Nonsmooth geometry and collapse of flexible structures under smooth loads

While static equilibria of flexible strings subject to various load types (gravity, hydrostatic pressure, Newtonian wind) is well understood textbook material, the combinations of the very same loads can give rise to complex spatial behaviour at the core of which is the unilateral material constraint prohibiting compressive loads. While the effects of such constraints have been explored in optimisation problems involving straight cables, the geometric complexity of physical configurations has not yet been addressed. Here we show that flexible strings subject to combined smooth loads may not have smooth solutions in certain ranges of the load ratios. This non-smooth phenomenon is closely related to the collapse geometry of inflated tents. After proving the nonexistence of smooth solutions for a broad family of loadings we identify two alternative, critical geometries immediately preceding the collapse. We verify these analytical results by dynamical simulation of flexible chains as well as with simple table-top experiments with an inflated membrane.

Self-assembled multilayer graphene oxide membrane and carbon nanotubes synthesized using a rare form of natural graphite

The fabrication of flexible multilayer graphene oxide (GO) membrane and carbon nanotubes (CNTs) using a rare form of high-purity natural graphite, vein graphite, is reported for the first time. Graphite oxide is synthesized using vein graphite following Hummer's method. By facilitating functionalized graphene sheets in graphite oxide to self-assemble, a multilayer GO membrane is fabricated. Electric arc discharge is used to synthesis CNTs from vein graphite. Both multilayer GO membrane and CNTs are investigated using microscopy and spectroscopy experiments, i.e., scanning electron microscopy (SEM), atomic force microscopy (AFM), high-resolution transmission electron microscopy (HRTEM), Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), thermogravimetric analysis (TGA), core level photoelectron spectroscopy, and C K-edge X-ray absorption spectroscopy (NEXAFS), to characterize their structural and topographical properties. Characterization of vein graphite using different techniques reveals that it has a large number of crystallites, hence the large number of graphene sheets per crystallite, preferentially oriented along the (002) plane. NEXAFS and core level spectra confirm that vein graphite is highly crystalline and pure. Fourier transform infrared (FT-IR) and C 1s core level spectra show that oxygen functionalities (-C-OH, -CO,-C-O-C-) are introduced into the basal plane of graphite following chemical oxidation. Carbon nanotubes are produced from vein graphite through arc discharge without the use of any catalyst. HRTEM confirm that multiwalled carbon nanotube (MWNTs) are produced with the presence of some structure in the central pipe. A small percentage of single-walled nanotubes (SWNTs) are also produced simultaneously with MWNTs. Spectroscopic and microscopic data are further discussed here with a view to using vein graphite as the source material for the synthesis of carbon nanomaterials. © 2013 American Chemical Society.

Flexible representations of dynamics are used in object manipulation.

To manipulate an object skillfully, the brain must learn its dynamics, specifying the mapping between applied force and motion. A fundamental issue in sensorimotor control is whether such dynamics are represented in an extrinsic frame of reference tied to the object or an intrinsic frame of reference linked to the arm. Although previous studies have suggested that objects are represented in arm-centered coordinates [1-6], all of these studies have used objects with unusual and complex dynamics. Thus, it is not known how objects with natural dynamics are represented. Here we show that objects with simple (or familiar) dynamics and those with complex (or unfamiliar) dynamics are represented in object- and arm-centered coordinates, respectively. We also show that objects with simple dynamics are represented with an intermediate coordinate frame when vision of the object is removed. These results indicate that object dynamics can be flexibly represented in different coordinate frames by the brain. We suggest that with experience, the representation of the dynamics of a manipulated object may shift from a coordinate frame tied to the arm toward one that is linked to the object. The additional complexity required to represent dynamics in object-centered coordinates would be economical for familiar objects because such a representation allows object use regardless of the orientation of the object in hand.