Zeroth Approximation Research Articles

Advanced computational approach to studying Rydberg and autoionization resonances in spectra of lanthanides: Ytterbium

We present the results of computing the Rydberg autoionization resonances in spectra of the ytterbium atom, in particular, data on the energies and widths of the autoionization resonances 4f13 [2F7/2]6s2np[5/2]2, 4f13 [2F7/2]6s2nf[5/2]2, which are arisen in result of excitation of the 4f-shell electrons. For some values of the principal quantum number the presented data are compared with the corresponding available experimental data by Jong-Hoon Yi et al, which are obtained by method of three-photon laser polarization spectroscopy. As the method of computing we apply the method of a relativistic many-body perturbation theory with the Dirac-Kohn-Sham zeroth approximation combined with the generalized relativistic energy approach. This approach takes effectively into account the important exchange-correlation corrections as the corrections of the perturbation theory second and higher orders (for example, the polarization interaction, quasiparticles screening corrections) and effect of the non-Coulomb grouping levels in the Rydberg spectra etc.

Advanced computational approach in electron-collisional spectroscopy of atoms and multicharged ions in plasmas

An advanced computational approach to determination of the electron-collisional strengths and cross-sections for atomic ions in the Debye plasmas is presented and used to calculate effective collision strengths of the Kr26+ Ne-like ion excitation states for temperature T=5×106K and density ne==1014cm−3 . The obtained results are compared with the R-matrix data by Griffin et al and other theoretical estimates. The approach is based on the generalized relativistic energy formalism and relativistic many-body perturbation theory with the Debye shielding model Hamiltonian for electron-nuclear and electron-electron systems. The optimized one-electron representation in the perturbation theory zeroth approximation is constructed by means of the correct treating the gauge dependent multielectron contribution of the lowest perturbation theory corrections to the radiation widths of atomic levels.

Temperature Field of a Turbulent Flow in a Well with Allowance for the Temperature Dependence of Heat Capacity

The article discusses a method to solve a field-matching problem that describes a nonstationary heat exchange between an upward flow of fluid in a pipe and an ambient medium with allowance for the variability of the coefficients due to the turbulence of a multiphase flow and the nonlinear dependence of the oil heat capacity on temperature and precipitation of paraffins. The method combines asymptotic methods of small and formal parameters. Analysis of the experimental data on the dependence of heat capacity on the temperature makes it possible to approximate it by a linear function that contains a small parameter in the form of the first terms of the Taylor series. Expansion of the problem by the small parameter in the zeroth approximation leads to a linear problem that is solved by the asymptotic method for a formal parameter for uncoupling of the first coefficient of the expansion. Expressions determining the temperature field in the well and surrounding rocks that take into account the orthotropy of the thermophysical properties of the media are obtained.

ANALYSIS OF POSSIBLE CAUSES AND MECHANISMS OF DESTRUCTION OF BUILDING STRUCTURES

In order to better understand the wave properties of the Timoshenko equation, the derivation of the refined equation from the equations of the plane elasticity problem for a long band is carried out. The simple iterations method is used for the derivation. It includes known methods: the semi-inverse method of Saint-Venant and Picard operator. In accordance with the semi-inverse method, a part of the unknowns is defined, which are interpreted as the values of the initial (zero) approximation. Proceeding from them, a sequential computation is carried out using a sequence of the four Picard operators in such a way that the outputs of the one operator are the inputs for the next. Calculating in this way all the unknowns in the zeroth approximation by the direct integration over the transverse coordinate, the values of the initial approximation are calculated in the first approximation. These quantities are small of the second order with respect to the dimensionless thickness. Expressions for the unknowns are obtained as power functions of the transverse coordinate and as a function of the deriva-tives along the longitudinal coordinate. By the Banach fixed point theorem, the computation process is asymptot-ically convergent one. After this, boundary conditions on the long sides are satisfied by means of the derivatives of the arbitrariness, depending only on the longitudinal coordinate. This gives us the ordinary differential equations for the determination of these arbitrary functions. In turn, the integration constants of the last equations can be found from the conditions on the short sides of the strip. The ordinary differential equations are split into equations for slowly varying and quickly varying quantities. The slowly changing values give the classical solu-tion of the beam oscillations. The quickly varying solutions give the perturbed solutions describing high-frequency oscillations and singularly perturbed wave solutions for time-concentrated effects. Some of these soluions are absent in the Timoshenko equation. It is assumed that the selected shear waves provoke in the buildings subjected to the rapid impacts (shock by airplane, explosions, and seismic movements of the base) the interruptions of interlayers between the floors and subsequent progressive collapse.

