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 interparticle collisions. For particles in the size range from a few centimeters to a few meters, a power-law distribution of radii, ∼ r −q with q ≈ 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 ≤ q ≤ 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 microstructures seen in Saturn's rings. (1-3) and the observation of rapid processes in the ring system (4) indicate that the shape of the particle size distribution is likely not primordial or a direct result of the ring-creating event. Rather, ring particles are believed to be involved in active accretion-destruction dynamics (5-13) and their sizes vary over a few orders of magnitude as a power law (14-17), with a sharp cutoff for large sizes (18-21). Moreover, tidal forces fail to explain the abrupt decay of the size distribution for house-sized particles (22). One wishes to understand the following: (i) Can the interplay between aggregation and fragmentation lead to the observed size distribution? And (ii) is this distribution peculiar for Saturn's rings, or is it universal for planetary rings in general? To answer these questions quantitatively, one needs to elaborate a detailed model of the kinetic processes in which the ring particles are involved. Here we develop a theory that quantitatively explains the observed properties of the particle size distribution and show that these properties are generic for a steady state, when a balance between aggregation and fragmentation holds. Our model is based on the hypothesis that collisions are binary and that they may be classified as aggregative, restitutive, or disruptive (including collisions with erosion); which type of collision is realized depends on the relative speed of colliding particles and their masses. We apply the kinetic theory of granular gases (23, 24) for the multicomponent system of ring particles to quantify the collision rate and the type of collision.
Results and DiscussionModel. Ring particles may be treated as aggregates built up of primary grains (9) of a certain size r 1 and mass m 1 . [Observations indicate that particles below a certain radius are absent in dense rings (16).] Denote by m k = km 1 the mass of rin...
Nitric oxide (NO) plays an important role in host defense against bacterial infections such as salmonellosis. NO and 4-bromophenacyl bromide (BPB) induce the formation of long tubulovesicular extensions (TVE, cytonemes, membrane tethers) from human neutrophils. These TVE serve as cellular sensory and adhesive organelles. In the present study, we demonstrated that in the presence of the NO donor, diethylamine NONOate or BPB human neutrophils bound and aggregated Salmonella enterica serovar Typhimurium bacteria extracellularly by TVE. In contrast, inhibition of NO-synthase activity by N(omega)-nitro-L-arginine methyl ester stimulated neutrophil phagocytosis (ingestion) of bacteria. Neutrophil TVE consisted of membrane-covered cytoplasm as was shown by the fluorescent cytoplasmic dye 2',7'-bis(2carboxyethyl)-5,(6)-carboxyfluorescein, and the fluorescent lipid, BODIPY-labeled sulfatide. Disruption and shedding of TVE were accompanied by the appearance of specific invaginations (porosomes) on neutrophil cell bodies. These invaginations corresponded to the variations in diameter of TVE (160-240 nm). We hypothesized that TVE represented protrusions of neutrophil exocytotic trafficking through special structures on the neutrophil surface. In conclusion, we propose a novel mechanism by which NO-induced TVE formation enables neutrophils to bind and aggregate bacteria at a distance.
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