A numerical investigation of a piezoelectric surface acoustic wave interaction with a one-dimensional channel

We investigate the propagation of a piezoelectric surface acoustic wave (SAW) across a GaAs/Al$_X$Ga$_{1-X}$As heterostructure surface, on which there is fixed a metallic split-gate. Our method is based on a finite element formulation of the underlying equations of motion, and is performed in three-dimensions fully incorporating the geometry and material composition of the substrate and gates. We demonstrate attenuation of the SAW amplitude as a result of the presence of both mechanical and electrical gates on the surface. We show that the incorporation of a simple model for the screening by the two-dimensional electron gas (2DEG), results in a total electric potential modulation that suggests a mechanism for the capture and release of electrons by the SAW. Our simulations suggest the absence of any significant turbulence in the SAW motion which could hamper the operation of SAW based quantum devices of a more complex geometry.Comment: 8 pages, 8 figure

Possible impacts of climate change on freezing rain in south-central Canada using downscaled future climate scenarios

Freezing rain is a major atmospheric hazard in mid-latitude nations of the globe. Among all Canadian hydrometeorological hazards, freezing rain is associated with the highest damage costs per event. Using synoptic weather typing to identify the occurrence of freezing rain events, this study estimates changes in future freezing rain events under future climate scenarios for south-central Canada. Synoptic weather typing consists of principal components analysis, an average linkage clustering procedure (i.e., a hierarchical agglomerative cluster method), and discriminant function analysis (a nonhierarchical method). Meteorological data used in the analysis included hourly surface observations from 15 selected weather stations and six atmospheric levels of six-hourly National Centers for Environmental Prediction (NCEP) upper-air reanalysis weather variables for the winter months (November&ndash;April) of 1958/59&ndash;2000/01. A statistical downscaling method was used to downscale four general circulation model (GCM) scenarios to the selected weather stations. Using downscaled scenarios, discriminant function analysis was used to project the occurrence of future weather types. The within-type frequency of future freezing rain events is assumed to be directly proportional to the change in frequency of future freezing rain-related weather types <br><br> The results showed that with warming temperatures in a future climate, percentage increases in the occurrence of freezing rain events in the north of the study area are likely to be greater than those in the south. By the 2050s, freezing rain events for the three colder months (December&ndash;February) could increase by about 85% (95% confidence interval &ndash; CI: &plusmn;13%), 60% (95% CI: &plusmn9%), and 40% (95% CI: &plusmn;6%) in northern Ontario, eastern Ontario (including Montreal, Quebec), and southern Ontario, respectively. The increase by the 2080s could be even greater: about 135% (95% CI: &plusmn;20%), 95% (95% CI: &plusmn;13%), and 45% (95% CI: &plusmn;9%). For the three warmer months (November, March, April), the percentage increases in future freezing rain events are projected to be much smaller with some areas showing either a decrease or little change in frequency of freezing rain. On average, northern Ontario could experience about 10% (95% CI: &plusmn;2%) and 20% (95% CI: &plusmn;4%) more freezing rain events by the 2050s and 2080s, respectively. However, future freezing rain events in southern Ontario could decrease about 10% (95% CI: &plusmn;3%) and 15% (95% CI: &plusmn;5%) by the 2050s and 2080s, respectively. In eastern Ontario (including Montreal, Quebec), the frequency of future freezing rain events is projected to remain the same as it is currently

Heat capacity of a thin membrane at very low temperature

We calculate the dependence of heat capacity of a free standing thin membrane on its thickness and temperature. A remarkable fact is that for a given temperature there exists a minimum in the dependence of the heat capacity on the thickness. The ratio of the heat capacity to its minimal value for a given temperature is a universal function of the ratio of the thickness to its value corresponding to the minimum. The minimal value of the heat capacitance for given temperature is proportional to the temperature squared. Our analysis can be used, in particular, for optimizing support membranes for microbolometers

Cosmic Calibration: Constraints from the Matter Power Spectrum and the Cosmic Microwave Background

Several cosmological measurements have attained significant levels of maturity and accuracy over the last decade. Continuing this trend, future observations promise measurements of the statistics of the cosmic mass distribution at an accuracy level of one percent out to spatial scales with k~10 h/Mpc and even smaller, entering highly nonlinear regimes of gravitational instability. In order to interpret these observations and extract useful cosmological information from them, such as the equation of state of dark energy, very costly high precision, multi-physics simulations must be performed. We have recently implemented a new statistical framework with the aim of obtaining accurate parameter constraints from combining observations with a limited number of simulations. The key idea is the replacement of the full simulator by a fast emulator with controlled error bounds. In this paper, we provide a detailed description of the methodology and extend the framework to include joint analysis of cosmic microwave background and large scale structure measurements. Our framework is especially well-suited for upcoming large scale structure probes of dark energy such as baryon acoustic oscillations and, especially, weak lensing, where percent level accuracy on nonlinear scales is needed.Comment: 15 pages, 14 figure

Efficient cosmological parameter sampling using sparse grids

We present a novel method to significantly speed up cosmological parameter sampling. The method relies on constructing an interpolation of the CMB-log-likelihood based on sparse grids, which is used as a shortcut for the likelihood-evaluation. We obtain excellent results over a large region in parameter space, comprising about 25 log-likelihoods around the peak, and we reproduce the one-dimensional projections of the likelihood almost perfectly. In speed and accuracy, our technique is competitive to existing approaches to accelerate parameter estimation based on polynomial interpolation or neural networks, while having some advantages over them. In our method, there is no danger of creating unphysical wiggles as it can be the case for polynomial fits of a high degree. Furthermore, we do not require a long training time as for neural networks, but the construction of the interpolation is determined by the time it takes to evaluate the likelihood at the sampling points, which can be parallelised to an arbitrary degree. Our approach is completely general, and it can adaptively exploit the properties of the underlying function. We can thus apply it to any problem where an accurate interpolation of a function is needed.Comment: Submitted to MNRAS, 13 pages, 13 figure

