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Many different physical systems, such as granular materials, colloids, foams and emulsions exhibit a jamming transition where the system changes from a liquid-like flowing state to a solid jammed state as the packing fraction increases. These systems are often modeled using soft-core particles with repulsive contact forces. In this thesis we explore several different dynamical models for these kinds of systems, and see how they affect the behavior around the jamming transition. We investigate the effect of different types of dissipative forces on the rheology, and study how different methods of preparing a particle configuration affect their probability to jam when quenched. We study the rheology of sheared systems close to the jamming transition. It has been proposed that the athermal jamming transition is controlled by a critical point, point J, with certain scaling properties. We investigate this using multivariable scaling analysis based on renormalization group theory to explore the scaling properties of the transition and determine the position of point J and some of the critical exponents.

In day to day life we encounter many different materials which are intermediate between crystalline solids and simple liquids that include paints , glues , suspensions, polymers, surfactants, food and cosmetic products and so on. ‘Soft condensed matter’ is an emerging field of science that aims to generalize the flow and various deformation mechanisms in this apparent diverse class of materials from a ‘mesoscopic’ point of view (important length scales for these systems is usually 10nm-1μm) where the actual atomic and molecular details governed by various quantum mechanical laws are not very important. These soft systems are held together by weaken tropic forces and therefore can be perturbed easily (the typical elastic modulus of these materials is many orders of magnitude lower compared to metallic solids). Moreover, very long relaxation times in these systems(∼10−3 to 1 s) have made them ideal candidates to study non-equilibrium physics. The present Thesis is an endeavor to understand linear and non-linear flow behavior and low Reynolds number instabilities in various soft matter systems like suspensions of flocculated carbon nanotubes and carbon black, surfactant gels, colloidal glasses, Langmuir monolayers etc probed mainly by bulk and interfacial rheology, in-situ light scattering, particle image velocimetry(PIV) techniques and Fourier transform rheology. We also use dynamic light scattering techniques for particle sizing and characterization of Brownian systems. Chapter 1 gives a general introduction to soft condensed matter, particularly, the important length and time scales, various interactions and the rich phase behavior emerged from the delicate balance between energy and entropy in these systems. In this context, We describe the detailed phase behavior of two such systems studied in this thesis. We next describe briefly a few important concepts which motivate the main problems studied in the present thesis like the shear-thickening in suspensions of Brownian and non-Brownian particles, non-equilibrium steady state fluctuation relations in driven systems, elasticity driven instabilities in complex fluids, jamming transitions and aging behavior. This is followed by a discussion of the experimental techniques like linear and nonlinear rheology, including the Fourier transform rheology. Chapter 2 discusses the experimental techniques used by us in detail. We first describe the different components and mode of operations of the MCR-300 stress-controlled rheometer (Paar Physica, Germany) and various experimental geometries. Next we discuss the set up for two dimensional rheological measurements. The homebuilt imaging set up for in-situ polarized light scattering and direct imaging studies is described along with the in-situ particle image velocimetry (PIV) to map out the exact spatially resolved velocity profiles in 2D systems. We give a brief account of the techniques of Fourier transform rheology. At the end of this chapter, we briefly describe the angle resolved dynamic light scattering (DLS) set up (Brookhaven Instruments, USA). In Chapter 3, we study colossal discontinuous shear-thickening transition in confined suspensions of fractal clusters formed by multi-wall carbon nanotubes (MWNT) by rheology and in-situ imaging experiments. Monotonic decrease in viscosity with increasing shear stress, known as shear thinning, is a known rheological response to shear flow in complex fluids in general and for flocculated suspensions in particular. In the present experiments we demonstrate a discontinuous shear thickening transition where the viscosity jumps sharply above a critical shear stress by four to six orders of magnitude in flocculated suspensions of MWNT even at very low weight fractions(∼0.5%). Rheo-optical observations reveal the shear-thickened state as a percolated structure of MWNT flocs spanning the system size. We present a dynamic phase diagram of the non-Brownian MWNT dispersions revealing a starting jammed state followed by shear-thinning and shear-thickened states. The present study further suggests that the shear-thickened state obtained as a function of shear stress is likely to be a generic feature of fractal clusters under flow, albeit under confinement. An understanding of the shear thickening phenomena in confined geometries is pertinent for flow controlled fabrication techniques in enhancing