Probabilistic properties of detrended fluctuation analysis for Gaussian processes

Detrended fluctuation analysis (DFA) is one of the most widely used tools for the detection of long-range dependence in time series. Although DFA has found many interesting applications and has been shown to be one of the best performing detrending methods, its probabilistic foundations are still unclear. In this paper, we study probabilistic properties of DFA for Gaussian processes. Our main attention is paid to the distribution of the squared error sum of the detrended process. We use a probabilistic approach to derive general formulas for the expected value and the variance of the squared fluctuation function of DFA for Gaussian processes. We also get analytical results for the expected value of the squared fluctuation function for particular examples of Gaussian processes, such as Gaussian white noise, fractional Gaussian noise, ordinary Brownian motion, and fractional Brownian motion. Our analytical formulas are supported by numerical simulations. The results obtained can serve as a starting point for analyzing the statistical properties of DFA-based estimators for the fluctuation function and long-memory parameter

Structure and oxidation kinetics of the Si(100)-SiO2 interface

We present first-principles calculations of the structural and electronic properties of Si(001)-SiO2 interfaces. We first arrive at reasonable structures for the c-Si/a-SiO2 interface via a Monte-Carlo simulated annealing applied to an empirical interatomic potential, and then relax these structures using first-principles calculations within the framework of density-functional theory. We find a transition region at the interface, having a thickness on the order of 20\AA, in which there is some oxygen deficiency and a corresponding presence of sub-oxide Si species (mostly Si^+2 and Si^+3). Distributions of bond lengths and bond angles, and the nature of the electronic states at the interface, are investigated and discussed. The behavior of atomic oxygen in a-SiO2 is also investigated. The peroxyl linkage configuration is found to be lower in energy than interstitial or threefold configurations. Based on these results, we suggest a possible mechanism for oxygen diffusion in a-SiO2 that may be relevant to the oxidation process.Comment: 7 pages, two-column style with 6 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#ng_sio

Nucleon axial and pseudoscalar form factors from the covariant Faddeev equation

We compute the axial and pseudoscalar form factors of the nucleon in the Dyson-Schwinger approach. To this end, we solve a covariant three-body Faddeev equation for the nucleon wave function and determine the matrix elements of the axialvector and pseudoscalar isotriplet currents. Our only input is a well-established and phenomenologically successful ansatz for the nonperturbative quark-gluon interaction. As a consequence of the axial Ward-Takahashi identity that is respected at the quark level, the Goldberger-Treiman relation is reproduced for all current-quark masses. We discuss the timelike pole structure of the quark-antiquark vertices that enters the nucleon matrix elements and determines the momentum dependence of the form factors. Our result for the axial charge underestimates the experimental value by 20-25% which might be a signal of missing pion-cloud contributions. The axial and pseudoscalar form factors agree with phenomenological and lattice data in the momentum range above Q^2 ~ 1...2 GeV^2.Comment: 17 pages, 7 figures, 1 tabl

Magnetic interactions in EuTe epitaxial layers and EuTe/PbTe superlattices

The magnetic properties of antiferromagnetic (AFM) EuTe epitaxial layers and short period EuTe/PbTe superlattices (SLs), grown by molecular beam epitaxy on (111) BaF$_2$ substrates, were studied by magnetization and neutron diffraction measurements. Considerable changes of the N\'eel temperature as a function of the EuTe layer thickness as well as of the strain state were found. A mean field model, taking into account the variation of the exchange constants with the strain-induced lattice distortions, and the nearest neighbor environment of a Eu atoms, was developed to explain the observed $T_{\text N}$ changes in wide range of samples. Pronounced interlayer magnetic correlations have been revealed by neutron diffraction in EuTe/PbTe SLs with PbTe spacer thickness up to 60 \AA. The observed diffraction spectra were analyzed, in a kinematical approximation, assuming partial interlayer correlations characterized by an appropriate correlation parameter. The formation of interlayer correlations between the AFM EuTe layers across the nonmagnetic PbTe spacer was explained within a framework of a tight-binding model. In this model, the interlayer coupling stems from the dependence of the total electronic energy of the EuTe/PbTe SL on the spin configurations in adjacent EuTe layers. The influence of the EuTe and PbTe layer thickness fluctuations, inherent in the epitaxial growth process, on magnetic properties and interlayer coupling is discussed.Comment: 17 pages, 19 figures, accepted to PR

