Emergent behaviors of discrete Lohe aggregation flows

<p style='text-indent:20px;'>The Lohe sphere model and the Lohe matrix model are prototype continuous aggregation models on the unit sphere and the unitary group, respectively. These models have been extensively investigated in recent literature. In this paper, we propose several discrete counterparts for the continuous Lohe type aggregation models and study their emergent behaviors using the Lyapunov function method. For suitable discretization of the Lohe sphere model, we employ a scheme consisting of two steps. In the first step, we solve the first-order forward Euler scheme, and in the second step, we project the intermediate state onto the unit sphere. For this discrete model, we present a sufficient framework leading to the complete state aggregation in terms of system parameters and initial data. For the discretization of the Lohe matrix model, we use the Lie group integrator method, Lie-Trotter splitting method and Strang splitting method to propose three discrete models. For these models, we also provide several analytical frameworks leading to complete state aggregation and asymptotic state-locking.</p>

Emergent Myxobacterial Behaviors Arise from Reversal Suppression Induced by Kin Contacts

In many species, large populations exhibit emergent behaviors whereby all related individuals move in unison. For example, fish in schools can all dart in one direction simultaneously to avoid a predator.

Vesicle shape transformations driven by confined active filaments

In active matter systems, deformable boundaries provide a mechanism to organize internal active stresses. To study a minimal model of such a system, we perform particle-based simulations of an elastic vesicle containing a collection of polar active filaments. The interplay between the active stress organization due to interparticle interactions and that due to the deformability of the confinement leads to a variety of filament spatiotemporal organizations that have not been observed in bulk systems or under rigid confinement, including highly-aligned rings and caps. In turn, these filament assemblies drive dramatic and tunable transformations of the vesicle shape and its dynamics. We present simple scaling models that reveal the mechanisms underlying these emergent behaviors and yield design principles for engineering active materials with targeted shape dynamics.

Competition for endothelial cell polarity drives vascular morphogenesis

Blood vessel formation generates unique vascular patterns in each individual. The principles governing the apparent stochasticity of this process remain to be elucidated. Using mathematical methods, we find that the transition between two fundamental vascular morphogenetic programs, sprouting angiogenesis and vascular remodeling, is established by a shift on collective front-rear polarity of endothelial cells. We demonstrate that the competition between biochemical (VEGFA) and mechanical (blood flow-induced shear stress) cues controls this collective polarity shift. Shear stress increases tension at focal adhesions overriding VEGFA-driven collective polarization, which relies on tension at adherens junctions. We propose that vascular morphogenetic cues compete to regulate individual cell polarity and migration through tension shifts that translates into tissue-level emergent behaviors, ultimately leading to uniquely organized vascular patterns.

Emergence of a periodically rotating one-point cluster in a thermodynamic Cucker-Smale ensemble

We study emergent behaviors of thermomechanical Cucker-Smale (TCS) ensemble confined in a harmonic potential field. In the absence of external force field, emergent dynamics of TCS particles has been extensively studied recently under various frameworks formulated in terms of initial configuration, system parameters and network topologies. Moreover, the TCS model does not exhibit rotating motions in the absence of an external force field. In this paper, we show the emergence of periodically rotating one-point cluster for the TCS model in a harmonic potential field using elementary energy estimates and continuity argument. We also provide several numerical simulations and compare them with analytical results.