Detecting periodicity in experimental data using linear modeling techniques

Fourier spectral estimates and, to a lesser extent, the autocorrelation function are the primary tools to detect periodicities in experimental data in the physical and biological sciences. We propose a new method which is more reliable than traditional techniques, and is able to make clear identification of periodic behavior when traditional techniques do not. This technique is based on an information theoretic reduction of linear (autoregressive) models so that only the essential features of an autoregressive model are retained. These models we call reduced autoregressive models (RARM). The essential features of reduced autoregressive models include any periodicity present in the data. We provide theoretical and numerical evidence from both experimental and artificial data, to demonstrate that this technique will reliably detect periodicities if and only if they are present in the data. There are strong information theoretic arguments to support the statement that RARM detects periodicities if they are present. Surrogate data techniques are used to ensure the converse. Furthermore, our calculations demonstrate that RARM is more robust, more accurate, and more sensitive, than traditional spectral techniques.Comment: 10 pages (revtex) and 6 figures. To appear in Phys Rev E. Modified styl

Comparative power demand of mechanical and aeration imposed shear in an immersed membrane bioreactor

The power demanded for the application of mechanically-imposed shear on an immersed flat sheet (iFS) membrane bioreactor (MBR) has been compared to that of conventional membrane air scouring. Literature correlations based on the Ostwald model were used to define the rheological characteristics of an MBR sludge. The correlation of specific power demand (, in Watts per m2 membrane area) with shear rate γ in s-1 was developed from first principles through a consideration of the force balance on the system in the case of mechanically-imposed shear. The corresponding aeration imposed shear correlation was interpreted from literature information. The analysis revealed the energy required to impose a shear mechanically through oscillation (or reciprocation) of the membrane to be between 20 and 70% less than that demanded for providing the same shear by conventional aeration of the immersed membrane. The energy saving increases with decreasing shear in accordance with a power demand ratio (aeration:mechanical) of 1400γ-1.4 for a specific sludge rheology. Whilst the absolute value is dependent on the sludge rheology, the aeration:mechanical power demand ratio is determined by the difference in the two exponents in the respective correlations between and γ. Consequently, aeration-imparted shear becomes energetically favoured beyond some threshold shear rate value (∼180 s-1, based on the boundary conditions applied in the current study). The outcomes qualitatively corroborate findings from the limited practical measurement of energy demand in MBRs fitted with reciprocating immersed membranes

Low-energy excitations of a linearly Jahn-Teller coupled orbital quintet

The low-energy spectra of the single-mode h x (G+H) linear Jahn-Teller model is studied by means of exact diagonalization. Both eigenenergies and photoemission spectral intensities are computed. These spectra are useful to understand the vibronic dynamics of icosahedral clusters with partly filled orbital quintet molecular shells, for example C60 positive ions.Comment: 14 pages revte

An efficient approach for spin-angular integrations in atomic structure calculations

A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional parentage nor unit tensors. It is based on the combination of second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin), and a generalized graphical technique. The latter allows us to calculate graphically the irreducible tensorial products of the second quantization operators and their commutators, and to formulate additional rules for operations with diagrams. The additional rules allow us to find graphically the normal form of the complicated tensorial products of the operators. All matrix elements (diagonal and non-diagonal with respect to configurations) differ only by the values of the projections of the quasispin momenta of separate shells and are expressed in terms of completely reduced matrix elements (in all three spaces) of the second quantization operators. As a result, it allows us to use standard quantities uniformly for both diagona and off-diagonal matrix elements

Toward Empirical Constraints on the Global Redshifted 21 cm Brightness Temperature During the Epoch of Reionization

Preliminary results are presented from a simple, single-antenna experiment designed to measure the all-sky radio spectrum between 100 and 200 MHz. The system used an internal comparison-switching scheme to reduce non-smooth instrumental contaminants in the measured spectrum to 75 mK. From the observations, we place an initial upper limit of 450 mK on the relative brightness temperature of the redshifted 21 cm contribution to the spectrum due to neutral hydrogen in the intergalactic medium (IGM) during the epoch of reionization, assuming a rapid transition to a fully ionized IGM at a redshift of 8. With refinement, this technique should be able to distinguish between slow and fast reionization scenarios. To constrain the duration of reionization to dz > 2, the systematic residuals in the measured spectrum must be reduced to 3 mK.Comment: Submitted to ApJ. 9 pages including 6 figure

