Double Potential Research Articles

Splittings of d8 configurations of late-transition metals with EOM-DIP-CCSD and FSCCSD methods.

Multireference methods are usually required for transition metal systems due to the partially filled d electrons. In this work, the single-reference equation-of-motion coupled-cluster method at the singles and doubles level for double ionization potentials (EOM-DIP-CCSD) is employed to calculate energies of states from the d8 configuration of late-transition metal atoms starting from a closed-shell reference. Its results are compared with those from the multireference Fock-space coupled-cluster method at the CCSD level (FSCCSD) for DIP from the same closed-shell reference. Both scalar-relativistic effects and spin-orbit coupling are considered in these calculations. Compared with all-electron FSCCSD results with four-component Dirac-Coulomb Hamiltonian, FSCCSD with relativistic effective core potentials can provide reasonable results, except for atoms with unstable reference. Excitation energies for states in the (n - 1)d8ns2 configuration are overestimated pronouncedly with these two methods, and this overestimation is more severe than those in the (n - 1)d9ns1 configuration. Error of EOM-CCSD on these excitation energies is generally larger than that of FSCCSD. On the other hand, relative energies of most of the states in the d8 configuration with respect to the lowest state in the same configuration are predicted reliably with EOM-DIP-CCSD, except for the 3P0 state of Hg2+ and states in Ir+. FSCCSD can provide reasonable relative energies for the several lowest states, while its error tends to be larger for higher states.

On the existence and formation of small amplitude electrostatic double‐layer structure in nonthermal dusty plasma

AbstractIn the present article, we studied the effect of nonthermal electrons on the formation and existence of double‐layer structures in a three‐species plasma consisting of positive ions, nonthermal electrons, and immobile negative dust‐charged grains. Employing the reductive perturbations, a modified Korteweg–de Vries (mKdV) type equation is derived for the dust‐ion‐acoustic waves (DIAWs) bearing nonthermality. We found that both positive and negative polarity shock structures (double layer) can exist such that it switches polarity while changing the dust charge concentrations. However, strong nonthemality favours only rarefactive structures irrespective of the ion temperature. It is also found that increasing the nonthermal electron in the system the width of the double layer is increased; furthermore, the shock structure forms with small dust charge concentration. For small ionic temperature, increasing the nonthermal electrons in the system makes the double layer potential to increase; however, for σ = 1 reverse phenomena occurs. Our results are relevant to the shock observations in Q machine experiments and in the ionospheric regime of the earth.

Cosmological consequences of a scalar field with oscillating equation of state: A possible solution to the fine-tuning and coincidence problems

We propose a new dark energy model for solving the cosmological fine-tuning and coincidence problems. A default assumption is that the fine-tuning problem disappears if we do not interpret dark energy as vacuum energy. The key idea to solving the coincidence problem is that the Universe may have several acceleration phases across the whole cosmic history. The specific example we study is a quintessence model with approximately repeated double exponential potential, which only introduces one Planck scale parameter and three dimensionless parameters of order unity. The cosmological background evolution equations can be recast into a four-dimensional dynamical system and its main properties are discussed in details. Preliminary calculations show that our model is able to explain the observed cosmic late-time acceleration.

Singular Integral Operators and Elliptic Boundary-Value Problems. Part I

The monograph consists of three parts. Part I is presented here. In this monograph, we develop a new approach (mainly based on papers of the author). Many results are published for the first time here. Chapter 1 is introductory. It provides the necessary background from functional analysis (for completeness). In this monograph, we mostly use weighted HOlder spaces; they are considered in Chap. 2. Chapter 3 plays the key role: in weighted HOlder spaces, we consider estimates of integral operators with homogeneous difference kernels, covering potential-type integrals and singular integrals as well as Cauchy-type integrals and double layer potentials. In Chap. 4, similar estimates in weighted Lebesgue spaces are proved. Integrals with homogeneous difference kernels will play an important role in Part III of the monograph, which will be devoted to elliptic boundary-value problems. They naturally arise in integral representations of solutions of first-order elliptic systems in terms of fundamental matrices or their parametrices. The investigation of boundary-value problems for second-order and higher-order elliptic equations or systems is reduced to first-order elliptic systems.

Hydration of Nucleobase as Probed by Electron Emission of Uridine-5′-Mono-Phosphate (UMP) in Aqueous Solution Induced by Nitrogen K-Shell Ionization

To identify the precise early radiation processes of DNA lesions, we measure electron kinetic energy spectra emitted from uridine-5′ monophosphate (UMP) in aqueous solution for the photoionization of the N 1s orbital electron and for the following Auger effect using a monochromatic soft X-ray synchrotron radiation at energies above the nitrogen K-shell ionization threshold. The change of photoelectron spectra for UMP in aqueous solutions at different proton concentrations (pH = 7.5 and 11.3) is ascribed to the chemical shift of the N3 nitrogen atom in uracil moiety of canonical and deprotonated forms. The lowest double ionization potentials for aqueous UMP at different pH obtained from the Auger electron spectra following the N 1s photoionization values show the electrostatic aqueous interaction of uracil moiety of canonical (neutral) and deprotonated (negatively charged) forms with hydrated water molecules.

