Absolute photoionization cross sections for Xe4+, Xe5+, and Xe6+ near 13.5 nm: Experiment and theory

Absolute photoionization cross-section measurements for a mixture of ground and metastable states of Xe4+, Xe5+, and Xe6+ are reported in the photon energy range of 4d -> nf transitions, which occur within or adjacent to the 13.5 nm window for extreme ultraviolet lithography light source development. The reported values allow the quantification of opacity effects in xenon plasmas due to these 4d -> nf autoionizing states. The oscillator strengths for the 4d -> 4f and 4d -> 5f transitions in Xeq+ (q=1-6) ions are calculated using nonrelativistic Hartree-Fock and random phase approximations. These are compared with published experimental values for Xe+ to Xe3+ and with the values obtained from the present experimental cross-section measurements for Xe4+ to Xe6+. The calculations assisted in the determination of the metastable content in the ion beams for Xe5+ and Xe6+. The experiments were performed by merging a synchrotron photon beam generated by an undulator beamline of the Advanced Light Source with an ion beam produced by an electron cyclotron resonance ion source.

Discretization of highly persistent correlated AR(1) shocks

The finite state Markov-chain approximation methods developed by Tauchen (1986) and Tauchen and Hussey (1991) are widely used in economics, finance and econometrics to solve functional equations in which state variables follow autoregressive processes. For highly persistent processes, the methods require a large number of discrete values for the state variables to produce close approximations which leads to an undesirable reduction in computational speed, especially in a multivariate case. This paper proposes an alternative method of discretizing multivariate autoregressive processes. This method can be treated as an extension of Rouwenhorst's (1995) method which, according to our finding, outperforms the existing methods in the scalar case for highly persistent processes. The new method works well as an approximation that is much more robust to the number of discrete values for a wide range of the parameter space.

Three-dimensional pattern formation, multiple homogeneous soft modes, and nonlinear dielectric electroconvection

Patterns forming spontaneously in extended, three-dimensional, dissipative systems are likely to excite several homogeneous soft modes (approximate to hydrodynamic modes) of the underlying physical system, much more than quasi-one- (1D) and two-dimensional (2D) patterns are. The reason is the lack of damping boundaries. This paper compares two analytic techniques to derive the pattern dynamics from hydrodynamics, which are usually equivalent but lead to different results when applied to multiple homogeneous soft modes. Dielectric electroconvection in nematic liquid crystals is introduced as a model for 3D pattern formation. The 3D pattern dynamics including soft modes are derived. For slabs of large but finite thickness the description is reduced further to a 2D one. It is argued that the range of validity of 2D descriptions is limited to a very small region above threshold. The transition from 2D to 3D pattern dynamics is discussed. Experimentally testable predictions for the stable range of ideal patterns and the electric Nusselt numbers are made. For most results analytic approximations in terms of material parameters are given. [S1063-651X(00)09512-X].

A comparison of nonstaggered compact FDTD schemes for the 3D wave equation

This paper aims at providing a better insight into the 3D approximations of the wave equation using compact finite-difference time-domain (FDTD) schemes in the context of room acoustic simulations. A general family of 3D compact explicit and implicit schemes based on a nonstaggered rectilinear grid is analyzed in terms of stability, numerical error, and accuracy. Various special cases are compared and the most accurate explicit and implicit schemes are identified. Further considerations presented in the paper include the direct relationship with other numerical approaches found in the literature on room acoustic modeling such as the 3D digital waveguide mesh and Yee's staggered grid technique.

Chemical processes in protoplanetary disks. II. On the importance of photochemistry and X-ray ionization

We investigate the impact of photochemistry and X-ray ionization on the molecular composition of, and ionization fraction in, a protoplanetary disk surrounding a typical T Tauri star. We use a sophisticated physical model, which includes a robust treatment of the radiative transfer of UV and X-ray radiation, and calculate the time-dependent chemical structure using a comprehensive chemical network. In previous work, we approximated the photochemistry and X-ray ionization; here, we recalculate the photoreaction rates using the explicit UV wavelength spectrum and wavelength-dependent reaction cross sections. We recalculate the X-ray ionization rate using our explicit elemental composition and X-ray energy spectrum. We find that photochemistry has a larger influence on the molecular composition than X-ray ionization. Observable molecules sensitive to the photorates include OH, HCO+, N2H+, H2O, CO2, and CH3OH. The only molecule significantly affected by the X-ray ionization is N2H+, indicating that it is safe to adopt existing approximations of the X-ray ionization rate in typical T Tauri star-disk systems. The recalculation of the photorates increases the abundances of neutral molecules in the outer disk, highlighting the importance of taking into account the shape of the UV spectrum in protoplanetary disks. A recalculation of the photoreaction rates also affects the gas-phase chemistry due to the adjustment of the H/H2 and C+/C ratios. The disk ionization fraction is not significantly affected by the methods adopted to calculate the photochemistry and X-ray ionization. We determine that there is a probable "dead zone" where accretion is suppressed, present in a layer, Z/R lsim 0.1-0.2, in the disk midplane, within R ˜ 200 AU.

