Condensed Matter Theory

Abstract:

Many strongly correlated states, such as those arising in the fractional quantum Hall effect and spin liquids, are described by wavefunctions obtained by dividing particles into multiple clusters, constructing a readily evaluable wavefunction in each cluster, and (anti)symmetrizing across these clusters. We introduce a method to compute quantities such as energies and correlators, using Monte Carlo simulations for these states. Our framework overcomes the factorial scaling of explicit (anti)symmetrization, allowing for studies of systems beyond the reach of exact diagonalization.

Abstract:

We investigate channel-confined, nematic liquid crystals using the Beris–Edwards model of nematohydrodynamics. Using strong homeotropic anchoring at the walls, we find multistability, i.e. multiple coexisting states where the uniform nematic state coexists with states having spatially varying scalar nematic order and director fields. When a pressure gradient is applied, flows develop, and the inherent multistability of the system organises a variety of complex dynamics. For low pressure gradients, steady flows are established, and the director fields that emerge from the multistable states at equilibrium correspond to Bowser and Dowser configurations similar to those reported in experiments. An increasing pressure gradient destabilises steady Bowser and Dowser flow states sequentially, leading to unsteady periodic and chaotic regimes featuring cyclical topological transitions, pulsating flows, advecting defects and spatiotemporal chaos. These findings demonstrate that modest variations in the scalar nematic order, as captured by the Beris–Edwards model, can qualitatively modify equilibrium structures and give rise to complex non-equilibrium behaviour in confined nematics – contrasting with the Ericksen–Leslie model, which assumes a constant scalar order parameter. Our key model predictions – multistability, periodically oscillating states and advecting defect-mediated turbulence – can be experimentally investigated in pressure-driven channel flows of nematic fluids.

Abstract:

Although cell monolayers typically remain confluent, they can spontaneously develop persistent holes as a result of collective cellular motion. Recent studies on MDCK monolayers cultured on soft substrates have revealed that cells can align to create regions of local nematic order, and topological defects that generate localised mechanical stresses which can spontaneously trigger hole formation. To investigate this process, we develop a continuum multi-phase field model that incorporates internal dissipation and active dipolar forces that drive cell shape anisotropy. Our simulations show that reducing substrate friction enhances cell-cell velocity correlations. In the low-friction regime, topological defects generate spiral flow patterns that concentrate stress and can trigger hole formation. By contrast, in the high-friction regime, holes do not nucleate. We further demonstrate that the number and stability of the holes—whether they close or persist—depends on both substrate friction and cellular activity, through a non-dimensional friction number. These findings highlight the importance of internal dissipation in modelling collective cell motion and the critical role of collective dynamics in maintaining tissue integrity.