Nanoscale Mapping of the Double Layer Potential at the Graphene-Electrolyte Interface.

The electrical double layer (EDL) governs the operation of multiple electrochemical devices, determines reaction potentials, and conditions ion transport through cellular membranes in living organisms. The few existing methods of EDL probing have low spatial resolution, usually only providing spatially averaged information. On the other hand, traditional Kelvin probe force microscopy (KPFM) is capable of mapping potential with nanoscale lateral resolution but cannot be used in electrolytes with concentrations higher than several mmol/L. Here, we resolve this experimental impediment by combining KPFM with graphene-capped electrolytic cells to quantitatively measure the potential drop across the EDL in aqueous electrolytes of decimolar and molar concentrations with a high lateral resolution. The surface potential of graphene in contact with deionized water and 0.1 mol/L solutions of CuSO4 and MgSO4 as a function of counter electrode voltage is reported. The measurements are supported by numerical modeling to reveal the role of the graphene membrane in potential screening and to determine the EDL potential drop. The proposed approach proves to be especially useful for imaging spatially inhomogeneous systems, such as nanoparticles submerged in an electrolyte solution. It could be suitable for in operando and in vivo measurements of the potential drop in the EDL on the surfaces of nanocatalysts and biological cells in equilibrium with liquid solutions.

Spectral Properties of the Neumann–Poincaré Operator in 3D Elasticity

AbstractWe consider the adjoint double layer potential (Neumann–Poincaré (NP)) operator appearing in 3-dimensional elasticity. We show that the recent result about the polynomial compactness of this operator for the case of a homogeneous media follows without additional calculations from previous considerations by Agranovich et al., based upon pseudodifferential operators. Further on, we define the NP operator for the case of a nonhomogeneous isotropic media and show that its properties depend crucially on the character of nonhomogeneity. If the Lamé parameters are constant along the boundary, the NP operator is still polynomially compact. On the other hand, if these parameters are not constant, two or more intervals of continuous spectrum may appear, so the NP operator ceases to be polynomially compact. However, after a certain modification, it becomes polynomially compact again. Finally, we evaluate the rate of convergence of discrete eigenvalues of the NP operator to the tips of the essential spectrum.

On the double layer potential ansatz for the n-dimensional Helmholtz equation with Neumann condition

In the present paper we consider the Neumann problem for the ndimensional Helmholtz equation. In particular we deal with the problem of representability of the solutions by means of double layer potentials.

Electrokinetic ion transport and fluid flow in a pH-regulated polymer-grafted nanochannel filled with power-law fluid.

In this article, we have discussed extensively electrokinetic ion transport and fluid flow through a slit polymer-grafted nanochannel filled with power-law fluid. The rigid walls of the channel are coated with the ion and fluid penetrable polymer layer containing a pH-regulated zwitterionic functional group (e.g., succinoglycan). The mathematical model is based on the non-linear Poisson-Boltzmann equation for electric double layer potential and the flow field within the polymer layer is governed by a modified Darcy-Brinkman equation; the Cauchy momentum equation governs the fluid flow outside of the polymer layer along with the equation of continuity for incompressible fluid. In order to consider a wide range of pertinent parameters, we adopt a finite difference based numerical tool to solve the coupled set of governing equations. We have analyzed several interesting features of electrokinetic transport phenomena through such a polymer-grafted nanochannel for a wide range of electrostatic and hydrodynamic properties of the polymer layer, parameters describing the non-Newtonian rheology of the background fluid, and the pH and concentration of the bulk electrolyte. In addition, we have also illustrated the ionic current across the undertaken nanochannel and observed that it can be either cation selective, anion selective or non-selective, depending on the critical choice of the pertinent parameters.

The carbon and oxygen K-edge NEXAFS spectra of CO.

We present and analyze high resolution near edge X-ray absorption fine structure (NEXAFS) spectra of CO+ at the carbon and oxygen K-edges. The spectra show a wealth of features that appear very differently at the two K-edges. The analysis of these features can be divided into three parts; (i) repopulation transition to the open shell orbital - here the C(1s) or O(1s) to 5σ transition, where the normal core hole state is reached from a different initial state and different interaction than in X-ray photoelectron spectroscopy; (ii) spin coupled split valence bands corresponding to C(1s) or O(1s) to π* transitions; (iii) remainder weak and long progressions towards the double ionization potentials containing a manifold of peaks. These parts, none of which has correspondence in NEXAFS spectra of neutral molecules, are dictated by the localization of the singly occupied 5σ orbital, adding a dimension of chemistry to the ionic NEXAFS technique.

