Higher-Order Properties of Analytic Wavelets

The influence of higher-order wavelet properties on the analytic wavelet transform behavior is investigated, and wavelet functions offering advantageous performance are identified. This is accomplished through detailed investigation of the generalized Morse wavelets, a two-parameter family of exactly analytic continuous wavelets. The degree of time/frequency localization, the existence of a mapping between scale and frequency, and the bias involved in estimating properties of modulated oscillatory signals, are proposed as important considerations. Wavelet behavior is found to be strongly impacted by the degree of asymmetry of the wavelet in both the frequency and the time domain, as quantified by the third central moments. A particular subset of the generalized Morse wavelets, recognized as deriving from an inhomogeneous Airy function, emerge as having particularly desirable properties. These "Airy wavelets" substantially outperform the only approximately analytic Morlet wavelets for high time localization. Special cases of the generalized Morse wavelets are examined, revealing a broad range of behaviors which can be matched to the characteristics of a signal.Comment: 15 pages, 6 Postscript figure

On the relation between sSFR and metallicity

In this paper we present an exact general analytic expression $Z(sSFR)=y/\Lambda(sSFR)+I(sSFR)$ linking the gas metallicity Z to the specific star formation rate (sSFR), that validates and extends the approximate relation put forward by Lilly et al. (2013, L13), where $y$ is the yield per stellar generation, $\Lambda(sSFR)$ is the instantaneous ratio between inflow and star formation rate expressed as a function of the sSFR, and $I$ is the integral of the past enrichment history, respectively. We then demonstrate that the instantaneous metallicity of a self-regulating system, such that its sSFR decreases with decreasing redshift, can be well approximated by the first term on the right-hand side in the above formula, which provides an upper bound to the metallicity. The metallicity is well approximated also by the L13 ideal regulator case, which provides a lower bound to the actual metallicity. We compare these approximate analytic formulae to numerical results and infer a discrepancy <0.1 dex in a range of metallicities and almost three orders of magnitude in the sSFR. We explore the consequences of the L13 model on the mass-weighted metallicity in the stellar component of the galaxies. We find that the stellar average metallicity lags 0.1-0.2 dex behind the gas-phase metallicity relation, in agreement with the data. (abridged)Comment: 14 pages, 6 figures, MNRAS accepte

Tunneling and nonlinear transport in a vertically coupled GaAs/AlGaAs double quantum wire system

We report low-dimensional tunneling in an independently contacted vertically coupled quantum wire system. This nanostructure is fabricated in a high quality GaAs/AlGaAs parallel double quantum well heterostructure. Using a novel flip chip technique to align top and bottom split gates to form low-dimensional constrictions in each of the independently contacted quantum wells we explicitly control the subband occupation of the individual wires. In addition to the expected 2D-2D tunneling results, we have found additional tunneling features that are related to the 1D quantum wires.Comment: 4 pages, 3 figures, submitted to APL Minor revision

Undoped Electron-Hole Bilayers in a GaAs/AlGaAs Double Quantum Well

We present the fabrication details of completely undoped electron-hole bilayer devices in a GaAs/AlGaAs double quantum well heterostructure with a 30 nm barrier. These devices have independently tunable densities of the two-dimensional electron gas and two-dimensional hole gas. We report four-terminal transport measurements of the independently contacted electron and hole layers with balanced densities from $1.2 \times 10^{11}$cm$^{-2}$ down to $4 \times 10^{10}$ cm$^{-2}$ at $T = 300 mK$. The mobilities can exceed $1 \times 10^{6}$ cm$^{2}$ V$^{-1}$ s$^{-1}$ for electrons and $4 \times 10^{5}$ cm$^{2}$ V$^{-1}$ s$^{-1}$ for holes.Comment: 3 pages, 3 figure

Frequency-Domain Stochastic Modeling of Stationary Bivariate or Complex-Valued Signals

There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has unique advantages depending on the system of interest and the application goals. In this paper we provide a joint framework for all three representations in the context of frequency-domain stochastic modeling. This framework allows us to extend many established statistical procedures for bivariate vector time series to complex-valued and rotary representations. These include procedures for parametrically modeling signal coherence, estimating model parameters using the Whittle likelihood, performing semi-parametric modeling, and choosing between classes of nested models using model choice. We also provide a new method of testing for impropriety in complex-valued signals, which tests for noncircular or anisotropic second-order statistical structure when the signal is represented in the complex plane. Finally, we demonstrate the usefulness of our methodology in capturing the anisotropic structure of signals observed from fluid dynamic simulations of turbulence.Comment: To appear in IEEE Transactions on Signal Processin

Near-Infrared Spectroscopy of 0.4<z<1.0 CFRS Galaxies: Oxygen Abundances, SFRs and Dust

Using new J-band VLT-ISAAC and Keck-NIRSPEC spectroscopy, we have measured Halpha and [NII] line fluxes for 0.47<z<0.92 CFRS galaxies which have [OII], Hbeta and [OIII]a line fluxes available from optical spectroscopy, to investigate how the properties of the star forming gas in galaxies evolve with redshift. We derive the extinction and oxygen abundances for the sample using a method based on a set of ionisation parameter and oxygen abundance diagnostics, simultaneously fitting the [OII], Hbeta,[OIII], Halpha, and [NII] line fluxes. The individual reddening measurements allow us to accurately correct the Halpha-based star formation rate (SFR) estimates for extinction. Our most salient conclusions are: a) in all 30 CFRS galaxies the source of gas ionisation is not due to AGN activity; b) we find a range of 0<AV<3, suggesting that it is important to determine the extinction for every single galaxy in order to reliably measure SFRs and oxygen abundances in high redshift galaxies; c) high values of [NII]/Halpha >0.1 for most (but not all) of the CFRS galaxies indicate that they lie on the high-metallicity branch of the R23 calibration; d) about one third of the 0.47<z<0.92 CFRS galaxies in our sample have lower metallicities than local galaxies with similar luminosities and star formation rates; e) comparison with a chemical evolution model indicates that these low metallicity galaxies are unlikely to be the progenitors of metal-poor dwarf galaxies at z~0.Comment: Accepted for publication in the Astrophysical Journa