相关论文: Compatible director fields in $\mathbb{R}^3$

We derive a phase diagram for amorphous solids and liquid supercooled water and explain why the amorphous solids of water exist in several different forms. Application of large-deviation theory allows us to prepare such phases in computer…

The relationship between the polymer orientation and the chaotic flow, in a dilute solution of rigid rodlike polymers at low Reynolds number, is investigated by means of direct numerical simulations. It is found that the rods tend to align…

We study the phase diagram of director structures in cholesteric liquid crystals of negative dielectric anisotropy in homeotropic cells of thickness d which is smaller than the cholesteric pitch p. The basic control parameters are the…

The three-dimensional $q$-state Potts model, forced into coexistence by fixing the density of one state, is studied for $q=2$, 3, 4, and 6. As a function of temperature and number of states, we studied the resulting equilibrium droplet…

When nematic liquid crystals are embedded in random polymer networks, the disordered environment disrupts the long-range order, producing a glassy state. If an electric field is applied, it induces large and fairly temperature-independent…

A nematic phase, previously seen in the d=3 classical Heisenberg spin-glass system, occurs in the n-component cubic-spin spin-glass system, between the low-temperature spin-glass phase and the high-temperature disordered phase, for number…

Conformal field theories (CFTs) with cubic global symmetry in 3D are relevant in a variety of condensed matter systems and have been studied extensively with the use of perturbative methods like the $\varepsilon$ expansion. In an earlier…

We introduce phase operators associated with the algebra su(3), which is the appropriate tool to describe three-level systems. The rather unusual properties of this phase are caused by the small dimension of the system and are explored in…

Geometrical constructions, such as the tangent construction on the molar free energy for determining whether a particular composition of a solution, is stable, are related to similar tangent constructions on the orientation-dependent…

Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and…

We propose a new algebraic approach to study compatibility of partial differential equations. The approach uses concepts from commutative algebra, algebraic geometry and Gr\"obner bases to clarify crucial notions concerning compatibility…

We propose a simple microscopic model of molecular dynamics simulation to study orientational glass in three dimensions. We present simulation results for mixtures of mildly anisotropic particles and spherical impurities. We realize fcc…

We review the impact of tetrahedral order on the macroscopic dynamics of bent-core liquid crystals. We discuss tetrahedral order comparing with other types of orientational order, like nematic, polar nematic, polar smectic, and active polar…

The geometric shape, symmetry, and topology of colloidal particles often allow for controlling colloidal phase behavior and physical properties of these soft matter systems. In liquid crystalline dispersions, colloidal particles with low…

We consider a random matrix model which describes the competition between chiral symmetry breaking and the formation of quark Cooper pairs in QCD at finite density. We study the evolution of the phase structure in temperature and chemical…

This thesis seeks to develop a general method for solving so-called quantum realizability problems, which are questions of the following form: under which conditions does there exist a quantum state exhibiting a given collection of…

We carry out Monte Carlo simulations on fluid membranes with orientational order and multiple edges in the presence and absence of external forces. The membrane resists bending and has an edge tension, the orientational order couples with…

We consider the broken phase of the n-vector model in n+1 dimensions with boundary conditions enforcing the presence of topological defect lines (Ising domain walls, XY vortex lines, and so on), and use field theory to argue an exact…

Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…

Phase behaviours of liquid crystals under external fields, conjugate to the nematic order and smectic order, are studied within the framework of mean field approximation developed by McMillan. It is found that phase diagrams, of temperature…