No description available.

No description available.

Des cellules allongées et apolaires cultivées à confluence s'alignent les unes avec les autres. Dans cette thèse, nous utilisons des concepts de la théorie de la matière active ainsi que de la physique des cristaux liquides afin d'étudier quantitativement l'émergence de cet ordre mésoscopique nématique pour des monocouches de cellules à deux dimension, avec et sans confinement. Il a été montré que les défauts topologiques jouent un rôle crucial durant l'auto-organisation de systèmes biologiques actifs. Ici, nous étudions la dynamique de ces défauts qui se forment dans le tissu nématique contractile. Étant intrinsèquement hors équilibre à cause de la consommation d'énergie par les cellules, la monocouche est parcourue par de complexes courants de cellules due à la migration spontanée des défauts et leur annihilation avec des défauts de charges opposées. En comparant nos résultats expérimentaux avec un modèle théorique, nous montrons que l'auto-organisation de la monocouche est liée à la minimisation de l'énergie de courbure du tissu. / Elongated, weakly interacting, apolar cells cultured at confluence align together, forming large domains where they are perfectly ordered. Using concepts from the active matter theory and the physics of liquid crystals, we study the emergence of this mesoscopic nematic order by quantifying the ordering dynamics in two-dimensional infinite monolayers or under confinement. Topological defects have been found to play a crucial role in the self-organization of active biological systems. We study the dynamics of the disclinations that form in these cellular contractile nematics. Being driven out of equilibrium by the consumption of energy by individual cells, the monolayer exhibits complex flow patterns as defects migrate spontaneously and annihilate pairwise. By comparing our experimental results to a nematic drop model, we show that the self-organization of the cellular nematic layer with no boundary conditions or under circular confinement is dictated by the minimization of the splay and bend distortions of the tissue.

In this thesis, we study six Ginzburg-Landau minimization problems in the context of two-dimensional nematic liquid crystals with the intention of finding conditions for the existence of boundary vortices. The first minimization problem consists of the standard Ginzburg-Landau energy on bounded, simply connected domains Ω ⊂ R2 with boundary energy penalizing minimizers who stray from being parallel to some smooth S1-valued boundary function g of degree D ≥ 1. The second and third minimization problems consider the same Ginzburg-Landau energy but now with divergence and curl penalization in the interior and boundary function taken to be g = τ, the positively oriented unit tangent vector to the boundary. The remaining three problems involve minimizing the same energies, but now over the set for which all functions are precisely parallel to the given boundary data (up to a set for which their norms can be zero). These six problems are classified under two categories called the weak and strong orthogonal problems. In each of the six problems, we show that conditions exist for which sequences of minimizers converge to a limiting S1-valued vector field describing an equilibrium configuration for nematic material with defects. In some cases, energy estimates are obtained that show vortices belong to the boundary exclusively and the exact number of these vortices are known. A special case is also studied in the strong orthogonality setting. The analysis here suggests that geometries exist for which boundary vortices may be energetically preferable to interior vortices in the case where interior and boundary vortices have similar energy contributions. / Thesis / Doctor of Philosophy (PhD)

No description available.

No description available.

In this thesis we studied theoretically and numerically dynamics, order and fluctuations in two dimensional active matter with specific reference to the nematic phase in collections of self-driven particles.The aim is to study the ways in which a nonequilibrium steady state with nematic order differs from a thermal equilibrium system of the same spatial symmetry. The models we study are closely related to “flocking”[1], as well as to equations written down to describe the interaction of molecular motors and filaments in a living cell[2,3] and granular nematics [4]. We look at (i) orientational and density fluctuations in the ordered phase, (ii) the way in which density fluctuations evolve in a nematic background, and finally (iii) the coarsening of nematic order and the density field starting from a statistically homogeneous and isotropic initial state. Our work establishes several striking differences between active nematics and their thermal equilibrium counterparts. We studied two-dimensional nonequilibrium active nematics. Two-dimensional nonequilibrium nematic steady states, as found in agitated granular-rod monolayers or films of orientable amoeboid cells, were predicted [5] to have giant number fluctuations, with the standard deviation proportional to the mean. We studied this problem more closely, asking in particular whether the active nematic steady state is intrinsically phase-separated. Our work has close analogy to the work of Das and Barma[6] on particles sliding downhill on fluctuating surfaces, so we looked at a model in which particles were advected passively by the broken-symmetry modes of a nematic, via a rule proposed in [5]. We found that an initially homogeneous distribution of particles on a well-ordered nematic background clumped spontaneously, with domains growing as t1/2, and an apparently finite phase-separation order parameter in the limit of large system size. The density correlation function shows a cusp, indicating that Porod’s Law does not hold here and that the phase-separation is fluctuation-dominated[7]. Dynamics of active particles can be implemented either through microscopic rules as in[8,9]or in a long-wavelength phenomenological approach as in[5]It is important to understand how the two methods are related. The purely phenomenological approach introduces the simplest possible (and generally additive)noise consistent with conservation laws and symmetries. Deriving the long-wavelength equation by explicit coarse-graining of the microscopic rule will in general give additive and multiplicative noise terms, as seen in e.g., in [10]. We carry out such a derivation and obtain coupled fluctuating hydrodynamic equations for the orientational order parameter (polar as well as apolar) and density fields. The nonequilibrium “curvature-induced” current term postulated on symmetry grounds in[5]emerges naturally from this approach. In addition, we find a multiplicative contribution to the noise whose presence should be of importance during coarsening[11]. We studied nonequilibrium phenomena in detail by solving stochastic partial differential equations for apolar objects as obtained from microscopic rules in[8]. As a result of “curvature-induced” currents, the growth of nematic order from an initially isotropic, homogeneous state is shown to be accompanied by a remarkable clumping of the number density around topological defects. The consequent coarsening of both density and nematic order are characterised by cusps in the short-distance behaviour of the correlation functions, a breakdown of Porod’s Law. We identify the origins of this breakdown; in particular, the nature of the noise terms in the equations of motion is shown to play a key role[12]. Lastly we studied an active nematic steady-state, in two space dimensions, keeping track of only the orientational order parameter, and not the density. We apply the Dynamic Renormalization Group to the equations of motion of the order parameter. Our aim is to check whether certain characteristic nonlinearities entering these equations lead to singular renormalizations of the director stiffness coefficients, which would stabilize true long-range order in a two-dimensional active nematic, unlike in its thermal equilibrium counterpart. The nonlinearities are related to those in[13]but free of a constraint that applies at thermal equilibrium. We explore, in particular, the intriguing but ultimately deceptive similarity between a limiting case of our model and the fluctuating Burgers/KPZequation. By contrast with that case, we find that the nonlinearities are marginally irrelevant. This implies in particular that 2-dactive nematics too have only quasi-long-range order[14].