Megastable quantization in generalized pilot-wave hydrodynamics.
Physical review. E 111:2 (2025) L022201
Abstract:
A classical particle in a harmonic potential gives rise to a continuous energy spectra, whereas the corresponding quantum particle exhibits countably infinite quantized energy levels. In recent years, classical non-Markovian wave-particle entities that materialize as walking droplets have been shown to exhibit various hydrodynamic quantum analogs, including quantization in a harmonic potential by displaying few coexisting limit cycle orbits. By considering a truncated-memory stroboscopic pilot-wave model of the system in the low dissipation regime, we obtain a classical harmonic oscillator perturbed by oscillatory nonconservative forces that display countably infinite coexisting limit-cycle states, also known as megastability. Using averaging techniques in the low-memory regime, we derive analytical approximations of the orbital radii, orbital frequency and Lyapunov energy function of this megastable spectrum, and further show average energy conservation along these quantized states. Our formalism extends to a general class of self-excited oscillators and can be used to construct megastable spectrum with different energy-frequency relations.Asymmetric limit cycles within Lorenz chaos induce anomalous mobility for a memory-driven active particle.
Physical review. E 110:5 (2024) L052203
Abstract:
On applying a small bias force, nonequilibrium systems may respond in paradoxical ways such as with giant negative mobility (GNM)-a large net drift opposite to the applied bias, or giant positive mobility (GPM)-an anomalously large drift in the same direction as the applied bias. Such behaviors have been extensively studied in idealized models of externally driven passive inertial particles. Here, we consider a minimal model of a memory-driven active particle inspired from experiments with walking and superwalking droplets, whose equation of motion maps to the celebrated Lorenz system. By adding a small bias force to this Lorenz model for the active particle, we uncover a dynamical mechanism for simultaneous emergence of GNM and GPM in the parameter space. Within the chaotic sea of the parameter space, a symmetric pair of coexisting asymmetric limit cycles separate and migrate under applied bias force, resulting in anomalous transport behaviors that are sensitive to the active particle's memory. Our work highlights a general dynamical mechanism for the emergence of anomalous transport behaviors for active particles described by low-dimensional nonlinear models.Erratum: “Utilizing bifurcations to separate particles in spiral inertial microfluidics” [Phys. Fluids 35, 011703 (2023)]
Physics of Fluids AIP Publishing 36:10 (2024) 109906
Inertial Focusing Dynamics of Spherical Particles in Curved Microfluidic Ducts with a Trapezoidal Cross Section
SIAM Journal on Applied Dynamical Systems Society for Industrial & Applied Mathematics (SIAM) 23:3 (2024) 1805-1835
Active particle motion in Poiseuille flow through rectangular channels.
Physical review. E 110:3-1 (2024) 034603