Related papers: Compatible director fields in $\mathbb{R}^3$
Compatibility conditions are investigated for planar network structures consisting of nodes and connecting bars; these conditions restrict the elongations of bars and are analogous to the compatibility conditions of deformation in continuum…
A nonlinear model due to Soddemann et al. [37] and Stewart [38] describing incompressible smectic-A liquid crystals under flow is studied. In comparison to previously considered models, this particular model takes into account possible…
The liquid and crystal phase of a single-component Fermi gas with dipolar interactions are investigated using quantum Monte Carlo methods in two spatial dimensions and at zero temperature. The dipoles are oriented by an external field…
We study the collective behavior of nonequilibrium systems subject to an external field with a dynamics characterized by the existence of non-interacting states. Aiming at exploring the generality of the results, we consider two types of…
There are at least three fundamental states of matter, depending upon temperature and pressure: gas, liquid, and solid (crystal). These states are separated by first-order phase transitions between them. In both gas and liquid phases the…
We put the theory of interacting topological crystalline phases on a systematic footing. These are topological phases protected by space-group symmetries. Our central tool is an elucidation of what it means to "gauge" such symmetries. We…
In this paper we prove the existence of a trajectory attractor (in the sense of V.V. Chepyzhov and M.I. Vishik) for a nonlinear PDE system coming from a 3D liquid crystal model accounting for stretching effects. The system couples a…
The geometric motion of small droplets placed on an impermeable textured substrate is mainly driven by the capillary effect, the competition among surface tensions of three phases at the moving contact lines, and the impermeable substrate…
Recent theoretical research has developed a general framework to understand director deformations and modulated phases in nematic liquid crystals. In this framework, there are four fundamental director deformation modes: twist, bend, splay,…
The movement of the triple contact line plays a crucial role in many applications such as ink-jet printing, liquid coating and drainage (imbibition) in porous media. To design accurate computational tools for these applications, predictive…
In this article is proposed the general approach to determination the character of the interaction between colloidal particles in a different liquid crystals. The main idea of this approach are in the presentation of the colloidal particle…
Effects of three-point direct correlation on properties of the phase field crystal (PFC) modeling are examined, for the control of various ordered and disordered phases and their coexistence in both three-dimensional and two-dimensional…
Although a great number of computational models of water are available today, the majority of current biological simulations are done with simple models, such as TIP3P and SPC, developed almost thirty years ago and only slightly modified…
In this paper, we consider a class of models for multiphase fluids, in the framework of mixture theory. The considered system, in its more general form, contains both the gradient of a hydrostatic pressure, generated by an incompressibility…
We introduce a Phase Field Crystal (PFC) model for particles with n-fold rotational symmetry in two dimensions. Our approach is based on a free energy functional that depends on the reduced one-particle density, the strength of the…
Tetrahedral frame fields have applications to certain classes of nematic liquid crystals and frustrated media. We consider the problem of constructing a tetrahedral frame field in three dimensional domains in which the boundary normal…
Using a phase field crystal model we study the structure and dynamics of a drop of colloidal suspension during evaporation of the solvent. We model an experimental system where contact line pinning of the drop on the substrate is…
If particles interact according to isotropic pair potentials that favor multiple length scales, in principle a large variety of different complex structures can be achieved by self-assembly. We present, motivate, and discuss a conjecture…
We study non-equilibrium stationary states of a cavity system consisting of many atoms interacting with a quantized cavity field mode, under a driving field in a dissipative environment. We derive a quantum master equation which is suitable…
While quasi-two-dimensional (layered) materials can be highly anisotropic, their asymptotic long-distance behavior generally reflects the properties of a fully three dimensional phase of matter. However, certain topologically ordered…