Global regularity for a 1D Euler-alignment system with misalignment

We study one-dimensional Eulerian dynamics with nonlocal alignment interactions, featuring strong short-range alignment, and long-range misalignment. Compared with the well-studied Euler-alignment system, the presence of the misalignment brings different behaviors of the solutions, including the possible creation of vacuum at infinite time, which destabilizes the solutions. We show that with a strongly singular short-range alignment interaction, the solution is globally regular, despite the effect of misalignment.

Circadian misalignment increases mood vulnerability in simulated shift work

Night shift work can associate with an increased risk for depression. As night workers experience a ‘misalignment’ between their circadian system and daily sleep–wake behaviors, with negative health consequences, we investigated whether exposure to circadian misalignment underpins mood vulnerability in simulated shift work. We performed randomized within-subject crossover laboratory studies in non-shift workers and shift workers. Simulated night shifts were used to induce a misalignment between the endogenous circadian pacemaker and sleep/wake cycles (circadian misalignment), while environmental conditions and food intake were controlled. Circadian misalignment adversely impacted emotional state, such that mood and well-being levels were significantly decreased throughout 4 days of continuous exposure to circadian misalignment in non-shift workers, as compared to when they were under circadian alignment (interaction of “circadian alignment condition” vs. “day”, mood: p < 0.001; well-being: p < 0.001; adjusted p-values). Similarly, in shift workers, mood and well-being levels were significantly reduced throughout days of misalignment, as compared to circadian alignment (interaction of “circadian alignment condition” vs. “day”, mood: p = 0.002; well-being: p = 0.002; adjusted p-values). Our findings indicate that circadian misalignment is an important biological component for mood vulnerability, and that individuals who engage in shift work are susceptible to its deleterious mood effects.

HYDRODYNAMICS OF SELF-ALIGNMENT INTERACTIONS WITH PRECESSION AND DERIVATION OF THE LANDAU–LIFSCHITZ–GILBERT EQUATION

We consider a kinetic model of self-propelled particles with alignment interaction and with precession about the alignment direction. We derive a hydrodynamic system for the local density and velocity orientation of the particles. The system consists of the conservative equation for the local density and a non-conservative equation for the orientation. First, we assume that the alignment interaction is purely local and derive a first-order system. However, we show that this system may lose its hyperbolicity. Under the assumption of weakly nonlocal interaction, we derive diffusive corrections to the first-order system which lead to the combination of a heat flow of the harmonic map and Landau–Lifschitz–Gilbert dynamics. In the particular case of zero self-propelling speed, the resulting model reduces to the phenomenological Landau–Lifschitz–Gilbert equations. Therefore the present theory provides a kinetic formulation of classical micromagnetization models and spin dynamics.

DIFFUSION IN A CONTINUUM MODEL OF SELF-PROPELLED PARTICLES WITH ALIGNMENT INTERACTION

In this paper, we provide the O(ε) corrections to the hydrodynamic model derived by Degond and Motsch from a kinetic version of the model by Vicsek and co-authors describing flocking biological agents. The parameter ε stands for the ratio of the microscopic to the macroscopic scales. The O(ε) corrected model involves diffusion terms in both the mass and velocity equations as well as terms which are quadratic functions of the first-order derivatives of the density and velocity. The derivation method is based on the standard Chapman–Enskog theory, but is significantly more complex than usual due to both the non-isotropy of the fluid and the lack of momentum conservation.