Spectral Deferred Correction Method for Landau-Brazovskii Model with Convex Splitting Technique

The Landau-Brazovskii model is a well-known Landau model for finding the complex phase structures in microphase-separating systems ranging from block copolymers to liquid crystals. It is critical to design efficient numerical schemes for the Landau-Brazovskii model with energy dissipation and mass conservation properties. Here, we propose a mass conservative and energy stable scheme by combining the spectral deferred correction (SDC) method with the convex splitting technique to solve the Landau-Brazovskii model efficiently. An adaptive correction strategy for the SDC method is implemented to reduce the cost time and preserve energy stability. Numerical experiments, including two- and three-dimensional periodic crystals in the Landau-Brazovskii model, are presented to show the efficiency of the proposed numerical method.Comment: 20 pages, 5 figure

Nucleation of stable cylinders from a metastable lamellar phase in a diblock copolymer melt

The nucleation of a droplet of stable cylinder phase from a metastable lamellar phase is examined within the single-mode approximation to the mean-field Landau–Brazovskii model for diblock copolymer melts. By employing a variational ansatz for the droplet interfacial profile, an analytic expression for the interfacial free energy of an interface of arbitrary orientation between cylinders and lamellae is found. The interfacial free energy is anisotropic and is lower when the cylinder axis is perpendicular to the interface than when the cylinders lie along the interface. Consequently, the droplet shape computed via the Wulff construction is lens like, being flattened along the axis of the cylinders. The size of the critical droplet and the nucleation barrier are determined within classical nucleation theory. Near the lamellar–cylinder phase boundary, where classical nucleation theory is applicable, critical droplets of size 30–400 cylinders across with aspect ratios of 4–10 and nucleation barriers of (30–40)kBT are typically found. The general trend is to larger critical droplets, higher aspect ratios, and smaller nucleation barriers as the mean-field critical point is approached

Modeling of dislocations in a CDW junction: interference of the CDW and the normal carriers

We derive and study equations for dissipative transient processes in a constraint incommensurate charge density wave (CDW) with remnant pockets or a thermal population of normal carriers. The attention was paid to give the correct conservation of condensed and normal electrons, which was problematic at presence of moving dislocation cores if working within an intuitive Ginzburg-Landau like model. We performed a numeric modelling for stationary and transient states in a rectangular geometry when the voltage V or the normal current are applied across the conducting chains. We observe creation of an array of electronic vortices, the dislocations, at or close to the junction surface; their number increases stepwise with increasing V. The dislocation core strongly concentrates the normal carriers but the CDW phase distortions almost neutralize the total charge. At other regimes, the lines of the zero CDW amplitude flash across the sample working as phase slips. The studies were inspired by, and can be applied to experiments on mesa-junctions in NbSe3 and TaS3 (Yu.I. Latyshev et al in proceedings of ECRYS 2008 and 2011).Comment: "Special Issue on the International Workshop on Electronic Crystals (ECRYS-2014)", Physica B (2015