Ordering dynamics of blue phases entails kinetic stabilization of amorphous networks

The cubic blue phases of liquid crystals are fascinating and technologically promising examples of hierarchically structured soft materials, comprising ordered networks of defect lines (disclinations) within a liquid crystalline matrix. We present the first large-scale simulations of their domain growth, starting from a blue phase nucleus within a supercooled isotropic or cholesteric background. The nucleated phase is thermodynamically stable; one expects its slow orderly growth, creating a bulk cubic. Instead, we find that the strong propensity to form disclinations drives the rapid disorderly growth of a metastable amorphous defect network. During this process the original nucleus is destroyed; re-emergence of the stable phase may therefore require a second nucleation step. Our findings suggest that blue phases exhibit hierarchical behavior in their ordering dynamics, to match that in their structure.Comment: 11 pages, 5 figures, 2 supplementary figures, 2 supplementary tables, accepted by PNA

Symmetric Interconnection Networks from Cubic Crystal Lattices

Torus networks of moderate degree have been widely used in the supercomputer industry. Tori are superb when used for executing applications that require near-neighbor communications. Nevertheless, they are not so good when dealing with global communications. Hence, typical 3D implementations have evolved to 5D networks, among other reasons, to reduce network distances. Most of these big systems are mixed-radix tori which are not the best option for minimizing distances and efficiently using network resources. This paper is focused on improving the topological properties of these networks. By using integral matrices to deal with Cayley graphs over Abelian groups, we have been able to propose and analyze a family of high-dimensional grid-based interconnection networks. As they are built over $n$-dimensional grids that induce a regular tiling of the space, these topologies have been denoted \textsl{lattice graphs}. We will focus on cubic crystal lattices for modeling symmetric 3D networks. Other higher dimensional networks can be composed over these graphs, as illustrated in this research. Easy network partitioning can also take advantage of this network composition operation. Minimal routing algorithms are also provided for these new topologies. Finally, some practical issues such as implementability and preliminary performance evaluations have been addressed

Spectral Renormalization Group for the Gaussian model and ψ4\psi^4 theory on non-spatial networks

We implement the spectral renormalization group on different deterministic non-spatial networks without translational invariance. We calculate the thermodynamic critical exponents for the Gaussian model on the Cayley tree and the diamond lattice, and find that they are functions of the spectral dimension, $\tilde{d}$. The results are shown to be consistent with those from exact summation and finite size scaling approaches. At $\tilde{d}=2$, the lower critical dimension for the Ising universality class, the Gaussian fixed point is stable with respect to a $\psi^4$ perturbation up to second order. However, on generalized diamond lattices, non-Gaussian fixed points arise for $2<\tilde{d}<4$.Comment: 16 pages, 14 figures, 5 tables. The paper has been extended to include a $\psi^4$ interactions and higher spectral dimension