Element Calculations Research Articles

Molecular QED of coherent and incoherent sum-frequency and second-harmonic generation in chiral liquids in the presence of a static electric field

Coherent second-order nonlinear optical processes are symmetry forbidden in centrosymmetric environments in the electric-dipole approximation. In liquids that contain chiral molecules, however, and which therefore lack mirror image symmetry, coherent sum-frequency generation is possible, whereas second-harmonic generation remains forbidden. Here we apply the theory of molecular quantum electrodynamics to the calculation of the matrix element, transition rate, and integrated signal intensity for sum-frequency and second-harmonic generation taking place in a chiral liquid in the presence and absence of a static electric field, to examine which coherent and incoherent processes exist in the electric-dipole approximation in liquids. Third- and fourth-order time-dependent perturbation theory is employed in combination with single-sided Feynman diagrams to evaluate two contributions arising from static field-free and field-induced processes. It is found that, in addition to the coherent term, an incoherent process exists for sum-frequency generation in liquids. Surprisingly, in the case of dc-field-induced second-harmonic generation, the incoherent contribution is found to always vanish for isotropic chiral liquids even though hyper-Rayleigh second-harmonic generation and electric-field-induced second-harmonic generation are both independently symmetry allowed in any liquid.

PREDICTION OF THE ANTICLASTIC SHAPE CHANGES OF HYBRID COMPOSITE MATERIAL

In search of structurally better and aesthetically more attractive solutions of the erection of various structures, non‐standard anticlastic elements are used more frequently. Therefore preservation of the initial shape of timber composite material sheets by using of reinforced plastic reinforcement has been investigated. Calculation model for determination of the thickness of rational reinforcement anticlastic sheet, which provides change of the original bending radius under variable moisture conditions (Baikovs and Rocens, 2006) within the limits of preferable intervals is developed by authors and using finite element method, calculations and modelling of sheet deformations are carried out with software package ANSYS v.11 (henceforth FEM) and by developed analytical method. Comparative research of the results calculated with the FEM and developed calculation model showed that the difference between results in the three cases investigated, when the composite timber material is reinforced on the top, bottom and both sides for the most of the cases does not exceed 3.3%. An opportunity to provide the original shape of anticlastic timber composite material sheets by using glass fibre reinforced plastic reinforcement under variable moisture conditions and not exceeding the difference of 5% has been demonstrated. Santrauka Ieškant ivairiu konstrukciju statiniu konstrukciškai geresniu ir estetiškai patrauklesniu sprendiniu, dažniausiai naudojami nestandartiniai antiklastiniai elementai. Todel buvo tyrinetas medienos kompozitines medžiagos lakštu pradinio pavidalo išsaugojimas naudojant sustiprinta plastiko armatūra. Skaičiuojamasis modelis, padedantis nustatyti racionaliai armuoto antiklastinio lakšto stori, kuris pakeičia pradini lenkimo spinduli kintamomis dregmes salygomis (Baikovs, Rocens 2006) tarp priimtinu intervalu ribu, yra sukurtas autoriu ir, taikant baigtiniu elementu metoda, lakšto deformaciju skaičiavimai bei modeliavimas atlikti kompiuteriniu programu paketu ANSYS v. 11 (toliau ‐ FEM) ir pagal sukurta analitini metoda. Rezultatu, apskaičiuotu su FEM ir pagal sukurta analitini modeli, lyginamasis tyrimas parode, kad skirtumas tarp triju tirtu atveju, kai medienos kompozitine medžiaga yra armuota viršuje, apačioje ir iš abieju pusiu, rezultatai daugeliu atveju neviršija 3,3%. Parodyta galimybe suteikti originalu pavidala antiklastiniams medienos kompozitiniams lakštams naudojant stiklo pluoštu sustiprinto plastiko armatūra ivairiomis dregmes salygomis ir neviršijant 5% skirtumo.

Reliability Analysis of Structure with Local Sunken Plate

The influence of the local sunken plate on ultimate strength is analyzed, and reliability calculation and sensitivity analysis expressions of the plate element are also given in this paper. Finally, taking a numerical example, the influence of each sunken factor on plate ultimate strength reliability is analyzed. The result indicates that the influence of sunken diameter and sunken depth on reliability is larger. The method that is given in this paper, it is a reference for reasonable maintenance of structure.

