We report on a theoretical discovery of a generic piezoelectric field in strained core-shell compound semiconductor nanowires. We show, using both an analytical model and numerical simulations based on fully electroelastically coupled continuum elasticity theory, that lattice-mismatch-induced strain in an epitaxial core-shell nanowire gives rise to an internal electric field along the axis of the nanowire. This piezoelectric field results predominantly from atomic layer displacements along the nanowire axis within both the core and shell materials and can appear in both zinc blende and wurtzite crystalline core-shell nanowires. The effect can be employed to separate photon-generated electron-hole pairs in the core-shell nanowires and thus offers a new device concept for solar energy conversion.

We compute strain distributions in core-shell nanowires of zinc blende structure. We use both continuum elasticity theory and an atomistic model, and consider both finite and infinite wires. The atomistic valence force-field (VFF) model has only few assumptions. But it is less computationally efficient than the finite-element (FEM) continuum elasticity model. The generic properties of the strain distributions in core-shell nanowires obtained based on the two models agree well. This agreement indicates that although the calculations based on the VFF model are computationally feasible in many cases, the continuum elasticity theory suffices to describe the strain distributions in large core-shell nanowire structures. We find that the obtained strain distributions for infinite wires are excellent approximations to the strain distributions in finite wires, except in the regions close to the ends. Thus, our most computationally efficient model, the finite-element continuum elasticity model developed for infinite wires, is sufficient, unless edge effects are important. We give a comprehensive discussion of strain profiles. We find that the hydrostatic strain in the core is dominated by the axial strain-component, εZZ . We also find that although the individual strain components have a complex structure, the hydrostatic strain shows a much simpler structure. All inplane strain components are of similar magnitude. The non-planar off-diagonal strain-components (εXZ and εY Z ) are small but nonvanishing. Thus the material is not only stretched and compressed but also warped. The models used can be extended for study of wurtzite nanowire structures, as well as nanowires with multiple shells.

Interpreting wave phenomena in terms of an underlying ray dynamics adds a new dimension to the analysis of linear wave equations. Forming explicit connections between spectra and wavefunctions on the one hand and the properties of a related ray dynamics on the other hand is a comparatively new research area, especially in elasticity and acoustics. The theory has indeed been developed primarily in a quantum context; it is increasingly becoming clear, however, that important applications lie in the field of mechanical vibrations and acoustics. We provide an overview over basic concepts in this emerging field of wave chaos. This ranges from ray approximations of the Green function to periodic orbit trace formulae and random matrix theory and summarizes the state of the art in applying these ideas in acoustics-both experimentally and from a theoretical/numerical point of view.

Energy distributions of high-frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics, vibroacoustics, seismology, electromagnetics and quantum mechanics. Related flow problems based on general conservation laws are used, for example, in weather forecasting or in molecular dynamics simulations. Solutions to these flow equations are often large-scale, complex and high-dimensional, leading to formidable challenges for numerical approximation methods. This paper presents an efficient and widely applicable method, called discrete flow mapping, for solving such problems on triangulated surfaces. An application in structural dynamics, determining the vibroacoustic response of a cast aluminium car body component, is presented.

The elastic and piezoelectric properties of zincblende and wurtzite crystalline InAs/InP nanowire heterostructures have been studied using electro-elastically coupled continuum elasticity theory. A comprehensive comparison of strains, piezoelectric potentials and piezoelectric fields in the two crystal types of nanowire heterostructures is presented. For each crystal type, three different forms of heterostructures-core-shell, axial superlattice, and quantum dot nanowire heterostructures-are considered. In the studied nanowire heterostructures, the principal strains are found to be insensitive to the change in the crystal structure. However, the shear strains in the zincblende and wurtzite nanowire heterostructures can be very different. All the studied nanowire heterostructures are found to exhibit a piezoelectric field along the nanowire axis. The piezoelectric field is in general much stronger in a wurtzite nanowire heterostructure than in its corresponding zincblende heterostructure. Our results are expected to be particularly important for analyzing and understanding the properties of epitaxially grown nanowire heterostructures and for applications in nanowire electronics, optoelectronics, and biochemical sensing.

Abstract.Several types of systems were put forward during the past decades to show that there exist isospectral systems which are metrically different. One important class consists of Laplace Beltrami operators for pairs of flat tori in R n with n ≥ 4. We propose that the spectral ambiguity can be resolved by comparing the nodal sequences (the numbers of nodal domains of eigenfunctions, arranged by increasing eigenvalues). In the case of isospectral flat tori in four dimensions -where a 4-parameters family of isospectral pairs is known-we provide heuristic arguments supported by numerical simulations to support the conjecture that the isospectrality is resolved by the nodal count. Thus -one can count the shape of a drum (if it is designed as a flat torus in four dimensions. . . ).

A matrix representation of the evolution operator associated with a nonlinear stochastic flow with additive noise is used to compute its spectrum. In the weak noise limit a perturbative expansion for the spectrum is formulated in terms of local matrix representations of the evolution operator centered on classical periodic orbits. The evaluation of perturbative corrections is easier to implement in this framework than in the standard Feynman diagram perturbation theory. The results are perturbative corrections to a stochastic analog of the Gutzwiller semiclassical spectral determinant computed to several orders beyond what has so far been attainable in stochastic and quantum-mechanical applications.

We present a new approach for modelling noise and vibration in complex mechanical structures in the mid-to-high frequency regime. It is based on a dynamical energy analysis (DEA) formulation which extends standard techniques such as statistical energy analysis (SEA) towards non-diffusive wave fields. DEA takes into account the full directionality of the wave field and makes sub-structuring obsolete. It can thus be implemented on mesh grids commonly used, for example, in the finite element method (FEM). The resulting mesh based formulation of DEA can be implemented very efficiently using discrete flow mapping (DFM) as detailed in [1] and described here for applications in vibro-acoustics. A mid-to-high frequency vibro-acoustic response can be obtained over the whole modelled structure. Abrupt changes of material parameter at interfaces are described in terms of reflection/transmission ma- systems are considered: a double-hull structure used in the ship-building industry and a cast aluminium shock tower from a Range Rover. We demonstrate that DEA with DFM implementation can handle multi-mode wave propagation effectively, taking into account mode conversion between shear, pressure and bending waves at interfaces, and on curved surfaces.