Related papers: Compatible director fields in $\mathbb{R}^3$
A numerical method is developed for solving a system of partial differential equations modeling the flow of a nematic liquid crystal fluid with stretching effect, which takes into account the geometrical shape of its molecules. This system…
We investigate the effect of three-body correlations on the phase behavior of hard rectangle two-dimensional fluids. The third virial coefficient, $B_3$, is incorporated via an equation of state that recovers scaled particle theory for…
So-called polar liquid crystals possess spontaneous long-range mutual orientation of their electric dipole moments, conferring bulk polarity to fluid phases of matter. The combination of polarity and fluidity leads to complex phase…
We show how the symmetry of attractors of equivariant dynamical systems can be observed by equivariant projections of the phase space. Equivariant projections have long been used, but they can give misleading results if used improperly and…
We examine Friedmann-Robertson-Walker models in three spacetime dimensions. The matter content of the models is composed of a perfect fluid, with a $\gamma$-law equation of state, and a homogeneous scalar field minimally coupled to gravity…
Colloidal particles moving in a fluid interact via the induced velocity field. The collective dynamic state for a class of actively forced colloids, driven by harmonic potentials via a rule that couples forces to configurations, to perform…
We investigate the phase diagram of a two-component associating fluid mixture in the presence of selectively adsorbing substrates. The mixture is characterized by a bulk phase diagram which displays peculiar features such as closed loops of…
We study photopolymerization in a low-molecular weight liquid crystal with non-uniform director gradients. Phase separation results in spatially non-uniform distribution of polymer density controlled by the distorted nematic matrix.…
The paper is concerned with various issues surrounding the mathematical description of defects in models of liquid crystals, drawing on experience from solid mechanics. The roles played by a suitable choice of function space and by the…
In the literature, for semidynamical systems in infinite dimensional phase spaces, different topological structures are used (Hilbert, Banach, Sobolev, locally convex, Hausdorf topology etc.). That is because there are neither set rules nor…
Superconductivity owes its properties to the phase of the electron pair condensate that breaks the $U(1)$ symmetry. In the most traditional ground state, the phase is uniform and rigid. The normal state can be unstable towards special…
It is difficult to derive the solid--fluid transition from microscopic models. We introduce particle systems whose potentials do not decay with distance and calculate their partition function exactly using a method similar to that for…
We study the Landau model of the class of incommensurate systems with a scalar order parameter where the modulated phase is driven by a gradient-squared term with negative coefficient. For example, theoretical studies of cholesteric liquid…
The non-equilibrium behavior of particle systems driven by reservoirs has been extensively studied in recent years. In one dimension, various regimes have been explored depending on the coupling strength to the reservoirs. In this paper, we…
In this article we show that the phase-ordering scaling state for binary fluids is not necessarily unique and that local correlations in the initial conditions can be responsible for selecting the scaling state. We describe a new scaling…
We use video microscopy to follow the phase-space trajectory of a two-dimensional colloidal model liquid and calculate three-point correlation functions from the measured particle configurations. Approaching the fluid-solid transition by…
Topology can manifest itself in colloids when quantified by invariants like Euler characteristics of nonzero-genus colloidal surfaces, albeit spherical colloidal particles are most often studied, and colloidal particles with complex…
Spatially uniform electric fields have been used to induce instabilities in liquids and polymers, and to orient and deform ordered phases of block-copolymers. Here we discuss the demixing phase transition occurring in liquid mixtures when…
An overview of results of models of coupled quantum rotors is presented. We focus on rotors with dipolar and quadrupolar potentials in two and three dimensions, potentials which correspond to approximate descriptions of real molecules…
In this contribution we discuss the role which incoherent boundary conditions can play in the study of phase transitions. This is a question of particular relevance for the analysis of disordered systems, and in particular of spin glasses.…