Influence Of Higher-order Modes In Coaxial Waveguide On Measurements Of Material Parameters

The use of a coaxial air-filled line as a test fixture for measuring complex permittivity and permeability often shows odd resonance-like behavior of material parameters as functions of frequency. This effect is typically either ascribed to the half-wavelength resonance at the sample length, or erroneously misinterpreted as intrinsic resonance behavior of the material. However, as is shown in this paper, such behavior can be attributed to excitation of the higher-order modes on the surface of the sample resulting in resonance absorption of electromagnetic energy in the test fixture. Herein, analytical, numerical, and experimental results show that there can actually be a significant impact of higher-order modes in a coaxial line on the extracted constitutive material parameters of samples

Multivariate Granger Causality and Generalized Variance

Granger causality analysis is a popular method for inference on directed interactions in complex systems of many variables. A shortcoming of the standard framework for Granger causality is that it only allows for examination of interactions between single (univariate) variables within a system, perhaps conditioned on other variables. However, interactions do not necessarily take place between single variables, but may occur among groups, or "ensembles", of variables. In this study we establish a principled framework for Granger causality in the context of causal interactions among two or more multivariate sets of variables. Building on Geweke's seminal 1982 work, we offer new justifications for one particular form of multivariate Granger causality based on the generalized variances of residual errors. Taken together, our results support a comprehensive and theoretically consistent extension of Granger causality to the multivariate case. Treated individually, they highlight several specific advantages of the generalized variance measure, which we illustrate using applications in neuroscience as an example. We further show how the measure can be used to define "partial" Granger causality in the multivariate context and we also motivate reformulations of "causal density" and "Granger autonomy". Our results are directly applicable to experimental data and promise to reveal new types of functional relations in complex systems, neural and otherwise.Comment: added 1 reference, minor change to discussion, typos corrected; 28 pages, 3 figures, 1 table, LaTe

Spectral Analysis of Multi-dimensional Self-similar Markov Processes

In this paper we consider a discrete scale invariant (DSI) process $\{X(t), t\in {\bf R^+}\}$ with scale $l>1$. We consider to have some fix number of observations in every scale, say $T$, and to get our samples at discrete points $\alpha^k, k\in {\bf W}$ where $\alpha$ is obtained by the equality $l=\alpha^T$ and ${\bf W}=\{0, 1,...\}$. So we provide a discrete time scale invariant (DT-SI) process $X(\cdot)$ with parameter space $\{\alpha^k, k\in {\bf W}\}$. We find the spectral representation of the covariance function of such DT-SI process. By providing harmonic like representation of multi-dimensional self-similar processes, spectral density function of them are presented. We assume that the process $\{X(t), t\in {\bf R^+}\}$ is also Markov in the wide sense and provide a discrete time scale invariant Markov (DT-SIM) process with the above scheme of sampling. We present an example of DT-SIM process, simple Brownian motion, by the above sampling scheme and verify our results. Finally we find the spectral density matrix of such DT-SIM process and show that its associated $T$-dimensional self-similar Markov process is fully specified by $\{R_{j}^H(1),R_{j}^H(0),j=0, 1,..., T-1\}$ where $R_j^H(\tau)$ is the covariance function of $j$th and $(j+\tau)$th observations of the process.Comment: 16 page

Adaptive density estimation for stationary processes

We propose an algorithm to estimate the common density $s$ of a stationary process $X_1,...,X_n$. We suppose that the process is either $\beta$ or $\tau$-mixing. We provide a model selection procedure based on a generalization of Mallows' $C_p$ and we prove oracle inequalities for the selected estimator under a few prior assumptions on the collection of models and on the mixing coefficients. We prove that our estimator is adaptive over a class of Besov spaces, namely, we prove that it achieves the same rates of convergence as in the i.i.d framework

AR and MA representation of partial autocorrelation functions, with applications

We prove a representation of the partial autocorrelation function (PACF), or the Verblunsky coefficients, of a stationary process in terms of the AR and MA coefficients. We apply it to show the asymptotic behaviour of the PACF. We also propose a new definition of short and long memory in terms of the PACF.Comment: Published in Probability Theory and Related Field

The potential to narrow uncertainty in projections of stratospheric ozone over the 21st century

