There are two classes of phononic structures that can support elastic waves with non-conventional topology, namely intrinsic and extrinsic systems. The non-conventional topology of elastic wave results from breaking time reversal symmetry (T-symmetry) of wave propagation. In extrinsic systems, energy is injected into the phononic structure to break T-symmetry. In intrinsic systems symmetry is broken through the medium microstructure that may lead to internal resonances. Mass-spring composite structures are introduced as metaphors for more complex phononic crystals with non-conventional topology. The elastic wave equation of motion of an intrinsic phononic structure composed of two coupled one-dimensional (1D) harmonic chains can be factored into a Dirac-like equation, leading to antisymmetric modes that have spinor character and therefore non-conventional topology in wave number space. The topology of the elastic waves can be further modified by subjecting phononic structures to externally-induced spatio-temporal modulation of their elastic properties. Such modulations can be actuated through photo-elastic effects, magneto-elastic effects, piezo-electric effects or external mechanical effects. We also uncover an analogy between a combined intrinsic-extrinsic systems composed of a simple one-dimensional harmonic chain coupled to a rigid substrate subjected to a spatio-temporal modulation of the side spring stiffness and the Dirac equation in the presence of an electromagnetic field. The modulation is shown to be able to tune the spinor part of the elastic wave function and therefore its topology. This analogy between classical mechanics and quantum phenomena offers new modalities for developing more complex functions of phononic crystals and acoustic metamaterials.

We present a sensing modality using the geometric phase of acoustic waves propagating in an underwater environment. We experimentally investigate the effect of scattering by a small subwavelength perturbation on a flat submerged surface. We represent the state of an acoustic field in the unperturbed and perturbed cases as multidimensional vectors. The change in geometric phase is obtained by calculating the angle between those vectors. This angle represents a rotation of the state vector of the wave due to scattering by the perturbation. We perform statistical analysis to define a signal-to-noise ratio to quantify the sensitivity of the geometric phase measurement and compare it to magnitude based measurements. This geometric phase sensing modality is shown to have higher sensitivity than the magnitude based sensing approach.

Starting with the equations for the total molecular wave function that describe the self-consistent coupling of electrons and nuclei over time, we consider the case of one active electron outside closed shells and apply the formalism to ion-atom collisions. We discuss the need for electron translation factors, basis set type and size, and the choice of effective potentials in the calculation of the total integral cross section, the state-to-state integral cross section, and the differential cross sections for electron transfer and excitation. Atomic orbital alignment is considered here as well. We concern ourselves with the ${\mathrm{H}}^{+}$-H and ${\mathrm{He}}^{2+}$-H systems and the lower end of collision energies, 10 keV and below, down to several eV. We emphasize the study of time-dependent populations and properties to provide a deeper understanding of the dynamics of slow ion-atom collisions. Numerical results for cross sections and polarization parameters are in good agreement with other theories and experiments. © 1996 The American Physical Society.