Dispersion interactions in room-temperature ionic liquids: Results from a non-empirical density functional

The role of dispersion or van de Waals (VDW) interactions in imidazolium-based room-temperature ionic liquids is studied within the framework of density functional theory, using a recently developed non-empirical functional [M. Dion, H. Rydberg, E. Schroder, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004)], as efficiently implemented in the SIESTA code [G. Roman-Perez and J. M. Soler, Phys. Rev. Lett. 103, 096102 (2009)]. We present results for the equilibrium structure and lattice parameters of several crystalline phases, finding a general improvement with respect to both the local density (LDA) and the generalized gradient approximations (GGA). Similar to other systems characterized by VDW bonding, such as rare gas and benzene dimers as well as solid argon, equilibrium distances and volumes are consistently overestimated by approximate to 7%, compared to -11% within LDA and 11% within GGA. The intramolecular geometries are retained, while the intermolecular distances and orientations are significantly improved relative to LDA and GGA. The quality is superior to that achieved with tailor-made empirical VDW corrections ad hoc [M. G. Del Popolo, C. Pinilla, and P. Ballone, J. Chem. Phys. 126, 144705 (2007)]. We also analyse the performance of an optimized version of this non-empirical functional, where the screening properties of the exchange have been tuned to reproduce high-level quantum chemical calculations [J. Klimes, D. Bowler, and A. Michaelides, J. Phys.: Condens. Matter 22, 074203 (2010)]. The results for solids are even better with volumes and geometries reproduced within 2% of experimental data. We provide some insight into the issue of polymorphism of [bmim][Cl] crystals, and we present results for the geometry and energetics of [bmim][Tf] and [mmim][Cl] neutral and charged clusters, which validate the use of empirical force fields. (C) 2011 American Institute of Physics. [doi:10.1063/1.3652897]

Mean field approach for tracking similar objects

In this paper, we consider the problem of tracking similar objects. We show how a mean field approach can be used to deal with interacting targets and we compare it with Markov Chain Monte Carlo (MCMC). Two mean field implementations are presented. The first one is more general and uses particle filtering. We discuss some simplifications of the base algorithm that reduce the computation time. The second one is based on suitable Gaussian approximations of probability densities that lead to a set of self-consistent equations for the means and covariances. These equations give the Kalman solution if there is no interaction. Experiments have been performed on two kinds of sequences. The first kind is composed of a single long sequence of twenty roaming ants and was previously analysed using MCMC. In this case, our mean field algorithms obtain substantially better results. The second kind corresponds to selected sequences of a football match in which the interaction avoids tracker coalescence in situations where independent trackers fail.

A curvilinear approach to the kinetic analysis of linoleate peroxidation in aqueous liposomes by 2,2'azobis(2-amidoinopropane) dihydrochloride

Lipid peroxidation is a common feature of many chemical and biological processes, and is governed by a complex kinetic scheme. A fundamental stage in kinetic investigations of lipid peroxidation is the accurate determination of the rate of peroxidation, which in many instances is heavily reliant on the method of finite differences. Such numerical approximations of the first derivative are commonly employed in commercially available software, despite suffering from considerable inaccuracy due to rounding and truncation errors. As a simple solution to this, we applied three empirical sigmoid functions (viz. the Prout-Tompkins, Richards & Gompertz functions) to data obtained from the AAPH-mediated peroxidation of aqueous linoleate liposomes in the presence of increasing concentrations of Trolox, evaluating the curve fitting parameters using the widely available Microsoft Excel Solver add-in. We have demonstrated that the five-parameter Richards' function provides an excellent model for this peroxidation, and when applied to the determination of fundamental rate constants, produces results in keeping with those available in the literature. Overall, we present a series of equations, derived from the Richards' function, which enables direct evaluation of the kinetic measures of peroxidation. This procedure has applicability not only to investigations of lipid peroxidation, but to any system exhibiting sigmoid kinetics.

