Related papers: A Model Problem for Nematic-Isotropic Transitions …
It was recently suggested that the sign of particle drift in inhomogeneous temperature or turbulence depends on the particle inertia: weakly inertial particles localize near minima of temperature or turbulence intensity (effects known as…
We introduce a new class of non-isothermal models describing the evolution of nematic liquid crystals and prove their consistency with the fundamental laws of classical Thermodynamics. The resulting system of equations captures all…
The paper addresses the problem of a a semi-infinite plane crack along the interface between two 3D isotropic half-spaces. Two methods of solution have been considered in the past: Lazarus and Leblond (1998) applied the "special" method by…
Polyhedral nematics are examples of exotic orientational phases that possess a complex internal symmetry, representing highly non-trivial ways of rotational symmetry breaking, and are subject to current experimental pursuits in colloidal…
The existence of substellar cold H2 globules in planetary nebulae and the mere existence of comets suggest that the physics of cold interstellar gas might be much richer than usually envisioned. We study the case of a cold gaseous medium in…
Liquid crystals in two dimensions do not support long-ranged nematic order, but a quasi-nematic phase where the orientational correlations decay algebraically is possible. The transition from the isotropic to the quasi-nematic phase can be…
We show that a minimal model for viscous fingering with a nematic liquid crystal in which anisotropy is considered to enter through two different viscosities in two perpendicular directions can be mapped to a two-fold anisotropy in the…
The dynamics of a spherical elastic capsule, containing a Newtonian fluid bounded by an elastic membrane and immersed in another Newtonian fluid, in a uniform DC electric field is investigated. Discontinuity of electrical properties such as…
We investigate the phase behavior of a single-component system in 3 dimensions with spherically-symmetric, pairwise-additive, soft-core interactions with an attractive well at a long distance, a repulsive soft-core shoulder at an…
We present new results for the ordering process of a two-dimensional Ising model with anisotropic frustrating next-nearest-neighbor interactions. We concentrate on a specific wide temperature and parameter region to confirm the existence of…
This paper studies a two-phase free boundary problem governed by the ElectroHydroDynamic equations, which describes a perfectly conducting, incompressible, irrotational fluid with gravity, surrounded by a dielectric gas. The interface…
We theoretically study the nematic ordering transition of rods that are able to elastically adjust their mutually excluded volumes. The model rods, which consist of a hard core surrounded by a deformable shell, mimic the structure of…
In vivo and in vitro systems of cells and extra-cellular matrix (ECM) systems are well known to form ordered patterns of orientationally aligned fibers. Here, we interpret them as active analogs of the (disordered) isotropic to the…
Field theories predict that phase transitions sequentially breaking continuous and discrete symmetries can generate hybrid topological structures in which defects of different dimensionalities merge. We report experimental and numerical…
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…
Anisotropic fluids appear in a diverse array of systems, from liquid-crystal displays to bacterial swarms, and are characterized by orientational order. Large colloidal particles immersed in such environments disturb the medium's…
We study the effective behavior of random, heterogeneous, anisotropic, second order phase transitions energies that arise in the study of pattern formations in physical-chemical systems. Specifically, we study the asymptotic behavior, as…
Phase transition problems on curved surfaces can lead to a panopticon of fascinating patterns. In this paper we consider finite element approximations of phase field models with a spatially inhomogeneous and anisotropic surface energy…
We analyze nonnegative solutions of the nonlinear elliptic problem $\Delta u=\frac{\lambda f(x)}{u^2}+P$, where $\lambda>0$ and $P\geq0$, on a bounded domain $\Omega$ of $\mathbb{R}^N$ ($N\geq 1$) with a Dirichlet boundary condition. This…
In this work we introduce a new system of partial differential equations as a simplified model for the evolution of reversible martensitic transformations under thermal cycling in low hysteresis alloys. The model is developed in the context…