Comprehensive T-matrix reference database: A 2007-2009 update

The T-matrix method is among the most versatile, efficient, and widely used theoretical techniques for the numerically exact computation of electromagnetic scattering by homogeneous and composite particles, clusters of particles, discrete random media, and particles in the vicinity of an interface separating two half-spaces with different refractive indices. This paper presents an update to the comprehensive database of T-matrix publications compiled by us previously and includes the publications that appeared since 2007. It also lists several earlier publications not included in the original database.     

The autoionizing energy levels of neon-like Al IV

The photoionization of the ground state of neon-like ions is investigated, and the autoionizing spectrum of 2s²2p⁵ (²P_1/2)ns,nd and 2s2p⁶ (²S_1/2)np Rydberg series of Al IV is studied by using the Breit-Pauli Hamiltonian within the R-matrix theory combining with the QB method of Quigly-Berrington (Quigley L, Berrington K A, Pelan J. Comput Phys Commun 1998;144:225). We predict the autoionizing energy levels and widths of four Rydberg series of Al IV.     

Model of light scattering by dust particles in the solar system: Applications to cometary comae and planetary regoliths

We analyze both the intensity and linear polarization of cosmic dust particles by using the physically exact superposition T-matrix method in a fixed orientation for various aggregates of spheres and DDA for the aggregates of Gaussian random spheres. We study both the spherical geometry (in cometary comae) and cylindrical slabs (for regoliths) up to 2000 monomers with size parameters less than ∼3. It is straightforward to produce the observed linear polarization in both geometries while the typically convex and strong opposition spike seems to require wide regolith geometries. The dependence of various parameters on light scattering has also been studied in a rather detailed form. In applications to the cometary polarization we can fit the data in six colors from UV to the J band at a very good accuracy. We, however, emphasize that we do not claim our model to be unique. The most important parameters here are the refractive index and the size distribution of submicron particles. Rest of the parameters has only a minor role. We also found that it is critically important to use several realizations from any assumed particle geometry model because corresponding scattering characteristics can vary quite a lot.     

An efficient approach for the implementation of the SNB based correlated-k method and its evaluation

The current implementation of the SNB based correlated-k method consumes a significant portion of the total cpu time on the on-line inversion of the cumulative distribution function. An approach was developed to pre-calculate the absorption coefficients of real gases from the inversion procedure. This approach results in significant improvement in the efficiency of the SNB based correlated-k method with slight loss in accuracy. This approach was evaluated against other implementation approaches of the SNB based correlated-k method in several non-isothermal and/or inhomogeneous problems.     

A multiple sphere T-matrix Fortran code for use on parallel computer clusters

A general-purpose Fortran-90 code for calculation of the electromagnetic scattering and absorption properties of multiple sphere clusters is described. The code can calculate the efficiency factors and scattering matrix elements of the cluster for either fixed or random orientation with respect to the incident beam and for plane wave or localized-approximation Gaussian incident fields. In addition, the code can calculate maps of the electric field both interior and exterior to the spheres. The code is written with message passing interface instructions to enable the use on distributed memory compute clusters, and for such platforms the code can make feasible the calculation of absorption, scattering, and general EM characteristics of systems containing several thousand spheres.     

From h to p efficiently: Implementing finite and spectral/hp element methods to achieve optimal performance for low- and high-order discretisations

The spectral/hp element method can be considered as bridging the gap between the – traditionally low-order – finite element method on one side and spectral methods on the other side. Consequently, a major challenge which arises in implementing the spectral/hp element methods is to design algorithms that perform efficiently for both low- and high-order spectral/hp discretisations, as well as discretisations in the intermediate regime. In this paper, we explain how the judicious use of different implementation strategies can be employed to achieve high efficiency across a wide range of polynomial orders. Furthermore, based upon this efficient implementation, we analyse which spectral/hp discretisation (which specific combination of mesh-size h and polynomial order P) minimises the computational cost to solve an elliptic problem up to a predefined level of accuracy. We investigate this question for a set of both smooth and non-smooth problems.     

Optimal cubature on the sphere and other orientation averaging schemes

We propose an orientation averaging scheme which we call optimal cubature on the sphere to be used in light scattering computations. The cubature points are optimally arranged on the sphere to produce non-biased and fast convergence in scattering problems requiring numerical orientation averaging. We will compare performance against other possible schemes.     

The T-matrix technique for calculations of scattering properties of ensembles of randomly oriented particles with different size

We develop a modification of the T-matrix method that allows efficient studies of scattering properties of ensembles of independent irregular particles of different size. The advantage of the modification is quick calculations using the so-called shape-matrices (Sh-matrices), which allow more rapid calculations of scattering by particles of different size and can be used for averaging scattering properties over particle size. To illustrate the advantage we calculate the scattering-angle dependence of the intensity and degree of linear polarization of ensembles of cubes and Chebyshev particles of different size using both the new and traditional methods. Our time savings in calculating scattering properties for the particles with the new methodology is approximately a factor of ten when calculating scattering properties of one hundred of the same type of particles with different size parameter. As can be anticipated, increasing the size interval results in a smoothing of the structure of the photometric curves and a decrease in the linear polarization.     