Clogging vs. fouling in immersed membrane bioreactors

Whilst the fouling of MBR membrane surfaces has been very extensively explored by the academic community, there is an increasingly widespread recognition by practitioners of the issue of clogging of membrane channels with sludge solids, sometimes termed “sludging”. The study undertaken has quantified this phenomenon using a bespoke test cell allowing a flat sheet membrane channel to be viewed directly during operation and the accumulated solids determined by digital image processing. Sludging behaviour has then been correlated both with the sludge properties, from sludge samples taken from both an industrial and municipal MBR, and the permeability decline rate data. The work has revealed the expected trends in fouling propensity, as quantified by the exponent n of the Δp/Δt = m.exp(nJ) correlation from classical flux-step tests. With zero membrane aeration the industrial samples exhibited sludging, the filling of the complete thickness of the membrane channel with sludge solids, whereas for municipal sludge the solids formed a cake layer which did not fill the channel. In the absence of sludging the permeability decline followed the expected pattern of increasing at the elevated soluble COD and capillary suction time values of the industrial sludge, compared with municipal sludge at the same solids concentration range (8–12 g.L−1). However, there was no evident correlation between fouling (permeability decline without sludging) and sludging: incipient sludging did not appear to influence permeability, though can be assumed to negatively impact on long-term operation, or relate to the sCOD concentration. Sludging instead appeared to depend on the sludge physical properties, and primarily the viscosity: sludge samples at high viscosities were found to exhibit a different air-scour pattern to that at normal MLSS concentrations. Outcomes suggest that sludging is caused by rheological conditions promoting bubble coalescence and bubble stream constriction, reducing the exposure of the membrane surface to scouring air

Geometric scaling in the spectrum of an electron captured by a stationary finite dipole

We examine the energy spectrum of a charged particle in the presence of a {\it non-rotating} finite electric dipole. For {\emph{any}} value of the dipole moment $p$ above a certain critical value p_{\mathrm{c}}$ an infinite series of bound states arises of which the energy eigenvalues obey an Efimov-like geometric scaling law with an accumulation point at zero energy. These properties are largely destroyed in a realistic situation when rotations are included. Nevertheless, our analysis of the idealised case is of interest because it may possibly be realised using quantum dots as artificial atoms.Comment: 5 figures; references added, outlook section reduce

Coupled tensorial form for atomic relativistic two-particle operator given in second quantization representation

General formulas of the two-electron operator representing either atomic or effective interactions are given in a coupled tensorial form in relativistic approximation. The alternatives of using uncoupled, coupled and antisymmetric two-electron wave functions in constructing coupled tensorial form of the operator are studied. The second quantization technique is used. The considered operator acts in the space of states of open-subshell atoms

Resonant Inelastic X-ray Scattering Studies of Elementary Excitations

In the past decade, Resonant Inelastic X-ray Scattering (RIXS) has made remarkable progress as a spectroscopic technique. This is a direct result of the availability of high-brilliance synchrotron X-ray radiation sources and of advanced photon detection instrumentation. The technique's unique capability to probe elementary excitations in complex materials by measuring their energy-, momentum-, and polarization-dependence has brought RIXS to the forefront of experimental photon science. We review both the experimental and theoretical RIXS investigations of the past decade, focusing on those determining the low-energy charge, spin, orbital and lattice excitations of solids. We present the fundamentals of RIXS as an experimental method and then review the theoretical state of affairs, its recent developments and discuss the different (approximate) methods to compute the dynamical RIXS response. The last decade's body of experimental RIXS data and its interpretation is surveyed, with an emphasis on RIXS studies of correlated electron systems, especially transition metal compounds. Finally, we discuss the promise that RIXS holds for the near future, particularly in view of the advent of x-ray laser photon sources.Comment: Review, 67 pages, 44 figure

Theory of Crystalline Electric Field and Kondo Effect in Pr Skutterudites

Possible Kondo effect in Pr skutterudite is studied with attention to characteristic features of low-lying crystalline electric field (CEF) levels and the conduction band. A mechanism for the small CEF splitting between a singlet and a triplet is proposed as combination of the point-charge interaction and hybridization of 4f with ligand p states. Provided 4f^3 configurations dominate over 4f^1 as intermediate states, p-f hybridization favors the triplet, while point-charge interaction favors the singlet. For realistic parameters for hybridization as well as 4f^1 and 4f^3 levels, these singlet and triplet can form a nearly degenerate pseudo-quartet. It is found that one of two spin 1/2 objects composing the pseudo-quartet has a ferromagnetic exchange, while the other has an antiferromagnetic exchange with conduction electrons. The magnitude of each effective exchange depends strongly on a parameter characterizing the triplet wave function under the T_h symmetry. It is argued that differences of this parameter among Pr skutterdudites are responsible for the apparent diversity of their physical properties. Numerical renormalization group is used to derive the renormalization flows going toward singlet, doublet, triplet or quaret according to the CEF splitting and exchange interactions.Comment: 19 pages, 6 figures, to be published in Special Invited Section (Kondo Effect) of Journal of Physical Society of Japa