Palynostratigraphy and Bayesian Age Stratigraphic Model of New CA-ID-TIMS Zircon Ages from the Walloon Coal Measures, Surat Basin, Australia

The Surat Basin hosts significant coal and coal seam gas resources. New high-precision CA-TIMS U/Pb zircon ages from tuffs and Bayesian age stratigraphic models are combined with palynology from fine-grained sedimentary rocks and zircon trace elements to provide further chronostratigraphic and biostratigraphic constrains on the Walloon Coal Measures in the eastern margin of the Surat Basin and infer the palaeoenvironment and tectonic setting. The tuff ages range from 165.88 ± 0.11 Ma to 158.84 ± 0.05 Ma, with those from the stratigraphically lower Taroom Coal Measures ranging from 165.88 ± 0.11 to 163.05 ± 0.08 Ma and Juandah Coal Measures ranging from 159.91 ± 0.04 to 158.84 ± 0.05 Ma. This corroborates that the lower part of the Walloon Coal Measures is Callovian and the upper part is Oxfordian. The palynology results from mudstones show that all samples are dominated by microfossils of spore-pollen with conifers being the most abundant. Our samples fall withinPrice’s (1997) stratigraphic zonation of APJ4.2 and APJ4.3. Posterior ages for palynology samples were estimated through Bayesian age stratigraphic modelling using stratigraphic depths and U-Pb zircon ages. The palaeoenvironment in the eastern portion of the basin is inferred to be predominantly fluvial, with spores and pollen derived from fresh water or terrestrial plants. Higher concentrations of green algae in one sample suggest that at times the water was somewhat stagnant. The zircons were derived from predominantly intermediate magmas, as indicated by the generally low Ti, Ta, and Nb values. The tectonic environment that the zircons were derived from was most likely a continental subduction zone due to their high U/Yb, low Nb/Yb and relatively low Hf concentrations. These new data support previous conclusions of the Surat Basin palaeoenvironment, contribute to the ongoing discussion about the tectonic setting of the basin and add new regional age marker horizons

e+e--pair production in Pb-Au collisions at 158 GeV per nucleon

We present the combined results on electron-pair production in 158 GeV/n {Pb-Au} ($\sqrt{s}$= 17.2 GeV) collisions taken at the CERN SPS in 1995 and 1996, and give a detailed account of the data analysis. The enhancement over the reference of neutral meson decays amounts to a factor of 2.31$\pm0.19 (stat.)\pm0.55 (syst.)\pm0.69 (decays)$ for semi-central collisions (28% $\sigma/\sigma_{geo}$) when yields are integrated over $m>$ 200 MeV/$c^2$ in invariant mass. The measured yield, its stronger-than-linear scaling with $N_{ch}$, and the dominance of low pair $p_t$ strongly suggest an interpretation as {\it thermal radiation} from pion annihilation in the hadronic fireball. The shape of the excess centring at $m\approx$ 500 MeV/$c^2$, however, cannot be described without strong medium modifications of the $\rho$ meson. The results are put into perspective by comparison to predictions from Brown-Rho scaling governed by chiral symmetry restoration, and from the spectral-function many-body treatment in which the approach to the phase boundary is less explicit.Comment: 39 pages, 40 figures, to appear in Eur.Phys.J.C. (2005

Well path design and stimulation treatments at the geothermal research well GtGrSk4/05 in Groß Schönebeck

see Abstract Volum

Recent results from Pb-Au collisions at 158 GeV/c per nucleon obtained with the CERES spectrometer

During the 1996 lead run time, CERES has accumulated 42 million events, corresponding to a factor of 5 more statistics than in 1995 and 2.5 million events of a special photon-run. We report on the results of the low-mass e$^+$e$^-$-pair analysis. Since the most critical item is the poor signal-to-background ratio we also discuss the understanding of this background, in absolute terms, with the help of a detailed Monte Carlo simulation. We show preliminary results of the photon analysis and summarize the results of the hadron analysis preliminarily reported on already at QM'97Comment: 10 pages, 9 figures, Proceedings of the XIV Int. Conf. on Nucleus-Nucleus Collisions,Quark Matter 99, Torino, Italy, May 10 - 15, 199