Finite Element Analysis and Calculation in Cracks of Stress Intensity Factor of Thick Walled Cylinder

Calculating stress intensity factor is an important task of fracture mechanics, specially in the thick walled cylinder with inner pressure, which has macro crack. The value of KІ is crucial for safety life. The software ANSYS was used to calculate the stress intensity factors of the walled cylinder in this paper. Crack along the axis in the inner face of the tube can be predigested a long plate with a center crack. According to the symmetry of this model, the calculated model was built. The results show that the relative error is under 5% and the method is available to satisfy the precision engineering requirements. In addition, the error and how to reduce it were analyzed.

Synthesis and Characterization of Dinuclear Metal Complexes Stabilized by Tetradentate Schiff Base Ligands

Problem statement: The synthesis, spectroscopic properties and theoretical calculations of acetylacetonimine and acetylacetanilidimine Schiff-base ligands, L1H and L2H, respectively and their dinuclear complexes of the type [M2LnCl2(H2O)2], where n = 1 or 2, M = Co(II), Ni(II), Cu(II), Zn(II) and Cd(II) are described. Approach: The new tetradentate dianion Schiff base ligand which was used as stabilizers for the complexes were prepared by condensation of hydrazine with acetylacetone or acetylacetanilide. The dinuclear complexes of theses ligands were synthesized by treating an ethanolic solution of the prepared ligand with hydrated metal salts in molar ratio of 1:2 (L:M). Results: The ligand and their dinuclear metal complexes were characterized by CHN elemental analysis, FT-IR, UV-Vis, 1HNMR (for the ligands), conductivity, magnetic susceptibility and theoretical calculation by using MM2 modeling program. Conclusion: The reaction of these ligands in a 1:2 (L:M) afford dinuclear M(II) metal complexes with tetrahedral arrangement around Co(II), Zn(II) and Cd(II) and square planar around Ni(II) and Cu(II).

Determining the energy barrier for decay out of superdeformed bands

An asymptotically exact quantum mechanical calculation of the matrix elements for tunneling through an asymmetric barrier is combined with the two-state statistical model for decay out of superdeformed bands to determine the energy barrier (as a function of spin) separating the superdeformed and normal-deformed wells for several nuclei in the 190 and 150 mass regions. The spin-dependence of the barrier leading to sudden decay out is shown to be consistent with the decrease of a centrifugal barrier with decreasing angular momentum. Values of the barrier frequency in the two mass regions are predicted.

Reducing Computational Time of Quantum Diagonalization Calculation for 2-Dimensional Strongly Correlated Systems

We reduce the computational time of the quantum Monte Carlo diagonalization (QMCD) (in De Raedt and von der Linden, Phys. Rev. B 45:8787, 1992) calculation for 2-dimensional strongly correlated systems by using several methods including symmetry operations. First, we subdivide each lattice into spin-up and spin-down lattices separately, thus allowing a bi-partite lattice. A valid base is then obtained from stacking up an up-spin configuration on top of a down-spin configuration. As a consequence, the memory space to be used in saving the trial basis reduces substantially. Secondly, we record the matrix elements of a Hamiltonian in a look-up table when making basis set. Thus we avoid the repeated calculation of the matrix elements of the Hamiltonian during the diagonalization process. Thirdly, by applying symmetry operations to the basis set, the original basis is transformed to a new basis, whose elements are the eigenvectors of the symmetry operations. The ground state wavefunction is constructed from the elements of symmetric (bonding state) basis set. As a result, the total number of bases involved in the quantum Monte Carlo diagonalization calculation is reduced significantly by using symmetry operations.

Calculation of accurate alignment elements of precision chip-resistors

Using conformal mapping method there is obtained analytical relations for form-factor and its dependence on depth of laser slit for accurate alignment elements in form of semicircular, triangle and rectangular chamfered regions in precision film and metal-foil chip-resistors.