Future stratospheric ozone concentrations will be determined both by changes in the concentration of ozone depleting substances (ODSs) and by changes in stratospheric and tropospheric climate, including those caused by changes in anthropogenic greenhouse gases (GHGs). Since future economic development pathways and resultant emissions of GHGs are uncertain, anthropogenic climate change could be a significant source of uncertainty for future projections of stratospheric ozone. In this pilot study, using an "ensemble of opportunity" of chemistry-climate model (CCM) simulations, the contribution of scenario uncertainty from different plausible emissions pathways for ODSs and GHGs to future ozone projections is quantified relative to the contribution from model uncertainty and internal variability of the chemistry-climate system. For both the global, annual mean ozone concentration and for ozone in specific geographical regions, differences between CCMs are the dominant source of uncertainty for the first two-thirds of the 21st century, up-to and after the time when ozone concentrations return to 1980 values. In the last third of the 21st century, dependent upon the set of greenhouse gas scenarios used, scenario uncertainty can be the dominant contributor. This result suggests that investment in chemistry-climate modelling is likely to continue to refine projections of stratospheric ozone and estimates of the return of stratospheric ozone concentrations to pre-1980 levels

Stochastic simulations of the quantum Zeno effect

Published versio

Ozone sensitivity to varying greenhouse gases and ozone-depleting substances in CCMI-1 simulations

Ozone fields simulated for the first phase of the Chemistry-Climate Model Initiative (CCMI-1) will be used as forcing data in the 6th Coupled Model Intercomparison Project. Here we assess, using reference and sensitivity simulations produced for CCMI-1, the suitability of CCMI-1 model results for this process, investigating the degree of consistency amongst models regarding their responses to variations in individual forcings. We consider the influences of methane, nitrous oxide, a combination of chlorinated or brominated ozone-depleting substances, and a combination of carbon dioxide and other greenhouse gases. We find varying degrees of consistency in the models' responses in ozone to these individual forcings, including some considerable disagreement. In particular, the response of total-column ozone to these forcings is less consistent across the multi-model ensemble than profile comparisons. We analyse how stratospheric age of air, a commonly used diagnostic of stratospheric transport, responds to the forcings. For this diagnostic we find some salient differences in model behaviour, which may explain some of the findings for ozone. The findings imply that the ozone fields derived from CCMI-1 are subject to considerable uncertainties regarding the impacts of these anthropogenic forcings. We offer some thoughts on how to best approach the problem of generating a consensus ozone database from a multi-model ensemble such as CCMI-1

Recent variability of the solar spectral irradiance and its impact on climate modelling

The lack of long and reliable time series of solar spectral irradiance (SSI) measurements makes an accurate quantification of solar contributions to recent climate change difficult. Whereas earlier SSI observations and models provided a qualitatively consistent picture of the SSI variability, recent measurements by the SORCE (SOlar Radiation and Climate Experiment) satellite suggest a significantly stronger variability in the ultraviolet (UV) spectral range and changes in the visible and near-infrared (NIR) bands in anti-phase with the solar cycle. A number of recent chemistry-climate model (CCM) simulations have shown that this might have significant implications on the Earth's atmosphere. Motivated by these results, we summarize here our current knowledge of SSI variability and its impact on Earth's climate. We present a detailed overview of existing SSI measurements and provide thorough comparison of models available to date. SSI changes influence the Earth's atmosphere, both directly, through changes in shortwave (SW) heating and therefore, temperature and ozone distributions in the stratosphere, and indirectly, through dynamical feedbacks. We investigate these direct and indirect effects using several state-of-the art CCM simulations forced with measured and modelled SSI changes. A unique asset of this study is the use of a common comprehensive approach for an issue that is usually addressed separately by different communities. We show that the SORCE measurements are difficult to reconcile with earlier observations and with SSI models. Of the five SSI models discussed here, specifically NRLSSI (Naval Research Laboratory Solar Spectral Irradiance), SATIRE-S (Spectral And Total Irradiance REconstructions for the Satellite era), COSI (COde for Solar Irradiance), SRPM (Solar Radiation Physical Modelling), and OAR (Osservatorio Astronomico di Roma), only one shows a behaviour of the UV and visible irradiance qualitatively resembling that of the recent SORCE measurements. However, the integral of the SSI computed with this model over the entire spectral range does not reproduce the measured cyclical changes of the total solar irradiance, which is an essential requisite for realistic evaluations of solar effects on the Earth's climate in CCMs. We show that within the range provided by the recent SSI observations and semi-empirical models discussed here, the NRLSSI model and SORCE observations represent the lower and upper limits in the magnitude of the SSI solar cycle variation. The results of the CCM simulations, forced with the SSI solar cycle variations estimated from the NRLSSI model and from SORCE measurements, show that the direct solar response in the stratosphere is larger for the SORCE than for the NRLSSI data. Correspondingly, larger UV forcing also leads to a larger surface response. Finally, we discuss the reliability of the available data and we propose additional coordinated work, first to build composite SSI data sets out of scattered observations and to refine current SSI models, and second, to run coordinated CCM experiments