Cost of excursions until first return for random walks and Lévy flights: an exact general formula
ArXiv 2403.16152 (2024)
Viscoelastic confinement induces periodic flow reversals in active nematics
Physical Review E American Physical Society 108:6 (2023) 064611
Abstract:
We use linear stability analysis and hybrid lattice Boltzmann simulations to study the dynamical behavior of an active nematic confined in a channel made of viscoelastic material. We find that the quiescent, ordered active nematic is unstable above a critical activity. The transition is to a steady flow state for high elasticity of the channel surroundings. However, below a threshold elastic modulus, the system produces spontaneous oscillations with periodic flow reversals. We provide a phase diagram that highlights the region where time-periodic oscillations are observed and explain how they are produced by the interplay of activity and viscoelasticity. Our results suggest experiments to study the role of viscoelastic confinement in the spatiotemporal organization and control of active matter.Nonlinear-cost random walk: Exact statistics of the distance covered for fixed budget.
Physical review. E 108:6-1 (2023) 064122
Abstract:
We consider the nonlinear-cost random-walk model in discrete time introduced in Phys. Rev. Lett. 130, 237102 (2023)10.1103/PhysRevLett.130.237102, where a fee is charged for each jump of the walker. The nonlinear cost function is such that slow or short jumps incur a flat fee, while for fast or long jumps the cost is proportional to the distance covered. In this paper we compute analytically the average and variance of the distance covered in n steps when the total budget C is fixed, as well as the statistics of the number of long or short jumps in a trajectory of length n, for the exponential jump distribution. These observables exhibit a very rich and nonmonotonic scaling behavior as a function of the variable C/n, which is traced back to the makeup of a typical trajectory in terms of long or short jumps, and the resulting entropy thereof. As a by-product, we compute the asymptotic behavior of ratios of Kummer hypergeometric functions when both the first and last arguments are large. All our analytical results are corroborated by numerical simulations.Optimal switching strategies for navigation in stochastic settings
ArXiv 2311.18813 (2023)
Nonlinear-Cost Random Walk: exact statistics of the distance covered for fixed budget
ArXiv 2310.08966 (2023)