterize the polydisperse spray evaporated mass by the evaporated mass of monodisperses sprays. New definitions of diameters from fluidized bed literature enable the use of D50%, which is close to D32. We propose to use this diameter to characterize the evaporation of a polydisperse spray. Finally, the last section studies the structure of two-phase flames in the MERCATO bench, using the Lagrangian formalism, monodisperse and polydisperse but also using the Eulerian formalism. The validation of FIM-UR model and improvements from the first section are used to represent liquid injection conditions. A polydisperse simulation is realized and two monodisperse simulations are computed using mean diameters D10 and D32, thanks to the previous section. Qualitative comparisons and validations are realized, comparing gaseous velocity profiles and liquid velocity profiles. Good agreements are found and the mean diameter D32 seems to be close to the polydisperse spray. A comparison between mean flames is done with an Abel transform of the flame from the experiments. The flame has an "M shape", anchored by small recirculation zones out of the swirler, and by a point at the tip of the central recirculation zone. Then, the impact of droplet distributions is analyzed. Even if few bigger droplets from the polydisperse distribution are convected in the hot gases due to bigger particular time and evaporation time, two-phase flow flame structures are equivalent. Different combustion regimes appeared with premixed flames and pockets of fuel burning in the hot gases

Le but de cette étude expérimentale est de caractériser la dynamique de particules solides, à flottabilité nulle, incluse dans un écoulement turbulent isotrope en décroissance libre. Les particules utilisées sont de forme sphérique et ont un diamètre de 4 à 5 fois plus grand que l'échelle spatial de Kolmogorov de l'écoulement. De part leur taille, les particules ont également un nombre de Stokes proche de l'unité. On s'attend alors à ce que ces particules aient une dynamique différente de celle du fluide environnant. Dans cette étude, ont se propose de quantifier les différences de vitesses entre les deux phases à l'aide d'une technique de vélocimétrie simultanée
In this experimental study, the focus is made on the characterization of the dynamics of solid neutrally buoyant particles embedded in a freely decaying, nearly isotropic turbulence, with a weak mean flow. The particles are spherical with diameters several times larger than the Kolmogorov scale. The study of this flow configuration is still challenging both theoretically and numerically. Due to large particle sizes, the local flow around particles can not be considered as uniform and due to fluid-particle density ratio of around unity, the history and Basset forces cannot be neglected in comparison with the viscous drag force. Particle equation of motion is then fully non-linear, in contrast to the equation for heavy particles with diameters smaller then the Kolmogorov scale, for which only the Stokes drag is considered. In several experimental and numerical studies, the effect of particle size on velocity and acceleration statistics has been investigated (Homann and Bec 2010 ; Qureshi et al. 2008 ; Ouellette et al. 2008 ; Xu and Bodenschatz 2008). In the case of isotropic turbulence, Homann and Bec (2010) show that while the PDF of the particle velocity normalized by the square root of its variance does not vary with particle size, the variance itself is size dependent. A scaling relation for particle velocity variance has been proposed by using the Faxen correction (Gatignol 1983) which takes into account the non uniformity of the fluid flow at the scale of the particle. The aim of our research is to further study the dependence of particle dynamics on particle size. To that purpose, a turbulence generator has been set-up and the resulting turbulence is characterized. Then the flow was seeded with millimeter sized, neutrally-buoyant particles and the velocity of the two phases have been measured simultaneously. Simultaneous measurements of particle and surrounding fluid velocities show that although the global velocity statistics of the two phases have comparable values, the particles may have different local velocity from the velocity of the neighboring fluid

Les liquides diffèrent des solides par une réponse retardée à la sollicitation en cisaillement; c’est-à-dire une absence d’élasticité de cisaillement et un comportement d'écoulement à basses fréquences (<1 Hz). Ce postulat pourrait ne pas être vrai à toutes échelles. A l’échelle submillimétrique, les mesures viscoélastiques (VE) réalisées en améliorant l'interaction entre le liquide et le substrat, montrent qu’une élasticité basses-fréquences existe dans des liquides aussi variés que les polymères, les surfondus, les liquides à liaison H, ioniques ou van der Waals. Ce résultat implique que les molécules à l'état liquide ne seraient pas dynamiquement libres, mais élastiquement corrélées.En utilisant les propriétés biréfringentes des fluctuations prétransitionnelles qui coexistent dans la phase isotrope des cristaux liquides, nous montrons qu'il est possible de visualiser ces corrélations « cachées ». Dans des conditionssimilaires aux mesures VE, une biréfringence optique synchrone à la déformation est observée dans la phase isotrope à des fréquences aussi basses que 0.01 Hz et des températures éloignées de toute transition. Le comportement dela biréfringence basses-fréquences a des similitudes avec l'élasticité; elle est en phase avec la déformation à faibles amplitudes de déformation, puis en phase avec le taux de déformation à plus grandes amplitudes. La biréfringence basses- fréquences est forte, sans défaut et réversible. Elle indique un ordre à longue portée. La synchronisation de la réponse à la sollicitation en fréquence et l’état ordonné qu’elle produit ne sont pas compatibles avec un état liquide isotrope mais montrent qu’il s’agit d’un état élastique soumis à déformation (entropie élastique)
Liquids differ from solids by a delayed response to a shear mechanical solicitation; i.e. they have no shearelasticity and exhibit a flow behaviour at low frequency (<1 Hz). This postulate might be not verified at thesub-millimeter scale. By optimizing the measurement in particular by improving the liquid/substrate interactions (wetting), a low frequency shear elasticity has been found in liquids including molten polymers, glass-formers, H-bond polar, ionic or van der Waals liquids. This result implies that molecules in the liquid state may not be dynamically free but weaklyelastically correlated. Using the birefringent properties of the pretransitional fluctuations coexisting in the isotropic phase of liquid crystals, we show that it is possible to visualize these “hidden” shear-elastic correlations. We detect a synchronized birefringent optical response in the isotropic phase that is observable at frequencies as low as 0.01 Hz and at temperatures far away from anyphase transition. The low-frequency birefringence exhibits a strain dependence similar to the low frequency elasticity: An optical signal that is in-phase with the strain at low strain amplitudes and in-phase with the strain-rate at larger strain amplitudes. The birefringent response is strong, defect-free, reversible and points out a collective response. This long-range ordering rules out the condition of an isotropic liquid and its synchronized response supports the existenceof long-range elastic (solid-like) correlations. In the light of this, the strain dependence of the harmonic birefringent signal and the shear elasticity may correspond to an entropy-driven transition

Les sources émettant dans la région du moyen infrarouge revêtent un grand intérêt environnemental et écologique. Les semiconducteurs de la branche électronique, tels que le séléniure de zinc ou l'arseniure de gallium, sont d'excellents candidats pour la conversion d'un rayonnement optique du proche vers le moyen infrarouge. Ces matériaux sont cependant isotropes, et seule la technique du quasi-accord de phase permet de réaliser une conversion efficace. Ce travail concerne le quasi-accord de phase par réflexion. Lés conditions d'accord de phase sont obtenues par biréfringence de Fresnel en réflexion interne totale. Il est montré que cette technique est analogue dans son principe à celle de l'accord de phase par biréfringence naturelle: on parle donc d'accord de phase de Fresnel. Deux situations schématiques sont analysées. La première est celle du quasi-accord de phase résonnant classique: le modèle théorique que nous avons développé prédit correctement les observations expérimentales. La seconde est une particularité de l'accord de Fresnel: il s'agit du quasi-accord de phase non résonnant, qui permet d'alléger considérablement les conditions d'accord de phase et autorise une grande accordabilité spectrale. L'influence de facteurs limitants est également quantifiée. Ainsi, le décalage de Goos-Hänchen rappelle, par ses effets, le walk-off classique. Ceci limite en fait les dimensions de la plaque. Cependant, le facteur le plus sévèrement limitant s'avère être la rugosité de surface: en effet, ce paramètre suffit seul à quantifier l'efficacité de toute la structure. Des calculs du seuil d'oscillation paramétrique optique sont développés sur la base de la formule de Brosnan et Byer. La fluorescence paramétrique a été observée dans une plaque en accord de Fresnel. Les premières estimations du seuil d'oscillation sont prometteuses
Mid-infrared tunable sources are becoming of considerable interest for applications in environmental monitoring. Semiconductors of the technological mainstream (such as gallium arsenide or zinc selenide) are excellent candidates for optical conversion of near-infrared waves into the mid-infrared range. However, these materials are isotropic, so that quasiphase-matching scenarios are needed to get an efficient conversion. Reflection quasiphase-matching techniques are studied here. We make use of the Fresnel birefringence at total internal reflection to reach the phase-matching conditions in a plane parallel plate. It is shown that this technique is very similar in its principle to the natural birefringence phase-matching : we thus call it Fresnel phase-matching. Two schematic situations are explored. First, a model of classical resonant quasi-phase matching scenario is presented; the agreement between theoretical predictions and experimental results is convincing. Second, the Fresnel birefringence allows a new non-resonant quasiphase-matching scenario: this appears to greatly alleviates the phase-matching conditions and provides a high tenability. The impact of restricting factors is also quantified. So, the Goos-Hänchen shift is similar, in terms of conversion yield, to the classical walk-off. This actually limits the dimensions of the plate. However, the most inhibiting parameter appears to be the surface roughness : indeed, this sole factor is enough to determine the conversion efficiency of the whole structure. Optical parametric oscillation threshold calculations based on the Brosnan and Byer formula are finally presented. Parametric fluorescence is measured in a Fresnel phase-matched plate. The first estimations of the oscillation threshold are promising

