We derive a microscopic expression for a quantity μ that plays the role of chemical potential of active Brownian particles (ABPs) in a steady state in the absence of vortices. We show that μ consists of (i) an intrinsic chemical potential similar to passive systems, which depends on density and self-propulsion speed, but not on the external potential, (ii) the external potential, and (iii) a newly derived one-body swim potential due to the activity of the particles. Our simulations on ABPs show good agreement with our Fokker-Planck calculations, and confirm that z m ( ) is spatially constant for several inhomogeneous active fluids in their steady states in a planar geometry. Finally, we show that phase coexistence of ABPs with a planar interface satisfies not only mechanical but also diffusive equilibrium. The coexistence can be well-described by equating the bulk chemical potential and bulk pressure obtained from bulk simulations for systems with low activity but requires explicit evaluation of the interfacial contributions at high activity.

Correlations between functional and biochemical outcomes of eccentric exercise and between these outcomes and "delayed-onset muscle soreness" (DOMS) were studied. Maximal isotonic force, extension and flexion angle of the elbow, creatine kinase activity, and myoglobin concentration in serum were measured in 27 male subjects during 5 days after 120 maximal eccentric contractions of the forearm flexors. Significant correlations were found between values at 1 to 96 h after exercise for force (r = 0.55 to 0.96), flexion (0.52 to 0.94), extension (0.41 to 0.95), and myoglobin (0.55 to 0.97) and at 24 to 96 h for creatine kinase (0.67 to 0.96) and DOMS (0.45 to 0.72). Clusters of significant correlations (0.32 to 0.91) were found among all functional and biochemical measures. DOMS, however, showed only few and lower correlations with the other parameters (0.34 to 0.63). These results can practically be interpreted as follows: 1) subjects need more time to recover completely when early deviations after eccentric exercise are large, 2) a large change in one measure is accompanied by large deviations in other measures, and 3) objective outcomes of eccentric exercise are more accurate parameters than a DOMS score for use in effect studies.

The effect of a combination of a warm-up, stretching exercises and massage on subjective scores for delayed onset muscle soreness (DOMS) and objective functional and biochemical measures was studied. Fifty people, randomly divided in a treatment and a control group, performed eccentric exercise with the forearm flexors for 30 min. The treatment group additionally performed a warm-up and underwent a stretching protocol before the eccentric exercise and massage afterwards. Functional and biochemical measures were obtained before, and 1, 24, 48, 72 and 96h after exercise. The median values at the five post-exercise time points differed significantly for DOMS measured when the arm was extended (p = 0.043). Significant main effects for treatment were found on the maximal force (p = 0.026), the flexion angle of the elbow (p = 0.014) and the creatine kinase activity in blood (p = 0.006). No time-by-treatment interactions were found. DOMS on pressure, extension angle and myoglobin concentration in blood did not differ between the groups. This combination of a warm-up, stretching and massage reduces some negative effects of eccentric exercise, but the results are inconsistent, since some parameters were significantly affected by the treatment whereas others were not, despite the expected efficacy of a combination of treatments. The objective measures did not yield more unequivocal results than the subjective DOMS scores.

To study the role of torque in motility-induced phase separation (MIPS), we simulate a system of self-propelled particles whose shape varies smoothly from isotropic (disks/spheres) to weakly elongated (rods). We construct the phase diagrams of 2D active disks, 3D active spheres and 2D/3D active rods of aspect ratio l/σ = 2. A stability analysis of the homogeneous isotropic phase allows us to predict the onset of MIPS based on the effective swimming speed and rotational diffusion of the particles. Both methods find suppression of MIPS as the particle shape is elongated. We propose a suppression mechanism based on the duration of collisions, and argue that this mechanism can explain both the suppression of MIPS found here for rodlike particles and the enhancement of MIPS found for particles with Vicsek interactions.