Related papers: Defects in Nematic Shells: a $\Gamma$-convergence …
We study nematic equilibria in an unbounded domain, with a two-dimensional regular polygonal hole with $K$ edges, in a reduced Landau-de Gennes framework. This complements our previous work on the "interior problem" for nematic equilibria…
In contrast to extensively studied defects in traditional materials, we report here for the first time a systematic investigation of the formation mechanism of intrinsic defects in self-assembled peptide nanostructures. The Monte Carlo…
Disclination lines in three-dimensional nematic liquid crystals generically form closed loops whose topology is classified by homotopy theory. While this classification successfully captures global topological features, it does not encode…
Topological defects constructed out of scalar fields and possessing chiral fermion zero modes are known to exhibit an anomaly inflow mechanism which cancels the anomaly in the effective theory of the zero modes through an inflow of current…
Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work…
We are interested in nonlinear hyperbolic systems in nonconservative form arising in fluid dynamics, and, for solutions containing shock waves, we investigate the convergence of finite difference schemes applied to such systems. According…
Through experiments, we studied defect turbulence, a type of spatiotemporal chaos in planar systems of nematic liquid crystals, to clarify the chaotic advection of weak turbulence. In planar systems of large aspect ratio, structural…
We investigate the effect of defect geometry in dictating the sensitivity of the critical buckling conditions of spherical shells under external pressure loading. Specifically, we perform a comparative study between shells containing…
Defects and impurities strongly affect the timing and the character of the (re)ordering or disordering transitions of thermodynamic systems captured in metastable states. In this paper we analyze the case of two-dimensional magnetic…
We present a unified theory of fracture in disordered brittle media that reconciles apparently conflicting results reported in the literature. Our renormalization group based approach yields a phase diagram in which the percolation fixed…
Topological defects are singularities within a field that cannot be removed by continuous transformations. The definition of these irregularities requires an ordered reference configuration, calling into question whether they exist in…
We consider an isolated point defect embedded in a homogeneous crystalline solid. We show that, in the harmonic approximation, a periodic supercell approximation of the formation free energy as well as of the transition rate between two…
We show that the anomalous dimension $\gamma_G$ of the scalar glueball operator contains information on the mechanism that leads to the onset of conformality at the lower edge of the conformal window in a non-Abelian gauge theory. In…
We study nematic equilibria on rectangular domains, in a reduced two-dimensional Landau-de Gennes framework. These reduced equilibria carry over to the three-dimensional framework at a special temperature. There is one essential model…
Recent experimental observations have suggested that topological defects can facilitate the creation of sharp features in developing embryos. Whereas these observations echo established knowledge about the interplay between geometry and…
We revisit the velocity-dependent one-scale model for topological defect evolution, and present a new alternative formulation in terms of a physical (rather than invariant) characteristic length scale. While the two approaches are…
We study a discrete version of a biaxial nematic liquid crystal model with external fields via an approach based on the solution of differential identities for the partition function. In the thermodynamic limit, we derive the free energy of…
A geometrically nonlinear continuum mechanical theory is formulated for deformation and failure behaviors of amorphous polymers. The model seeks to capture material response over a range of loading rates, temperatures, and stress states…
In this paper we discuss the behavior of the Oseen-Frank model for nematic liquid crystals in the limit of vanishing thickness. More precisely, in a thin slab~$\Omega\times (0,h)$ with~$\Omega\subset \mathbb{R}^2$ and $h>0$ we consider the…
Topological defects are at the root of the large-scale organization of liquid crystals. In two-dimensional active nematics, two classes of topological defects of charges $\pm 1/2$ are known to play a major role due to active stresses.…