Stable absorbing boundary conditions for molecular dynamics in general domains

A new type of absorbing boundary conditions for molecular dynamics simulations are presented. The exact boundary conditions for crystalline solids with harmonic approximation are expressed as a dynamic Dirichlet- to-Neumann (DtN) map. It connects the displacement of the atoms at the boundary to the traction on these atoms. The DtN map is valid for a domain with general geometry. To avoid evaluating the time convo- lution of the dynamic DtN map, we approximate the associated kernel function by rational functions in the Laplace domain. The parameters in the approximations are determined by interpolations. The explicit forms of the zeroth, first, and second order approximations will be presented. The stability of the molecular dynamics model, supplemented with these absorbing boundary conditions is established. Two numerical simulations are performed to demonstrate the effectiveness of the methods.

Kinetics of CO Molecules Taking into Account Resonant VE Exchanges in a Nonequilibrium Nozzle Flow

The kinetics of CO molecules with excited electronic levels for a nonequilibrium flow in nozzles is studied. Three electronic energy levels are taken into account; the VV exchanges of the vibrational energy within each electronic energy level, VT transitions from the vibrational energy to the translational energy, and VE exchanges between the vibrational energy and the electronic terms occur in the system. The system of equations of vibrational level kinetics and gasdynamics, which is written in the zeroth approximation of the Chapman–Enskog method, is solved numerically. Special attention is paid to estimating the effect of the VE exchanges of the vibrational energy on the formation of nonequilibrium populations of the vibrational levels. It is shown that resonant VE transitions considerably affect the relaxation process and noticeably change the population of the upper vibrational levels even in the absence of recombination and dissociation processes; VE exchanges also affect the time dependence of the vibrational temperature.

Coefficient-by-Coefficient Averaging in a Problem of Laminar Gas Flow in a Well

This paper describes the problem of determining the temperature of laminar gas flow, in which the equation of convective heat transfer contains two variable coefficients, is reduced to nonclassical problems for zeroth and first asymptotic expansion coefficient with respect to a formal parameter. The Laplace–Carson transform are used to obtain analytical expressions for the temperature field of ascending laminar gas flow in a well with account for the relationships of density and velocity with spatial coordinates in zeroth and first asymptotic approximations. Expressions for the temperature asymptotically averaged along the cross section of the well and temperature distributions over the cross-sectional radius are obtained.

Heuristic derivation of Brinkman's seepage equation

Brinkman’s law is describing the seepage of viscous fluid through a porous medium and is more acurate than the classical Darcy’s law. Namely, Brinkman’s law permits to conform the flow through a porous medium to the free Stokes’ flow. However, Brinkman’s law, similarly as Schro¨dinger’s equation was only devined. Fluid in its motion through a porous solid is interacting at every point with the walls of pores, but the interactions of the fluid particles inside pores are different than the interactions at the walls, and are described by Stokes’ equation. Here, we arrive at Brinkman’s law from Stokes’ flow equation making use of successive iterations, in type of Born’s approximation method, and using Darcy’s law as a zero-th approximation.

Associations and dissociations with time-dependent reaction coefficients in finite polymer mixtures: The model and analytical-numerical method for solution by successive approximations

• The conservation-law-based derivation of the model for finite homopolymer mixtures. • Association and dissociation reactions with time-dependent reaction coefficients. • Analytical-numerical method of the successive-approximation type for efficient computing. • Complete analysis and examples of simulation of monomer-dimer mixtures with time-independent coefficients. • Emphasized importance of the obtained results for manufacturing of spatially heterogeneous polymer products. The work deals with the association and dissociation reactions with time-dependent coefficients in finite mixtures of polymers dispersed in fluid media with solid components. The polymers are regarded to be formed by identical units, polymer-forming units (PFUs) and, thus, present homopolymers. The model takes into account the porosity of the dispersion-medium/polymer-mixture system. The work derives the model for the reactions in the finite mixtures. The model presents a non-autonomous quadratic finite ODE system in a time-independent hyperplane and is based on the conservation law for the total number of PFUs. A variety of engineering applications of the derived finite-mixture model are discussed. The simplest case of the finite mixtures, i.e., the monomer-dimer mixtures with time-independent reaction coefficients is completely analyzed. An analytical-numerical (AN) method of the successive-approximations (SA) type is proposed for solving the derived model. The AN/SA method includes explicit analytical expressions for each of the approximations in terms of the preceding approximation. The method is exact in the dissociation-only case. The approximations are expected to converge if the association-reaction coefficients are not too large and the zeroth approximations are not very far from the solution. The AN/SA method comprises two sequences of the approximations. If the first one converges uniformly in the entire time axis, then the limit function is a steady-state (or “dynamic equilibrium”) solution of the non-autonomous quadratic ODE system. The second sequence presumes that the first sequence is convergent in the above mentioned sense. The second sequence is intended for calculation of the solutions of initial-value problems for the above ODE system in a semi-infinite time interval. The main differences from common computational methods are formulated. The AN/SA method is quantitatively illustrated with a few examples of the settings in the aforementioned case of monomer-dimer mixtures, also in comparison with the explicit Euler method. The form of the AN/SA method allows especially efficient implementation on multi-processor/multi-core personal computers with graphic processing units even if the dimension of the state space is large. The developed model and method form a constructive framework for analysis or design of polymer mixtures dispersed in fluid-solid media. An application to prospective manufacturing of spatially heterogeneous polymer products is noted. A few directions for future research are proposed as well.