Dynamic and quasi-static FE calculation of impact from 9 metre drop of spent fuel transport cask

Abstract The drop from 9 m height onto a rigid target is one of the required proofs of safety for packages of radioactive materials. Direct dynamic finite element method (FEM) calculations and combined two step analytical quasi-static finite element (FE) calculations are both applied for the simulation of a 9 m drop test. This paper gives a comparative example of both approaches for the 9 m side drop simulation of the spent fuel transport cask with wood filled impact limiter. The model for dynamic FEM consists of cask body and impact limiter. Detailed material properties and geometry descriptions from each component of the impact limiter are required. The results (stress fields in the cask body) are obtained directly from the calculation. The combined method provides as intermediate results the force–deformation characteristic of impact limiter. The maximum impact limiter force determined by the law of energy conservation during the drop is then – in a second step – applied on the cask body in a quasi-sta...

Application of FIRE for the calculation of photon matrix elements

The next-to-next-to-leading order (the order αα s 2 ) corrections to the first moment of the polarized virtual photon structure function g 1 γ (x,Q 2, P 2) are studied in perturbative QCD for the kinematical region Λ2 ≪ P 2 ≪ Q 2, where −Q 2 (−P 2) is the mass square of the probe (target) photon and Λ is the QCD scale parameter. In order to evaluate the two-loop Feynman diagrams for the photon matrix element of the gluon operator, I apply the recently developed algorithm FIRE which reduces a complicated sum of scalar Feynman integrals to a linear combination of a few master integrals. The details of the calculation are presented.

Recursive method for calculation of tree-level elements of arbitrary order S matrix in scalar electrodynamics

The possibility of creating a recursive method for the calculation of tree-level elements of an S-matrix based on the functional integration method is considered, as exemplified by scalar electrodynamics. One of the advantages of this method is the gauge invariance of amplitudes provided without additional operations with them.

Numerical study of the extinction matrix for a plate crystal

Energy and polarization characteristics of optical radiation passed through a semitransparent plate crystal with a preset orientation in space are studied numerically within the framework of the method of physical optics. Results of calculations of the extinction matrix elements versus particle size, refractive index, crystal orientation, and incident radiation wavelength (from 0.5 to 15 μm) are presented. It is demonstrated that K 11 , K 12 , and K 34 are most informative among the elements of the extinction matrix. It is established that the first of them is most sensitive to changes in the microphysical and orientational parameters of the particle when the angle of radiation incidence on the plate changes from 0 to 20°, and the nondiagonal elements are most sensitive when the angle of radiation incidence is greater than 40°. The characteristics of the total field scattered near the forward direction are determined. It is established that their dependence on the physical parameters of the crystal is most strong at scattering angles smaller than or equal to 4° and wavelengths from the IR range (in particular, from the atmospheric transparency window).

Computational strategy using improved virtual orbitals to ensure orthogonality of excited states to the ground state and to each other for calculation of transition matrix elements

Computational strategy using improved virtual orbitals to ensure orthogonality of excited states to the ground state and to each other for calculation of transition matrix elements

The construction of symmetry-adapted functions in configuration interaction calculations for molecules with one principal axis of symmetry

A scheme is presented for the automatic generation on the computer of lists of many-electron functions of definite spin and symmetry, for use in configuration interaction calculations of the electronic wave functions of molecules having one principal axis of symmetry. All such linearly independent functions that can be obtained from a given basis set may be generated, or a limit may be put on the number of electron promotions, relative to a ground-state function, to be considered. The many-electron functions are expressed in terms of complex symmetry orbitals, but are generally real, and practically all computations may be performed without the use of complex arithmetic. The calculation of matrix elements of the Hamiltonian for these functions is discussed.

Localized defects in semiconductors

A method of calculating the energies of bound states associated with imperfections described by short-range potentials in semiconductors is presented and applied. The method is based on solid-state scattering theory and involves expansion of physical quantities in terms of the Wannier functions for a many-band system. The properties of Bloch functions and Wannier functions are investigated to enable the numerical computation of matrix elements. Application is made to the neutral vacancy in silicon. A pseudopotential is employed to represent the change in the crystal potential produced by the vacancy. It is found that the vacancy produces a localized state in which low-lying energy bands and interband couplings are important, in contrast to the shallow donor and acceptor states which have been studied in the past.

