相关论文: Compatible director fields in $\mathbb{R}^3$
In this paper, we investigate the Cauchy problem for the incompressible nematic liquid crystal flows in three-dimensional whole space. First of all, we establish the global existence of solution by energy method under assumption of small…
A phase field theory of polycrystalline solidification is presented that is able to describe the nucleation and growth of anisotropic particles with different crystallographic orientation in three dimensions. As opposed with the…
The late-stage phase ordering, in $d=2$ dimensions, of symmetric fluid mixtures violates dynamical scaling. We show however that, even at 50/50 volume fractions, if an asymmetric droplet morphology is initially present then this sustains…
We studied in-plane bistable alignments of nematic liquid crystals confined by two frustrated surfaces by means of Monte Carlo simulations of the Lebwohl-Lasher spin model. The surfaces are prepared with orientational checkerboard patterns,…
We consider the homogeneous five-vertex model on a rectangle domain of the square lattice with so-called scalar-product boundary conditions. Peculiarity of these boundary conditions is that the configurations of the model are in an…
Phase field crystal (PFC) models constitute central tools for a microscopic understanding of the dynamics of complex systems in soft matter physics. They have found widespread application in the modeling of the uniaxial orientational…
Many physical systems involve two types of orientational order, which are coupled together. For example, ferroelectric nematic liquid crystals have coupled polar and nematic order, and tilted hexatic phases have coupled polar and hexatic…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
The three-state Potts model is numerically investigated on three-dimensional simple cubic lattices of up to \(128^3\) volume, concentrating on the neighborhood of the first-order phase transition separating the ordered and disordered…
In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…
Fractional quantum Hall liquids can accomodate various degrees of spatial ordering. The most likely scenarios are a Hall hexatic, Hall smectic, and Hall crystal, in which respectively orientational, one--dimensional translational, and…
The present contribution investigates the well-posedness of a PDE system describing the evolution of a nematic liquid crystal flow under kinematic transports for molecules of different shapes. More in particular, the evolution of the {\em…
The world of two-dimensional crystals is of great significance for the design and study of structural and functional materials with novel properties. The world of two-dimensional crystals is of great significance for the design and study of…
The phase diagram of the attractive Hubbard model with spatially inhomogeneous interactions is obtained using a single site dynamical mean field theory like approach. The model is characterized by three parameters: the interaction strength,…
Colloidal fluids can exhibit complex phase behavior and determining phase diagrams via experiments or computer simulations can be laborious. We demonstrate that the dispersion relation $\omega(k)$, obtained from dynamical density functional…
A general field-theoretic framework for the treatment of liquid-gas phase transitions is developed. Starting from a fundamental four-dimensional field theory at nonzero temperature and density, an effective three-dimensional field theory…
Field induced assembly of reconfigurable structures with complex hierarchical configurations has recently become an area of intense research with the promise for exciting applications in programmable self-assembly and nano/microstructure…
We investigate the possibility to control the symmetry of ordered states in phase-field crystal models by tuning nonlinear resonances. In two dimensions, we find that a state of square symmetry as well as coexistence between squares and…
Topological field theory in three dimensions provides a powerful tool to construct correlation functions and to describe boundary conditions in two-dimensional conformal field theories.
Through extensive molecular simulations we determine a phase diagram of attractive, flexible polymer chains in two and three dimensions. A surprisingly rich collection of distinct crystal morphologies appear, which can be finely tuned…