ADVANCED RELATIVISTIC APPROACH IN SPECTROSCOPY OF COMPLEX AUTOIONIZATION RESONANCES IN ATOMIC SPECTRA

We applied a generalized energy approach (Gell-Mann and Low S-matrix formalism) combined with the relativistic multi-quasiparticle (QP) perturbation theory (PT) with the Dirac-Kohn-Sham zeroth approximation and accounting for the exchange-correlation, relativistic corrections to studying autoionization resonances in the helium spectrum, in particular, we predicted the energies and widths of the number of the Rydberg resonances. There are presented the results of comparison of our theory data for the autoionization resonance 3s3p 1Р0 with the available experimental data and those results of other theories, including, method of complex rotation by Ho, algebraic approach by Wakid-Callaway, diagonalization method by Senashenko-Wague etc.

OPTIMIZED RELATIVISTIC DIRAC-FOCK APPROACH TO CALCULATING THE HYPERFINE LINE SHIFT AND BROADENING FOR HEAVY ATOMS IN THE BUFFER GAS

It is presented a new consistent relativistic approach to description of the energetic and spectral properties of the heavy atoms in an atmosphere of the inert gases, based on the atomic gauge-invariant relativistic perturbation theory with the optimized Dirac-Fock zeroth approximation with density functional correlation potential and the exchange perturbation theory for construction of the interatomic potential function. As illustration it is applied to calculating the interatomic potentials, hyperfine structure line collision shift and broadening for alkali and thallium atoms, in an atmosphere of the buffer inert gas. It is shown that an accurate accounting of relativistic and exchange-correlation provides physically reasonable description of the energetic and spectral properties of the heavy atoms in an atmosphere of the inert gases.

Buckling delamination of the PZT/Metal/PZT sandwich circular plate-disc with penny-shaped interface cracks

The axisymmetric buckling delamination of the Piezoelectric/Metal/Piezoelectric (PZT/Metal/PZT) sandwich circular plate with interface penny-shaped cracks is investigated. The case is considered where open-circuit conditions with respect to the electrical displacement on the upper and lower surfaces, and short-circuit conditions with respect to the electrical potential on the lateral surface of the face layers are satisfied. It is assumed that the edge surfaces of the cracks have an infinitesimal rotationally symmetric initial imperfection and the development of this imperfection with rotationally symmetric compressive forces acting on the lateral surface of the plate is studied by employing the exact geometrically non-linear field equations and relations of electro-elasticity for piezoelectric materials. The sought values are presented in the power series form with respect to the small parameter which characterizes the degree of the initial imperfection. The zeroth and first approximations are used for investigation of stability loss and buckling delamination problems. It is established that the equations and relations related to the first approximation coincide with the corresponding ones of the three-dimensional linearized theory of stability of electro-elasticity for piezoelectric materials. The quantities related to the zeroth approximation are determined analytically, however the quantities related to the first approximation are determined numerically by employing Finite Element Method (FEM). Numerical results on the critical radial stresses acting in the layers of the plate are presented and discussed. In particular, it is established that the piezoelectricity of the face layer material causes an increase (a decrease) in the values of the critical compressive stress acting in the face (core) layer.

SPECTROSCOPY OF THE COMPLEX AUTOIONIZATION RESONANCES IN SPECTRUM OF BERYLLIUM

We applied a generalized energy approach (Gell-Mann and Low S-matrix formalism) combined with the relativistic multi-quasiparticle (QP) perturbation theory (PT) with the Dirac-Kohn-Sham zeroth approximation and accounting for the exchange-correlation, relativistic corrections to studying autoionization resonances in the beryllium Be spectrum, in particular, we predicted the energies and widths of the number of the Rydberg resonances. There are presented the results of comparison of our theory data for the autoionization resonance 3s3p 1 Р0 with the available experimental data and those results of other theories, including, method Greene, by Tully-Seaton-Berrington and by Kim-TayalZhou-Manson etc.