the mechanical strength and transport properties of thin films and wires of nanostructured composites as well as in lubrication issues. We try to understand the flow of jammed and shear-thickened states under constant applied strain rate by studying the building up and relaxation of individual stress fluctuation events similar to the flow in dense granular materials. We also characterize the metastable shear thickened states by superposing a small sinusoidal stress component on a steady applied stress as well as by studying the a thermal entropy consuming fluctuations which are also observed for other jammed systems under an applied steady shear stress as described in the next chapter. Chapter 4 reports the study of non-equilibrium fluctuations in concentrated gels and glassy systems(in jammed state), the nature of fluctuations and their systemsize dependence in the framework of fluctuation relation and Generalized Gumbel distribution. In the first part, we show that the shear rate at a fixed shear stress in a micellar gel in a jammed state exhibits large fluctuations, showing positive and negative values, with the mean shear rate being positive. The resulting probability distribution functions (PDFs) of the global power flux to the system vary from Gaussian to non-Gaussian, depending on the driving stress and in all cases show similar symmetry properties as predicted by Gallavotti-Cohen steady state fluctuation relation. The fluctuation relation allows us to determine an effective temperature related to the structural constraints of the jammed state. We have measured the stress dependence of the effective temperature. Further, experiments reveal that the effective temperature and the standard deviation of the shear rate fluctuations increase with the decrease of the systemsize. In the second part of this chapter, we report a universal large deviation behavior of spatially averaged global injected power just before the rejuvenation of the jammed state formed by an aging suspension of laponite clay under an applied stress. The probability distribution function (PDF) of these entropy consuming strongly non-Gaussian fluctuations follow an universal large deviation functional form described by the Generalized Gumbel (GG) distribution like many other equilibrium and non-equilibrium systems with high degree of correlations but do not obey Gallavotti-Cohen Steady State Fluctuation Relation (SSFR). However, far from the unjamming transition (for smaller applied stresses) SSFR is satisfied for both Gaussian as well as non-Gaussian PDF. The observed slow variation of the mean shear rate with system size supports a recent theoretical prediction for observing GG distribution. We also establish the universality of the observations reported in this chapter in the light of other jammed systems under shear. We examine in the first part of Chapter 5, the shear-thinning behavior of a two dimensional yield stress bearing monolayer of sorbitan tristearate at air/water interface. The flow curve (stress vs shear rate) consists of a linear region at low shear stresses/shear rates, followed by a stress plateau at higher values. The velocity profile obtained from particle imaging velocimetry indicates that shear banding occurs showing coexistence of fluidized region near the rotor and solid region with vanishing shear-rate away from the rotor. In the fluidized region, the velocity profile which is linear at low shear rates becomes exponential at the onset of shear-thinning, followed by a time varying velocity profile in the plateau region. At low values of constant applied shear rates, the viscosity of the film increases with time, thus showing aging behavior like in soft glassy three-dimensional (3D) systems. Further, at the low values of the applied stress in the yield stress regime, the shear-rate fluctuations in time show both positive and negative values, similar to that observed in sheared 3D jammed systems. By carrying out a statistical analysis of these shear-rate fluctuations, we estimate the effective temperature of the soft glassy monolayer using the Galavatti-Cohen steady state fluctuation relation. In the second part of this chapter, we study in detail the non-linear viscoelastic behavior of Langmuir monolayers. Under oscillatory shear usually observed in many 3D metastable complex fluids with large structural relaxation times. At large strain amplitudes(γ), the storage modulus (G”) decreases monotonically whereas the loss modulus (G”) exhibits a peak above a critical strain amplitude before it decreases at higher strain amplitudes. The power law decay exponents of G” and G” are in the ratio 2:1. The peak in G” is absent at high temperatures and low concentration of sorbitan tristearate. Strain-rate frequency sweep measurements on the monolayers do indicate a strain-rate dependence of the structural relaxation time. The present study on sorbitan tristearate monolayers clearly indicates that the nonlinear viscoelastic behavior in 2D Langmuir monolayers is very general and exhibits many of the features observed in 3D complex fluids. We report in the first part of Chapter 6 scattering dichroism experiments to quantify the spatio-temporal nematodynamics of shear-thinning worm like micellar gels of surfactant Cetyltrimethylammonium Tosylate (CTAT) in the presence of salt sodium chloride (NaCl) enroute to rheochaos. For shear rates past the plateau onset, we observe a presence of alternating bright and dark‘ intertwined’ birefringent structures along the vorticity direction. The