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The stability to dislocations of the elastic phase, or ``Bragg glass'', of a randomly pinned elastic medium in two dimensions is studied using the minimum-cost-flow algorithm for a disordered fully-packed loop model. The elastic phase is…
The pinning of an inhomogeneous elastic medium by a disordered substrate is studied analytically and numerically. The static and dynamic properties of a $D$-dimensional system are shown to be equivalent to those of the well known problem of…
In recent years there has been renewed interest in the behavior of dislocations in crystals that exhibit strong atomic scale disorder, as typical of compositionally complex single phase alloys. The behavior of dislocations in such crystals…
The simultaneous effect of both disorder and crystal-lattice pinning on the equilibrium behavior of oriented elastic objects is studied using scaling arguments and a functional renormalization group technique. Our analysis applies to…
The equilibrium behavior of a system of elastic layers under tension in the presence of correlated disorder is studied using functional renormalization group techniques. The model exhibits many of the features of the Bose glass phase of…
Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple…
A description of a dislocation-free elastic glass phase in terms of domain walls is developed and used as the basis of a renormalization group analysis of the energetics of dislocation loops added to the system. It is found that even after…
These notes are devoted to the statistical mechanics of directed polymers interacting with one-dimensional spatial defects. We are interested in particular in the situation where frozen disorder is present. These polymer models undergo a…
The competing effect of a periodic pinning potential and random point disorder is studied for arrays of elastic lines or directed polymers. The groundstates are investigated by exact combinatorial optimization. In both two and three…
We study, using functional renormalization (FRG), two copies of an elastic system pinned by mutually correlated random potentials. Short scale decorrelation depend on a non trivial boundary layer regime with (possibly multiple) chaos…
Spatially confined rigid membranes reorganize their morphology in response to the imposed constraints. A crumpled elastic sheet presents a complex pattern of random folds focusing the deformation energy while compressing a membrane resting…
While the dynamics of polymer chains in equilibrium media is well understood by now, the polymer dynamics in active non-equilibrium environments can be very different. Here we study the dynamics of polymers in a viscous medium containing…
In this thesis I discuss analytical approaches to disordered systems using field theory. Disordered systems are characterized by a random energy landscape due to heterogeneities, which remains fixed on the time scales of the phenomena…
We study a disordered network of bistable bonds subjected to periodic strain. The model is inspired by experiments on crumpled sheets and it features behaviors associated with glasses, including a complex energy landscape, memories, and…
Polynomial chaos is a powerful technique for propagating uncertainty through ordinary and partial differential equations. Random variables are expanded in terms of orthogonal polynomials and differential equations are derived for the…
We report evidence of irregular unsteady flow of two-dimensional polymer solutions in the absence of inertia in cross-slot geometry using numerical simulations of Oldroyd-B model. By exploring the transition to time-dependent flow versus…
We examine here various aspects of the statics and dynamics of disordered elastic systems such as manifolds and periodic systems. Although these objects look very similar and indeed share some underlying physics, periodic systems constitute…
The effects of weak point-like disorder on periodic systems at their upper critical dimension D_c for disorder are studied. The systems studied range from simple elastic systems with D_c=4 to systems with long range interactions with D_c=2…
We discuss the question of the generation of topological defects (dislocations) by quenched disorder in two dimensional periodic systems. In a previous study [Phys. Rev. B {\bf 52} 1242 (1995)] we found that, contrarily to $d=3$, unpaired…
We investigate the roughening phase transition of a $(3+1)$-dimensional elastic manifold driven by the completion between a periodic pinning potential and a randomly distributed impurities. The elastic manifold is modeled by a…