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Abstract:

We show that Hubbard models with nearest-neighbor hopping and a nearest-neighbor hardcore constraint exhibit “maximal” Hilbert space fragmentation in many lattices of arbitrary dimension 𝑑. Focusing on the 𝑑 =1 rhombus chain and the 𝑑 =2 Lieb lattice, we demonstrate that the fragmentation is strong for all fillings in the thermodynamic limit, and explicitly construct all emergent integrals of motion, which include an extensive set of higher-form symmetries. Blockades consisting of frozen particles partition the system in real space, leading to anomalous dynamics. Our results are potentially relevant to optical lattices of dipolar and Rydberg-dressed atoms.

Abstract:

Complex tissue flows in epithelia are driven by intra- and inter-cellular processes that generate, maintain, and coordinate mechanical forces. There has been growing evidence that cell shape anisotropy, manifested as nematic order, plays an important role in this process. Here we extend an active nematic vertex model by replacing substrate friction with internal viscous dissipation, dominant in epithelia not supported by a substrate or the extracellular matrix, which are found in many early-stage embryos. When coupled to cell shape anisotropy, the internal viscous dissipation allows for long-range velocity correlations and thus enables the spontaneous emergence of flows with a large degree of spatiotemporal organisation. We demonstrate sustained flow in epithelial sheets confined to a channel, providing a link between the cell-level vertex model of tissue dynamics and continuum active nematics, whose behaviour in a channel is theoretically understood and experimentally realisable. Our findings also show a simple mechanism that could account for collective cell migration correlated over distances large compared to the cell size, as observed during morphogenesis.

Abstract:

An idealised mesoscale model of the enzymatic digestion of starch modelled as a polymer aggregate is used to study the effect of various enzyme properties, such as the enzyme efficiency, range and radius, on the rate at which monomers are released from the aggregate. Depending on the enzyme efficiency the process is found to be either reaction- or diffusion-limited. Additionally the digestion rate is found to be proportional to the volume around each bond that is accessible to the enzyme, which is determined by the range and radius of the enzyme. Simulations of uniformly mixed susceptible and resistant polymers reveal no significant effect on the digestion of the susceptible polymers due to the presence of the resistant polymers.