Related papers: Exact equations of state for nematics
We present experimental evidence for a first-order freezing/melting phase transition in a nonequilibrium system -- an oscillated two-dimensional isobaric granular fluid. The steady-state transition occurs between a gas and a crystal and is…
Using a version of density-functional theory which combines Onsager approximation and fundamental-measure theory for spatially nonuniform phases, we have studied the phase diagram of freely rotating hard rectangles and hard discorectangles.…
Nematic liquid crystals exhibit configurations in which the underlying ordering changes markedly on macroscopic length scales. Such structures include topological defects in the nematic phase and tactoids within nematic-isotropic…
Liquid crystals consisting of biaxial particles can exhibit a much richer phase behavior than their uniaxial counterparts. Usually, one has to rely on simulation results to understand the phase diagram of these systems, since very few…
The celebrated van der Waals model describes simple fluids in the thermodynamic limit and predicts the existence of a critical point associated to the gas-liquid phase transition. However the behaviour of critical isotherms according to the…
We use density-functional theory, of the fundamental-measure type, to study the relative stability of the biaxial nematic phase, with respect to non-uniform phases such as smectic and columnar, in fluids made of hard board-like particles…
Liquid crystal droplets are of great interest from physics and applications. Rigorous mathematical analysis is challenging as the problem involves harmonic maps (and in general the Oseen-Frank model), free interfaces and topological defects…
Liquid crystals in two dimensions undergo a first-order isotropic-to-quasi-nematic transition, provided the particle interactions are sufficiently ``sharp and narrow''. This implies phase coexistence between isotropic and quasi-nematic…
Simulations of nematic-isotropic transition of liquid crystals in two dimensions are performed using an O(2) vector model characterised by non linear nearest neighbour spin interaction governed by the fourth Legendre polynomial $P\_4$. The…
Modeling and simulation studies using a high-order Landau-de Gennes type model for the direct isotropic/smectic-A liquid crystal transition are presented showing the existence of meta-stable nematic pre-ordering under certain conditions, in…
In this paper, we characterize a class of solutions to the unsteady 2-dimensional flow of a van der Waals fluid involving shock waves, and derive an asymptotic amplitude equation exhibiting quadratic and cubic nonlinearities including…
The phase-field-crystal model for liquid crystals is solved numerically in two spatial dimensions. This model is formulated with three position-dependent order parameters, namely the reduced translational density, the local nematic order…
We study phases and phase transitions that can take place in the newly discovered banana (bow-shaped or bent-core) liquid crystal molecules. We show that to completely characterize phases exhibited by such bent-core molecules a third-rank…
This article is focused on a multidimensional nonlinear variational wave equation which is the Euler-Lagrange equation of a variational principle arising form the theory of nematic liquid crystals. By using the method of characteristics, we…
This study establishes the global well-posedness of the compressible non-isentropic Navier-Stokes/Allen-Cahn system governed by the van der Waals equation of state $p(\rho,\theta)=- a\rho^2+\frac{R\theta\rho}{1-b\rho}$ and degenerate…
The paradigm of spontaneous symmetry breaking encompasses the breaking of the rotational symmetries $O(3)$ of isotropic space to a discrete subgroup, i.e. a three-dimensional point group. The subgroups form a rich hierarchy and allow for…
We propose and study a local map capable of describing the full variety of dynamical states, ranging from regular to chaotic, obtained when a nematic liquid crystal is subjected to a steady shear flow. The map is formulated in terms of a…
We propose a model that describes phase transition including meta\-stable states present in the van der Waals Equation of State. From a convex optimization problem on the Helmoltz free energy of a mixture, we deduce a dynamical system that…
We use lattice Boltzmann simulations of the Beris--Edwards formulation of nematodynamics to probe the response of a nematic liquid crystal with conflicting anchoring at the boundaries under shear and Poiseuille flow. The geometry we focus…
An intermediate nematic phase is proposed for the interpretation of recent experimental results on phase biaxiality in bent-core nematics. The phase is macroscopically uniaxial but consists of microscopic biaxial, and possibly polar,…