The bulk, surface and corner free energies of the anisotropic triangular Ising model

We consider the anisotropic Ising model on the triangular lattice with finite boundaries, and use Kaufman’s spinor method to calculate low-temperature series expansions for the partition function to high order. From these, we can obtain 108-term series expansions for the bulk, surface and corner free energies. We extrapolate these to all terms and thereby conjecture the exact results for each. Our results agree with the exactly known bulk-free energy and with Cardy and Peschel’s conformal invariance predictions for the dominant behaviour at criticality. For the isotropic case, they also agree with Vernier and Jacobsen’s conjecture for the 60 ° corners.

Mechanisms of Phase Transformation and Creating Mechanical Strength in a Sustainable Calcium Carbonate Cement

Calcium carbonate cements have been synthesized by mixing amorphous calcium carbonate and vaterite powders with water to unravel the mechanisms of creating mechanical strength during the setting reaction. In-situ XRD was used to monitor the transformation of ACC and vaterite phases into calcite. Unlike this transformation of crystals suspended in a stirred solution, the transformation in the cement is controlled by vaterite dissolution. The supersaturation within the cement paste, Ω, depends not only on the bulk free energy difference of the phases, ΔG, but also on the grain size evolution. Among the strengthening mechanisms, an initial geometric reorganization of CaCO3 particles has been identified by rheological measurements; followed by the formation of an interconnected network of calcite crystals that increases in strength as the crystals grow and form bridges among them. All compositions yield microporous calcite structures with diverse transformation history, crystal bridging efficiency, and hence final mechanical properties.

Nematic liquid crystals on curved surfaces: a thin film limit

We consider a thin film limit of a Landau–de Gennes Q-tensor model. In the limiting process, we observe a continuous transition where the normal and tangential parts of the Q-tensor decouple and various intrinsic and extrinsic contributions emerge. The main properties of the thin film model, like uniaxiality and parameter phase space, are preserved in the limiting process. For the derived surface Landau–de Gennes model, we consider an L 2 -gradient flow. The resulting tensor-valued surface partial differential equation is numerically solved to demonstrate realizations of the tight coupling of elastic and bulk free energy with geometric properties.

Solutions to a model for interface motion by interface diffusion

Existence of weak solutions is proved for a phase field model describing an interface in an elastically deformable solid, which moves by diffusion of atoms along the interface. The volume of the different regions separated by the interface is conserved, since no exchange of atoms across the interface occurs. The diffusion is driven only by reduction of the bulk free energy. The evolution of the order parameter in this model is governed by a degenerate parabolic fourth-order equation. If a regularizing parameter in this equation tends to zero, then solutions tend to solutions of a sharp interface model for interface diffusion. The existence proof is valid only for a 1½-dimensional situation.

Two component lattice Boltzmann model with flux limiters

A two-dimensional finite difference lattice Boltzmann model for two-component fluid systems is introduced. Phase separaton is achieved using an appropriate expression of the bulk free energy. Flux limiter techniques are used to improve the numberical accuracy of this model.