Anomalous quantum chaotic behavior in nanoelectromechanical structures

It is predicted that for sufficiently strong electron-phonon coupling an anomalous quantum chaotic behavior develops in certain types of suspended electro-mechanical nanostructures, here comprised by a thin cylindrical quantum dot (billiard) on a suspended rectangular dielectric plate. The deformation potential and piezoelectric interactions are considered. As a result of the electron-phonon coupling between the two systems the spectral statistics of the electro-mechanic eigenenergies exhibit an anomalous behavior. If the center of the quantum dot is located at one of the symmetry axes of the rectangular plate, the energy level distributions correspond to the Gaussian Orthogonal Ensemble (GOE), otherwise they belong to the Gaussian Unitary Ensemble (GUE), even though the system is time-reversal invariant.Comment: 4 pages, pdf forma

Quantum chaos in nanoelectromechanical systems

We present a theoretical study of the electron-phonon coupling in suspended nanoelectromechanical systems (NEMS) and investigate the resulting quantum chaotic behavior. The phonons are associated with the vibrational modes of a suspended rectangular dielectric plate, with free or clamped boundary conditions, whereas the electrons are confined to a large quantum dot (QD) on the plate's surface. The deformation potential and piezoelectric interactions are considered. By performing standard energy-level statistics we demonstrate that the spectral fluctuations exhibit the same distributions as those of the Gaussian Orthogonal Ensemble (GOE) or the Gaussian Unitary Ensemble (GUE), therefore evidencing the emergence of quantum chaos. That is verified for a large range of material and geometry parameters. In particular, the GUE statistics occurs only in the case of a circular QD. It represents an anomalous phenomenon, previously reported for just a small number of systems, since the problem is time-reversal invariant. The obtained results are explained through a detailed analysis of the Hamiltonian matrix structure.Comment: 14 pages, two column

Role of confined phonons in thin film superconductivity

We calculate the critical temperature $T_c$ and the superconducting energy gaps $\Delta_n$ of a thin film superconductor system, where $\Delta_n$ is the superconducting energy gap of the $n$-th subband. Since the quantization of both the electron energy and phonon spectrum arises due to dimensional confinement in one direction, the effective electron-electron interaction mediated by the quantized confined phonons is different from that mediated by the bulk phonon, leading to the modification of $T_c$ in the thin film system. We investigate the dependence of $T_c$ and $\Delta_n$ on the film thickness $d$ with this modified interaction.Comment: 4 pages, 2 figure

CMB likelihood approximation by a Gaussianized Blackwell-Rao estimator

We introduce a new CMB temperature likelihood approximation called the Gaussianized Blackwell-Rao (GBR) estimator. This estimator is derived by transforming the observed marginal power spectrum distributions obtained by the CMB Gibbs sampler into standard univariate Gaussians, and then approximate their joint transformed distribution by a multivariate Gaussian. The method is exact for full-sky coverage and uniform noise, and an excellent approximation for sky cuts and scanning patterns relevant for modern satellite experiments such as WMAP and Planck. A single evaluation of this estimator between l=2 and 200 takes ~0.2 CPU milliseconds, while for comparison, a single pixel space likelihood evaluation between l=2 and 30 for a map with ~2500 pixels requires ~20 seconds. We apply this tool to the 5-year WMAP temperature data, and re-estimate the angular temperature power spectrum, $C_{\ell}$, and likelihood, L(C_l), for l<=200, and derive new cosmological parameters for the standard six-parameter LambdaCDM model. Our spectrum is in excellent agreement with the official WMAP spectrum, but we find slight differences in the derived cosmological parameters. Most importantly, the spectral index of scalar perturbations is n_s=0.973 +/- 0.014, 1.9 sigma away from unity and 0.6 sigma higher than the official WMAP result, n_s = 0.965 +/- 0.014. This suggests that an exact likelihood treatment is required to higher l's than previously believed, reinforcing and extending our conclusions from the 3-year WMAP analysis. In that case, we found that the sub-optimal likelihood approximation adopted between l=12 and 30 by the WMAP team biased n_s low by 0.4 sigma, while here we find that the same approximation between l=30 and 200 introduces a bias of 0.6 sigma in n_s.Comment: 10 pages, 7 figures, submitted to Ap

Explicit asymptotic modelling of transient Love waves propagated along a thin coating

The official published version can be obtained from the link below.An explicit asymptotic model for transient Love waves is derived from the exact equations of anti-plane elasticity. The perturbation procedure relies upon the slow decay of low-frequency Love waves to approximate the displacement field in the substrate by a power series in the depth coordinate. When appropriate decay conditions are imposed on the series, one obtains a model equation governing the displacement at the interface between the coating and the substrate. Unusually, the model equation contains a term with a pseudo-differential operator. This result is confirmed and interpreted by analysing the exact solution obtained by integral transforms. The performance of the derived model is illustrated by numerical examples.This work is sponsored by the grant from Higher Education of Pakistan and by the Brunel University’s “BRIEF” research award