Diverses applications, telles que la détection de polluants ou neurotoxiques, nécessitent de disposer de sources optiques accordables intenses dans l’infrarouge (IR) moyen (8–12 µm). Une voie bien adaptée pour répondre à ces besoins est d’utiliser l’optique non linéaire pour convertir vers l’IR moyen le rayonnement d’un laser émettant dans l’IR proche. Cependant, les matériaux non linéaires usuels ne peuvent être utilisés pour la bande 8–12 µm car ils absorbent au-delà de 4 µm. Afin de s’affranchir de cette limitation, nous étudions ici l’utilisation des semiconducteurs isotropes comme matériaux non linéaires alternatifs. En effet, ces matériaux (GaAs, ZnSe, etc. ) présentent de forts coefficients non linéaires, et sont transparents dans l’IR moyen. Comme ces matériaux sont isotropes, des techniques de quasi-accord de phase doivent être mises en place pour une conversion non linéaire efficace. La technique choisie ici est celle de la biréfringence de Fresnel. Nous avons étudié cette technique aussi bien d’un point de vue expérimental par des expériences de différence de fréquences dans GaAs entre deux faisceaux proche IR accordables (~1,9 µm et 2,4 µm), que d’un point de vue théorique par le développement de nouveaux modèles prenant en compte tous les processus linéaire et non linéaire intrinsèques à la biréfringence de Fresnel. Enfin, cette technique d’accord de phase a été appliquée à l’auto-différence de fréquences dans les lasers ZnSe:Cr afin de générer une onde IR moyen à partir d’un faisceau pompe unique. L’onde à 10 µm est alors générée par différence de fréquences entre l’onde pompe à 1,9 µm et l’onde laser émise par les ions Cr2+ autour de 2,3 µm
Tunable mid-infrared (IR) sources are of high interest for many applications, including chemical monitoring, gas analysis, remote sensing, and IR countermeasures. A promising way to obtain such mid-IR emission is to use optical sources based on parametric conversion in nonlinear materials. However, apart from few materials (ZnGeP2, AgGaSe2, CdSe,…), most of usual nonlinear materials exhibit strong multiphonon absorption beyond 5 µm. Therefore, an important issue is to find adequate materials for the 8﷓12 µm band. In this context, semiconductors of the technological mainstream, such as GaAs or ZnSe, are excellent candidates for mid-infrared parametric generation. Indeed, they display high non linear susceptibility and they are transparent from the near-infrared up to 20 µm. However, since these materials are isotropic, quasi-phase-matching techniques have to be implemented to get an efficient conversion. Nonetheless, this limitation can be overcome using Fresnel birefringence that takes place at total internal reflection. We present here an experimental and theoretical study of this phase matching technique : difference frequency generation experiments are carried out and new models are developped to take into account all the physical processes involved. We investigate then self-difference frequency mixing in Cr:ZnSe laser using Fresnel phase matching. Taking advantage of both the lasing and nonlinear properties of this material, we demonstrate that 8–12 µm radiation can be produced using a single pump beam at 1. 9 µm. Subsequently, difference frequency mixing between the 1. 9µm pump beam and 2. 3µm laser beam produces a mid-IR radiation in the 9 µm range

Synthèses et caractéristiques de polyesters thermotropes nématiques. Étude des propriétés optiques à la transition anisotrope-isotrope. L'existence d'une biphase nématique-isotrope est démontrée. Les conditions de formation de cette biphase, sa cinétique de séparation, la répartition des chaînes polymères selon leur longueur sont caractérisées en fonction du type de polymère, sa masse moléculaire, la durée et la température du recuit

L'objectif de ce travail consiste en l'étude in vitro des phénomènes d'autoassemblage des molécules de collagène de type I en phases denses. Dans un premier temps nous nous sommes consacrés à l'étude de solutions colloïdales de collagène solubilisé en milieu acide. Nous avons étudié la transition isotrope/cholestérique ainsi que la structure de la phase cristal-liquide obtenue à l'aide de la microscopie optique à lumière polarisée et de la diffusion des rayons X aux petits angles. De plus, nous avons décrit les propriétés rhéologiques de ces solutions à l'aide d'expériences en régime oscillant en géométrie cône-plan. Ensuite, nous avons cherché à déterminer l'influence de quelques paramètres physicochimiques simples sur la formation de gels fibrillaires à partir des solutions acides (la « fibrillogenèse »). Ces gels ont été caractérisés par diffusion des rayons X et microscopie électronique à transmission sur coupes ultrafines. Enfin, nous présentons quelques expériences de minéralisation de ces matrices fibrillaires ordonnées ; nous y montrons comment nous avons réussi à obtenir une phase minérale coalignée avec la phase organique. Ce travail s'inscrit dans un contexte plus large de compréhension de la morphogenèse tissulaire et de la synthèse de biomatériaux ordonnés.

Pour poutres de materiaux parfaitement colles, determination de deux coefficients de cisaillement par la notion de variables homogeneisees, calcules en fonction de la frequence pour poutre en vibrations libre-libre. Etude comparatives sur poutres sandwich; determination de la fonction de gauchissement des sections par la resolution d'un probleme de neumann poisson. Calcul par elements finis: adaptation de codes industriels pour poutres homogenes (frequences et modes propres), elaboration d'un code specifique

Cette thèse vise à améliorer la résolution en trois dimensions grâce à une technique récente d’imagerie : la microscopie tomographique diffractive (MTD). Son principe est d’éclairer l’objet successivement sous différents angles en lumière cohérente, de détecter le champ diffracté en phase et en amplitude, et de reconstruire la carte 3D de permittivité de l’objet par un algorithme d’inversion. La MTD s’est avérée capable de combiner plusieurs modalités utiles pour la microscopie sans marquage, telles que plein champ, champ sombre, à contraste de phase, confocale, ou encore la microscopie à synthèse d’ouverture 2D ou 3D. Toutes sont basées sur des approximations scalaires et linéaires, ce qui restreint leur domaine d’application pour restituer l’objet de manière quantitative. A l’aide d’une inversion numérique rigoureuse prenant en compte la polarisation du champ et le phénomène de diffusion multiple, nous sommes parvenus à reconstruire la carte 3D de permittivité d’objets avec une résolution de λ/4. Une amélioration supplémentaire la portant à λ/10 a été rendue possible par l’insertion d’information a priori sur l’objet dans l’algorithme d’inversion. Enfin, la résolution axiale est moins bonne du fait de l’asymétrie des schémas d’illumination et de détection dans les microscopes. Pour s’affranchir de cette limitation, une configuration de tomographie assistée par miroir a été implémentée et a mis en évidence un pouvoir de séparation axial meilleur que λ/2. Au final, la MTD s’est illustrée comme un outil de caractérisation puissant pour reconstruire en 3D les objets ainsi que leurs indices optiques, à des résolutions bien supérieures à celles des microscopes conventionnels
This PhD thesis is devoted to the three-dimensional isotropic resolution improvement using optical tomographic diffraction microscopy (TDM), an emerging optical microscope technique. The principle is to illuminate the sample successively with various angles of coherent light, collect the complex (amplitude and phase) diffracted field and reconstruct the sample 3D permittivity map through an inversion algorithm. A single TDM measurement was shown to combine several popular microscopy techniques such as bright-field microscope, dark-field microscope, phase-contrast microscope, confocal microscope, 2D and 3D synthetic aperture microscopes. All rely on scalar and linear approximations that assume a linear link between the object and the field diffracted by it, which limit their applicability to retrieve the object quantitatively. Thanks to a rigorous numerical inversion of the TDM diffracted field data which takes into account the polarization of the field and the multiple scattering process, we were able to reconstruct the 3D permittivity map of the object with a λ/4 transverse resolution. A further improvement to λ/10 transverse resolution was achieved by providing a priori information about the sample to the non-linear inversion algorithm. Lastly, the poor axial resolution in microscopes is due to the fundamental asymmetry of illumination and detection. To overcome this, a mirror-assisted tomography configuration was implemented, and has demonstrated a sub-λ/2 axial resolution capability. As a result, TDM can be seen as a powerful tool to reconstruct objects in three-dimensions with their optical material properties at resolution far superior to conventional microscopes

In this thesis, based on the Onsager excluded volume interaction model, two nematic ordering problems of wormlike (semiflexible) polymer are studied: one is to investigate the isotropic-nematic interface of polymers for three typical cases—the flexible one, the rigid-rod one and the intermediate one; the other is to investigate a very long polymer confined between two infinite flat hard walls.

Many previous studies of the isotropic-nematic phase coexistence are mainly focused on either rigid rod-like polymers with small flexibility, or flexible polymers with large flexibility. The phase coexistence of polymers with intermediate flexibility is desired to be investigated. For these three typical cases (flexible, rigid-rod and intermediate), the profiles for density, order parameter and tension contribution were shown for different tilt angles. The interface tension was studied. The simulation results are consistent with those reported by other people.

We investigated the confinement of a long polymer between two flat hard walls, which are separated by a distance comparable to the effective Kuhn length of polymer chain by the wormlike chain model with or without the Onsager excluded volume interaction. Without the interaction, the results are compared with those of the Gaussian chain model. Including the interaction, the phase diagram is analyzed.

Dans ce travail de thèse, une transition isotrope-nématique induite par cisaillement dans les fondus de polymères cristaux liquides en peigne a été pour la première fois mise en évidence. Cette transition de phase hors équilibre est caractérisée principalement par l'apparition, au delà d'un taux de cisaillement critique, d'une phase fortement biréfringente en phase isotrope (T > T_NI) et par un plateau de contrainte dans les courbes d'écoulement de contrainte en fonction du taux de cisaillement. Ces résultats sont interprétés comme révélateurs d'une transition de phase hors équilibre analogue à une transition du premier ordre, donnant lieu à une région du diagramme de phase hors équilibre (contrainte en fonction de la température) où la phase isotrope et la phase nématique induite coexistent. Deux bandes de biréfringences différentes sont directement visualisées dans le plan de cisaillement (vitesse, gradient de vitesse). Enfin, le mécanisme envisagé donnant lieu à cette transition isotrope-nématique hors équilibre est la déformation de chaînes connectées dans des amas élastiques. Des expériences de diffusion des neutrons aux petits angles, réalisées in situ, dans une cellule de Couette spécialement conçue, permettent l'étude de la conformation des chaînes en phase nématique induite. On a ainsi pu démontrer que la conformation des chaînes subit une réorientation de perpendiculaire au directeur de la phase nématique à l'équilibre à parallèle dans la phase nématique induite. Enfin, dans le cas d'un polymère caractérise par une conformation de chaîne de type parallèle au directeur, en phase nématique induite ainsi qu'à l'équilibre, nous avons relevé l'apparition d'oscillations temporelles auto-entretenues de la contrainte en réponse à un taux de cisaillement imposé en phase nématique induite. Ce phénomène oscillant est interprété en termes de déformation élastique suivie d'une relaxation du milieu
In this work, a shear induced isotropic to nematic phase transition in melts of side chain liquid crystal polymers is pointed out for the first time. This non-equilibrium transition has been revealed through rheo-optical measurements: a high birefringence emerges from the isotropic phase when sheared above a critical shear rate. Furthermore, a stress plateau in the flow curves of stress versus shear rate is observed and interpreted as relevant of a non-equilibrium transition achieved through shear banding. Two bands of different birefringence have been observed in the shear plane (velocity, velocity gradient). The mechanism considered for the formation of the shear induced nematic phase is the deformation of connected chains forming elastic clusters. Small angle neutron scattering experiments, performed in situ, in an especially designed Couette shear cell, allow the determination of the main-chain conformation in the shear induced nematic phase. The oblate conformation observed in the equilibrium nematic phase (at T < T_NI) is changed into a prolate one characterizing the shear induced nematic phase. Lastly, in the case of a side chain liquid crystal polymer characterized by a prolate main chain conformation, in the induced nematic phase as well as in the equilibrium one, we pointed out the appearance of undamped stress oscillations in response to an applied shear rate in the shear induced nematic phase. This oscillating phenomenon is interpreted in terms of an elastic deformation followed by a relaxation of the sample

