Measure of combined effects of morphological parameters of inclusions within composite materials via stochastic homogenization to determine effective mechanical properties

In our previous papers we have described efficient and reliable methods of generation of representative volume elements (RVE) perfectly suitable for analysis of composite materials via stochastic homogenization. In this paper we profit from these methods to analyze the influence of the morphology on the effective mechanical properties of the samples. More precisely, we study the dependence of main mechanical characteristics of a composite medium on various parameters of the mixture of inclusions composed of spheres and cylinders. On top of that we introduce various imperfections to inclusions and observe the evolution of effective properties related to that. The main computational approach used throughout the work is the FFT-based homogenization technique, validated however by comparison with the direct finite elements method. We give details on the features of the method and the validation campaign as well. Keywords: Composite materials, Cylindrical and spherical reinforcements, Mechanical properties, Stochastic homogenization.Comment: 23 pages, updated figures, version accepted to Composite Structures 201

Unfolding the Sulcus

Sulci are localized furrows on the surface of soft materials that form by a compression-induced instability. We unfold this instability by breaking its natural scale and translation invariance, and compute a limiting bifurcation diagram for sulcfication showing that it is a scale-free, sub-critical {\em nonlinear} instability. In contrast with classical nucleation, sulcification is {\em continuous}, occurs in purely elastic continua and is structurally stable in the limit of vanishing surface energy. During loading, a sulcus nucleates at a point with an upper critical strain and an essential singularity in the linearized spectrum. On unloading, it quasi-statically shrinks to a point with a lower critical strain, explained by breaking of scale symmetry. At intermediate strains the system is linearly stable but nonlinearly unstable with {\em no} energy barrier. Simple experiments confirm the existence of these two critical strains.Comment: Main text with supporting appendix. Revised to agree with published version. New result in the Supplementary Informatio

Dynamical tunnelling with ultracold atoms in magnetic microtraps

The study of dynamical tunnelling in a periodically driven anharmonic potential probes the quantum-classical transition via the experimental control of the effective Planck's constant for the system. In this paper we consider the prospects for observing dynamical tunnelling with ultracold atoms in magnetic microtraps on atom chips. We outline the driven anharmonic potentials that are possible using standard magnetic traps, and find the Floquet spectrum for one of these as a function of the potential strength, modulation, and effective Planck's constant. We develop an integrable approximation to the non-integrable Hamiltonian and find that it can explain the behaviour of the tunnelling rate as a function of the effective Planck's constant in the regular region of parameter space. In the chaotic region we compare our results with the predictions of models that describe chaos-assisted tunnelling. Finally we examine the practicality of performing these experiments in the laboratory with Bose-Einstein condensates.Comment: V1: 12 pages, 10 figures. V2: 14 pages, 12 figures, significantly updated in response to referee report. Some figures are lower quality to reduce file sizes, please contact submitter for high quality versions. V3: Introduction rewritten, but mostly unchanged; updated to published versio

Wave packet approach to transport in mesoscopic systems

Wave packets provide a well established and versatile tool for studying time-dependent effects in molecular physics. Here, we demonstrate the application of wave packets to mesoscopic nanodevices at low temperatures. The electronic transport in the devices is expressed in terms of scattering and transmission coefficients, which are efficiently obtained by solving an initial value problem (IVP) using the time-dependent Schroedinger equation. The formulation as an IVP makes non-trivial device topologies accessible and by tuning the wave packet parameters one can extract the scattering properties for a large range of energies.Comment: 12 pages, 4 figure