Potential Model Theory Research Articles

Comments on the paper "Quantum defect and Rydberg energy level calculations for 85Rb and 87Rb by Weakest Bound Electron Potential Model"

The manuscript highlights some issues in the recently published paper "Quantum defect and Rydberg energy level calculations for 85Rb and 87Rb by Weakest Bound Electron Potential Model". The issues stem from fundamental and conceptual miscues. We resolved them, and new results are presented based on quantum defect theory and the weakest bound electron potential. The necessary input data to calculate the quantum defects in the 85Rb series were obtained from the NIST site. In the first step, the quantum defect theory determined the quantum defect for the series ns, np, and nd. In the second step, the calculated quantum defects were employed in the Weakest Bound Electron Potential Model theory to calculate the energy of 85Rb I levels. The quantum defects and energies of 85Rb I were determined for the series ns, np, and nd. The spectral coefficients were compared with the published work, and the energies with the NIST database showed good agreement. Our results differ significantly from the previously reported findings, highlighting key errors in methodology.

On the study of electrical transport properties of some liquid metals by pseudopotential method

ABSTRACT Our recently evolved pseudopotential is used to study the electrical transport properties such as electrical resistivity ( ρ ), thermal conductivity ( σ ) and thermoelectric power ( TEP ) of some monovalent (Li, Na, K, Rb, Cs), divalent (Mg, Zn, Ca) and polyvalent (Al, Ga, In, Pb, Sn, Bi, Sb) liquid metals. The model potential theory in conjunction with Ziman, mean free path, t-matrix, and Kubo models are implemented in the above-mentioned work for the first time. The Taylor’s local field correction function (T) is taken for observing the exchange and correlation effect with one component plasma (OCP) structure factor method of liquid metals with Hartree dielectric function (H). The presently computed findings are extremely comparable with available data, either theoretical or experimental results that exist in the literature.

A coupled damped harmonic oscillator model for arbitrary arrays of floating cylinders using homotopy methods

A coupled damped harmonic oscillator model is derived for the long-time motion of an array of floating cylinders moving in heave, forced by a prescribed initial displacement. Eigenmodes of the coupled damped harmonic oscillator model are set to be the complex resonances of the corresponding linear potential theory model of the array. Thus, the solution of the coupled damped harmonic oscillator model has the same form as the singularity expansion method. The derivation of the coupled damped harmonic oscillator model is underpinned by a homotopy method to calculate the complex resonances for arbitrary arrays. A recursive homotopy method is used to study the complex resonances as one of the geometrical parameters is varied. The coupled damped harmonic oscillator model is shown to give accurate approximations of the full linear solutions, except for exceptional cases in which additional complex resonances appear.

Anti-plane fracture behavior of n nano-cracks emanating from a magnetoelectrically semi-permeable regular n-polygon nano-hole in magnetoelectroelastic materials

Based on Gurtin–Murdoch surface/interface model and complex potential theory, by constructing a new conformal mapping function, the fracture behavior on n nano-cracks emanating from a n-polygon nano-hole under far-field anti-plane mechanical load, inplane electrical load and magnetic load is studied. The analytical solutions of stress intensity factor, electric displacement intensity factor and magnetic induction intensity factor at the crack tip are given under the boundary conditions of magnetoelectrically semi-permeable. In addition, numerical examples show that when considering the surface effect, the stress field intensity factor, electric displacement intensity factor and magnetic induction intensity factor have obvious size-dependence. The results of this paper show that when the defect size increases to a certain extent, the influence of the surface effect begins to decrease, and finally tends to the results of classical elastic theory.

Observing Second Harmonic Generation and Enhancing Second-Order Nonlinearity from Germanium-on-Insulator

Second-order nonlinear χ2 processes hold the key to realizing various promising classical and quantum applications. Only conventional non-centrosymmetric materials like aluminium nitride (AlN) and lithium niobate (LN) exhibit a strong second-order nonlinearity. While germanium (Ge) has the advantage of mature foundry processing due to its complementary metal-oxide-semiconductor (CMOS) compatibility compared to conventional χ2 materials, it has a weak second-order nonlinearity owning to its inversion symmetry. It is predicted that exploiting micro-scale strain gradients induced by silicon nitride (SiN) stressors can break the inversion symmetry of Ge and enable more efficient second harmonic generation (SHG) in mid-infrared (MIR). We herein demonstrate SHG in visible and telecom S-band ranges by pumping our germanium-on-insulator (GOI) sample with a tunable femtosecond pulse laser. The signature quadratic power dependence curve of SHG has also been experimentally observed. In this report, we also propose a novel approach to breaking the inversion symmetry of Ge, which can amplify its weak second-order nonlinearity. We designed a Ge micro-bridge with a periodically changing nano-scale strain gradient that is orders of magnitude higher than the previously proposed structures utilizing SiN stressors. This results in a 3-orders of magnitude enhancement in χ2 according to both a classic anharmonic model and density potential theory. Our work paves the way toward a CMOS compatible and high χ2 nonlinear material for integrated photonic applications.