La première partie de ce travail a consisté en l'étude des effets prétransitionnels qui apparaissent en chauffant dans les phases ordonnées du mélange binaire lyotrope C12EO6/H2O à l'approche de la transition vers la phase isotrope. En employant une technique de photoblanchiment, nous avons déterminé les coefficients de diffusion de sondes fluorescentes en fonction de la température. Nous avons montré que des défauts structuraux connectant les agrégats de surfactant apparaissent dans les phases lamellaire et hexagonale et nous avons déterminé leur structure et leur densité. Nous en avons déduit que la phase isotrope est fortement connectée au voisinage des mésophases. Cette conclusion est confirmée par le fait que le coefficient de diffusion ne varie pas à la transition entre la phase isotrope et la phase cubique, elle-même fortement connectée.

Nous avons ensuite exploré les propriétés dynamiques de la phase isotrope à haute concentration en combinant la diffusion dynamique de la lumière avec des expériences de rhéologie à haute fréquence. Nous avons mis en évidence un temps de relaxation terminale extrêmement court (de l'ordre de la microseconde) et avons expliqué ce comportement dans le cadre de théories déjà existantes sur la rhéologie des micelles connectées en incluant l'effet de l'ordre local.

La première partie de ce travail a consisté en l'étude des effets prétransitionnels qui apparaissent en chauffant dans les phases ordonnées du mélange binaire lyotrope C12EO6/H20 à l'approche de la transition vers la phase isotrope. En employant une technique de photoblanchiment, nous avons déterminé les coefficients de diffusion de sondes fluorescentes en fonction de la température. Nous avons montré que des défauts structuraux connectant les agrégats de surfactant apparaissent dans les phases lamellaire et hexagonale et nous avons déterminé leur structure et leur densité. Nous en avons déduit que la phase isotrope est fortement connectée au voisinage des mésophases. Cette conclusion est confirmée par le fait que le coefficient de diffusion ne varie pas à la transition entre la phase isotrope et la phase cubique, elle-même fortement connectée. Nous avons ensuite exploré les propriétés dynamiques de la phase isotrope à haute concentration en combinant la diffusion dynamique de la lumière avec des expériences de rhéologie à haute fréquence. Nous avons mis en évidence un temps de relaxation terminale extrêmement court (de l'ordre de la microseconde) et avons expliqué ce comportement dans le cadre de théories déjà existantes sur la rhéologie des micelles connectées en incluant l'effet de l'ordre local.

CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
Este trabalho propõe uma técnica do tipo rotação de fase para migração em profundidade de dados sísmicos para meios com simetria polar local (localmente transversalmente isotrópicos, LTI), nos quais a direção do eixo de simetria varia continuamente ao longo das camadas. São testadas, através de simulações numéricas de levantamentos sísmicos, a precisão e a estabilidade do método, em função da variação do eixo de simetria. Para a realização das simulações, desenvolveu-se um método a partir da solução da equação elástica da onda usando-se a técnica das diferenças finitas, que possibilita a modelagem em meios LTI, onde cada ponto da malha tem suas características definidas pelas velocidades de fase P e SV, parâmetros de Thomsen, densidade e inclinação do eixo de simetria. Na separação dos modos de onda qP e qSV dos sismogramas, implementou-se um algoritmo baseado na solução da equação de Christoffel para determinar os operadores de separação. A migração para cada família de tiro comum é realizada por soluções da equação da onda usando somente técnicas de rotações de fase. De fato, tanto a depropagação do campo registrado quanto a geração das matrizes de tempo utilizadas na condição de imageamento, são realizadas por soluções que envolvem rotações de fase para cada conjunto de parâmetros, em cada nível de profundidade. Nos resultados das migrações usando reflexões dos tipos qP-qP, e qP-qSV, os horizontes foram localizados precisamente e verificou-se que o processo é estável em relação à variação do eixo de simetria. Vale ressaltar que o método não está restrito a aquisições sísmicas multicomponentes, podendo ser aplicado em dados sísmicos marítimos convencionais, como também em dados provenientes de aquisições do tipo OBC (Ocean Bottom Cable) e com cabo vertical. Como o método proposto se baseia em algoritmos que utilizam técnicas de rotação de fase, a sua implementação conta com o beneficio de ser altamente paralelizável.
This work proposes a technique based on the phase-shift method to implement pre-stack depth migration on locally transverse isotropic media (LTI), in which the direction of the symmetry axis varies continually along the layers. Through numerical seismic data simulations the methods robustness and stability were tested in relation to the axis symmetry variations. For seismic modeling, a generalization of the finite differences method for the solution of the elastic wave equation was used. With this procedure, it was possible to accommodate seismic modeling on LTI media defined by six parameters at each grid point, i.e., density, P and S wave propagation velocities along the local symmetry axis, Thomsen parameters and, the direction of the local symmetry axis itself. In order to separate from the seismograms the qP and qSV wavefields, an algorithm based on the Christoffel equation was implemented. The migration for each common shot gather is implemented solely by phase-shift based algorithms, which means that not only the depropagation of the registered wavefield, but also the generation of the time matrices involved in the imaging condition were obtained in this manner for each set of parameters at each depth level. The migration results using qP-qP and qP-qSV reflections show that the horizons were located precisely, and that the process is stable in relation to the symmetry axis variations. The proposed method is not restricted to multicomponent seismic acquisitions, but it can be applied to marine seismic data using streamers, or Ocean Bottom Cables or vertical cables. Since the proposed method uses phaseshift algorithms, its parallel implementation can be highly efficient.

La présente thèse rassemble des études expérimentales portant sur le sujet de la dynamique des fluctuations thermiques dans les phases nématiques uniaxes (ND-biréfringence positive- et NC-biréfringence négative), nématique biaxe et isotrope, du système lyotrope K-Laurate, Décanol, D₂O. En contraste avec les cristaux liquides nématiques classiques ou thermotropes, constitués par des molécules allongées, les nématiques lyotropes sont formés par des agrégats (ou micelles) en solution dans l'eau. Dans les systèmes que nous avons étudiés, la phase biaxe apparaît entre deux phases uniaxes dans l'ordre suivant, à température croissante : Isotrope→ND→Nbx→NC→Isotrope. La technique de base utilisée est la diffusion quasi-élastique de la lumière (Rayleigh). L'analyse par battement de photons permet de mettre en évidence les fluctuations lentes originaires du couplage direct de la lumière avec le paramètre d'ordre via le tenseur diélectrique. Dans les études faites en présence de la phase nématique biaxe, nous avons mis en évidence l'existence des fluctuations de biaxialité dans les deux phases uniaxes voisinantes (NC et ND) et mesuré l'effet de ralentissement critique de ces fluctuations lorsque les températures de transition ND-Nbx et NC-Nbx sont approchées. Ces mesures ont permis d'estimer la longueur de corrélation ε des fluctuations de biaxialité. Près de TC nous avons trouvé ε ~ 500 A, c'est-à-dire de l'ordre de 10 tailles micellaires. Ensuite, nous avons entrepris une étude combinée des transitions de phase uniaxe-biaxe et isotrope-nématique. Pour analyser les mesures obtenues, nous avons estimé, en utilisant le formalisme de Landau­Khalatnikov, les dépendances en température des taux de relaxation des 5 modes de fluctuation associés au paramètre d'ordre. Ces estimations permettent de décrire les 5 modes. D'autre part, un mode supplémentaire a été trouvé. Nous avons interprété ce mode en termes des fluctuations de densité micellaire
This thesis groups experimental studies on the subject of the dynamics of thermal fluctuations in the uniaxial nematic (ND: positive birefringence; NC: negative birefringence), biaxial nematic, and isotropic phases of the lyotropic system K-Laurate, Decanol, D₂O. Differently from classical thermotropic nematics in which the building blocks are elongated molecules, lyotropic nematics are formed by aggregates (or micelles) dispersed in water. In the system which we have studied the biaxial phase appears between the two uniaxial phases, in the following temperature sequence: Isotrope→ND→Nbx→NC→Isotrope. The main technique employed was Rayleigh light scattering. The sJow fluctuations, originated from the coupling of the light waves with the order parameter via the dielectric tensor can be adequately followed by photocorrelation techniques. In the main part of the thesis (text in english) we have performed studies in a system exhibiting the biaxial phase. We have demonstrated the existence of biaxiality fluctuations in the neighbours ND and NC uniaxial phases. Such measurements did allow us to estimate the correlation length associated to biaxiality fluctuations. Near TC we found ε ~ 500 A, i. E. About 10 micellar sizes. Next we have performed a combined study of both uniaxial­biaxial and isotropic-nematic phase transitions in the same system. In order to analyze these measurements we have estimated, by using a Landau­Khalatnikov formalism, the temperature dependence of the relaxation rates of the 5 fluctuation modes associated to the order parameter. These estimates have accounted for the description of such modes. On the other hand a new unexpected mode has been found. We have interpretated it in terms of a mechanism of micellar density fluctuations, a special feature from lyotropic materials

Probability distributions of electric field and electric potential in two-phase particulate composite materials with spherical inclusions are found in the limit of small particle concentration. Additionally a method for the approximation of local fields within random statistically isotropic composites with a finite number of field fluctuations which retain potentiality is presented and an approximate solution with the variational principal for homogenization in statistical terms for three fluctuations within one phase and a homogeneous second phase is found.