Application of the vector ε and ρ extrapolation methods in the acceleration of the Richardson-Lucy algorithm

The vector ε and ρ extrapolation methods are applied in accelerating the convergence of the Richardson-Lucy (R-L) algorithm and its damped version. The theory and implementation are discussed in detail, and relevant numerical results are given, including the cases of noise-free images and images corrupted by the Poisson noise. The results show that the vector ε and ρ extrapolations of 9 orders can speed the convergence quite efficiently, and the ρ(9) method is more powerful than the ε(9) method for noisy degraded images. The extra computation burden due to the extrapolation is limited, and is well paid back by the accelerated convergence. The performances of these two methods are compared with the famous automatic acceleration method. For noise-free degraded images, the vector ε(9) and ρ(9) methods are more stable than the automatic method. For noisy degraded images, the damped R-L algorithm accelerated by vector ρ(9) or automatic methods is more powerful, and the instability of the automatic method is restrained by the damping strategy. We explain the instability of the method in accelerating the normal R-L algorithm by the numerical noise due to its frequent applications in the run.     

Theoretical analysis of fluorine-passivated germanium surface for high-k/Ge gate stack by molecular orbital method

Energy state and coordination of fluorine (F)-passivated Ge surface have been theoretically analyzed by semi-empirical molecular orbital method in comparison with hydrogen-passivated Ge surface to predict usefulness of F for passivation element and surface stabilization. Heat of formation for the reaction of F atoms and Ge layer system decreased simultaneously without energy barrier. Resultantly, F-Ge bonds were formed on Ge layer system and Ge surface dangling bonds were passivated by F dissimilar to the reaction of H atoms and Ge layer system. Furthermore, it was confirmed experimentally that the electrical properties of HfO₂/Ge gate stack were improved by F₂-ambient treatment of Ge substrate prior to HfO₂ deposition. It is concluded that F-passivation of Ge surface is useful in making stable and low-defective Ge substrate for high-k dielectric layer deposition.     

Comparison of the structural and magnetic properties of ground-state SrTcO3 and CaTcO3 from first principles

The generalized gradient approximation (GGA) plus on-site Coulomb interaction corrections (GGA+U) method is employed for the total energies and electronic structure calculations of SrTcO₃ and CaTcO₃. G-type antiferromagnetic (G-AFM) is found to be ground state for both compounds, in consistence with the previous experimental results. The mechanism of Neel temperature of SrTcO₃ being higher than that of CaTcO₃ is explored. The insulating band gaps of SrTcO₃ and CaTcO₃ are found to be 1.71 eV and 1.74 eV, respectively. The magnetic moment of Tc1 is found to be 2.237μ_B in SrTcO₃ unit cell and 2.266μ_B in CaTcO₃ unit cell. Structural parameters and electronic structure of the two compounds are examined to explore the origin of their different electrical and magnetic characters.     

Gastric cancer screening by combined assay for serum anti-Helicobacter pylori IgG antibody and serum pepsinogen levels - "ABC method"

The current status of screening for gastric cancer-risk (gastritis A, B, C, D) method using combined assay for serum anti-Helicobacter pylori (Hp) IgG antibody and serum pepsinogen (PG) levels, "ABC method", was reviewed and the latest results of our ongoing trial are reported. It was performed using the following strategy: Subjects were classified into 1 of 4 risk groups based on the results of the two serologic tests, anti-Hp IgG antibody titers and the PG I and II levels: Group A [Hp(-)PG(-)], infection-free subjects; Group B [Hp(+)PG(-)], chronic atrophic gastritis (CAG) free or mild; Group C [Hp(+)PG(+)], CAG; Group D [Hp(-)PG(+)]), severe CAG with extensive intestinal metaplasia. Continuous endoscopic follow-up examinations are required to detect early stages of gastric cancer. Asymptomatic Group A, which accounts for 50-80% of all the subjects may be excluded from the secondary endoscopic examination, from the viewpoint of efficiency. Hp-infected subjects should be administered eradication treatment aimed at the prevention of gastric cancer.     