Spectroscopic properties of lithium like ions: Prospective elements for quantum computation

Rydberg physics is the most exquisite playground for the exploration of quantum technologies. Therefore, in this spectral investigation based on weakest bound electron potential model theory (WBEPMT). The quantum defects and Rydberg energies of low-lying and high-lying spectral Rydberg energy sequence in the following configurations: 1s2ns2Se1/2 and 1s2np2Po1/2 in Lithium-like ions (Z=4-6) Beryllium (Be II), Boron (B III) and Carbon (C IV) are computed with their radial expected values. Total 43 low-lying energies and quantum defects are computed and compared with 25 low lying radial expected values. The results are in good agreement with the previously published experimental / theoretical results. Based on the good agreement of low-lying data, total 257 new values of high-lying Rydberg energies and quantum defects are computed with 575 radial expected values currently not listed at NIST. The deviation in both sets of data doesn’t exceed 1 cm-1 .

Enhanced predictive corrosion modeling of crevice evolution at e‐coat defects under cyclic climate conditions

AbstractE‐coated galvanized steel sheets are widespread parts of the automotive industry. Hence, the undermining of the organic coating due to defects is a crucial issue. The delamination of an e‐coating is simulated for different cyclic climate conditions using the finite element method to predict the corrosion behavior over several weeks. A semiempirical mixed potential theory model is developed incorporating the time‐of‐wetness, the temperature, and the effect of corrosion products. Furthermore, the spatial orientation of the sheets is considered in the simulation. The trends of experimental delamination widths of corrosion tests are well described by the simulation.

Surface effect on two nanocracks emanating from an electrically semi-permeable regular 2n-polygon nanohole in one-dimensional hexagonal piezoelectric quasicrystals under anti-plane shear

In this paper, the conformal mapping from a regular 2[Formula: see text]-polygon hole with two collinear asymmetric cracks into a circle is constructed. Based on the Gurtin–Murdoch surface/ interface model and complex potential theory, two collinear asymmetric nanocracks emanating from an electrically semi-permeable regular 2[Formula: see text]-polygon nanohole embedded in an infinite one-dimensional hexagonal piezoelectric quasicrystals with surface effect are investigated. The size-dependent stress intensity factors of phonon field and phason field, electric displacement intensity factor at the nanocrack tip are derived for electrically semi-permeable boundary condition. Numerical examples are illustrated to show that the size of the hole, mechanical load, electric load, cracks relative size change with stress intensity factor of phonon field and electric displacement intensity factor. Also analyzed the change of the electric displacement intensity factor with different electric permeability at the nanocrack tip and the dimensionless intensity factor with [Formula: see text].

Theoretical prediction of intrinsic carrier mobility of monolayer C7N6: First-principles study

One porous carbon-nitride monolayer of C7N6, a two-dimensional graphene-derivative material, has been synthesized recently. Herein we performed polarization Wannier interpolation (PWI) calculations to study the inherent mobility of monolayer C7N6 at various temperatures. The electron (hole) mobilities, of 146.77 (79.66) and 140.55 (76.52) cm2V−1s−1 along x and y directions, were calculated at 300 K, respectively. In order to analyze contributing factors of the mobility, we also treated the carrier mobility via deformation potential theory model (DPTM) of both longitudinal acoustic (LA) phonon and optical phonon. Our findings demonstrated that the optical phonon is the dominant scattering process with the electron (hole) mobility of 1.38 × 103 (1.35 × 102) cm2V−1s−1 and 1.36 × 103 (1.30 × 102) cm2V−1s−1 in x and y directions, respectively, via optical phonon of DPTM.

Prediction of theoretical strength of diamond under complex loadings

The strength of diamond under uniaxial loading has been widely studied, but little attention has been paid to its strength under complex loadings. In this study, we investigate the theoretical strength under complex loadings based on a nonequilibrium energy model. Two atomistic modeling approaches based on the empirical potential model and density functional theory are applied. Using these two approaches, we derived the strength, strength contours, and strength surfaces under uniaxial, biaxial, and triaxial loadings along the <100> direction. The results are in good agreement with the results of some previous studies, and they show that diamond has a strong tension–compression strength asymmetry effect.