Le mémoire traite des effets d'une très importante chiralité dans de nouveaux cristaux liquides, présentant des phases smectiques helicoidales frustrees (s#c#*fi ferrielectrique, s#c#*, phases a torsion par joints de grains tgb#a et tgb#c, phases bleues tgb) et phases isotropes anomales. Dans un premier temps est présentée une nouvelle méthode de mesure du pas helicoidal, fondée sur l'étude de franges d'ellipticite, dites franges de friedel, obtenues sur gouttes très aplaties observées au microscope polarisant en lumière réfléchie. Cette technique, élaborée pour la phase s#c#*, a permis d'en démontrer le caractère helicoidal, et de suivre les variations de la torsion avec la température. L'étude d'une série de thiobenzoates montre que le pas peut atteindre des valeurs très faibles (0. 05 m), et présenter d'apparentes divergences et inversions. Ces résultats sont confrontes a trois modeles de structure de la phase s#c#*. L'étude de nombreux autres composes vient confirmer les résultats expérimentaux obtenus pour la série de thiobenzoates
Une nouvelle séquence de phases, ainsi que la présence d'une phase s#c#* entre les phases s#c#* et tgb#a, ont de plus été mises en évidence. Dans un deuxième temps a été étudiée une série présentant les phases s#c#*, tgb#a tgb#c et phases bleues tgb. Les mesures de pas effectuées dans les trois premières phases ont révèle une torsion tres forte ; il est ainsi montre que l'existence de ces nouvelles phases bleues tgb est, comme pour l'habituelle phase bleue cholesterique, une conséquence d'une très forte chiralité. Les trois phases bleues tgb sont mises en évidence avec des textures optiques bien définies, en particulier pour la phase bpiii qui n'avait jamais été observée auparavant. Enfin les phases isotropes anomales présentées par deux types de matériaux sont étudiées optiquement, amenant a la détermination d'une texture particulière, et a l'observation de plusieurs phases de ce type dans la séquence d'un des composes

Cette thèse est consacrée à l'étude du mouvement de petites bulles dans des écoulements turbulents homogènes isotropes. Le travail aborde différentes questions liées à la description statistique des forces hydrodynamiques exercées sur une bulle ainsi qu'à leur modélisation stochastique tenant compte des effets d'intermittence. Nous proposons tout d'abord un modèle pour l'accélération de bulles de taille inférieures à l'échelle dissipative de l'écoulement soumises à la traînée et aux forces d'inertie du fluide. Ce modèle, qui dépend du nombre de Stokes, du nombre de Reynolds et du rapport de densité, reproduit l'évolution de la variance d'accélération ainsi que l'importance relative et l'alignement des deux forces observées à partir de simulations numériques directes (DNS). Deuxièmement, sur la base de l’observation selon laquelle les statistiques d’accélération conditionnelles au taux de dissipation de l’énergie cinétique locale sont invariantes avec le nombre de Stokes et le taux de dissipation, nous proposons un modèle stochastique du vecteur d’accélération instantanée de la bulle, qui tient compte de l’intermittence à petite échelle de la turbulence. La norme de l'accélération de la bulle est obtenue en modélisant le taux de dissipation le long de la trajectoire de la bulle à partir d'un processus stochastique lognormal, tandis que son orientation est donnée par deux marches aléatoires couplées sur une même sphère afin de modéliser l'évolution de l'orientation conjointe la traînée et les forces d'inertie agissant sur la bulle. Le modèle stochastique proposé pour l'accélération des bulles permet d'améliorer les simulations de grandes turbulences (LES) d'écoulements turbulents transportant de petites bulles. Il peut reproduire efficacement l’effet des échelles turbulentes inférieures à la résolution du maillage en ajoutant une contribution aléatoire en fonction du taux de dissipation moyen local. Les comparaisons avec le DNS et les LES standard montrent que le modèle proposé améliore considérablement les statistiques de la phase de formation de bulles. Troisièmement, nous étendons les résultats précédents dans le cas de bulles à plus grand nombre de Reynolds en prenant en compte les lois de traînée non-linéaires. Nous définissons un temps de relaxation effectif basé sur le coefficient de traînée pour caractériser le mouvement de la bulle (accélération, vitesse). Finalement, nous étudions l’effet de la flottabilité et de la force de portance sur la dynamique des bulles et analysons la réduction de la vitesse moyenne ascensionnelle dans les écoulements turbulents par rapport aux écoulements au repos. On observe que la bulle explore de préférence une région ayant une accélération de fluide vers le bas qui contribue, par le biais de la force d’inertie, à réduire la vitesse de montée. De plus, comme déjà observée, la force de portance amène de préférence les bulles dans un mouvement de fluide en aval qui réduit également leur vitesse de montée
This thesis is devoted to the study of the motion of small bubbles in homogeneous isotropic turbulent flows. The work addresses several questions related to the statistical description of the hydrodynamic forces exerted on a bubble as well as the stochastic modeling of their high frequency fluctuations. First, we propose a model for the acceleration of micro-bubbles (smaller than the dissipative scale of the flow) subjected to the drag and the fluid inertia forces. This model, that depends on the Stokes number, the Reynolds number and the density ratio, reproduces the evolution of the acceleration variance as well as the relative importance and alignment of the two forces as observed from Direct Numerical Simulations (DNS). Second, based on the observation that acceleration statistics conditional to the local kinetic energy dissipation rate are invariant with the Stokes number and the dissipation rate, we propose a stochastic model for the instantaneous bubble acceleration vector accounting for the small-scale intermittency of the turbulent flows. The norm of the bubble acceleration is obtained by modeling the dissipation rate along the bubble trajectory from a log-normal stochastic process, whereas its orientation is given by two coupled random walk on a unit sphere in order to model the evolution of the joint orientation of the drag and inertia forces acting on the bubble. Furthermore, the proposed stochastic model for the bubble acceleration is used in the context of large eddy simulations (LES) of turbulent flows laden with small bubbles. It can effectively reproduce effect of turbulent motion at scales smaller than the mesh resolution by adding a random contribution depending on local average dissipation rate. Comparisons with DNS and standard LES, show that the proposed model improves significantly the statistics of the bubbly phase. Third, we extend the previous results in the case of bubbles with large Reynolds number by considering non-linear drag laws. We define an effective relaxation time based on the drag coefficient to characterize bubble motion (acceleration,velocity). Eventually we study the effect of buoyancy and lift force on the bubble dynamics, and analyze the reduction of the average rising velocity in turbulent flow compared to quiescent flows. It is observed that bubbles preferentially explore region having downward fluid acceleration which contributes through the inertia force to reduction of the rising velocity. In addition, as already observed, the lift force brings preferably bubbles into downstream fluid motion which also reduce their rising velocity

La caractérisation des réseaux de polymères, obtenus par photopolymérisation radicalaire, a été faite par gonflement en masse du réseau de poly(n-butylacrylate) dans des solvants organiques isotropes. L’étude a montré que le taux de gonflement dépend à la fois de la nature du solvant, de la densité de réticulation ainsi que de la température. Ce dernier paramètre influe seulement sur les réseaux gonflés dans des mauvais solvants, comme par exemple le méthanol. L’étude a été suivie d’une caractérisation par gonflement en volume des réseaux de poly(n-butyl-acrylate) et de poly(2-éthyl-hexyl-acrylate) dans des solvants anisotropes, tels que les cristaux liquides 5CB et E7. L’analyse a été effectuée par microscopie optique dans une grande plage de température. Le E7 présente une meilleure compatibilité avec le PABu qu’avec le PEHA. Le 5CB a une miscibilité supérieure à celle du E7 dans le PABu. L’étude comparative de gonflement dans des solvants isotropes et anisotropes a mis en évidence, qu’en termes de miscibilité, les cristaux liquides E7 et 5CB se situent entre le toluène comme bon solvant isotrope, et le méthanol, comme mauvais solvant isotrope. Le modèle de diffusion de Fick a été appliqué aux résultats expérimentaux de cinétique de gonflement des systèmes « polymères isotropes et solvants isotropes ». Une méthode d’optimisation a été utilisée qui consiste à déterminer les facteurs influant sur le gonflement et la réponse quand ces facteurs varient. A partir d’un minimum d’expériences, on aboutit à une surface de réponse qui couvre toute la gamme de l’étude. La méthode utilisée est le plan d’expériences factoriel 2k
The characterization of polymer networks, obtained by radical photopolymerization, was made by swelling of the network of poly (n-butylacrylate ) in isotropic organic solvents. The study showed that the swelling rate depends on the nature of the solvent, on the density of crosslinking as well as on the temperature. This last parameter influences only networks swollen in bad solvents, such as methanol. The study was followed by a characterization by swelling in volume of the networks of poly (n-butyl-acrylate ) and of poly (2-ethyl-hexyl-acrylate) in anisotropic solvents, such as the liquid crystals 5CB and E7. The analysis was made by optical microscopy on a large range of temperature. E7 presents a better compatibility with the PABu than with the PEHA. 5CB has a higher miscibility to that of E7 in PABu. The comparative study of swelling in isotropic and anisotropic solvents put in evidence, that in terms of miscibility, the liquid crystals E7 and 5CB are situated between the good isotropic solvent toluene and the bad isotropic solvent methanol.The model of diffusion of Fick was applied to the experimental results of swelling kinetics of the systems " isotropic polymers and isotropic solvents ". A method of optimization was used which consists in determining the factors influencing the swelling and the answer when these factors vary. From a minimum of experiments, we end up in a surface of answers which covers the whole range of the study. The used method is the factorial plan of experiments 2k

Thesis (M. S.)--Civil and Environmental Engineering, Georgia Institute of Technology, 2010.
Committee Chair: Laurence J. Jacobs; Committee Member: Jianmin Qu; Committee Member: Jin-Yeon Kim. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Com uma mistura de laurato de potássio, decanol e agua, determina-se a birrefringência induzida, na fase isotrópica, por gradientes de velocidade, no interior da amostra. Os movimentos são provocados através de vibrações periódicas nas paredes do porta amostras. O tempo de relaxação, da estrutura de rolos, e determinado experimental e teoricamente. É determinado, também, o parâmetro T AST (temperatura em torno da temperatura de transição), ate então desconhecido, em cristais líquidos liotrópicos. Como uma provável aplicação pratica, e proposta a confecção de dispositivos sensíveis a vibrações.
With a mixture of the Potassium Laurate, Decanol and water, the birefringence induced by gradient of the velocity, in the isotropic phase, is determinated. The movement are provocated through periodic vibrations of the superface of the sample holder. The relaxation time of the roll structure is determinated experimental an theorically. The temperature T* (temperature around the transition temperature), well-known in thermotropic liquid crystals, is determinated in liotropic liquid crystals. The confection of the sensible vibration dispositive is proposed.

