Structure of Periodic Crystals and Quasicrystals in Ultrathin Films of Ba-Ti-O.

We model the remarkable thin-film Ba-Ti-O structures formed by heat treatment of an initial perovskite BaTiO thin film on a Pt(111) surface. All structures contain a rumpled Ti-O network with all Ti threefold coordinated with O, and with Ba occupying the larger. mainly TiO, pores.

How grow-and-switch gravitropism generates root coiling and root waving growth responses in Medicago truncatula.

Experimental studies show that plant root morphologies can vary widely from straight gravity-aligned primary roots to fractal-like root architectures. However, the opaqueness of soil makes it difficult to observe how environmental factors modulate these patterns. Here, we combine a transparent hydrogel growth medium with a custom built 3D laser scanner to directly image the morphology of Medicago truncatula primary roots.

Classical topological order in Abelian and non-Abelian generalized height models.

We present Monte Carlo simulations on a new class of lattice models in which the degrees of freedom are elements of an Abelian or non-Abelian finite symmetry group G, placed on directed edges of a two-dimensional lattice. The plaquette group product is constrained to be the group identity. In contrast to discrete gauge models (but similar to past work on height models), only elements of symmetry-related subsets S∈G are allowed on edges.

Emergent spin excitations in a Bethe lattice at percolation.

We study the spin-1/2 quantum Heisenberg antiferromagnet on a Bethe lattice diluted to the percolation threshold. Dilution creates areas of even or odd sublattice imbalance resulting in "dangling spins" [L. Wang and A.

3D imaging and mechanical modeling of helical buckling in Medicago truncatula plant roots.

We study the primary root growth of wild-type Medicago truncatula plants in heterogeneous environments using 3D time-lapse imaging. The growth medium is a transparent hydrogel consisting of a stiff lower layer and a compliant upper layer. We find that the roots deform into a helical shape just above the gel layer interface before penetrating into the lower layer.

Classical height models with topological order.

I discuss a family of statistical-mechanics models in which (some classes of) elements of a finite group G occupy the (directed) edges of a lattice; the product around any plaquette is constrained to be the group identity e. Such a model may possess topological order, i.e.

Order by disorder and gaugelike degeneracy in a quantum pyrochlore antiferromagnet.

The (three-dimensional) pyrochlore lattice antiferromagnet with Heisenberg spins of large spin length S is a highly frustrated model with a macroscopic degeneracy of classical ground states. The zero-point energy of (harmonic-order) spin-wave fluctuations distinguishes a subset of these states. I derive an approximate but illuminating effective Hamiltonian, acting within the subspace of Ising spin configurations representing the collinear ground states.