Acoustic vibrations of anisotropic nanoparticles

Acoustic vibrations of nanoparticles made of materials with anisotropic elasticity and nanoparticles with non-spherical shapes are theoretically investigated using a homogeneous continuum model. Cubic, hexagonal and tetragonal symmetries of the elasticity are discussed, as are spheroidal, cuboctahedral and truncated cuboctahedral shapes. Tools are described to classify the different vibrations and for example help identify the modes having a significant low-frequency Raman scattering cross-section. Continuous evolutions of the modes starting from those of an isotropic sphere coupled with the determination of the irreducible representation of the branches permit some qualitative statements to be made about the nature of various modes. For spherical nanoparticles, a more accurate picture is obtained through projections onto the vibrations of an isotropic sphere.Comment: 11 pages, 9 tables, 6 figure

Vibrations of free and embedded anisotropic elastic spheres: Application to low-frequency Raman scattering of silicon nanoparticles in silica

Vibrational mode frequencies and damping are calculated for an elastic sphere embedded in an infinite, homogeneous, isotropic elastic medium. Anisotropic elasticity of the sphere significantly shifts the frequencies in comparison to simplified calculations that assume isotropy. New low frequency Raman light scattering data are presented for silicon spheres grown in a SiO2 glass matrix. Principal features of the Raman spectrum are not correctly described by a simple model of the nanoparticle as a free, isotropic sphere, but require both matrix effects and the anisotropy of the silicon to be taken into account. Libration, not vibration, is the dominant mechanism

Delayed Sampling and Automatic Rao-Blackwellization of Probabilistic Programs

We introduce a dynamic mechanism for the solution of analytically-tractable substructure in probabilistic programs, using conjugate priors and affine transformations to reduce variance in Monte Carlo estimators. For inference with Sequential Monte Carlo, this automatically yields improvements such as locally-optimal proposals and Rao-Blackwellization. The mechanism maintains a directed graph alongside the running program that evolves dynamically as operations are triggered upon it. Nodes of the graph represent random variables, edges the analytically-tractable relationships between them. Random variables remain in the graph for as long as possible, to be sampled only when they are used by the program in a way that cannot be resolved analytically. In the meantime, they are conditioned on as many observations as possible. We demonstrate the mechanism with a few pedagogical examples, as well as a linear-nonlinear state-space model with simulated data, and an epidemiological model with real data of a dengue outbreak in Micronesia. In all cases one or more variables are automatically marginalized out to significantly reduce variance in estimates of the marginal likelihood, in the final case facilitating a random-weight or pseudo-marginal-type importance sampler for parameter estimation. We have implemented the approach in Anglican and a new probabilistic programming language called Birch.Comment: 13 pages, 4 figure

Far infrared absorption by acoustic phonons in titanium dioxide nanopowders

We report spectral features of far infrared electromagnetic radiation absorption in anatase TiO2 nanopowders which we attribute to absorption by acoustic phonon modes of nanoparticles. The frequency of peak excess absorption above the background level corresponds to the predicted frequency of the dipolar acoustic phonon from continuum elastic theory. The intensity of the absorption cannot be accounted for in a continuum elastic dielectric description of the nanoparticle material. Quantum mechanical scale dependent effects must be considered. The absorption cross section is estimated from a simple mechanical phenomenological model. The results are in plausible agreement with the absorption being due to a sparse layer of charge on the nanoparticle surface.Comment: 8 pages, 5 figures, submitted to Journal of Nanoelectronics and Optoelectronic

Inelastic neutron scattering due to acoustic vibrations confined in nanoparticles: theory and experiment

The inelastic scattering of neutrons by nanoparticles due to acoustic vibrational modes (energy below 10 meV) confined in nanoparticles is calculated using the Zemach-Glauber formalism. Such vibrational modes are commonly observed by light scattering techniques (Brillouin or low-frequency Raman scattering). We also report high resolution inelastic neutron scattering measurements for anatase TiO2 nanoparticles in a loose powder. Factors enabling the observation of such vibrations are discussed. These include a narrow nanoparticle size distribution which minimizes inhomogeneous broadening of the spectrum and the presence of hydrogen atoms oscillating with the nanoparticle surfaces which enhances the number of scattered neutrons.Comment: 3 figures, 1 tabl

Chimera States for Coupled Oscillators

Arrays of identical oscillators can display a remarkable spatiotemporal pattern in which phase-locked oscillators coexist with drifting ones. Discovered two years ago, such "chimera states" are believed to be impossible for locally or globally coupled systems; they are peculiar to the intermediate case of nonlocal coupling. Here we present an exact solution for this state, for a ring of phase oscillators coupled by a cosine kernel. We show that the stable chimera state bifurcates from a spatially modulated drift state, and dies in a saddle-node bifurcation with an unstable chimera.Comment: 4 pages, 4 figure