L'interaction réciproque entre une turbulence fluide et des inclusions dispersées a été étudiée à l'aide de simulations numériques directes (DNS) en turbulence homogène isotrope stationnaires forcée. Le temps de relaxation des particules va de l'échelle turbulente de Kolmogorov à celle eulérienne et la charge de 0 à 1. L'analyse a été effectuée dans le cadre du modèle eulérien complété de l'approche lagrangienne développés au Laboratoire National d'Hydraulique et étendue au couplage inverse et aux effets de Reynolds. On trouve que les particules dissipent en moyenne de l'énergie turbulente. Les spectres de taux d'échange d'énergie entre phases montrent que les particules entraînent le fluide sur les grands nombres d'onde, expliquant la croissance relative constatée des petites échelles turbulentes. Une analyse spectrale révèle que le mécanisme physique responsable est celui du transfert de covariance fluide-particules par la turbulence. Concernant la modélisation, la dépendance en Reynolds et la contribution directe de la charge s'avèrent essentielles pour bien prédire les moments de la phase dispersée. Une étude prospective pour des applications pratiques par simulations des grandes échelles (LES) a donné les résultats suivants : la LES peut s'utiliser pour les écoulements diphasiques totalement couplés à condition d'employer le modèle dynamique mixte de sous-maille et de prendre des particules de temps de relaxation supérieur à celui de coupure : le couplage inverse dépendrait davantage de la position de ce temps de relaxation par rapport au temps eulérien que par rapport à celui de Kolmogorov.

De nombreux liquides subissent un changement de volume lorsqu'ils gèlent. Pour l'eau et certaines solutions aqueuses, l'expansion volumétrique au cours de la solidification peut entraîner une série de problèmes mécaniques. Dans l'industrie automobile, l'expansion de changement de phase (ECP) met en cause la sécurité des réservoirs des véhicules aux saisons froides. Une des questions les plus problématiques est l'expansion de la solution aqueuse d'urée (SAU) dans le réservoir du système SCR des véhicules diesels. Lorsque le liquide gèle, les composants intérieurs ainsi que le réservoir lui-même peuvent être endommagés dû à la pression apportée par la dilatation du liquide solidifié. Dans le centre , une méthode numérique est fortement attendue afin de prévoir la répartition de la température, des contraintes ainsi que de la déformation des composants lors d'un processus de solidification. Du fait que les informations sur la solution d'urée restent limitées, la structure de la glace cristalline ainsi que ses comportements mécaniques sont principalement passés en revue. La préférence d'orientation de croissance des grains de glace à l'interface de cristallisation met en évidence, l'hypothèse de l'ECP non-isotropique pour des problèmes de solidification. Une série de tests mécaniques a été réalisée afin d'obtenir les propriétés basiques de SAU à l'état solide à différentes températures. Une méthode « différence-volume » a été appliquée pour mesurer la variation de la densité de la SAU lors du processus de solidification. Pour la suite, des études analytiques thermiques et mécaniques sont effectuées. Pour l'aspect thermique, le problème classique de Stefan est passé en revue. Un schéma de différence-finie est proposé et il permet de calculer la position de l'interface et les profils de température pour un modèle sphérique. Pour l'aspect mécanique, un modèle sphérique similaire est établi à la base de l'ECP non-isotropique. Les solutions analytiques des contraintes et de la pression liquide sont présentées en fonction de la position de l'interface. Une méthode éléments-finis thermo-mécaniquement couplée est développée afin de simuler efficacement les contraintes thermiques, les déformations et la pression liquide dans un problème de solidification avec des relations constitutives de comportement non-linéaires. Les contraintes thermiques sont calculées en chaque point d'intégration en résolvant les équations elasto-viscoplastiques avec l'ECP non-isotropique. Le problème aux limites est résolu par la méthode de Newton-Raphson. Cette procédure est implémentée dans le package Abaqus via un UMAT. La méthode est validée d'abord pour les aspects algorithmiques par les solutions analytiques, puis pour les paramètres de comportement retenus par une série de tests expérimentaux. De plus, une étude de cas réaliste sur un réservoir de la SAU est introduite. Les avantages et les limitations de la méthode numérique lors d'une application sont évalués
Many liquids involve a change in volume when they freeze. For water and some aqueous solutions, the volumetric expansion during solidification may invoke a series of mechanical issues. In automobile industries, the security of tanks installed in vehicles is challenged by the Phase-Change Expansion (PCE) of the freezing liquid in cold conditions. One of the most problematic issues is the expansion of Aqueous Urea Solution (AUS) in the SCR tank of diesel vehicles. As the liquid freezes, interior components may be deformed under the stress or pressure of the expanding AUS, potentially leading to failures of the storage tank. In the product center, a numerical method is of high demand to perform thermo-mechanical analysis to predict the temperature and stress distribution during a liquid solidification process in their tanks. In this work, a bibliographic study is carried out first on the basic knowledge of the ice and AUS. Due to the very limited information on urea solution in the literature, the structure and behaviors of freshwater ice are mainly reviewed. The grain orientation preference at the growth interface of polycrystalline ice provides the evidence of non-isotropic PCE for the solidification problem. A series of mechanical tests have been performed to characterize the basic properties of the solidified AUS at different temperatures. The density evolution is measured using a volume-difference method. Then, both thermal and mechanical analytical studies are performed. The classical thermal Stefan problem is reviewed and a finite-difference scheme is proposed to calculate the interface position and temperature profiles of a spherical solidification model. Mechanically, a similar spherical model is established based on the non-isotropic PCE phenomenon of ice growth. The solutions of stress distribution and liquid pressure evolution are given as a function of the solidification interface position. Finally, an efficient thermo-mechanical FEM is proposed to evaluate the thermal stress, strain, displacement and pressure in solidification problems with highly nonlinear relations. Three particular methods for treating the liquid phase with fixed-grid approaches are introduced. The thermal stress is computed at each integration point by integrating the elasto-viscoplastic constitutive equations with non-isotropic PCE. Then, the boundary value problem is solved using the full Newton-Raphson method. This procedure is implemented into the FE package Abaqus via a UMAT subroutine. The numerical model is validated first for the algorithmic aspect by the analytical solutions, and then for the parametric calibration by a series of benchmark tests. In the end, a realistic study case on a real-size AUS storage tank is introduced. Advantages and limitations of the numerical method in the application are evaluated

Phased array feeds (PAFs) are a promising new technology for astronomical radio telescopes. While PAFs have been used in other fields, the demanding sensitivity and calibration requirements in astronomy present unique new challenges. This dissertation presents some of the first astronomical PAF results demonstrating the lowest noise temperature and highest sensitivity at the time (66 Kelvin and 3.3 m^2/K, respectively), obtained using a narrowband (425 kHz bandwidth) prototype array of 19 linear co-polarized L-band dipoles mounted at the focus of the Green Bank 20 Meter Telescope at the National Radio Astronomy Observatory (NRAO) in Green Bank, West Virginia. Results include spectral line detection of hydroxyl (OH) sources W49N and W3OH, and some of the first radio camera images made using a PAF, including an image of the Cygnus X region. A novel array Y-factor technique for measuring the isotropic noise response of the array is shown along with experimental measurements for this PAF. Statistically optimal beamformers (Maximum SNR and MVDR) are used throughout the work. Radio-frequency interference (RFI) mitigation is demonstrated experimentally using spatial cancelation with the PAF. Improved RFI mitigation is achieved in the challenging cases of low interference-to-noise ratio (INR) and moving interference by combining subspace projection (SP) beamforming with a polynomial model to track a rank 1 subspace. Limiting factors in SP are investigated including sample estimation error, subspace smearing, noise bias, and spectral scooping; each of these factors is overcome with the polynomial model and prewhitening. Numerical optimization leads to the polynomial subspace projection (PSP) method, and least-squares fitting to the series of dominant eigenvectors over a series of short term integrations (STIs) leads to the eigenvector polynomial subspace projection (EPSP) method. Expressions for the gradient, Hessian, and Jacobian are given for use in numerical optimization. Results are given for simulated and experimental data, demonstrating deeper beampattern nulls by 6 to 30dB. To increase the system bandwidth toward the hundreds of MHz bandwidth required by astronomers for a fully science-ready instrument, an FPGA digital backend is introduced using a 64-input analog-to-digital converter running at 50 Msamp/sec and the ROACH processing board developed at the University of California, Berkeley. International efforts to develop digital back ends for large antenna arrays are considered, and a road map is proposed for development of a hardware correlator/beamformer at BYU using three ROACH boards communicating over 10 gigabit Ethernet.

Dissertation (Ph.D.) -- Worcester Polytechnic Institute.
Keywords: smectic-A to smectic-C; nematic to smectic-A; isotropic-nematic; phase transition; quenched random disorder; liquid crystal; gel structure; turbidity; gel dynamics; x-ray intensity fluctuation spectroscopy ( XIFS ); ac-calorimetry; x-ray diffraction Includes bibliographical references (p. 210-218).

