Thermal activation, long-range ordering, and topological frustration of artificial spin ice

Frustrated systems, typically characterized by competing interactions that cannot all be simultaneously satisfied, are ubiquitous in nature and display many rich phenomena and novel physics. Artificial spin ices (ASIs), arrays of lithographically patterned Ising-like single-domain magnetic nanostructures, are highly tunable systems that have proven to be a novel method for studying the effects of frustration and associated properties. The strength and nature of the frustrated interactions between individual magnets are readily tuned by design and the exact microstate of the system can be determined by a variety of characterization techniques. Recently, thermal activation of ASI systems has been demonstrated, introducing the spontaneous reversal of individual magnets and allowing for new explorations of novel phase transitions and phenomena using these systems. In this work, we introduce a new, robust material with favorable magnetic properties for studying thermally active ASI and use it to investigate a variety of ASI geometries. We reproduce previously reported perfect ground-state ordering in the square geometry and present studies of the kagome lattice showing the highest yet degree of ordering observed in this fully frustrated system. We consider theoretical predictions of long-range order in ASI and use both our experimental studies and kinetic Monte Carlo simulations to evaluate these predictions. Next, we introduce controlled topological defects into our square ASI samples and observe a new, extended frustration effect of the system. When we introduce a dislocation into the lattice, we still see large domains of ground-state order, but, in every sample, a domain wall containing higher energy spin arrangements originates from the dislocation, resolving a discontinuity in the ground-state order parameter. Locally, the magnets are unfrustrated, but frustration of the lattice persists due to its topology. We demonstrate the first direct imaging of spin configurations resulting from topological frustration in any system and make predictions on how dislocations could affect properties in numerous materials systems.

Strong shift equivalence, algebraic K-theory, and isolating zero-dimensional dynamics on manifolds

We study the relations of shift equivalence and strong shift equivalence for matrices over a ring $\mathcal{R}$, and establish a connection between these relations and algebraic K-theory. We utilize this connection to obtain results in two areas where the shift and strong shift equivalence relations play an important role: the study of finite group extensions of shifts of finite type, and the Generalized Spectral Conjectures of Boyle and Handelman for nonnegative matrices over subrings of the real numbers. We show the refinement of the shift equivalence class of a matrix $A$ over a ring $\mathcal{R}$ by strong shift equivalence classes over the ring is classified by a quotient $NK_{1}(\mathcal{R}) / E(A,\mathcal{R})$ of the algebraic K-group $NK_{1}(\calR)$. We use the K-theory of non-commutative localizations to show that in certain cases the subgroup $E(A,\mathcal{R})$ must vanish, including the case $A$ is invertible over $\mathcal{R}$. We use the K-theory connection to clarify the structure of algebraic invariants for finite group extensions of shifts of finite type. In particular, we give a strong negative answer to a question of Parry, who asked whether the dynamical zeta function determines up to finitely many topological conjugacy classes the extensions by $G$ of a fixed mixing shift of finite type. We apply the K-theory connection to prove the equivalence of a strong and weak form of the Generalized Spectral Conjecture of Boyle and Handelman for primitive matrices over subrings of $\mathbb{R}$. We construct explicit matrices whose class in the algebraic K-group $NK_{1}(\mathcal{R})$ is non-zero for certain rings $\mathcal{R}$ motivated by applications. We study the possible dynamics of the restriction of a homeomorphism of a compact manifold to an isolated zero-dimensional set. We prove that for $n \ge 3$ every compact zero-dimensional system can arise as an isolated invariant set for a homeomorphism of a compact $n$-manifold. In dimension two, we provide obstructions and examples.

Dynamic Coculture of a Prevascularized Engineered Bone Construct

The generation of functional, vascularized tissues is a key challenge for the field of tissue engineering. Before clinical implantations of tissue engineered bone constructs can succeed, in vitro fabrication needs to address limitations in large-scale tissue development, including controlled osteogenesis and an inadequate vasculature network to prevent necrosis of large constructs. The tubular perfusion system (TPS) bioreactor is an effective culturing method to augment osteogenic differentiation and maintain viability of human mesenchymal stem cell (hMSC)-seeded scaffolds while they are developed in vitro. To further enhance this process, we developed a novel osteogenic growth factors delivery system for dynamically cultured hMSCs using microparticles encapsulated in three-dimensional alginate scaffolds. In light of this increased differentiation, we characterized the endogenous cytokine distribution throughout the TPS bioreactor. An advantageous effect in the ‘outlet’ portion of the uniaxial growth chamber was discovered due to the system’s downstream circulation and the unique modular aspect of the scaffolds. This unique trait allowed us to carefully tune the differentiation behavior of specific cell populations. We applied the knowledge gained from the growth profile of the TPS bioreactor to culture a high-volume bone composite in a 3D-printed femur mold. This resulted in a tissue engineered bone construct with a volume of 200cm3, a 20-fold increase over previously reported sizes. We demonstrated high viability of the cultured cells throughout the culture period as well as early signs of osteogenic differentiation. Taking one step closer toward a viable implant and minimize tissue necrosis after implantation, we designed a composite construct by coculturing endothelial cells (ECs) and differentiating hMSCs, encouraging prevascularization and anastomosis of the graft with the host vasculature. We discovered the necessity of cell to cell proximity between the two cell types as well as preference for the natural cell binding capabilities of hydrogels like collagen. Notably, the results suggested increased osteogenic and angiogenic potential of the encapsulated cells when dynamically cultured in the TPS bioreactor, suggesting a synergistic effect between coculture and applied shear stress. This work highlights the feasibility of fabricating a high-volume, prevascularized tissue engineered bone construct for the regeneration of a critical size defect.