Related papers: Wulff Construction for Deformable Media
This is a report on the derivation and application of a generalized version of the Wulff construction in two dimensions. The construction is used to find the shape of a domain containing an XY-like order parameter. In such a domain the…
Finite domains of a Langmuir monolayer in a phase with tilted molecules can be modeled by a simple elastic free energy of an XY order parameter with isotropic and anisotropic line tension terms. The domains can and often do contain…
Two-dimensional domains containing an XY-like order parameter exhibit non-trivial internal structure and take on shapes controlled by the configuration that the order parameter adopts. The textures exhibited by the order parameter in such…
Structure of monolayers built during adsorption process is strongly related to the properties of adsorbed particles. The most important factor is their shape. For example, adsorption of elongated molecules on patterned surfaces may produce…
Domains in Langmuir monolayers support a texture that is the two-dimensional version of the feature known as a boojum. Such a texture has a quantifiable effect on the shape of the domain with which it is associated. The most noticeable…
We use surface tension to distinguish between phases with isotropic internal structure from phases which are microscopically anisotropic. There are many interesting open problems, especially in two dimensions, and in phase coexistence.
The spatiotemporal structure formation problem is investigated in the region far above the transverse ferromagnetic resonance instability. The investigations are based on the dissipative Landau-Lifshitz equation and have been performed on a…
In this work, the influence of geometry and domain size on spatiotemporal pattern formation is investigated to establish parameter spaces for a cross-diffusive reaction-diffusion model on an annulus. By applying linear stability theory, we…
The formation of normal-state domains in type-I superconducting indium films is investigated using the high resolution magneto-optical imaging technique. The observed patterns consist of coexisting circular and lamellar normal-phase domains…
Highly anisotropic interfaces play an important role in the development of material microstructure. Using the diffusive atomistic phase-field crystal (PFC) formalism, we determine the capability of the model to quantitatively describe these…
We present the geometric solutions to some variational problems of statistical mechanics and combinatorics. Together with the Wulff construction, which predicts the shape of the crystals, we discuss the construction which exhibits the shape…
Based on the dissipative Landau-Lifshitz equation, the spatiotemporal structure formation problem is investigated in the region far above the transverse ferromagnetic resonance instability. Apart from the external fields, the model contains…
Domain walls form at phase transitions which break discrete symmetries. In a cosmological context they often overclose the universe (contrary to observational evidence), although one may prevent this by introducing biases or forcing…
We investigate the formation of stable one-dimensional N\'eel walls in a ferromagnetic slab with finite thickness and finite width. Taking into account the dipolar, the exchange and the uniaxial anisotropic crystalline field interactions,…
Topologically protected magnetic structures such as skyrmions and domain walls (DWs) have drawn a great deal of attention recently due to their thermal stability and potential for manipulation by spin current, which is the result of chiral…
The dilational viscosity $\epsilon'$ of Langmuir monolayer is considered in a theoretical model taking into account an orientational effect of the dilational wave on surface molecules. This orientational order is described by the surface…
Discrete symmetry-breaking phase transitions in the early universe may have caused the formation of networks of sheet-like topological defects, usually referred to as domain walls, which separate regions that have settled into different…
Domain patterns are simulated by the Landau-Lifshitz-Gilbert (LLG) equation with an easy-axis anisotropy. If the Gilbert damping is removed from the LLG equation, it merely describes the precession of magnetization with a ferromagnetic…
The effect of sample shape on the depinning of the domain wall (DW) driven by an applied magnetic field or a spin-polarized current is studied theoretically. The shape effect resulting from the modulation of the sample width (geometric…
We study numerically the coarsening kinetics of a two-dimensional ferromagnetic system with aleatory bond dilution. We show that interfaces between domains of opposite magnetisation are fractal on every lengthscale, but with different…