This thesis, which contains fourteen chapters in two parts, presents theoretical and computer simulation studies of dynamics in supercooled liquids and thermotropic liquid crystals. These two apparently diverse physical systems are unified by a startling similarity in their complex slow dynamics. Part I consists of six chapters on supercooled liquids while Part II comprises seven chapters on thermotropic liquid crystals. The fourteenth chapter provides a concluding note. Part I starts with an introduction to supercooled liquids given in chapter 1. This chapter discusses basic features of supercooled liquids and the glass transition and portrays some of the theoretical frameworks and formalisms that are widely recognized to have contributed to our present understanding. Chapter 2 introduces a new model of binary mixture in order to study dynamics across the supercooled regime. The system consists of an equimolar mixture of the Lennard-Jones spheres and the Gay-Berne ellipsoids of revolution, and thus one of its components has orientational degrees of freedom (ODOF). A decoupling between trans-lational diffusion and rotational diffusion is found to occur below a temperature where the second rank orientational correlation time starts showing a steady deviation from the Arrhenius temperature behavior. At low temperatures, the optical Kerr effect (OKE) signal derived from the system shows a short-to-intermediate time power law decay with a very weak dependence on temperature, if at all, of the power law exponent as has been observed experimentally. At the lowest temperature investigated, jump motion is found to occur in both the translational and orientational degrees of freedom. Chapter 3 studies how the binary mixture, introduced in the previous chapter, explores its underlying potential energy landscape. The study reveals correlations between the decoupling phenomena, observed almost universally in supercooled molecular liquids, and the manner of exploration of the energy landscape of the system. A significant deviation from the Debye model of rotational diffusion in the dynamics of ODOF is found to begin at a temperature at which the average inherent structure energy of the system starts falling as the temperature decreases. Further, the coupling between rotational diffusion and translational diffusion breaks down at a still lower temperature, where a change occurs in the temperature dependence of the average inherent structure energy. Chapters 4-6 describe analytical and numerical approaches to solve kinetic models of glassy dynamics for various observables. The β process is modeled as a thermally activated event in a two-level system and the a process is described as a β relaxation mediated cooperative transition in a double-well. The model resembles a landscape picture, conceived by Stillinger [Science 267, 1935 (1995)], where the a process is assumed to involve a concerted series of the β processes, the latter being identified as elementary relaxations involving transitions between contiguous basins. For suitable choice of parameter values, the model could reproduce many of the experimentally observed features of anomalous heat capacity behavior during a temperature cycle through the glass transition as described in chapter 4. The overshoot of the heat capacity during the heating scan that marks the glass transition is found to be caused by a delayed energy relaxation. Chapter 5 shows that the model can also predict a frequency dependent heat capacity that reflects the two-step relaxation behavior. The high-frequency peak in the heat capacity spectra appears with considerably larger amplitude than the low-frequency peak, the latter being due to the a relaxation. The model, when simplified with a modified description of the a process that involves an irreversible escape from a metabasin, can be solved analytically for the relaxation time. This version of the model captures salient features of the structural relaxation in glassy systems as described in chapter 6. In Part II, thermotropic liquid crystals are studied in molecular dynamics simulations using primarily the family of the Gay-Berne model systems. To start with, chapter 7 provides a brief introduction to thermotropic liquid crystals, especially from the perspective of the issues discussed in the following chapters. This chapter ends up with a detail description of the family of the Gay-Berne models. Chapter 8 demonstrates that a model system for calamitic liquid crystal (comprising rod-like molecules) could capture the short-to-intermediate time power law decay in the OKE signal near the isotropic-nematic (I-N) phase transition as observed experimentally. The single-particle second rank orientational time correlation function (OTCF) for the model liquid crystalline system is also found to sustain a power law decay regime in the isotropic phase near the I-N transition. On transit across the I-N phase boundary, two power law decay regimes, separated by a plateau, emerge giving rise to a step-like feature in the single-particle second rank OTCF. When the time evolution of the rotational non-Gaussian parameter is monitored as a diagnostic of spatially heterogeneous dynamics, a dominant peak is found to appear following a shoulder at short times, signaling the growth of pseudonematic domains. These observations are compared with those relevant ones obtained for the supercooled binary mixture, as discussed in chapter 2, in the spirit of the analogy suggested recently by Fayer and coworkers [J. Chem. Phys. 118, 9303 (2003)]. In chapter 9, orientational dynamics across the I-N transition are investigated in a variety of model systems of thermotropic liquid crystals. A model discotic system that consists of disc-like molecules as well as a lattice system have been considered in the quest of a universal short-to-intermediate time power law decay in orientational relaxation, if any. A surprisingly general power law decay at short to intermediate times in orientational relaxation is observed in all these systems. While the power law decay of the OKE signal has been recently observed experimentally in calamitic systems near the I-N phase boundary and in the nematic phase by Fayer and coworkers [J. Chem. Phys. 116, 6339 (2002), J. Phys. Chem. B 109, 6514 (2005)], the prediction for the discotic system can be tested in experiments. Chapter 10 presents the energy landscape view of phase transitions and slow dynamics in thermotropic liquid crystals by determining the inherent structures of a family of one-component Gay-Berne model systems. This study throws light on the interplay between the orientational order and the translational order in the mesophases the systems exhibit. The onset of the growth of the orientational order in the parent phase is found to induce a translational order, resulting in a smectic-like layer in the underlying inherent structures. The inherent structures, surprisingly, never seem to sustain orientational order alone if the parent nematic phase is sandwiched between the high-temperature isotropic phase and the low-temperature smectic phase. The Arrhenius temperature dependence of the orientational relaxation time breaks down near the I-N transition and this breakdown is found to occur at a temperature below which the system explores increasingly deeper potential energy minima. There exists a remarkable similarity in the manner of exploration of the potential energy landscape between the Gay-Berne systems studied here and the well known Kob-Andersen binary mixture reported previously [Nature, 393, 554 (1998)]. In search of a dynamical signature of the coupling between orientational order and translational order, anisotropic translational diffusion in the nematic phase has been investigated in the Gay-Berne model systems as described in chapter 11. The translational diffusion coefficient parallel to the director D// is found to first increase and then decrease as the temperature drops through the nematic phase. This reversal occurs where the smectic order parameter of the underlying inherent structures becomes significant for the first time. The non-monotonic temperature behavior of D// can thus be viewed from an energy landscape analysis as a dynamical signature of the coupling between orientational and translational order at the microscopic level. Such a view is likely to form the foundation of a theoretical framework to explain the anisotropic translation diffusion. Chapter 12 investigates the validity of the Debye model of rotational diffusion near the I-N phase boundary with a molecular dynamics simulation study of a Gay-Berne model system for calamitic liquid crystals. The Debye model is found to break down near the I-N phase transition. The breakdown, unlike the one observed in supercooled molecular liquids where a jump diffusion model is often invoked, is attributed to the growth of orientational pair correlation. A mode-coupling theory analysis is provided in support of the explanation. Chapter 13 presents a molecular dynamics study of a binary mixture of prolate ellipsoids of revolution with different aspect ratios interacting with each other through a generalized Gay-Berne potential. Such a study allows to investigate directly the aspect ratio dependence of the dynamical behavior. In the concluding note, chapter 14 starts with a brief summary of the outcome of the thesis and ends up with suggestion of a few relevant problems that may prove worthwhile to be addressed in future.

After giving a brief background on the subject we introduce in section two the Phase-Integral Method of Fröman & Fröman in terms of the platform function of Yngve and Thidé. In section three we derive a different form of the radial Bohr-Sommerfeld condition in terms of the apsidal angle of the corresponding classical motion. Using the derived expression, we then show how easily one can calculate the exact energy eigenvalues of the hydrogen atom and the isotropic three-dimensional harmonic oscillator, we also derive an expression for higher order quantization condition. In section four we derive an expression for the angular frequencies of a restricted (0≤φ≤β) soap bubble and also give a proposition concerning the parameters l and m of the associated Legendre differential equation.
Vi använder Fröman & Frömans Fas-Integral Metod tillsammans med Yngve & Thidés plattformfunktion för att härleda kvantiseringsvilkoret för högre ordningar. I sektion tre skriver vi Bohr-Sommerfelds kvantiseringsvillkor på ett annorlunda sätt med hjälp av den så kallade apsidvinkeln (definierad i samma sektion) för motsvarande klassiska rörelse, vi visar också hur mycket detta underlättar beräkningar av energiegenvärden för väteatomen och den isotropa tredimensionella harmoniska oscillatorn. I sektion fyra tittar vi på en såpbubbla begränsad till området 0≤φ≤β för vilket vi härleder ett uttryck för dess (vinkel)egenfrekvenser. Här ger vi också en proposition angående parametrarna l och m tillhörande den associerade Legendreekvationen.

Dissertation (Ph.D.) -- Worcester Polytechnic Institute.
Keywords: random-field interactions; radio frequency field heating; modulation calorimetry technique; heat capacity; aerosil; nematic; isotropic; phase transitions Includes bibliographical references.