orientational order corresponding to these structures are predominantly oriented at +45deg and−45deg to the flow (v) in the (v,∇v) plane. The orientational dynamics of the nematics especially at the interface between the structures, has a one-to-one correspondence with the temporal behavior of the stress. Experiments show that the spatial motion of the vorticity structures depend on the gap thickness of the Couette cell. We next discuss the random temporal flow behavior of this system at high values of applied shear rate/stress in the framework of elastic turbulence in the second part of this chapter. Here, we study the statistical properties of spatially averaged global injected power fluctuations for the worm-like micellar system described above. At sufficiently high Weissenberg numbers (Wi) the shear rate and hence the injected power p(t) at a constant applied stress shows large irregular fluctuations in time. The nature of the probability distribution function (PDF) of p(t) and the power-law decay of its power spectrum are very similar to that observed in recent studies of elastic turbulence for polymer solutions. Remarkably, these non-Gaussian pdf scan be well described by an universal large deviation functional form given by the Generalized Gumbel (GG) distribution observed in the context of spatially averaged global measures in diverse classes of highly correlated systems. We show by in-situ rheology and polarized light scattering experiments that in the elastic turbulent regime the flow is spatially smooth but random in time, in agreement with a recent hypothesis for elastic turbulence. In Chapter 7, we study the vorticity banding under large amplitude oscillatory shear (LAOS) in a dilute worm-like micellar gel formed by surfactant CTAT by Fourier transform rheology and in-situ polarized light scattering. Under LAOS we found the signature of a non-trivial order-disorder transition of Taylor vortices. In the non-linear regime, higher harmonicde composition of the resulting stress signal reveals that the third harmonic I3 shows a very prominent maximum at the strain value where the number density (nv) of the Taylor vortices is maximum for a wide range of angular frequencies both above and below the linear crossover point. Subsequent increase in applied strain results in distortions of the vortices and a concomitant decrease in nv when I3 also drops very sharply and acts like an order parameter for this order-disorder transition. We further quantify the transition by defining an independent order parameter like quantity from the spatial correlation function of the scattered intensity and equivalently its Fourier transform which essentially captures the non monotonous third harmonic behavior. Lissajous plots indicate an intra-cycle strain hardening for the values of γ corresponding to the peak of I3 similar to that observed for hard-sphere glasses. Our study is an important step forward to correlating the structures developed in the system under LAOS to the appearances of the higher harmonics in the non-linear regime. The Thesis concludes with a summary of the main results and a brief account on the scope of future work as described in Chapter 8.

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Les méthodes classiques de physique de l'état solide telles que la diffraction des rayons X et la microscopie électronique ont permis la compréhension de la structure des membranes cellulaires. Aujourd'hui, leur composition et structure étant bien connues, les recherches se concentrent sur les processus actifs des membranes. Des processus tels que l'endocytose impliquent des modifications substantielles de la forme des membranes lipidiques, réalisées par des protéines induisant la courbure membranaire. L'une des méthodes expérimentales parmi les plus populaires est dite « TLM-pulling », où la membrane lipidique tubulaire (TLM) est formée à partir de la vésicule en tirant par une force externe. Des structures similaires relient les vésicules endocytiques aux compartiments du donneur et servent de canaux pour le transfert de matière dans la cellule et entre les cellules adjacentes, établissant ainsi une voie de communication intercellulaire. De tels systèmes formés in vitro en raison de leur simplicité et grande homogénéité peuvent être décrits avec précision par la physique théorique.Dans la première partie de la thèse, nous développons un modèle théorique de TLM, basé sur la mécanique classique et la thermodynamique, et l'appliquons aux expériences de « TLM-pulling » avec adsorption de protéines induisant la courbure. Le modèle tient compte de l'asymétrie de la bicouche lipidique, de la tension superficielle, de la force longitudinale appliquée au TLM et de la différence de pression dans le système. Nous modélisons l'action que les protéines exercent sur la TLM via des ensembles de forces normales à la surface de la membrane à l'équilibre mécanique. Cette nouvelle approche multipolaire permet de modéliser les interactions anisotropes, entre les protéines adsorbées à la membrane, qui sont induites par sa déformation. Notre théorie décrit les premiers stades de la formation des échafaudages protéiques, c-à-d la disposition caractéristique des protéines et leur grande affinité avec les extrémités de la TLM. Le comportement collectif des protéines induisant la courbure est extrêmement important pour effectuer des déformations à grande échelle des membranes au cours de processus tels que l'endo et l'exocytose, l'entrée du virus dans la cellule hôte ainsi que la formation et la