Study of interaction of butyl p-hydroxybenzoate with human serum albumin by molecular modeling and multi-spectroscopic method

Study of the interaction between butyl p-hydroxybenzoate (butoben) and human serum albumin (HSA) has been performed by molecular modeling and multi-spectroscopic method. The interaction mechanism was predicted through molecular modeling first, then the binding parameters were confirmed using a series of spectroscopic methods, including fluorescence spectroscopy, UV-visible absorbance spectroscopy, circular dichroism (CD) spectroscopy and Fourier transform infrared (FT-IR) spectroscopy. The thermodynamic parameters of the reaction, standard enthalpy ΔH⁰ and entropy ΔS⁰, have been calculated to be −29.52 kJ mol⁻¹ and −24.23 J mol⁻¹ K⁻¹, respectively, according to the Van’t Hoff equation, which suggests the van der Waals force and hydrogen bonds are the predominant intermolecular forces in stabilizing the butoben-HSA complex. Results obtained by spectroscopic methods are consistent with that of the molecular modeling study. In addition, alteration of secondary structure of HSA in the presence of butoben was evaluated using the data obtained from UV-visible absorbance, CD and FT-IR spectroscopies.     

Coupled fractional nonlinear differential equations and exact Jacobian elliptic solutions for exciton–phonon dynamics

An improved quantum model for exciton–phonon dynamics in an α-helix is investigated taking into account the interspine coupling and the influence of power-law long-range exciton–exciton interactions. Having constructed the model Hamiltonian, we derive the lattice equations and employ the Fourier transforms to go in continuum space showing that the long-range interactions (LRI) lead to a nonlocal integral term in the equations of motion. Indeed, the non-locality originating from the LRI results in the dynamic equations with space derivatives of fractional order. New theoretical frameworks are derived, such that: fractional generalization of coupled Zakharov equations, coupled nonlinear fractional Schrödinger equations, coupled fractional Ginzburg–Landau equations, coupled Hilbert–Zakharov equations, coupled nonlinear Hilbert–Ginzburg–Landau equations, coupled nonlinear Schrödinger equations and coupled nonlinear Hilbert–Schrödinger equations. Through the F-expansion method, we derive a set of exact Jacobian solutions of coupled nonlinear Schrödinger equations. These solutions include Jacobian periodic solutions as well as bright and dark soliton which are important in the process of energy transport in the molecule. We also discuss of the impact of LRI on the energy transport in the molecule.     

A numerical methodology for the Painlevé equations

The six Painlevé transcendents P_I − P_VI have both applications and analytic properties that make them stand out from most other classes of special functions. Although they have been the subject of extensive theoretical investigations for about a century, they still have a reputation for being numerically challenging. In particular, their extensive pole fields in the complex plane have often been perceived as ‘numerical mine fields’. In the present work, we note that the Painlevé property in fact provides the opportunity for very fast and accurate numerical solutions throughout such fields. When combining a Taylor/Padé-based ODE initial value solver for the pole fields with a boundary value solver for smooth regions, numerical solutions become available across the full complex plane. We focus here on the numerical methodology, and illustrate it for the P_I equation. In later studies, we will concentrate on mathematical aspects of both the P_I and the higher Painlevé transcendents.     

Short-range interacting skyrmion charges in the long-range interacting skyrmion lattice

A topological excitation-skyrmion in p-wave superconductors is studied in the context of Landau-Ginzburg-Wilson (LGW) theory. Interaction between skyrmion charge densities is shown to be short ranged from a derived effective field model. The computed energy per single skyrmion of skyrmion lattice suggests a long ranged lattice interaction.     

Extension of the weak-line approximation and application to correlated-k methods

Global climate models require accurate and rapid computation of the radiative transfer through the atmosphere. Correlated-k methods are often used. One of the approximations used in correlated-k models is the weak-line approximation. We introduce an approximation T_γ which reduces to the weak-line limit when optical depths are small, and captures the deviation from the weak-line limit as the extinction deviates from the weak-line limit. This approximation is constructed to match the first two moments of the gamma distribution to the k-distribution of the transmission. We compare the errors of the weak-line approximation with T_γ in the context of a water vapor spectrum. The extension T_γ is more accurate and converges more rapidly than the weak-line approximation.     

Near-field computation using the null-field method

In this paper we analyze three methods for computing the total field in the near-zone region. These methods use the expansion of the scattered field outside the minimum circumscribing sphere, an integral representation of the scattered field and a vector spherical wave expansion of the near-zone field. Calculations of the total field within the circumscribing sphere are presented for dielectric prolate spheroids to compare the different methods.     

Differential algebraic method for time of flight property of electrostatic electron lenses

Differential algebraic method is a powerful technique in computer numerical analysis. It presents a straightforward method for computing arbitrary order derivatives of functions with extreme high accuracy limited only by the truncation error of the computer. When applied to nonlinear dynamical systems, the arbitrary high-order transfer properties of the systems can be computed directly with high precision. In this article, the time of flight (TOF) property of electrostatic electron lens systems is studied by differential algebraic method and their arbitrary order TOF transfer properties can be numerically calculated. As an example, Schiske's model electrostatic lens has been studied by the efficient differential algebraic TOF method.