Cantonnée à la physique mathématique depuis des décennies, la gravitation quantique entre désormais dans le giron de la science expérimentale. Suivant cette mouvance nous considérons dans cette thèse trois cadres d’application de la gravitation quantique à boucles (LQG) : le système Univers, les trous noirs et les astroparticules. Le troisième n’est qu’esquissé tandis que les deux premiers sont présentés plus en détails.Le secteur cosmologique étant l’un des domaines les plus prometteurs pour tester et contraindre des théories de gravité quantique, le développement de différents modèles tentant d’appliquer les idées de la LQG à l’Univers primordial ne s’est pas fait attendre. Les travaux que nous présentons portent sur la phénoménologie associée à ces modèles; tant dans le secteur homogène (où nous nous focalisons notamment sur la durée de la phase d’inflation), que dans le secteur inhomogène (nous étudions ce coup-ci le devenir des spectres de puissance primordiaux). Ces études combinées nous permettent alors de préciser dans quelle mesure des effets de gravité quantique (à boucles) peuvent être observés dans les anisotropies du fond diffus cosmologique.D’autre part les trous noirs, non contents de faire partie des objets les plus étranges et les plus fascinants de l’Univers, constituent également des sondes privilégiées pour tester des théories de gravitation. Nous développons la phénoménologie associée à différents traitements des trous noirs en gravitation quantique à boucles. Celle-ci intervient sur une grande variété de fronts : de l’évaporation de Hawking aux ondes gravitationnelles, en passant par la matière noire. C’est sans nul doute un domaine riche et vaste.Finalement, l’existence d’une échelle de longueur minimale, prédite par la majorité des théories de gravité quantique, suggère une généralisation du principe d’incertitude de Heisenberg. Partant de ce constat nous présentons également dans ce manuscrit une méthodologie permettant de calculer une nouvelle relation de dispersion de la lumière à partir du principe d’incertitude généralisé le plus couramment répandu
After decades of being confined to mathematical physics, quantum gravity now enters the field of experimental science. Following this trend, we consider throughout this thesis three implementation frameworks of Loop Quantum Gravity (LQG): the Universe as a system, black holes and astroparticles. The last one is only outlined while the first two are presented in more detail.Since the cosmological sector is one of the most promising areas for testing and constraining quantum gravity theories, it was not long before the development of different models attempting to apply the ideas of the LQG to the primordial Universe. The work we present deals with the phenomenology associated with these models; both in the homogeneous sector (where we focus particularly on the duration of the inflation phase), as in the inhomogeneous sector (where this time, we study the fate of the primordial power spectra). These combined studies then allow us to specify to what extent effects of (loop) quantum gravity can be observed in the anisotropies of the cosmic microwave background.On the other hand black holes, not content to be among the strangest and most fascinating objects of the Universe, are also prominent probes to test the theories of gravitation. We develop the phenomenology associated with different treatments of black holes in the loop quantum gravity framework, which intervenes on multiple levels: from the evaporation of Hawking to gravitational waves, including dark matter. This is undoubtedly a rich and vast area.Finally, the existence of a minimal length scale, predicted by the majority of quantum gravity theories, suggests a generalization of the Heisenberg uncertainty principle. On the basis of this observation, we also present in this manuscript a methodology to derive a new relation dispersion of light from the most widely used generalized uncertainty principle

博士
國立中央大學
機械工程研究所
91
This thesis focuses on the topic of laboratory isotropic turbulence and its applications to two-phase flows. The aim of this study is to provide a comprehensive and systematic analysis of what and how the spatio-temporal relationships between turbulence and two-phase flows. Experiments were conducted in an aqueous vibrating-grids-turbulence (VGT) and a gas phase near-isotropic turbulence to generate low to moderate Reynolds number turbulence with zero-mean velocity, where the Reynolds number, Rel, based on the Taylor microscale λ can be varied from 20 to 200 for the present study. In an effort to ascertain both the spatial and temporal properties of turbulence that are related to the large hierarchy of scales involved, a high-resolution, high-speed digital particle image velocimetry (DPIV) technique, together with the wavelet analyses, is developed so that the detailed three-dimensional spatio-temporal (x-y-t) measurements of the kinematic aspects of small-scale turbulent structures can be obtained simultaneously without any assumption and hypothesis. The first objective of the present work is to identify the turbulent spatiotemporal intermittency in the dissipation and inertial ranges. We found that the characteristic spatial and temporal intermittent scales of intense vorticity structures in the dissipation range occur around 10 h and tk, where h and tk are the Kolmogorov length and time scales, respectively. These results are useful for further study of particle settling and/or premixed flames interacting with stationary near-isotropic turbulence. On the other hand, using the extended self-similarity (ESS) scaling, we found that in the inertial range the spatiotemporal scaling exponents for both high-order longitudinal and transverse velocity structure functions are identical. The second objective is to investigate the solid particle settling behaviours in a stationary homogeneous isotropic turbulence. The mean settling velocity, Vs, of solid particles was measured using both particle tracking velocimetry (PTV) in the VGT system and DPIV in the gaseous system. For the VGT system, we found that Vs > Vt and (Vs - Vt)/Vt reaches its maximum of about 7 % around St » 1, even when the particle Reynolds number Rep is as large as 25 at which Vt/vk » 10, where the Stokes number St = tp/tk, tp is the particle’s relaxation time, vk is the Kolmogorov velocity scale, and Vt is the particle’s terminal velocity. On the other hand, for the gaseous system the mean settling velocity reaches its maximum of 0.13 u¢ when St 1.0 and Vt/u¢ 0.5 for Rep ≤ 1 and Reλ = 120. In addition, non-uniform particle concentration fields (preferential accumulation) are observed and most significant when St 1.0. It is also found that the particle preferential accumulation is highly related to the scaling of the small intense vorticity structures; the particle cluster thickness is nearly the spacing between the small intense vorticity structures, and the time passage of the clustered particle is tk. By comparing the average wavelet spectra between unladen (neutral particle) and laden (heavy particle) turbulent flows at a fixed Rel, turbulence augmentation of energy spectra in the gravitational direction is found over the entire frequency domain, whereas in the transverse direction augmentation occurs only at higher frequencies beyond the Taylor microscale. Finally, a simple physical model based on the phenomenology of the energy balance concept for turbulence generation and dissipation by the descending heavy particles is proposed to predict the value of ul’/u’, where ul’ and u’ are the r.m.s. fluctuating velocity of laden and unladen turbulent flows, respectively. The predicted values agree reasonably well with the experimental results. This suggests that the assumptions based on the scaling of the small intense vorticity structures and the slip velocity at which the maximum probability distribution occurs are adequate, especially when St 1.0 for the present study.

碩士
國立臺灣大學
機械工程學研究所
106
Because cells are thin and transparent objects, they usually have to be dyed to be observable at a bright field microscope. But fluorescently labeled methodology will lead to a phototoxicity and photo-bleaching problem. After observing dyed cells, they will stop growing and gradually die. In order to observe a transparent cell without poisoning them, it is important to develop label-free microscopic techniques. Label-free microscopic techniques include qualitative and quantitative types. Since a quantitative label-free microscope can provide quantitative optical thickness which is helpful to analyze the process of cells changes. The purpose of this thesis is to develop quantitative label-free microscopy. Due to the advantages of wide-field based measurement, quantitative differential phase contrast microscopy (QDPC), compared to other label-free quantification phase microscopic techniques, it is more efficient to capture images without point-by-point plane scanning or depth scanning. In this study, a thin-film transistor (TFT) shield is placed on the Fourier plane to generate structured light by variable pupil control. After light passes through the TFT shield, the intensity of the light is modulated by the proposed gradient light intensity modulation pattern. After two sets of 4 complementary images are acquired, the phase contrast value of a specimen is obtained by using lab developed Matlab software. Compared with the method proposed by other research groups, which utilized contrast structured light for multiple image acquisition to achieve an isotropic phase transfer function. The color gradient light intensity modulation pattern further makes the system achieve isotropic phase transfer functions at high acquisition speed. The proposed method improves the efficiency and accuracy of phase reconstruction. For experimental verification, micro-plastic spheres have been used standard targets to verify the quantitative measurement capability and accuracy of proposed QDPC system. With the measured phase contrast value and the refractive index of the microspheres, the geometric thickness of the microspheres can be calculated. Furthermore, the developed automatic microscopic image-acquisition is used for acquiring time-lapse QDPC photography of mouse label-free 3T3 fibroblasts cells and human lung cancer cells CYL2 . QDPC reconstructed images provide high contrast and the reconstruction result is independent of viewing angles. The detailed structures and apoptosis process of cells can be clearly observed. While the 3T3 fibroblasts cells shrinks, their phase difference value gradually increases from ~1.5 to ~2.5 rad. While the lung cancer cells CYL2, their phase difference value gradually decrease from ~4.5 to ~2.5 rad. The optical thickness of the cells can be further calculate, and quantitative thickness change data is helpful for the analysis of the cells’ long-time monitoring. Keyword：Optical microscopy, Structured illumination, Variable pupil control, Phase retrieval, Differential phase contrast imaging

For the past few decades, tremendous progress has been made on liquid crystal display (LCD) technologies in terms of stability, resolution, contrast ratio, and viewing angle. The remaining challenge is response time. The state-of-the-art response time of a nematic liquid crystal is a few milliseconds. Faster response time is desirable in order to reduce motion blur and to realize color sequential display using RGB LEDs, which triples the optical efficiency and resolution density. Polymer-stabilized blue phase liquid crystal (PS-BPLC) is a strong candidate for achieving fast response time because its self-assembled cubic structure greatly reduces the coherence length. The response time is typically in the submillisecond range and can even reach microsecond under optimized conditions. Moreover, it exhibit several attractive features, such as no need for surface alignment layer, intrinsic wide viewing angle, and cell gap insensitivity if an in-plane-switching (IPS) cell is employed. In this dissertation, recent progresses in polymer-stabilized blue phases, or more generally optically-isotropic liquid crystals, are presented. Potential applications in display and photonic devices are also demonstrated. In Chapter 1, a brief introduction of optically isotropic liquid crystals is given. In Chapter 2, we investigate each component of polymer-stabilized blue phase materials and provide guidelines for material preparation and optimization. In Chapter 3, the electro-optical properties of PS-BPLCs, including electric-field-induced birefringence and dynamic behaviors are characterized. Theoretical models are proposed to explain the physical phenomena. Good agreements between experimental data and models are obtained. The proposed models also provide useful guidelines for both material and device optimizations. Four display and photonic devices using PS-BPLCs are demonstrated in Chapter 4. First, by red-shifting the Bragg reflection and using circular polarizers, we reduce the LCD driving voltage by 35% as compared to a short-pitch BPLC while maintaining high contrast ratio and submillisecond response time. Second, a turning film which is critically needed for widening the viewing angle of a vertical field switching (VFS) BPLC mode is designed. With this film, the viewing angle of VFS is widened to [plus or minus] 80[degrees] in horizontal direction and [plus or minus] 50[degrees] in vertical direction. Without this turning film, the viewing angle is only [plus or minus]30[degrees], which is too narrow for most applications. Third, a reflective BPLC display with vivid colors, submillisecond response time, and natural grayscales is demonstrated for the first time. The proposed BPLC reflective display opens a new gateway for 3D reflective displays; it could make significant impact to display industry. Finally, we demonstrate a tunable phase grating with a high diffraction efficiency of 40% and submillisecond response time. This tunable grating exhibits great potential for photonic and display applications, such as optical interconnects, beam steering, and projection displays.
Ph.D.
Doctorate
Optics and Photonics
Optics and Photonics
Optics and Photonics

