Polymer materials of reduced size and dimensionality, such as thin films, polymer nanofibres and nanotubes, exhibit exceptional mechanical properties compared with those of their macroscopic counterparts. We discuss here the abrupt increase in Young's modulus in polymer nanofibres. Using scaling estimation we show that this effect occurs when, in the amorphous (non-crystalline) part of the nanofibres, the transversal size of regions consisting of orientation-correlated macromolecules is comparable to the nanofibre diameter, thereby resulting in confinement of the supramolecular structure. We suggest that in polymer nanofibres the resulting supramolecular microstructure plays a more dominant role in the deformation process than previously thought, challenging the commonly held view that surface effects are most significant. The concept we develop also provides a way to interpret the observed--but not yet understood--temperature dependence of Young's modulus in nanofibres of different diameters.

We study energy pumping in an impulsively excited, two-degrees-of-freedom damped system with essential (nonlinearizable) nonlinearities by means of two analytical techniques. First, we transform the equations of motion using the action-angle variables of the underlying Hamiltonian system and bring them into the form where two-frequency averaging can be applied. We then show that energy pumping is due to resonance capture in the 1:1 resonance manifold of the system, and perform a perturbation analysis in an Oε neighborhood of this manifold in order to study the attracting region responsible for the resonance capture. The second method is based on the assumption of 1:1 internal resonance in the fast dynamics of the system, and utilizes complexification and averaging to develop analytical approximations to the nonlinear transient responses of the system in the energy pumping regime. The results compare favorably to numerical simulations. The practical implications of the energy pumping phenomenon are discussed.

The systems considered in this work are composed of weakly coupled, linear and essentially nonlinear (nonlinearizable) components. In Part I of this work we present numerical evidence of energy pumping in coupled nonlinear mechanical oscillators, i.e., of one-way (irreversible) “channeling” of externally imparted energy from the linear to the nonlinear part of the system, provided that the energy is above a critical level. Clearly, no such phenomenon is possible in the linear system. To obtain a better understanding of the energy pumping phenomenon we first analyze the dynamics of the underlying Hamiltonian system (corresponding to zero damping). First we reduce the equations of motion on an isoenergetic manifold of the dynamical flow, and then compute subharmonic orbits by employing nonsmooth transformation of coordinates which lead to nonlinear boundary value problems. It is conjectured that a 1:1 stable subharmonic orbit of the underlying Hamiltonian system is mainly responsible for the energy pumping phenomenon. This orbit cannot be excited at sufficiently low energies. In Part II of this work the energy pumping phenomenon is further analyzed, and it is shown that it is caused by transient resonance capture on a 1:1 resonance manifold of the system.

Journal reference: Phys. Rev. B 97, 035161 (2018) We propose a framework for the connection between local symmetries of discrete Hamiltonians and the design of compact localized states. Such compact localized states are used for the creation of tunable, local symmetry-induced bound states in an energy continuum and flat energy bands for periodically repeated local symmetries in one-and two-dimensional lattices. The framework is based on very recent theorems in graph theory which are here employed to obtain a block partitioning of the Hamiltonian induced by the symmetry of a given system under local site permutations. The diagonalization of the Hamiltonian is thereby reduced to finding the eigenspectra of smaller matrices, with eigenvectors automatically divided into compact localized and extended states. We distinguish between local symmetry operations which commute with the Hamiltonian, and those which do not commute due to an asymmetric coupling to the surrounding sites. While valuable as a computational tool for versatile discrete systems with locally symmetric structures, the approach provides in particular a unified, intuitive, and efficient route to the flexible design of compact localized states at desired energies.

No abstract