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1. Enhanced diffusivity in perturbed senile reinforced random walk models

   https://doi.org/DOI: 10.3233/ASY-201611  

   Dinh, Thu; Xin, Jack (October 2020, Asymptotic analysis)

   We consider diffusivity of random walks with transition probabilities depending on the number of consecutive traversals of the last traversed edge, the so called senile reinforced random walk (SeRW). In one dimension, the walk is known to be sub-diffusive with identity reinforcement function. We perturb the model by introducing a small probability δ of escaping the last traversed edge at each step. The perturbed SeRW model is diffusive for any δ > 0 , with enhanced diffusivity (≫ O ( δ^2 ) ) in the small δ regime. We further study stochastically perturbed SeRW models by having the last edge escape probability of the form δ ξ n with ξ n ’s being independent random variables. Enhanced diffusivity in such models are logarithmically close to the so called residual diffusivity (positive in the zero δ limit), with diffusivity between O ( 1/| log δ | ) and O ( 1/ log | log δ | ) . Finally, we generalize our results to higher dimensions where the unperturbed model is already diffusive. The enhanced diffusivity can be as much as O ( 1/log ^2 δ ) 

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2. Computational exploration of treadmilling and protrusion growth observed in fire ant rafts

   https://doi.org/10.1371/journal.pcbi.1009869  

   Wagner, Robert J.; Vernerey, Franck J. (February 2022, PLOS Computational Biology)

   Maini, Philip K. (Ed.)

   Collective living systems regularly achieve cooperative emergent functions that individual organisms could not accomplish alone. The rafts of fire ants (Solenopsis invicta) are often studied in this context for their ability to create aggregated structures comprised entirely of their own bodies, including tether-like protrusions that facilitate exploration of and escape from flooded environments. While similar protrusions are observed in cytoskeletons and cellular aggregates, they are generally dependent on morphogens or external gradients leaving the isolated role of local interactions poorly understood. Here we demonstrate through an ant-inspired, agent-based numerical model how protrusions in ant rafts may emerge spontaneously due to local interactions. The model is comprised of a condensed structural network of agents that represents the monolayer of interconnected worker ants, which floats on the water and gives ant rafts their form. Experimentally, this layer perpetually contracts, which we capture through the pairwise contraction of all neighboring structural agents at a strain rate of d ˙ . On top of the structural layer, we model a dispersed, on-lattice layer of motile agents that represents free ants, which walk on top of the floating network. Experimentally, these self-propelled free ants walk with some mean persistence length and speed that we capture through an ant-inspired phenomenological model. Local interactions occur between neighboring free ants within some radius of detection, R , and the persistence length of freely active agents is tuned through a noise parameter, η as introduced by the Vicsek model. Both R and η where fixed to match the experimental trajectories of free ants. Treadmilling of the raft occurs as agents transition between the structural and free layers in accordance with experimental observations. Ultimately, we demonstrate how phases of exploratory protrusion growth may be induced by increased ant activity as characterized by a dimensionless parameter, A . These results provide an example in which functional morphogenesis of a living system may emerge purely from local interactions at the constituent length scale, thereby providing a source of inspiration for the development of decentralized, autonomous active matter and swarm robotics. 

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3. Hitting probabilities for fast stochastic search ^*

   https://doi.org/10.1088/1751-8121/ad5ee2  

   Linn, Samantha; Lawley, Sean D (July 2024, Journal of Physics A: Mathematical and Theoretical)

   Abstract Many physical phenomena are modeled as stochastic searchers looking for targets. In these models, the probability that a searcher finds a particular target, its so-called hitting probability, is often of considerable interest. In this work we determine hitting probabilities for stochastic search processes conditioned on being faster than a random short time. Such times have been used to model stochastic resetting or stochastic inactivation. These results apply to any search process, diffusive or otherwise, whose unconditional short-time behavior can be adequately approximated, which we characterize for broad classes of stochastic search. We illustrate these results in several examples and show that the conditional hitting probabilities depend predominantly on the relative geodesic lengths between the initial position of the searcher and the targets. Finally, we apply these results to a canonical evidence accumulation model for decision making. 

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4. Escape dynamics of confined undulating worms

   https://doi.org/10.1039/D3SM00211J  

   Biswas, Animesh; Kudrolli, Arshad (June 2023, Soft Matter)

   We investigate the escape dynamics of oligochaeta Lumbriculus variegatus by confining them to a quasi-2D circular chamber with a narrow exit passage. The worms move by performing undulatory and peristaltic strokes and use their head to actively probe their surroundings. We show that the worms follow the chamber boundary with occasional reversals in direction and with velocities determined by the orientation angle of the body with respect to the boundary. The average time needed to reach the passage decreases with its width before approaching a constant, consistent with a boundary-following search strategy. We model the search dynamics as a persistent random walk along the boundary and demonstrate that the head increasingly skips over the passage entrance for smaller passage widths due to body undulations. The simulations capture the observed exponential time-distributions taken to reach the exit and their mean as a function of width when starting from random locations. Even after the head penetrates the passage entrance, we find that the worm does not always escape because the head withdraws rhythmically back into the chamber over distances set by the dual stroke amplitudes. Our study highlights the importance of boundary following and body strokes in determining how active matter escapes from enclosed spaces. 

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5. Actin Turnover Required for Adhesion-Independent Bleb Migration

   https://doi.org/10.3390/fluids7050173  

   Copos, Calina; Strychalski, Wanda (May 2022, Fluids)

   Cell migration is critical for many vital processes, such as wound healing, as well as harmful processes, such as cancer metastasis. Experiments have highlighted the diversity in migration strategies employed by cells in physiologically relevant environments. In 3D fibrous matrices and confinement between two surfaces, some cells migrate using round membrane protrusions, called blebs. In bleb-based migration, the role of substrate adhesion is thought to be minimal, and it remains unclear if a cell can migrate without any adhesion complexes. We present a 2D computational fluid-structure model of a cell using cycles of bleb expansion and retraction in a channel with several geometries. The cell model consists of a plasma membrane, an underlying actin cortex, and viscous cytoplasm. Cellular structures are immersed in viscous fluid which permeates them, and the fluid equations are solved using the method of regularized Stokeslets. Simulations show that the cell cannot effectively migrate when the actin cortex is modeled as a purely elastic material. We find that cells do migrate in rigid channels if actin turnover is included with a viscoelastic description for the cortex. Our study highlights the non-trivial relationship between cell rheology and its external environment during migration with cytoplasmic streaming. 

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