Time-dependent numerical renormalization group method for multiple quenches: towards exact results for the long time limit of thermodynamic observables and spectral functions

We develop an alternative time-dependent numerical renormalization group (TDNRG) formalism for multiple quenches and implement it to study the response of a quantum impurity system to a general pulse. Within this approach, we reduce the contribution of the NRG approximation to numerical errors in the time evolution of observables by a formulation that avoids the use of the generalized overlap matrix elements in our previous multiple-quench TDNRG formalism [Nghiem {\em et al.,} Phys. Rev. B {\bf 89}, 075118 (2014); Phys. Rev. B {\bf 90}, 035129 (2014)]. We demonstrate that the formalism yields a smaller cumulative error in the trace of the projected density matrix as a function of time and a smaller discontinuity of local observables between quenches than in our previous approach. Moreover, by increasing the switch-on time, the time between the first and last quench of the discretized pulse, the long-time limit of observables systematically converges to its expected value in the final state, i.e., the more adiabatic the switching, the more accurately is the long-time limit recovered. The present formalism can be straightforwardly extended to infinite switch-on times. We show that this yields highly accurate results for the long-time limit of both thermodynamic observables and spectral functions, and overcomes the significant errors within the single quench formalism [Anders {\em et al.}, Phys. Rev. Lett. {\bf 95}, 196801 (2005); Nghiem {\em et al.}, Phys. Rev. Lett. {\bf 119}, 156601 (2017)]. This improvement provides a first step towards an accurate description of nonequilibrium steady states of quantum impurity systems, e.g., within the scattering states NRG approach [Anders, Phys. Rev. Lett. {\bf 101}, 066804 (2008)].Comment: 15 pages and 10 figures; Additional figures and references added; typos fixed; references fixe

A Linear Errors-in-Variables Model with Unknown Heteroscedastic Measurement Errors

In the classic measurement error framework, covariates are contaminated by independent additive noise. This paper considers parameter estimation in such a linear errors-in-variables model where the unknown measurement error distribution is heteroscedastic across observations. We propose a new generalized method of moment (GMM) estimator that combines a moment correction approach and a phase function-based approach. The former requires distributions to have four finite moments, while the latter relies on covariates having asymmetric distributions. The new estimator is shown to be consistent and asymptotically normal under appropriate regularity conditions. The asymptotic covariance of the estimator is derived, and the estimated standard error is computed using a fast bootstrap procedure. The GMM estimator is demonstrated to have strong finite sample performance in numerical studies, especially when the measurement errors follow non-Gaussian distributions

Application of theoretical models to active and passive remote sensing of saline ice

The random medium model is used to interpret the polarimetric active and passive measurements of saline ice. The ice layer is described as a host ice medium embedded with randomly distributed inhomogeneities, and the underlying sea water is considered as a homogeneous half-space. The scatterers in the ice layer are modeled with an ellipsoidal correlation function. The orientation of the scatterers is vertically aligned and azimuthally random. The strong permittivity fluctuation theory is employed to calculate the effective permittivity and the distorted Born approximation is used to obtain the polarimetric scattering coefficients. We also calculate the thermal emissions based on the reciprocity and energy conservation principles. The effects of the random roughness at the air-ice, and ice-water interfaces are accounted for by adding the surface scattering to the volume scattering return incoherently. The above theoretical model, which has been successfully applied to analyze the radar backscatter data of the first-year sea ice near Point Barrow, AK, is used to interpret the measurements performed in the CRRELEX program

Expansion of Major Urban Areas in the US Great Plains from 2000 to 2009 Using Satellite Scatterometer Data

A consistent dataset delineating and characterizing changes in urban environments will be valuable for socioeconomic and environmental research and for sustainable urban development. Remotely sensed data have been long used to map urban extent and infrastructure at various spatial and spectral resolutions. Although many datasets and approaches have been tried, there is not yet a universal way to map urban extents across the world. Here we combined a microwave scatterometer (QuikSCAT) dataset at ~1 km posting with percent impervious surface area (%ISA) data from the National Land Cover Dataset (NLCD) that was generated from Landsat data, and ambient population data from the LandScan product to characterize and quantify growth in nine major urban areas in the US Great Plains from 2000 to 2009. Nonparametric Mann-Kendall trend tests on backscatter time series from urban areas show significant expanding trends in eight of nine urban areas with p-values ranging 0.032 to 0.001. The sole exception is Houston, which has a substantial non-urban backscatter at the northeastern edge of the urban core. Strong power law scaling relationships between ambient population and either urban area or backscatter power (r2 of 0.96 in either model) with sub-linear exponents (β of 0.911 and 0.866, respectively) indicate urban areas become more compact with more vertical built-up structure than lateral expansion to accommodate the increased population. Increases in backscatter and %ISA datasets between 2001 and 2006 show agreement in both magnitude and direction for all urban areas except Minneapolis-St. Paul (MSP), likely due to the presence of many lakes and ponds throughout the MSP metropolitan area. We conclude discussing complexities in the backscatter data caused by large metal structures and rainfall