sortie des virions. L'étude de ce dernier processus pourrait conduire au développement de nouvelles méthodes de traitement en virologie.La deuxième partie de la thèse est consacrée à l'étude de l'aorte dorsale (DA) de l'embryon de poisson Danio-Rerio. On étudie l'évolution de la forme du DA pendant la transition endothélio-hématopoïétique (EHT). Le processus EHT conduit à l'extrusion des cellules souches/hématopoïétiques qui coloniseront en suite la moelle osseuse permettant l'hématopoïèse tout au long de la vie. Ce processus semble être universel et devrait s'appliquer aussi bien aux mammifères qu'aux oiseaux, ce qui fait de son étude un problème fondamental de l'embryologie.Le DA a une géométrie cylindrique et semblable aux TLM, mais en même temps, il est beaucoup plus gros que les tubes lipidiques, a un module de cisaillement non nul et est incorporé dans la matrice des tissus environnants : un système beaucoup plus complexe du point de vue mécanique. Nous relions les changements globaux de forme de l'aorte pendant l'EHT aux principes génériques de la mécanique et montrons que les instabilités mécaniques conduisant à l'évolution de la forme de l'aorte sont invoquées par des stress résultant des inhomogénéités de croissance et de l'interaction avec les tissus environnants. Sur la base de l'analyse théorique et des données en microscopie confocale 4D, nous proposons un schéma détaillé du processus et postulons que les instabilités mécaniques préparent l'ensemble du processus EHT avant son contrôle génétique spécifique, suggérant un mécanisme universel et auto-organisé du processus de réorganisation collective des tissus dans les organismes en croissance. / Applications of classical solid state physics methods such as X-ray diffraction analysis and electron microscopy allowed making a giant step in understanding of cellular membranes’ structure. Today since their composition and structure are well known, the focus of research has shifted to active processes involving cell membranes. As we know, such processes as endocytosis involve substantial shape changes of cell membranes, which are performed by curvature-inducing proteins. One of the most popular methods to study how these proteins interact with lipid membranes and each other is TLM-pulling experiment, where tubular lipid membrane (TLM) is formed from the vesicle by pulling. Similar structures connect endocytic vesicles with the donor compartments and serve as channels for the matter transfer within the cell and between adjacent cells establishing cell-to-cell communication pathway. Such systems formed in vitro due to their simplicity and high homogeneity can be accurately described by the means of theoretical physics.In the first part of the present thesis, we develop a theoretical model of the TLM pulled out of the vesicle on the basis of classical mechanics and thermodynamics and apply it to the TLM-pulling experiments with curvature-inducing proteins adsorption. The developed model takes into account asymmetry of the lipid bilayer, surface tension, longitudinal force applied to the TLM and pressure difference in the system. We model the action that proteins exert on TLM via sets of forces normal to the membrane’s surface and satisfying conditions of mechanical equilibrium. This novel force multipole approach allows us to model anisotropic interactions between proteins adsorbed at the membrane surface that are induced by the membrane deformation. Our theory describes early stages of protein scaffolds formation i.e. characteristic arrangement of proteins and their high affinity to the membrane ends. Collective behavior of curvature-inducing proteins is extremely important for performing large scale deformations of lipid membranes during such processes as endo and exocytosis, virus entry in the host cell as well as formation and exit of daughter virions later on. Studying of the latter process can possibly lead to the development of fundamentally new methods of viral disease treatment.The second part of the thesis is devoted to the study of zebrafish embryo’s dorsal aorta (DA). It focuses on DA’s shape evolution during the Endothelio-Haematopoietic Transition (EHT). The EHT process leads to the extrusion of haematopoietic stem/progenitor cells (HSPCs) which will later on colonize haematopoietic organs allowing haematopoiesis throughout adult life. This process seems to be universal and should also apply for both mammals and birds, which makes its investigation a fundamental problem of embryology.DA has a cylindrical geometry that makes it similar to the TLM’s, however at the same time DA is much bigger than lipid tubes, has a non-zero share modulus and is embedded in the matrix of surrounding tissues, which makes it a much more complex system from the mechanical perspective. We relate the global shape changes of the aorta during EHT to generic principles of mechanics and show that mechanical instabilities leading to the aorta shape evolution are invoked by different stresses resulting from the growth inhomogeneities and interaction with surrounding tissues. Based on the performed theoretical analysis and the data obtained with a help of 4D confocal microscopy we propose a detailed scheme of the process and postulate that mechanical instabilities prepare and support the whole EHT process prior to its specific genetic control. Our interpretation suggests a universal and self-organized mechanism underlying collective tissue reorganization processes in the growing organisms such as EHT.

No description available.