Planar aromaticity of D N h -symmetrical systems as a perturbed two-dimensional (2D) rigid rotor.

Energy levels for D N h -symmetrical cyclic polyenes with planar aromaticity were obtained using two-dimensional (2D) rigid rotor as the zeroth approximation. The addition of nuclei was simulated by the cosine-type potential and treated at the first-order perturbation theory. The result is qualitatively equivalent to that obtained using Hückel's molecular orbital theory. As an addition, the energetic shift between σ and π orbitals is obtained using the model of electron oscillating around the center of a positively charged ring.

Analytical solutions and genuine multipartite entanglement of the three-qubit Dicke model

We present analytical solutions to three qubits and a single-mode cavity coupling system beyond the rotating-wave approximation (RWA). The zero-th order approximation gives correct solutions when the qubits are far detuned from the cavity. The first order approximation, called generalized rotating-wave approximation (GRWA), produces an effective solvable Hamiltonian with the same form as the ordinary RWA one and exhibits substantial improvements of energy levels over the RWA even on resonance. Based on these analytical eigen-solutions, we study both the bipartite entanglement and genuine multipartite entanglement (GME). The dynamics of the concurrence and the GME using the GRWA are in consistent with the numerical ones. Interestingly, the well known sudden death of entanglement occurs in the bipartite entanglement dynamics but not in GME dynamics.

Determination of sample surface topography using electron back-scatter diffraction patterns

The background of an electron backscattered diffraction pattern contains quantitative surface topography data. We propose a new approach to extract this topography from the location of the maximum background intensity in each diffraction pattern. Using specular reflection as a zero-th order approximation, we employ Monte Carlo simulations to determine corrections to the scattering angles, which then allow us to accurately determine the local surface normal. We derive the theoretical model and illustrate the approach experimentally using a β-Sn sphere, for which we determine the local surface normal orientation from the background intensity shifts in electron backscatter diffraction patterns.

SPECTROSCOPY OF THE COMPLEX AUTOIONIZATION RESONANCES IN SPECTRUM OF HELIUM: TEST AND NEW SPECTRAL DATA

We applied a generalized energy approach (Gell-Mann and Low S-matrix formalism) combined with the relativistic multi-quasiparticle (QP) perturbation theory (PT) with the Dirac-Kohn-Sham zeroth approximation and accounting for the exchange-correlation, relativistic corrections to studying autoionization resonances in the helium spectrum, in particular, we predicted the energies and widths of the number of the Rydberg resonances. There are presented the results of comparison of our theory data for the autoionization resonance 3s3p 1Р0 with the available experimental data and those results of other theories, including, method of complex rotation by Ho, algebraic approach by Wakid-Callaway, diagonalization method by Senashenko-Wague etc.

Longwave stability of two-layer fluid flow in the inclined plane

The exact invariantOstroumov–Birikh solution of the Oberbeck–Bussinesq equationswhich describes two-layer advective thermocapillary flows in the inclined plane is analyzed. The spectrum of the characteristic perturbations of all classes of the flows is investigated and analytical representations of the eigennumbers and eigenfunctions of the corresponding spectral problem are obtained in the zeroth approximation. Stability of the flows with respect to longwave perturbations and the possibility of existence of oscillatory regimes are proved.

SPECTROSCOPY OF ATOMS IN A STRONG LASER FIELD: NEW METHOD TO SENSING AC STARK EFFECT, MULTIPHOTON RESONANCES PARAMETERS AND IONIZATION CROSS-SECTIONS

The resonant multiphoton resonances shifts and widths and ionization cross-sections for multielectron atoms in a intense laser radiation field are studied. It is carried out a new consistent approach to atom in a strong realistic laser field, based on the relativistic energy formalism (S-matrix adiabatic formalism), relativistic Dirac equation Green function method and relativistic many-body perturbation theory with the Dirac-Kohn-Sham zeroth approximation. In relativistic theory, the Gell-Mann and Low adiabatic formula for energy shift is connected with electrodynamical scattering matrice, which includes interaction with as a laser field as a photon vacuum field (radiative decay). The optimized basis of the relativistic orbitals is generated with using a minimization procedure for the gauge-non-invariant contribution (the fourth-order of the QED perturbation theory) to the radiation width of atomic state. An approach to treating the multiphoton atomic processes is outlined on example of H, Cs, Kr,Mg etc. Analysis shows that the shift and width of the multi-photon resonance line for the interaction “atom- multimode laser pulse” is greater than the corresponding shift and width for a case of the “atom- single-mode pulse” (the Lorenz pulse model) interaction. From the physical point of view it is naturally provided by action of the photon-correlation effects and influence of the laser pulse multi-modity.

