Narrow Results

We study the low-energy excitation of the quantum spin tube with the triangular lattice structure, using density matrix renormalization group. Taking account of the edge spin effect, we particularly investigate the spin gap behavior and the low-field magnetization curve near the quantum phase transition point in contrast with the usual free boundary condition. We then find that the bulk behavior of the spin tube can be extracted easier for the single spin termination.

Nanoscale beams might not be considered uniform isotropic since the energy of the surface layer and microstructure of the bulk material highly affect the mechanical characteristics of the beams. Herein, the simultaneous effects of energy of the surface and microstructure of the bulk on the dynamic response and stability of beam-type electromechanical nanocantilevers are investigated. A bilayer model has been developed which incorporates the strain energy of the surface atoms as well as the microstructure-dependent strain energy of the bulk. The Gurtin–Murdoch surface elasticity in conjunction with the modified couple stress theory (MCST) is applied to derive the governing equation. Since the classical assumption for zero normal surface stresses is not consistent with the surface equilibrium assumption in Gurtin–Murdoch elasticity, the presence of normal surface stresses is incorporated. The von Karman nonlinear strain is employed to derive the governing equation. The presence of gas rarefaction at various Knudsen numbers is considered as well as the edge effect on the distribution of Coulomb and dispersion forces. The mode shapes of the nanobeam are determined as a function of the surface and microstructure parameter and the nonlinear governing equation is solved using Galerkin method. The dynamic response, phase plane and stability threshold of the nanocantilever are discussed.

Metal (iron and nickel) films have been deposited on soft elastic polydimethylsiloxane (PDMS) substrates by direct current sputtering technique and the impurity induced wrinkling patterns are investigated by using optical microscopy and atomic force microscopy. It is found that the metal films can spontaneously form disordered wrinkles due to the isotropic compressive stress. In the vicinity of film impurities such as extraneous particles, linear defects, cracks and thickness-gradient film edges, the stress field becomes anisotropic owing to symmetry breaking and thus complex wrinkling patterns including straight stripes, herringbones, crossings, labyrinths and their transitions can be observed. The morphological evolutions, structural characteristics and physical mechanisms of the impurity induced wrinkles have been discussed and analyzed based on the continuum elastic theory.