Self-assembly of colloidal particles into ordered structures is hailed as the preferred route to production of functional devices on the nanometre and micron length scales. The shape of a colloidal particle is one of the most influential factors determining the type of ordered structure that is assembled. Thus this thesis is devoted to understanding the role of particle shape on phase behaviour of colloidal systems. The effect of particle shape is isolated by using computer simulations to model particles as hard, anisotropic bodies which interact via purely repulsive interactions. Two particle models are studied which are representative of real colloids: non-convex wireframe polyhedra, and convex spherical caps. This thesis investigates the densest packings of several wireframe polyhedra. By comparing packings of six distinct polyhedra some general conclusions are drawn regarding the effects of rounded polyhedra edges, and a new shape descriptor is given which can suggest whether a wireframe polyhedron is likely to form new interpenetrating crystal structures. Wireframe cubes were studied in more detail, where the full phase behaviour was mapped out. A curious phenomenon was found whereby crystals formed by cubic wireframes exhibit plastic fluctuations. This unusual behaviour, if reproduced experimentally, may lead to useful optical properties. A systematic study of spherical caps demonstrates the effect of shape on collective behaviour as the particle model interpolates between a sphere and a thin platelet. Purely repulsive interactions are responsible for a range of different crystal structures, but the nucleation of these structures is challenging due to slow dynamics. Furthermore, there are often many ways for a spherical cap to pack in a given volume, which leads to multiple metastable states. The self-assembly of spherical caps was directed by sedimentation on a solid template which resulted in increased nucleation rates and more stable crystals. However, there is still a lack of control over the exact crystal structure due to the degeneracy in ways to pack.

The constituents of a quantum many-body system can be inextricably linked, a phenomenon known as quantum entanglement. Entanglement can be used as a resource for quantum computing, quantum communication and detecting phase transitions, among others. The amount of entanglement can be quantified via the von Neumann and Rényi entropies, which have their origins in information theory. In this work, the quantum entanglement between subsystems of a one dimen- sional lattice model of fermions is quantified. The von Neumann and Rényi entropies were calculated for two types of subsystems. In the first study, the subsystems were treated as two subsets of particles, and in the second, as two spatial subregions. Finally, by considering particle superselection rules, the amount of entanglement that can actually be accessed as a resource was calcu- lated. In all cases, the quantum entanglement served to detect phase transitions in the model.

Granular materials are abundant in the natural and industrial environment. Typical granular materials are collections of inert, passive particles in which the constituent grains of the material are macroscopic; thus they fill space, are athermal, and interact through only local contact forces. This definition can be broadened to include non-inert particles as well-active particles-in which the grains of an active granular material possess an internal energy source which drives motion. Active granular materials are found in many areas of the biological world, from cattle stampedes and pedestrian traffic flow, to the subterranean world of ant colonies and their collective motion within the nest. We study the rheology and dynamics of inert granular material, and an active granular system of collections of fire-ants, which together we call matter with granularity. In both of these systems we observe bifurcations in the force and flow dynamics which results from confinement effects of the effectively rigid granular materials. In inert granular systems, the onset of flow among particles that are closely packed together causes them to dilate as particles must separate away from each other to accommodate flow. Dilation is a property unique to matter with granularity and other complex fluids in which particles interact locally and occupy space. We explore how dilation influences the inert granular system in situations of local and global forcing: drag of an immersed intruder and avalanche flow respectively. We next study collections of fire ants which also interact with each other locally through contact forces and exclude volume. We study the construction of, and locomotion within subterranean tunnels by groups of fire ants. We find that the traffic dynamics of ants within confined tunnels are significantly affected by tunnel diameter. Reducing tunnel diameter increases the formation of traffic jams due to the inability of ants to pass each other easily. However, we show that jamming within tunnels may have beneficial effects on subterranean locomotion. Individual ants jam there bodies against the walls of vertical tunnels to resist falling. From physics studies of fire ant mobility in confined spaces, we show that subterranean tunnel size has a significant effect on the stability and mobility of ants within these environments.

We examine various models of soft matter, and one model of quasicrystals, focusing on abrupt changes as density is varied. We consider in detail two models, one of granular matter and another of confined wires, showing that the models become ordered as density is increased, with crystalline order observed in the former and nematic order observed in the latter. We associate the phenomenon of random close packing with the onset of crystalline order in our granular model, and we conjecture that crumpled wires should exhibit a nematic transition with increasing compaction. We also consider two other models of granular matter: one which describes dilatancy onset as a second order phase transition, and one which describes random loose packing as a precise, well- defined density. Finally, we examine an equilibrium model of quasicrystals with a first order phase transition to a solid phase without any crystalline order. / text