We introduce a deterministic model for scale-free networks, whose degree distribution follows a power law with the exponent gamma. At each time step, each vertex generates its offspring, whose number is proportional to the degree of that vertex with proportionality constant m-1 (m>1). We consider the two cases: First, each offspring is connected to its parent vertex only, forming a tree structure. Second, it is connected to both its parent and grandparent vertices, forming a loop structure. We find that both models exhibit power-law behaviors in their degree distributions with the exponent gamma = 1+ln(2m-1)/ln m. Thus, by tuning m, the degree exponent can be adjusted in the range, 2 < gamma < 3. We also solve analytically a mean shortest-path distance d between two vertices for the tree structure, showing the small-world behavior, that is, d approximately ln N/ln K macro, where N is system size, and k macro is the mean degree. Finally, we consider the case that the number of offspring is the same for all vertices, and find that the degree distribution exhibits an exponential-decay behavior.

Animals have developed a range of drinking strategies depending on physiological and environmental constraints. Vertebrates with incomplete cheeks use their tongue to drink; the most common example is the lapping of cats and dogs. We show that the domestic cat (Felis catus) laps by a subtle mechanism based on water adhesion to the dorsal side of the tongue. A combined experimental and theoretical analysis reveals that Felis catus exploits fluid inertia to defeat gravity and pull liquid into the mouth. This competition between inertia and gravity sets the lapping frequency and yields a prediction for the dependence of frequency on animal mass. Measurements of lapping frequency across the family Felidae support this prediction, which suggests that the lapping mechanism is conserved among felines.

Raindrop impact on infected plants can disperse micron-sized propagules of plant pathogens (e.g., spores of fungi). Little is known about the mechanism of how plant pathogens are liberated and transported due to raindrop impact. We used high-speed photography to observe thousands of dry-dispersed spores of the rust fungus Puccinia triticina being liberated from infected wheat plants following the impact of a single raindrop. We revealed that an air vortex ring was formed during the raindrop impact and carried the dry-dispersed spores away from the surface of the host plant. The maximum height and travel distance of the airborne spores increased with the aid of the air vortex. This unique mechanism of vortex-induced dispersal dynamics was characterized to predict trajectories of spores. Finally, we found that the spores transported by the air vortex can reach beyond the laminar boundary layer of leaves, which would enable the long-distance transport of plant pathogens through the atmosphere.

Caenorhabditis elegans (C. elegans) is a nematode that often swims in saturated soil in nature. We investigated the locomotive behavior of C. elegans swimming in a fluid with particles of various sizes and found that the nematode swims a greater distance per undulation than it does in a fluid without particles. The Strouhal number (a ratio of lateral to forward velocity) of C. elegans significantly decreases in a saturated particulate medium (0.50±0.13) in comparison to a fluid without particles (1.6±0.27). This result was unexpected due to the generally low performance of a body moving in a high drag medium. In our model, a saturated granular system is approximated as a porous medium where only the hydrodynamic forces on the body are considered. Combining these assumptions with resistive force theory, we find that a porous medium provides more asymmetric drag on a slender body, and consequently that C. elegans locomotes with a greater distance per undulation.

Soft organisms such as earthworms can access confined, narrow spaces, inspiring scientists to fabricate soft robots for in vivo manipulation of cells or tissues and minimally invasive surgery. We report a super‐soft and super‐elastic magnetic DNA hydrogel‐based soft robot (DNA robot), which presents a shape‐adaptive property and enables magnetically driven navigational locomotion in confined and unstructured space. The DNA hydrogel is designed with a combinational dynamic and permanent crosslinking network through chain entanglement and DNA hybridization, resulting in shear‐thinning and cyclic strain properties. DNA robot completes a series of complex magnetically driven navigational locomotion such as passing through narrow channels and pipes, entering grooves and itinerating in a maze by adapting and recovering its shape. DNA robot successfully works as a vehicle to deliver cells in confined space by virtue of the 3D porous networked structure and great biocompatibility.