The present thesis reports computer simulation studies of several phase transition related phenomena in a range of soft-condensed matter systems. A coherent unifying theme of the thesis is the understanding of dynamics of phase transitions through free energy calculations using recently developed efficient non-Boltzmann sampling methods. Based on the system/phenomena of interest, the thesis has been classified into four major parts: I. Isotropic-nematic (IN) phase transition in liquid crystals. II. Nucleation phenomena in gas-liquid transition with particular emphasis on the systems close to the spinodal curve. III. Collapse transition in linear hydrocarbon (n-alkane) chains for a varying range of length, solvent and temperature. IV. Crystallization of unbranched polymer chains in dilute solution, with particular emphasis on the temperature dependent crossover between the rod-like crystalline state and spherical molten globule state. The thesis has been further divided into ten chapters running through the four parts mentioned before. In the following we provide a brief chapter-wise outline of the thesis. Part I deals with the power law relaxation and glassy dynamics in thermotropic liquid crystals close to the IN transition and consists of two chapters. To start with, Chapter I.1 provides an introduction to thermotropic liquid crystals. Here we briefly introduce various liquid crystalline phases, the order parameter used to characterize the IN transition, a few well established theoretical models, and we conclude with describing the recent experimental and computer simulation studies that have motivated the work described in the next chapter. In Chapter I.2, we present our molecular dynamics simulation studies on single particle and collective orientational dynamics across the IN transition for Lebwohl Lasher model, which is a well-known lattice model for thermotropic liquid crystals. Even this simplified model without any translational degrees of freedom successfully captures the short-tointermediate time power law decay recently observed in optical heterodyne detected optical Kerr effect (OHDOKE) measurements near the IN transition. The angular velocity time correlation function also exhibits a rather pronounced power law decay near the IN boundary. In the mean squared angular displacement at comparable time scales, we observe the emergence of a sub-diffusive regime which is followed by a super-diffusive regime before the onset of the longtime diffusive behavior. We observe signature of dynamical heterogeneity through pronounced non-Gaussian behavior in the orientational motion particularly at lower temperatures. Interestingly, this behavior closely resembles what is usually observed in supercooled liquids. We obtain the free energy as a function of orientational order parameter by the use of recently developed transition matrix Monte Carlo (TMMC) method. The free energy surface is flat for the system considered here and the barrier between isotropic and nematic phases is vanishingly small for this weakly first-order transition, hence allowing for large scale, collective, and correlated orientational density fluctuations. We attribute this large scale fluctuations as the reason for the observed power law decay of the orientational time correlation functions. Part II consists of three chapters, where we focus on the age old problem of nucleation and growth, both from the perspective of thermodynamics and kinetics. We account for the rich history of the problem in the introductory Chapter II.1. In this chapter we describe various types and examples of the nucleation phenomena, and a brief account of the major theoretical approaches used so far. We begin with the most successful Classical Nucleation Theory (CNT), and then move on to more recent applications of Density Functional Theory (DFT) and other mean-field types of models. We conclude with a comparison between the experiments, theories and computational studies. In the next chapter (Chapter II.2) we attempt to elucidate the mechanism of nucleation near the gas-liquid spinodal from a microscopic point of view. Here we construct a multidimensional free energy surface of nucleation of the liquid phase from the parent supercooled and supersaturated vapor phase near the gas-liquid spinodal. In particular, we remove the Becker-Doring constraint of having only one growing cluster in the system. The free energy, as a function of the size of the largest cluster, develops a pronounced minimum at a subcritical cluster size close to the spinodal. This signifies a two step nature of the process of nucleation, where the rapid formation of subcritical nuclei is followed by further growth by slower density fluctuations on an uphill free energy surface. An alternative free energy pathway involving the participation of many subcritical clusters is envisaged near the spinodal where the growth of the nucleus is found to be promoted by a coalescence mechanism in contrast to the single particle addition assumption within CNT. The growth of the stable phase becomes progressively collective and spatially diffuse, and the significance of a “critical nucleus” is lost for deeper quenches. In this chapter we present our studies both in 3dimensional Lennard-Jones (LJ) system and Ising model (both 2and 3dimensions). Our general findings seem to be independent of the model chosen. While the previous chapter focuses on relatively well-studied 3-dimensional (3D) LJ system, in Chapter II.3 we present our studies on the characteristics of the nucleation phenomena in 2dimensional (2D) Lennard-Jones fluid. To the best of our knowledge this is the first extensive computer simulation study to check the accuracy of CNT in 2D. Using various Monte Carlo methods, we calculate the free energy barrier for nucleation, line tension, and bulk densities of equilibrium liquid and vapor phases, and also investigate the size and shape of the critical nucleus. The study is carried out at an intermediate level of supersaturation (away from the spinoidal limit). In 2D, a surprisingly large cutoff (rc ≥ 7.0σ where σ is the diameter of LJ particles) in the truncation of the LJ potential is required to obtain converged results. A lower cutoff leads to a substantial error in the values of the line tension, nucleation barrier, and characteristics of the critical cluster. Note that typically 2.5σ is sufficient for 3D LJ fluids. We observe that in 2D system CNT fails to provide a reliable estimate of the free energy barrier. While it is known to slightly overestimate the nucleation barrier in 3D, it underestimates the barrier by as much as 50% at the saturation ratio S = 1.1(defined as S = P/Pc, where Pc is the coexistence pressure) and at the reduced temperature T* = 0.427(defined as T* = KBT/ ε, where ε is the depth of the potential well). The reason for the marked inadequacy of the CNT in 2D can be attributed to the non-circular nature of the critical clusters. Although the shape becomes increasingly circular and the clusters become more compact with increase in cutoff radius, an appreciable non-circular nature remains even without any cutoff to make the simple CNT inaccurate. Part III again consists of three chapters and focuses on the conformational equilibria. Collapse transition and self-organized structures of n-alkanes in solution. In Chapter III.1 we carry out a brief survey of the existing theories of polymer in solution, with particular emphasis on the collapse process in poor solvents. We also introduce the concept of “hydrophobicity” and “hydrophobic collapse”, which is now a subject enormous interest, partly because it my help in understanding the initial processes involved in protein folding. We briefly discuss the subject of formation of beautiful self-organized structures by block copolymers, and also simple homopolymers which is essentially the focus of the work embodied in the next two chapters. In Chapter III.2 we demonstrated a chain length dependent crossover in the structural properties of linear hydrocarbon (n-alkane) chains using detailed atomistic simulations in explicit water. We identify a number of exotic structures o the polymer chain through energy minimization of representative snapshots collected from molecular dynamics trajectory. While the collapsed state is ring-like(circular) for small chains(CnH2n+2; n ≤ 20) and spherical for very long ones( n = 100), we find the emergence of ordered helical structures at intermediate lengths (n ~ 40). We find different types of disordered helices and toroid-like structures at n = 60. We also report a sharp transition in the stability of the collapsed state as a function of the chain length through relevant free energy calculations. While the collapsed state is only marginally metastable for C20H42, a clear bistable free energy surface emerges only when the chain is about 30 monomers long. For n = 30, the polymer exhibits an intermittent oscillation(characterized by well-developed 1/f noise, where f is the frequency ) between the collapsed and the coil structures, characteristic of two stable states separated by a small barrier. This appears to support a weakly first order phase transition between the extended and the collapsed states. Chapter III.3 extends the study of previous chapter to much longer chains (n ≥ 100), which irreversibly collapse in water into globular forms. Even though the collapsed form has a nearly spherical shape, close inspection shows a propensity towards local ordering in the alignment of the polymer segments. This tendency to maintain alignment in order to maximize the number of contacts leads to a core-shell like structure, where the shell is often characterized by a bent rod-like shape consisting of two adjacent segments running in parallel. A key event associated with the initial stage of collapse seems to be the formation of a skewed ring (or loop) that serves as a “nucleation center” for rest of the chain to collapse into. Time evolution of the radial distribution function of water surrounding the polymer, shows that the density of neighboring water decreases by only about 15-20% from that of bulk water. Even though interior of the ting-like structures is fully devoid of water, solvent accessible surface representation shows that these regions are geometrically/spatially inaccessible to water molecules. We suggest that the role of water is to stabilize such ring-like structures once formed by natural conformational fluctuations of the polymer chain. This view is confirmed by observation of spontaneous formation and melting away of such ring-like entities in a polar aprotic solvent(DMSO). We also comment on the role of the flexibility of polymer chains in determining the collapse kinetics. The last part(Part IV) of the thesis consists of two chapters that deal with the crystallization of linear polymer chains from dilute solution. The way long chain polymers crystallize is drastically different from their small molecule counterparts due to their topological connectivity. Linear polymers often crystallize from dilute solution in the form of thin lamellae with well-defined crystallographic features. In Chapter IV.1 we briefly survey the current theoretical understanding and confusions associated with the highly debated field of polymer crystallization. While the last few decades have seen the development of many successful phenomenological theories, the molecular mechanism of formation of such self-organized lamellae is extremely complex and very poorly understood. There are clearly two distinct steps in polymer crystallization. Firstly, the individual linear polymers must self-organize into bundles of somewhat regular structures. These structures then further aggregate to lamellar form and crystallize into a lattice. In this respect , it has marked similarity to the problem of protein crystallization. In chapter IV.2 we present Brownian dynamics simulation studies of a single polythelene chain of length 500. Such systems can reasonably mimic the process of crystallization from dilute solutions. Our simulations could successfully reproduce some of the interesting phenomena observed in experiments and very recent computer simulation studies, including multi-center nucleation of rod-like structures within a single polymer chain, an inverse relation between lamellar thickness and temperature etc. But our primary focus has been to understand the nature of the phase transition as one traverses along the melting temperature and the underlying free energy surface. Near the melting temperature we observe a very intriguing fluctuation between the disordered molten globule state and the ordered rod-like crystalline, where these two forms have highly different shape and structure. These fluctuations have strong signature of 1/f noise or intermittency. This clearly indicates the existence of a weakly first order transition, where two widely different states with large difference in values of order parameter are separated by a rather small free energy barrier. This can be related to the experimentally observed density fluctuations that resemble spinodal decomposition. It is important to note that very similar fluctuations have been observed in our previous studies on liquid crystals (Chapter 1.2) and intermediate sized alkalines in water(Chapter III.2) that signifies a universal underlying energy landscape for these systems. We have discussed the scope of future work at the end of each chapter whenever appropriate.