Effects of shearing on biogas production and microbial community structure during anaerobic digestion with recuperative thickening

© 2017 Recuperative thickening can intensify anaerobic digestion to produce more biogas and potentially reduce biosolids odour. This study elucidates the effects of sludge shearing during the thickening process on the microbial community structure and its effect on biogas production. Medium shearing resulted in approximately 15% increase in biogas production. By contrast, excessive or high shearing led to a marked decrease in biogas production, possibly due to sludge disintegration and cell lysis. Microbial analysis using 16S rRNA gene amplicon sequencing showed that medium shearing increased the evenness and diversity of the microbial community in the anaerobic digester, which is consistent with the observed improved biogas production. By contrast, microbial diversity decreased under either excessive shearing or high shearing condition. In good agreement with the observed decrease in biogas production, the abundance of Bacteroidales and Syntrophobaterales (which are responsible for hydrolysis and acetogenesis) decreased due to high shearing during recuperative thickening

Sixty GHz IMPATT diode development

The objective of this program is to develop 60 GHz GaAs IMPATT Diodes suitable for communications applications. The performance goal of the 60 GHz IMPATT is 1W CW output power with a conversion efficiency of 15 percent and 10 year life time. During the course of the program, double drift (DD) GaAs IMPATT Diodes have been developed resulting in the state of the art performance at V band frequencies. A CW output power of 1.12 W was demonstrated at 51.9 GHz with 9.7 percent efficiency. The best conversion efficiency achieved was 15.3 percent. V band DD GaAs IMPATTs were developed using both small signal and large signal analyses. GaAs wafers of DD flat, DD hybrid, and DD Read profiles using molecular beam epitaxy (MBE) were developed with excellent doping profile control. Wafer evaluation was routinely made by the capacitance versus voltage (C-V) measurement. Ion mass spectrometry (SIMS) analysis was also used for more detailed profile evaluation

Anaerobic digestion of soft drink beverage waste and sewage sludge

© 2018 Soft drink beverage waste (BW) was evaluated as a potential substrate for anaerobic co-digestion with sewage sludge to increase biogas production. Results from this study show that the increase in biogas production is proportional to the increase in organic loading rate (OLR) rate due to BW addition. The OLR increase of 86 and 171% corresponding to 10 and 20% BW by volume in the feed resulted in 89 and 191% increase in biogas production, respectively. Under a stable condition, anaerobic co-digestion with BW did not lead to any significant impact on digestate quality (in terms of COD removal and biosolids odour) and biogas composition. The results suggest that existing nutrients in sewage sludge can support an increase in OLR by about 2 kg COD/m3/d from a carbon rich substrate such as soft drink BW without inhibition or excessive impact on subsequent handling of the digestate

Likelihood-based surrogate dimension reduction

We consider the problem of surrogate sufficient dimension reduction, that is, estimating the central subspace of a regression model, when the covariates are contaminated by measurement error. When no measurement error is present, a likelihood-based dimension reduction method that relies on maximizing the likelihood of a Gaussian inverse regression model on the Grassmann manifold is well-known to have superior performance to traditional inverse moment methods. We propose two likelihood-based estimators for the central subspace in measurement error settings, which make different adjustments to the observed surrogates. Both estimators are computed based on maximizing objective functions on the Grassmann manifold and are shown to consistently recover the true central subspace. When the central subspace is assumed to depend on only a few covariates, we further propose to augment the likelihood function with a penalty term that induces sparsity on the Grassmann manifold to obtain sparse estimators. The resulting objective function has a closed-form Riemann gradient which facilitates efficient computation of the penalized estimator. We leverage the state-of-the-art trust region algorithm on the Grassmann manifold to compute the proposed estimators efficiently. Simulation studies and a data application demonstrate the proposed likelihood-based estimators perform better than inverse moment-based estimators in terms of both estimation and variable selection accuracy