Related papers: Front Propagation at the Isotropic Nematic Transit…
An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be formulated as a Laplacian growth model regularized by a 'kinetic undercooling' boundary condition. Using this model we study both the…
The motion of a contact line is examined, and comparisons drawn, for a variety of models proposed in the literature. Pressure and stress behaviours at the contact line are examined in the prototype system of quasistatic spreading of a thin…
Linear defects such as dislocations and disclinations in ordered materials attract foreign particles since they replace strong elastic distortions at the defect cores. In this work, we explore the behavior of isotropic droplets nucleating…
Computer simulations are presented of the isotropic-to-nematic transition in a liquid crystal confined between two parallel plates a distance H apart. The plates are neutral and do not impose any anchoring on the particles. Depending on the…
This paper exploits the theory of geometric gradient flows to introduce an alternative regularization of the thin-film equation. The solution properties of this regularization are investigated via a sequence of numerical simulations whose…
We investigate the evolution of interfaces among phases of the interstellar medium with different temperature. It is found that, for some initial conditions, the dynamical effects related to conductive fronts are very important even if…
We study the existence and uniqueness of mild and strong solutions of nonlocal nonlinear diffusion problems of $p$-Laplacian type with nonlinear boundary conditions posed in metric random walk spaces. These spaces include, among others,…
We study the radial-hedgehog solution in a three-dimensional spherical droplet, with homeotropic boundary conditions, within the Landau-de Gennes theory for nematic liquid crystals. The radial-hedgehog solution is a candidate for a globally…
We analyze the global phase diagram of a Maier-Saupe lattice model with the inclusion of disorder degrees of freedom to mimic a mixture of oblate and prolate molecules (discs and cylinders). In the neighborhood of a Landau multicritical…
We study a model that intermediates among the wave, heat, and transport equations. The approach considers the propagation of initial disturbances in a one-dimensional medium that can vibrate. The medium is nonlinear in such a form that…
In this paper, we consider a family of seamlessly coupled nonlocal models associated with transmission conditions across an interface. The models are derived from the variation of a parameterized family of energies consisting of a…
The transition from a nematic to an isotropic state in a self-closing spherical liquid crystal shell with tangential alignment is a stimulating phenomenon to investigate, as the topology dictates that the shell exhibits local isotropic…
When captured by a flat nematic-isotropic interface, colloidal particles can be dragged by it. As a result spatially periodic structures may appear, with the period depending on a particle mass, size, and interface…
We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains. Assuming smooth and uniaxial (e.g. homeotropic) boundary conditions and a corresponding physically…
The Landau-de Gennes free energy is used to calculate the interaction between long cylindrical colloids and the nematic-isotropic (NI) interface. This interaction has two contributions: one is specific of liquid crystals and results from…
Within the macroscopic Landau-de Gennes approach, we examine the Gaussian normal mode fluctuations of semi-infinite nematic liquid crystals in a regime of critical wetting. It is argued that surface free-energy potentials that strongly…
We analyze the effect of nonlinear boundary conditions on an advection-diffusion equation on the half-line. Our model is inspired by models for crystal growth where diffusion models diffusive relaxation of a displacement field, advection is…
Aqueous dispersions of exfoliated, bile-salt stabilized single-wall carbon nanotubes exhibit a first order transition to a nematic liquid-crystalline phase. The nematic phase presents itself in the form of micron-sized nematic droplets also…
We develop a novel finite element method for a phase field model of nematic liquid crystal droplets. The continuous model considers a free energy comprised of three components: the Ericksen's energy for liquid crystals, the Cahn-Hilliard…
In this paper, we mainly study a hydrodynamic system modeling the flow of nematic liquid crystals. In three dimensions, we first establish local well-posedness of the initial-boundary value problem of the system. Then, we prove the…