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

No abstract

The manufacturing of water droplets wrapped with two different powders, carbon black (semiconductor) and polytetrafluoroethylene (dielectric), is presented. Droplets composed of two hemispheres (Janus droplets) characterized by various physical and chemical properties are reported first. Watermelon-like striped liquid marbles are reported. Janus droplets remained stable on solid and liquid supports and could be activated with an electric field.

A series of two papers is devoted to detailed investigation of the response regimes of linear oscillator with attached nonlinear energy sink (NES) under harmonic external forcing and assessment of possible application of the NES for vibration absorption and mitigation. The first paper of the series is devoted to analytic and numeric description of the attractors (response regimes) of the system. Analytic approach is based on averaging and multiple-scales analysis, the mass ratio being used as the small parameter. The problem of possible coexistence of different attractors is reduced to analysis of flow on slow invariant manifolds (SIM) of the system. Numeric simulation confirms the predictions of the analytic model concerning the number, the shape, and the structure of the response regimes and reveals some other features of these attractors.