Pavel Krapivsky | Searcharxiv

arXiv2024

Flocking in One Dimension: Asters and Reversals

We study the one-dimensional active Ising model in which aligning particles undergo diffusion biased by the signs of their spins. The phase diagram obtained varying the density of particles, their hopping rate and the temperature controlling the alignment shows a homogeneous disordered phase but no homogeneous ordered one, as well as two phases with localized dense structures. In the flocking phase, large ordered aggregates move ballistically and stochastically reverse their direction of motion. In what we termed the "aster" phase, dense immobile aggregates of opposite magnetization face each other, exchanging particles, without any net motion of the aggregates. Using a combination of numerical simulations and mean-field theory, we study the evolution of the shapes of the flocks, the statistics of their reversal times, and their coarsening dynamics. Solving exactly for the zero-temperature dynamics of an aster allows us to understand their coarsening, which shows extremal dynamics, while mean-field equations account for their shape.

cond-mat.stat-mech↗

arXiv2015

Size distribution of particles in Saturn's rings from aggregation and fragmentation

Saturn's rings consist of a huge number of water ice particles, with a tiny addition of rocky material. They form a flat disk, as the result of an interplay of angular momentum conservation and the steady loss of energy in dissipative inter-particle collisions. For particles in the size range from a few centimeters to a few meters, a power-law distribution of radii, $\sim r^{-q}$ with $q \approx 3$, has been inferred; for larger sizes, the distribution has a steep cutoff. It has been suggested that this size distribution may arise from a balance between aggregation and fragmentation of ring particles, yet neither the power-law dependence nor the upper size cutoff have been established on theoretical grounds. Here we propose a model for the particle size distribution that quantitatively explains the observations. In accordance with data, our model predicts the exponent $q$ to be constrained to the interval $2.75 \le q \le 3.5$. Also an exponential cutoff for larger particle sizes establishes naturally with the cutoff-radius being set by the relative frequency of aggregating and disruptive collisions. This cutoff is much smaller than the typical scale of micro-structures seen in Saturn's rings.

astro-ph.EP↗