Methodology for Validating Artifact Removal Techniques for Physiological Signals

Artifact removal from physiological signals is an essential component of the biosignal processing pipeline. The need for powerful and robust methods for this process has become particularly acute as healthcare technology deployment undergoes transition from the current hospital-centric setting toward a wearable and ubiquitous monitoring environment. Currently, determining the relative efficacy and performance of the multiple artifact removal techniques available on real world data can be problematic, due to incomplete information on the uncorrupted desired signal. The majority of techniques are presently evaluated using simulated data, and therefore, the quality of the conclusions is contingent on the fidelity of the model used. Consequently, in the biomedical signal processing community, there is considerable focus on the generation and validation of appropriate signal models for use in artifact suppression. Most approaches rely on mathematical models which capture suitable approximations to the signal dynamics or underlying physiology and, therefore, introduce some uncertainty to subsequent predictions of algorithm performance. This paper describes a more empirical approach to the modeling of the desired signal that we demonstrate for functional brain monitoring tasks which allows for the procurement of a ground truth signal which is highly correlated to a true desired signal that has been contaminated with artifacts. The availability of this ground truth, together with the corrupted signal, can then aid in determining the efficacy of selected artifact removal techniques. A number of commonly implemented artifact removal techniques were evaluated using the described methodology to validate the proposed novel test platform. © 2012 IEEE.

Semiring induced valuation algebras: Exact and approximate local computation algorithms

Local computation in join trees or acyclic hypertrees has been shown to be linked to a particular algebraic structure, called valuation algebra.There are many models of this algebraic structure ranging from probability theory to numerical analysis, relational databases and various classical and non-classical logics. It turns out that many interesting models of valuation algebras may be derived from semiring valued mappings. In this paper we study how valuation algebras are induced by semirings and how the structure of the valuation algebra is related to the algebraic structure of the semiring. In particular, c-semirings with idempotent multiplication induce idempotent valuation algebras and therefore permit particularly efficient architectures for local computation. Also important are semirings whose multiplicative semigroup is embedded in a union of groups. They induce valuation algebras with a partially defined division. For these valuation algebras, the well-known architectures for Bayesian networks apply. We also extend the general computational framework to allow derivation of bounds and approximations, for when exact computation is not feasible.

Electronic properties of interfaces and defects from many-body perturbation theory: Recent developments and applications

We review some recent developments in many body perturbation theory (MBPT) calculations that have enabled the study of interfaces and defects. Starting from the theoretical basis of MBPT, Hedin's equations are presented, leading to the CW and CWI' approximations. We introduce the perturbative approach, that is the one most commonly used for obtaining quasiparticle (QP) energies. The practical strategy presented for dealing with the frequency dependence of the self energy operator is based on either plasmon-pole models (PPM) or the contour deformation technique, with the latter being more accurate. We also discuss the extrapolar method for reducing the number of unoccupied states which need to be included explicity in the calculations. The use of the PAW method in the framework of MBPT is also described. Finally, results which have been obtained using, MBPT for band offsets a interfaces and for defects presented, with companies on the main difficulties and cancels.

Schematic representation of the QP corrections (marked with ) to the band edges (E and E-v) and a defect level (F) for a Si/SiO2 interface (Si and O atoms are represented in blue and red, respectively, in the ball and stick model) with an oxygen vacancy leading to a Si-Si bond (the Si atoms involved in this bond are colored light blue).

Density functionals from many-body perturbation theory: The band gap for semiconductors and insulators

Theoretically the Kohn-Sham band gap differs from the exact quasiparticle energy gap by the derivative discontinuity of the exchange-correlation functional. In practice for semiconductors and insulators the band gap calculated within any local or semilocal density approximations underestimates severely the experimental energy gap. On the other hand, calculations with an "exact" exchange potential derived from many-body perturbation theory via the optimized effective potential suggest that improving the exchange-correlation potential approximation can yield a reasonable agreement between the Kohn-Sham band gap and the experimental gap. The results in this work show that this is not the case. In fact, we add to the exact exchange the correlation that corresponds to the dynamical (random phase approximation) screening in the GW approximation. This accurate exchange-correlation potential provides band structures similar to the local density approximation with the corresponding derivative discontinuity that contributes 30%-50% to the energy gap. Our self-consistent results confirm substantially the results for Si and other semiconductors obtained perturbatively [R. W. Godby , Phys. Rev. B 36, 6497 (1987)] and extend the conclusion to LiF and Ar, a wide-gap insulator and a noble-gas solid. (c) 2006 American Institute of Physics.

