RESUMEN
We develop and study the hydrodynamic theory of flocking with autochemotaxis. This describes large collections of self-propelled entities all spontaneously moving in the same direction, each emitting a substance which attracts the others (e.g., ants). The theory combines features of the Keller-Segel model for autochemotaxis with the Toner-Tu theory of flocking. We find that sufficiently strong autochemotaxis leads to an instability of the uniformly moving state (the "flock"), in which bands of different density form moving parallel to the mean flock velocity with different speeds. This instability is, therefore, completely different from the well-known "banding instability," in which bands form perpendicular to the mean flock velocity. The bands we find, which are reminiscent of ant trails, coarsen over time to reach a phase-separated state, in which one high-density and one low-density band fill the entire system. The same instability, described by the same hydrodynamic theory, can occur in flocks phase separating due to any microscopic mechanism (e.g., sufficiently strong attractive interactions). Although in many ways analogous to equilibrium phase separation via spinodal decomposition, the two steady-state densities here are determined not by a common tangent construction, as in equilibrium, but by an uncommon tangent construction very similar to that found for motility-induced phase separation of disordered active particles. Our analytic theory agrees well with our numerical simulations of our equations of motion.
RESUMEN
We develop the hydrodynamic theory of dry, polar ordered, active matter ("flocking") with autochemotaxis; i.e., self-propelled entities moving in the same direction, each emitting a substance which attracts the others (e.g., ants). We find that sufficiently strong autochemotaxis leads to an instability to phase separation into one high and one low density band. This is very analogous to both equilibrium phase separation, and "motility induced phase separation" and can occur in flocks due to any microscopic mechanism (e.g., sufficiently strong attractive interactions) that makes the entities cohere.
RESUMEN
BACKGROUND: Educators and trainees both recognise that autonomy, the number of patient encounters and setting learning outcomes are all vital for a successful residency. This study examined whether these clinical rotation characteristics have an impact on trainee success in an orthotic and prosthetic clinical residency. METHODS: Two cohorts of resident trainees rated their rotation characteristics (autonomy, patient encounters and learning outcomes [1, significantly below expectations; 5, exceeds expectations]) and self-competency (77 items [1, not at all able; 5, very able]) at three points during an 18-month residency. Rotation performance (0-100, where 100 is the highest score) was ascertained with preceptor ratings and test scores. Means and correlations were derived. RESULTS: Data from 38 trainees were examined. The mean self-competency and rotation performance scores improved from time 1 to time 3 (from 4.14 ± 0.43 to 4.36 ± 0.38 [p < 0.01]; from 90.74 ± 5.15 to 92.62 ± 4.55 [p < 0.05]). Autonomy correlated with performance at time 1 (p < 0.05) only, and did not relate to self-competency at any point. Neither the number of patient encounters nor the presence of learning outcomes were associated with performance or self-competency at any point. CONCLUSIONS: These data show that over time our trainees become more competent, as rated by both themselves and their preceptors. These data do not suggest that the number of patient encounters and the presence of learning outcomes have an impact on trainee competence. Autonomy may play the largest role at the beginning of the residency as students make the transition to clinical practice.