Dmitry Golovaty

On Minimizers of a Landau-de Gennes Energy Functional on Planar Domains

We study tensor-valued minimizers of the Landau–de Gennes energy functional on a simply-connected planar domain Ω with non-contractible boundary data. Here the tensorial field represents the second moment of a local orientational distribution of rod-like molecules of a nematic liquid crystal. Under the assumption that the energy depends on a single parameter—a dimensionless elastic constant

Swimming Photochromic Azobenzene Single Crystals in Triacrylate Solution

{\varepsilon > 0}

On-line control of solid–liquid interface by state feedback

ε>0 —we establish that, as

Snell’s law of refraction observed in thermal frontal polymerization

{\varepsilon \to 0}

On Step‐Function Reaction Kinetics Model in the Absence of Material Diffusion

ε→0 , the minimizers converge to a projection-valued map that minimizes the Dirichlet integral away from a single point in Ω. We also provide a description of the limiting map.

Continuum model of polygonization of carbon nanotubes

We consider an evolution system, describing the time-dependent behavior of nematic liquid crystals with variable degree of orientation within the continuum model of Ericksen. We establish a dissipation relation and prove both the global existence of weak solutions and the local existence of classical solutions. Furthermore, we investigate the stability and long-time behavior of solutions and obtain an exact solution of the corresponding stationary system in a one-dimensional case.