(Invited) Rate-Determining Step for Oxygen Reduction Reaction on Oxide Cathode in SOFC and Its Interpretation Based on Band Energy Diagram

It is well known that the rate-determining step (RDS) of highly reactive oxide cathodes like La1-xSrxCoO3 (LSC), La1-xSrxCo1-yFeyO3 (LSCF), and Ba1-xSrxCo1-yFeyO3 (BSCF), for solid oxide fuel cells (SOFCs) is the surface reaction of oxygen reduction reaction (ORR), shown as 1/2O2(g) + Vö -> Oo + 2h, while its elementary step is still under discussion to date. The authors focus on the surface reactivity, defined as interfacial conductivity, σe, which is inverse of area-specific resistance, using dense thin film cathode. In the present study, σe was estimated using conventional triple-electrode cells composed of thin dense cathodes with additional thin surface modified layer, either polycrystalline pellet of Gd-doped CeO2 (GDC) or single crystalline yttria-stabilized zirconia (YSZ) with GDC barrier layer, and porous platinum anode. Various type of cathodes of LaCoO3 (LC) and LSC with variable (La+Sr)/Co ratios as well as pure and BaPrO3 coated PrOx, which shows stoichiometric composition of Pr6O11 at low temperatures below ≈480˚C in high oxygen pressure regime. The compact cathode films of LC/LSC with typically 500 nm thick coated with surface modification layer of 0, 10, 20 and 40nm are sputtered at RT, followed by a post heat-treatment at 600 ˚C. PrOx is selected to examine the influence of electronic band structure by comparison with LC and LSC systems, since PrOx is known as a mixed Vö and electron conductor in contrast to Vö and electron hole dominance in nonstoichiometric LC and LSCs. The measurements were made from 400 to 600˚C in pure O2 gas flow and the oxygen partial pressure (Po2) dependence of σe was examined at 600˚C from 10-2 to 1 atm. All the impedance data show three distinct semicircles in the impedance spectra, and specific types of resistance, corresponding to the electrolyte impedance, REl, middle frequency impedance, RMF, and low frequency impedance, RLF were extracted for further analyses. Although the origin of RMF is not well understood, it is reasonable to assume as the impedance that occurs out of cathode region; presumably an interfacial impedance between cathode and electrolyte. Although RMF of all the samples does not show the Po2 dependence, RLF clearly exhibits 1/2 power dependence for all the cathode materials from LC/LSC to PrOx system. The σe values of PrOx were 3-5 and 1-2 orders of magnitude lower than LSC and LC, respectively, which were greatly improved by adding merely 1nm thick surface layer of BaPrO3, presumably due to increased surface basicity. The rate equation with square root dependence of Po2 can be interpreted that the RDS is the reaction between the peroxide ion (O2 2-) adsorbed on the oxide cathode surface and Vö diffusing from cathode/electrolyte interface. Therefore, σe is proportional to the probability for bi-dentate immobile O2 2- to meet with Vö, expressed by the concentration product of [O2 2-][Vö]. Poor performance of PrOx can be attributed to a low [O2 2-] due to low basicity. The ab initio molecular dynamics were employed to observe the surface reaction of oxygen molecules on NiO with and without Vö at the surface. NiO was selected as a model system and GGA functional without spin correlation were employed. O2 molecules are adsorbed on NiO surface in step-by-step manner from mono-dentate O2 - to bi-dentate O2 2-. The increase of coordination number of O2 immediately increase the number of donated electron, maintaining one electron per coordination as average, and no further electron donation occurs without a help of Vö. Upon meeting of O2 2- and Vö, O2 2- splits and the third electron is donated to decompose O2 2- into OoX and O- ad. The observation above justify our conclusion from the experiments that the reaction between O2 2- and Vö is the RDS for ORR. A combination of O1s XAS and XPS measurements were made to estimate the electronic structure of oxide cathode materials to understand the energy level alignment between adsorbed O2 2- and cathode oxide surface. A higher EF of cathode material contributes to easy transfer of electrons, which is assumed to be represented, as a zeroth approximation, by the energy separation between EF and the maximum occupied partial DOS of O2p orbital in the valence band, ΔE, which corresponds to the basicity of the oxides. The σe for ORR observed shows excellent proportionality with ΔE, suggesting an important role of O2 2- in the cathodic ORR.