How wind and sun shape trees into fractals?

Trees are self-similar branching structures, hierarchically organized with longer and thicker branches near the roots. With a mechanically-based numerical model, we show how self-similarity can emerge through natural selection. In this model, trees grow into fractal structures to promote efficient photosynthesis in a competing environment. In addition, branch diameters increase in response to wind-induced loads. Remarkably, the virtual tree species emerging from this model have the same self-similar properties as those measured on conifers and angiosperms.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Flow-Induced Draping

Crumpled paper or drapery patterns are everyday examples of how elastic sheets can respond to external forcing. In this Letter, we study experimentally a novel sort of forcing. We consider a circular flexible plate clamped at its center and subject to a uniform flow normal to its initial surface. As the flow velocity is gradually increased, the plate exhibits a rich variety of bending deformations: from a cylindrical taco-like shape, to isometric developable cones with azimuthal periodicity two or three, to eventually a rolled-up period-three cone. We show that this sequence of flow-induced deformations can be qualitatively predicted by a linear analysis based on the balance between elastic energy and pressure force work

Shape of optimal active flagella

Many eukaryotic cells use the active waving motion of flexible flagella to self-propel in viscous fluids. However, the criteria governing the selection of particular flagellar waveforms among all possible shapes has proved elusive so far. To address this question, we derive computationally the optimal shape of an internally-forced periodic planar flagellum deforming as a travelling wave. The optimum is here defined as the shape leading to a given swimming speed with minimum energetic cost. To calculate the energetic cost though, we consider the irreversible internal power expanded by the molecular motors forcing the flagellum, only a portion of which ending up dissipated in the fluid. This optimisation approach allows us to derive a family of shapes depending on a single dimensionless number quantifying the relative importance of elastic to viscous effects: the Sperm number. The computed optimal shapes are found to agree with the waveforms observed on spermatozoon of marine organisms, thus suggesting that these eukaryotic flagella might have evolved to be mechanically optimal.Comment: 10 pages, 5 figure

Surveying the Three-Dimensional Fixed Points of T-Duality

We explore the family of fixed points of T-Duality transformations in three dimensions. For the simplest nontrivial self-duality conditions it is possible to show that, additionally to the spacelike isometry in which the T-Duality transformation is performed, these backgrounds must be necessarily stationary. This allows to prove that for nontrivial string coupling, the low energy bosonic string backgrounds which are additionally self-T-dual along an isometry direction generated by a constant norm Killing vector are uniquely described by a two-parametric class, including only three nonsingular cases: the charged black string, the exact gravitational wave propagating along the extremal black string, and the flat space with a linear dilaton. Besides, for constant string coupling, the only self-T-dual lower energy string background under the same assumptions corresponds to the Coussaert-Henneaux spacetime. Thus, we identify minimum criteria that yield a classification of these quoted examples and only these. All these T-dual fixed points describe exact backgrounds of string theory.Comment: 11 Page