Fixed-domain asymptotic properties of tapered maximum likelihood estimators

When the spatial sample size is extremely large, which occurs in many environmental and ecological studies, operations on the large covariance matrix are a numerical challenge. Covariance tapering is a technique to alleviate the numerical challenges. Under the assumption that data are collected along a line in a bounded region, we investigate how the tapering affects the asymptotic efficiency of the maximum likelihood estimator (MLE) for the microergodic parameter in the Mat\'ern covariance function by establishing the fixed-domain asymptotic distribution of the exact MLE and that of the tapered MLE. Our results imply that, under some conditions on the taper, the tapered MLE is asymptotically as efficient as the true MLE for the microergodic parameter in the Mat\'ern model.Comment: Published in at http://dx.doi.org/10.1214/08-AOS676 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Deep-subwavelength features of photonic skyrmions in a confined electromagnetic field with orbital angular momentum

In magnetic materials, skyrmions are nanoscale regions where the orientation of electron spin changes in a vortex-type manner. Here we show that spin-orbit coupling in a focused vector beam results in a skyrmion-like photonic spin distribution of the excited waveguided fields. While diffraction limits the spatial size of intensity distributions, the direction of the field, defining photonic spin, is not subject to this limitation. We demonstrate that the skyrmion spin structure varies on the deep-subwavelength scales down to 1/60 of light wavelength, which corresponds to about 10 nanometre lengthscale. The application of photonic skyrmions may range from high-resolution imaging and precision metrology to quantum technologies and data storage where the spin structure of the field, not its intensity, can be applied to achieve deep-subwavelength optical patterns

Tuning Strain in Flexible Graphene Nanoelectromechanical Resonators

The structural flexibility of low dimensional nanomaterials offers unique opportunities for studying the impact of strain on their physical properties and for developing innovative devices utilizing strain engineering. A key towards such goals is a device platform which allows the independent tuning and reliable calibration of the strain. Here we report the fabrication and characterization of graphene nanoelectromechanical resonators(GNEMRs) on flexible substrates. Combining substrate bending and electrostatic gating, we achieve the independent tuning of the strain and sagging in graphene and explore the nonlinear dynamics over a wide parameter space. Analytical and numerical studies of a continuum mechanics model, including the competing higher order nonlinear terms, reveal a comprehensive nonlinear dynamics phase diagram, which quantitatively explains the complex behaviors of GNEMRs

Kinetic simulations of X-B and O-X-B mode conversion

We have performed fully-kinetic simulations of X-B and O-X-B mode conversion in one and two dimensional setups using the PIC code EPOCH. We have recovered the linear dispersion relation for electron Bernstein waves by employing relatively low amplitude incoming waves. The setups presented here can be used to study non-linear regimes of X-B and O-X-B mode conversion.Comment: 4 pages, 3 figure

Fabrication and Electric Field Dependent Transport Measurements of Mesoscopic Graphite Devices

We have developed a unique micromechanical method to extract extremely thin graphite samples. Graphite crystallites with thicknesses ranging from 10 - 100 nm and lateral size $\sim$ 2 $\mu$m are extracted from bulk. Mesoscopic graphite devices are fabricated from these samples for electric field dependent conductance measurements. Strong conductance modulation as a function of gate voltage is observed in the thinner crystallite devices. The temperature dependent resistivity measurements show more boundary scattering contribution in the thinner graphite samples.Comment: 3 pages, 3 figures included, submitted to Appl. Phys. Let

Anomalous Hall effect in NiPt thin films

We study Hall effect in sputtered NixPt1-x thin films with different Ni concentrations. Temperature, magnetic field and angular dependencies are analyzed and the phase diagram of NiPt thin films is obtained. It is found that films with sub-critical Ni concentration exhibit cluster-glass behavior at low temperatures with a perpendicular magnetic anisotropy below the freezing temperature. Films with over-critical Ni concentration are ferromagnetic with parallel anisotropy. At the critical concentration the state of the film is strongly frustrated. Such films demonstrate canted magnetization with the easy axis rotating as a function of temperature. The magnetism appears via consecutive paramagnetic - cluster glass - ferromagnetic transitions, rather than a single second-order phase transition. But most remarkably, the extraordinary Hall effect changes sign at the critical concentration. We suggest that this is associated with a reconstruction of the electronic structure of the alloy at the normal metal - ferromagnet quantum phase transition.Comment: 12 pages, 17 figure