A unified study of electrical transport properties of some liquid metals by pseudopotential method

A well-recognized local pseudopotential is utilized to study the electrical transport properties such as electrical resistivity (ρ), thermal conductivity (σ) and thermoelectric power (TEP) of some liquid metals. The model potential theory in combination with Ziman, mean free path and Kubo models are implemented in the aforesaid study. The Taylor’s local field correction function is taken for studying the exchange and correlation effect with one component plasma (OCP) structure factor method of liquid metals. The computed data is found highly appreciated order with available either theoretical or experimental outcomes wherever exits.

Anti-plane fracture problem of three nano-cracks emanating from a magnetoelectrically permeable regular triangle nano-hole in magnetoelectroelastic materials

Based on the Gurtin–Murdoch surface/interface model and complex potential theory, by constructing a new conformal mapping, the anti-plane fracture problem of three nano-cracks emanating from a magnetoelectrically permeable triangle nano-hole in magnetoelectroelastic materials with surface effect is studied. The exact solutions of the stress intensity factor, the electric displacement intensity factor, the magnetic induction intensity factor, and the energy release rate are obtained under the boundary conditions of magnetoelectrically permeable and impermeable. The numerical examples show the influence of surface effect on the stress intensity factor, the electric displacement intensity factor, the magnetic induction intensity factor, and the energy release rate under two different boundary conditions. It can be seen that the surface effect leads to the coupling of stress, electric and magnetic field, and with the increase of cavity size, the influence of surface effect begins to decrease until it tends to classical elasticity theory.

Kuramoto-Like Synchronization Mediated through Faraday Surface Waves

A new class of problems in free surface hydrodynamics appeared after the groundbreaking discovery by Yves Couder and Emmanuel Fort. A bouncing droplet in association with Faraday surface waves gives rise to new nonlinear dynamics, in analogy with the pilot-wave proposed by de Broglie. The droplet and the underlying vibrating bath are of silicon oil. A weakly viscous potential theory model should be used. Numerical simulations are presented with one and two bouncing droplets oscillating while confined to their cavities. These oscillators are implicitly coupled by the underlying surface wave field. In certain regimes, the oscillators can spontaneously synchronize, even when placed at a distance. Cavity parameters are varied in order to highlight the sensitive wave-mediated coupling. The present nonlinear wave-mediated oscillator synchronization is more general than that displayed by the celebrated Kuramoto model and therefore of general interest.

Antiplane Fracture Problem of Three Nanocracks Emanating from an Electrically Permeable Hexagonal Nanohole in One-Dimensional Hexagonal Piezoelectric Quasicrystals

Based on the Gurtin-Murdoch surface/interface model and complex potential theory, by constructing a new conformal mapping, the electrically permeable boundary condition with surface effect is established, and the antiplane fracture problem of three nanocracks emanating from a hexagonal nanohole in one-dimensional hexagonal piezoelectric quasicrystals with surface effect is studied. The exact solutions of the stress intensity factor of the phonon field and the phason field, the electric displacement intensity factor, and the energy release rate are obtained under the two electrically permeable and the electrically impermeable boundary conditions. The numerical examples show the influence of surface effect on the stress intensity factors of the phonon field and the phason field, the electric displacement intensity factor, and the energy release rate under the two boundary conditions. It can be seen that the surface effect leads to the coupling of the phonon field, phason field, and electric field, and with the decrease of cavity size, the influence of surface effect is more obvious.

Anti-plane problem of nano-cracks emanating from a regular hexagonal nano-hole in one-dimensional hexagonal piezoelectric quasicrystals**Project supported by the National Key R&D Program of China (Grant No. 2017YFC1405605), the Innovation Youth Fund of the Ocean Telemetry Technology Innovation Center of the Ministry of Natural Resources, China (Grant No. 21k20190088), the Natural Science Foundation of Inner Mongolia, China (Grant No. 2018MS01005), and

By constructing a new conformal mapping function, we study the surface effects on six edge nano-cracks emanating from a regular hexagonal nano-hole in one-dimensional (1D) hexagonal piezoelectric quasicrystals under anti-plane shear. Based on the Gurtin–Murdoch surface/interface model and complex potential theory, the exact solutions of phonon field, phason field and electric field are obtained. The analytical solutions of the stress intensity factor of the phonon field, the stress intensity factor of the phason field, the electric displacement intensity factor and the energy release rate are given. The interaction effects of the nano-cracks and nano-hole on the stress intensity factor of the phonon field, the stress intensity factor of the phason field and the electric displacement intensity factor are discussed in numerical examples. It can be seen that the surface effect leads to the coupling of phonon field, phason field and electric field. With the decrease of cavity size, the influence of surface effect is more obvious.