STO and GTO field-induced polarization functions for H to Kr

Field-induced polarization (FIP) functions were proposed over two decades ago to improve the accuracy of calculated response properties, and the FIP functions in GTO form for H and C to F were tested on small molecules, with encouraging results. The concept of FIP,is now extended to all atoms up to Kr. New simplifying approximations for the description of asymptotic highest occupied atomic orbitals. (HOAOs) are introduced in this study. They provide the basis for STO and GTO exponents of a complete set of FIP functions from H to Kr, which are both listed for the convenience of the users. Tests on the polarizabilities of a series of atoms and molecules demonstrate that addition of the FIP basis functions to a series' of standard basis sets drastically improves the performance of all these basis sets compared to converged results. Moreover, the byproduct of this study (approximate asymptotic HOAOs) provides information for the construction of accurate basis sets for long-range ground state properties. (C) 2003 Wiley Periodicals, Inc.

Exchange-correlation energy and potential as approximate functionals of occupied and virtual Kohn-Sham orbitals: Application to dissociating H-2

The standard local density approximation and generalized gradient approximations fail to properly describe the dissociation of an electron pair bond, yielding large errors (on the order of 50 kcal/mol) at long bond distances. To remedy this failure, a self-consistent Kohn-Sham (KS) method is proposed with the exchange-correlation (xc) energy and potential depending on both occupied and virtual KS orbitals. The xc energy functional of Buijse and Baerends [Mol. Phys. 100, 401 (2002); Phys. Rev. Lett. 87, 133004 (2001)] is employed, which, based on an ansatz for the xc-hole amplitude, is able to reproduce the important dynamical and nondynamical effects of Coulomb correlation through the efficient use of virtual orbitals. Self-consistent calculations require the corresponding xc potential to be obtained, to which end the optimized effective potential (OEP) method is used within the common energy denominator approximation for the static orbital Green's function. The problem of the asymptotic divergence of the xc potential of the OEP when a finite number of virtual orbitals is used is addressed. The self-consistent calculations reproduce very well the entire H-2 potential curve, describing correctly the gradual buildup of strong left-right correlation in stretched H-2. (C) 2003 American Institute of Physics.

Exchange potential from the common energy denominator approximation for the Kohn-Sham Green's function: Application to (hyper)polarizabilities of molecular chains

An approximate Kohn-Sham (KS) exchange potential v(xsigma)(CEDA) is developed, based on the common energy denominator approximation (CEDA) for the static orbital Green's function, which preserves the essential structure of the density response function. v(xsigma)(CEDA) is an explicit functional of the occupied KS orbitals, which has the Slater v(Ssigma) and response v(respsigma)(CEDA) potentials as its components. The latter exhibits the characteristic step structure with "diagonal" contributions from the orbital densities \psi(isigma)\(2), as well as "off-diagonal" ones from the occupied-occupied orbital products psi(isigma)psi(j(not equal1)sigma). Comparison of the results of atomic and molecular ground-state CEDA calculations with those of the Krieger-Li-Iafrate (KLI), exact exchange (EXX), and Hartree-Fock (HF) methods show, that both KLI and CEDA potentials can be considered as very good analytical "closure approximations" to the exact KS exchange potential. The total CEDA and KLI energies nearly coincide with the EXX ones and the corresponding orbital energies epsilon(isigma) are rather close to each other for the light atoms and small molecules considered. The CEDA, KLI, EXX-epsilon(isigma) values provide the qualitatively correct order of ionizations and they give an estimate of VIPs comparable to that of the HF Koopmans' theorem. However, the additional off-diagonal orbital structure of v(xsigma)(CEDA) appears to be essential for the calculated response properties of molecular chains. KLI already considerably improves the calculated (hyper)polarizabilities of the prototype hydrogen chains H-n over local density approximation (LDA) and standard generalized gradient approximations (GGAs), while the CEDA results are definitely an improvement over the KLI ones. The reasons of this success are the specific orbital structures of the CEDA and KLI response potentials, which produce in an external field an ultranonlocal field-counteracting exchange potential. (C) 2002 American Institute of Physics.