Analytical evaluation of three-center one-electron integrals of rNYML (θ,ϕ) with slater-type atomic orbitals

Theoretical prediction of molecular properties, such as quadrupole coupling tensor, electron-proton hyperfine interaction, chemical shift, and spin-orbit coupling, requires computation of matrix elements of rNYML, where YML is a spherical harmonic. Formulas for two- and three-center one-electron integrals of rNYML with Slater-type atomic orbitals are derived. Use is made of Fourier-transforms, generalized-function theory, and complex variable theory. The final formulas involve spherical harmonics and functions related to exp (x) and to the exponential integral, but nothing more complicated. Two alternative sets of formulas are given, but only one is valid when N–L is an even, negative integer.

Systematic study of multiquark states:qqq−qq¯configuration

Group theoretic method for the systematic study of five-quark states with meson-baryon ($q\overline{q}\text{\ensuremath{-}}{q}^{3}$) configuration is developed. The calculation of matrix elements of many-body Hamiltonian is simplified by transforming the physical bases (meson-baryon quark cluster bases) to symmetry bases (group chain classified bases), where the fractional parentage expansion method can be used. Three quark models, the Glashow-Isgur naive model, the Salamanca chiral quark model, and the quark delocalization color screening model, are used to show the general applicability of the method and general results of constituent quark models for five-quark states are given. The method is also useful in the study of the five-quark components effect in baryon structure, the calculation of meson-baryon scattering, and the meson-baryon open channel coupling effect on baryon resonances. The physical contents of different model configurations for the same five-quark system can also be compared through the transformation between different physical bases to the same set of symmetry bases.

FT-IR spectra, vibrational assignments, and density functional calculations of imidazo[1,2-a]pyridine molecule and its Zn(II) halide complexes

The geometry, frequency, and intensity of the vibrational bands of imidazo[1,2-a]pyridine (which is abbreviated as impy) were obtained by the density functional theory (DFT) calculations with BLYP, B3LYP, and B3PW91 functionals and 6-31G(d) basis set. The optimized geometric bond lengths and bond angles are in good agreement with the available X-ray data. The infrared spectrum of imidazo[1,2-a]pyridine was computed by the DFT method in order to reproduce the vibrational wavenumbers and intensities with an accuracy, which allows reliable vibrational assignments. Total energy distribution and isotopic shifts have been calculated in order to help for the perfect assignment of the vibrational modes. The zinc halide complexes Zn(impy)2X2 [X = Cl, Br, and I] have also been synthesized. The compounds were characterized using the elemental analysis, FT-IR spectra, and quantum chemical calculations. The geometry optimization of Zn(impy)2X2 yields distorted tetrahedral environment around Zn ion.

Calculation of the 1s–2s two-photon excitation cross-section in atomic hydrogen

The two-photon excitation cross-section of atomic hydrogen is calculated using explicit summation over intermediate states within the framework of dipole approximation. The matrix element for two-photon excitation is transformed into finite sums, consisting of the product of a radial and angular part. Nine intermediate states are employed in the calculation of the transition matrix element. The two-photon excitation cross-section obtained for the transition 1s 2S1/2–2s 2S1/2in atomic hydrogen is a good agreement with the literature.

Mechanism and efficiency of photochemical transformation of ≡SiNNO• radicals grafted to activated Aerosil surface: Calculation of potential energy surface elements for the lower excited state of the radical

Assignment of the bands in the optical absorption spectrum of ≡SiNNO• radicals grafted to activated Aerosil surface was performed. A photochemical transformation mechanism was proposed, and the quantum yields of the reaction of ≡SiNNO• radicals relevant to the long-wavelength absorption band at 77 K were determined in the absence and presence of adsorbed CO2 and SF6 on the surface. For the model radical F3SiNNO•, the parameters characterizing the equilibrium geometry of excited states and the geometry of transition states involved in the reaction were determined by quantum-chemical calculations.