Water sorption on composite material “zeolite 13X modified by LiCl and CaCl2”

Abstract The article presents the synthesis of composite adsorbents by impregnating zeolite 13X with binary salts (LICl + CaCl2). The phase composition and element content of the composite adsorbent were characterized by X-ray diffraction (XRD) and Inductively coupled plasma (ICP). And its pore structure was discussed through N2 adsorption-desorption analysis. The results show that the formation of the solid solution changes the pore structure of the composite adsorbent which affects its adsorption performance. At the temperature of 25 °C and the relative humidity of 80%, CS6 exhibits the maximum adsorption capacity of 1.1 g/g compared with other adsorbents. The recycling test of CS6 shows that the adsorption capacity is 91.8% of the first time after 12 cycles. Finally, the dynamic adsorption curve and sorption isotherm were fitted by the LDF model and Polanyi Potential Adsorption Theory. It is shown that the simulation curve has good consistency with the measured data.

Simplified mechanical model for seismic design of horizontal storage tank considering soil-tank-liquid interaction

Based on potential fluid theory and soil model theory, this paper derived a simplified mechanical model for horizontal storage tanks considering soil-tank-liquid interaction (STLI), which can be used for seismic design of horizontal storage tanks. Then the paper studied the ground motion response of STLI and Non-STLI under different shear wave velocity. We find the seismic response of the horizontal storage tank is more severe after considering the STLI, and the main control targets such as the base shear force, overturning bending moment and sloshing wave height increase by 25%~58%. Moreover, the effects of soft and medium soft fields are more significant.

Collective dynamics of Zr-based bulk metallic glasses

The collective dynamics for the longitudinal as well as the transverse modes of the phonon eigenfrequencies are carried out for three Zr-based bulk metallic glasses (BMGs) in the present paper by employing pseudopotential theory. The theoretical phonon models proposed by Hubbard-Beeby (HB), Takeno-Goda (TG) and Bhatia-Singh (BS) are used to generate the phonon dispersion curves (PDC). The elastic and thermodynamic properties have also been investigated for the said BMGs by using the elastic limit of the phonon dispersion curves. The screening impact was also observed by using five different forms of local field functions due to Hartree (H), Taylor (T), Ichimaru and Utsumi (IU), Faridet al. (F) and Sarkaret al. (S) for the aforesaid properties. The derived results are seen to be in qualitative agreement with the available experimental and theoretically calculated data, as they confirm the applicability of Shaw's constant core model potential and self-consistent phonon theory for such studies.

Rydberg energy levels and quantum defects of B II, Ge II, Si II of subgroups III and IV

Theoretical computations of Rydberg energy levels series and atomic lifetimes for singly ionized boron (B II), silicon (Si II), and germanium (Ge II) have been performed. In the theoretical computation weakest bound electron potential model theory (WBEPMT) is employed. Regularities of changes in quantum defects for the following Rydberg states series: 2sns (1S0), 2snp ([Formula: see text]), 2snf ([Formula: see text], [Formula: see text], [Formula: see text]), 2snf ([Formula: see text]) of B II; 3s2ns (2S1/2), 3s2nd (2D3/2,5/2), 3s2nf ([Formula: see text]), 3s2ng (2G7/2,9/2) of Si II; and 4s2nf ([Formula: see text]), 4s2nf ([Formula: see text]), 4s2ng (2G7/2,9/2) of Ge II, up to n = 50 are presented. The atomic lifetimes of the following series: 1s22sns (1S0), 1s22snp ([Formula: see text]), 1s22snd (1D2) of B II; 3s2ns (2S1/2), 3s2nf ([Formula: see text]) of Si II; and 4s2ns (2S1/2) of Ge II are predicted with good accuracy. Some high-lying Rydberg energy levels and atomic lifetimes have been presented for the first time. The series for which Rydberg energy levels are computed in this work are unperturbed series.

Precise Computation of Energy Levels and Radiative Lifetimes in the s, p, d, and f Sequence of Hydrogen Isotope, with Natural Line Widths

Energy levels and Radiative lifetimes in Deuterium for the following: ns 2 S 1/2 (n≥2), np 2 P o (1/2,3/2) (n≥2), nd 2 D (3/2,5/2) (n≥3), and nf 2 F o (5/2,7/2) (n≥4) sequence have been evaluated with uncertainties in energies caused due to uncertainty principal. Theoretical calculations performed utilizing the Weakest Bound Electron Potential Model Theory (WBEPMT). Both sets of data show quite an excellent agreement with the experimental data listed at NIST. This theoretical computation is also a continuation of the work by Raza. S. et al. in Neutral Hydrogen. The high ‘n’ (principal quantum number) values for both sets of data are presented very first time by utilizing WBEPMT. Keywords: Energy levels, Radiative lifetimes, Quantum defects, Weakest bound electron, Natural line width. DOI : 10.7176/JNSR/9-10-07 Publication date :May 31 st 2019