Anderson Localization of Polar Eigenmodes in Random Planar Composites

Anderson localization of classical waves in disordered media is a fundamental physical phenomenon that has attracted attention in the past three decades. More recently, localization of polar excitations in nanostructured metal-dielectric films (also known as random planar composite) has been subject of intense studies. Potential applications of planar composites include local near-field microscopy and spectroscopy. A number of previous studies have relied on the quasistatic approximation and a direct analogy with localization of electrons in disordered solids. Here I consider the localization problem without the quasistatic approximation. I show that localization of polar excitations is characterized by algebraic rather than by exponential spatial confinement. This result is also valid in two and three dimensions. I also show that the previously used localization criterion based on the gyration radius of eigenmodes is inconsistent with both exponential and algebraic localization. An alternative criterion based on the dipole participation number is proposed. Numerical demonstration of a localization-delocalization transition is given. Finally, it is shown that, contrary to the previous belief, localized modes can be effectively coupled to running waves.Comment: 22 pages, 7 figures. Paper was revised and a more precise definition of the participation number given, data for figures recalculated accordingly. Accepted to J. Phys.: Cond. Mat

Comments on the nonpharmaceutical interventions in New York City and Chicago during the 1918 flu pandemic

This commentary was originally published in CIDRAP News and it is here reported almost verbatim to allow divulgation through open access. The Editorial summarizes John Barry's concerns about the value of accurate historical reporting and its implications in public policy determination. This short abstract was written by the Editor-in-Chief of the Journal of Translational Medicine to introduce the Editorial

Bound whispering gallery modes in circular arrays of dielectric spherical particles

Low-dimensional ordered arrays of optical elements can possess bound modes having an extremely high quality factor. Typically, these arrays consist of metal elements which have significantly high light absorption thus restricting performance. In this paper we address the following question: can bound modes be formed in dielectric systems where the absorption of light is negligible? Our investigation of circular arrays of spherical particles shows that (1) high quality modes in an array of 10 or more particles can be attained at least for a refractive index $n_{r}>2$, so optical materials like TiO$_{2}$ or GaAs can be used; (2) the most bound modes have nearly transverse polarization perpendicular to the circular plane; (3) in a particularly interesting case of TiO$_{2}$ particles (rutile phase, $n_{r}=2.7$), the quality factor of the most bound mode increases almost by an order of magnitude with the addition of 10 extra particles, while for particles made of GaAs the quality factor increases by almost two orders of magnitude with the addition of ten extra particles. We hope that this preliminary study will stimulate experimental investigations of bound modes in low-dimensional arrays of dielectric particles.Comment: Submitted to Physical Review

Phonons in a Nanoparticle Mechanically Coupled to a Substrate

The discrete nature of the vibrational modes of an isolated nanometer-scale solid dramatically modifies its low-energy electron and phonon dynamics from that of a bulk crystal. However, nanocrystals are usually coupled--even if only weakly--to an environment consisting of other nanocrystals, a support matrix, or a solid substrate, and this environmental interaction will modify the vibrational properties at low frequencies. In this paper we investigate the modification of the vibrational modes of an insulating spherical nanoparticle caused by a weak {\it mechanical} coupling to a semi-infinite substrate. The phonons of the bulk substrate act as a bath of harmonic oscillators, and the coupling to this reservoir shifts and broadens the nanoparticle's modes. The vibrational density of states in the nanoparticle is obtained by solving the Dyson equation for the phonon propagator, and we show that environmental interaction is especially important at low frequencies. As a probe of the modified phonon spectrum, we consider nonradiative energy relaxation of a localized electronic impurity state in the nanoparticle, for which good agreement with experiment is found.Comment: 10 pages, Revte

Electron-Phonon Dynamics in an Ensemble of Nearly Isolated Nanoparticles

We investigate the electron population dynamics in an ensemble of nearly isolated insulating nanoparticles, each nanoparticle modeled as an electronic two-level system coupled to a single vibrational mode. We find that at short times the ensemble-averaged excited-state population oscillates but has a decaying envelope. At long times, the oscillations become purely sinusoidal about a ``plateau'' population, with a frequency determined by the electron-phonon interaction strength, and with an envelope that decays algebraically as t^-{1/2} We use this theory to predict electron-phonon dynamics in an ensemble of Y_2 O_3 nanoparticles.Comment: 11 pages, 3 figure

Characterization of the inflammatory response to four commercial bone graft substitutes using a murine biocompatibility model

Bone grafting is utilized in nearly all orthopedic subspecialties and in most anatomic regions. Bone graft substitutes have the potential to offer similar efficacy as autogenous grafts without the morbidity of harvest. Several studies have noted the efficacy of new-generation bone substitute products, but few studies have evaluated their safety. This study characterizes and quantifies the inflammatory reaction to four different commercially available bone graft substitutes, which were examined using the in vivo murine air pouch biocompatibility model. One coralline hydroxyapatite product was chosen as an example of a purely osteoconductive material. Three demineralized bone matrix products were chosen to represent products that are both osteoconductive and osteoinductive. Samples were implanted in a murine air pouch and harvested after 14 days in situ. Pouch fluid was extracted, mRNA isolated, and reverse transcription polymerase chain reactions carried out to detect interleukin-1 gene expression as a marker for inflammation. In addition, multiple histological characteristics were examined to quantify cellular responses to the implanted materials. All bone graft substitutes induced a significant inflammatory response compared with negative controls. Histology and polymerase chain reaction data indicated that the level of inflammatory reaction was elevated in materials with a higher demineralized bone matrix to carrier proportion. The hydroxyapatite product generated a low inflammatory reaction. In conclusion, this study used an in vivo model of biocompatibility to demonstrate that a significant inflammatory reaction occurs when using implanted bone graft substitutes. When choosing a bone grafting method, surgeons should consider both the efficacy and safety of methods and materials used. Further studies are necessary to determine the ideal bone graft material to maximize efficacy while minimizing morbidity