Projector augmented-wave method: an analysis in a one-dimensional setting

In this article, a numerical analysis of the projector augmented-wave (PAW) method is presented, restricted to the case of dimension one with Dirac potentials modeling the nuclei in a periodic setting. The PAW method is widely used in electronic ab initio calculations, in conjunction with pseudopotentials. It consists in replacing the original electronic Hamiltonian H by a pseudo-Hamiltonian HPAW via the PAW transformation acting in balls around each nuclei. Formally, the new eigenvalue problem has the same eigenvalues as H and smoother eigenfunctions. In practice, the pseudo-Hamiltonian HPAW has to be truncated, introducing an error that is rarely analyzed. In this paper, error estimates on the lowest PAW eigenvalue are proved for the one-dimensional periodic Schrödinger operator with double Dirac potentials.

Deep quench approximation and optimal control of general Cahn–Hilliard systems with fractional operators and double obstacle potentials

<p style='text-indent:20px;'>Recently, the authors derived well-posedness and regularity results for general evolutionary operator equations having the structure of a Cahn–Hilliard system. The involved operators were fractional versions in the spectral sense of general linear operators that have compact resolvents and are densely defined, unbounded, selfadjoint, and monotone in a Hilbert space of functions. The class of admissible double-well potentials driving the phase separation process modeled by the Cahn–Hilliard system included polynomial, logarithmic, and double obstacle nonlinearities. In a subsequent paper, distributed optimal control problems for such systems were investigated, where only differentiable polynomial and logarithmic potentials were admitted. Existence of optimizers and first-order optimality conditions were derived. In this paper, these results are complemented for nondifferentiable double obstacle nonlinearities. It is well known that for such nonlinearities standard constraint qualifications to construct Lagrange multipliers cannot be applied. To overcome this difficulty, we follow the so-called "deep quench" method, which has proved to be a powerful tool in optimal control problems with double obstacle potentials. We give a general convergence analysis of the deep quench approximation, including an error estimate, and demonstrate that its use leads to meaningful first-order necessary optimality conditions.

An analysis of cross-sections of 9Be+28Si interaction in the framework of the double-folding model

In this paper the experimental data on the differential cross sections for elastic scattering of 9 Be ions on 28 Si nucleus at the energies of the incident nucleus ranging from 12 to 201.6 MeV were analyzed in the framework of the double folding model using the Paris NN-potential CDM3Y. A good agreement with the experimental angular distributions of differential cross sections for elastic scattering was obtained and the values of the total reaction cross sections were calculated. When the double folding potential was used as real and imaginary parts, no manifestation of the threshold anomaly was detected. The reason for such a behavior of the potential can be explained by the presence of break up and/or transfer channels at low energies.

Excited states via coupled cluster theory without equation-of-motion methods: Seeking higher roots with application to doubly excited states and double core hole states.

In this work, we revisited the idea of using the coupled-cluster (CC) ground state formalism to target excited states. Our main focus was targeting doubly excited states and double core hole states. Typical equation-of-motion (EOM) approaches for obtaining these states struggle without higher-order excitations than doubles. We showed that by using a non-Aufbau determinant optimized via the maximum overlap method, the CC ground state solver can target higher energy states. Furthermore, just with singles and doubles (i.e., CCSD), we demonstrated that the accuracy of ΔCCSD and ΔCCSD(T) (triples) far surpasses that of EOM-CCSD for doubly excited states. The accuracy of ΔCCSD(T) is nearly exact for doubly excited states considered in this work. For double core hole states, we used an improved ansatz for greater numerical stability by freezing core hole orbitals. The improved methods, core valence separation (CVS)-ΔCCSD and CVS-ΔCCSD(T), were applied to the calculation of the double ionization potential of small molecules. Even without relativistic corrections, we observed qualitatively accurate results with CVS-ΔCCSD and CVS-ΔCCSD(T). Remaining challenges in ΔCC include the description of open-shell singlet excited states with the single-reference CC ground state formalism as well as excited states with genuine multireference character. The tools and intuition developed in this work may serve as a stepping stone toward directly targeting arbitrary excited states using ground state CC methods.

Tunneling through Double Electrostatic Barriers in Strained Graphene

Herein, the electronic structure of Dirac fermions scattered by double barrier potential in graphene under strain effect is studied. It is shown that traction and compression strains can be used to generate fermion beam collimation, 1D transport channels, surface states, and confinement. The corresponding transmission probability and conductance at zero temperature are calculated and their numerical computations are performed taking into account various alterations of physical parameters, enabling the analysis of some important features of the system. It is shown that the transmissions satisfy three symmetry relations depending on the incident angle and strain parameters, while the conductance is reduced compared to that of the strained single barrier.

Current-Free Electric Double Layer in a Small Collisional Plasma Thruster Nozzle Simulation

A computational fluid dynamics and plasma model of a collisional (∼ a few Torr) radiofrequency (at 13.56 MHz) argon plasma capacitively coupled in a converging-diverging nozzle (applied to the optimisa- tion of electrothermal plasma thrusters for space use) shows the formation of a strong stationary current-free double layer (CFDL) at the 1.5 mm diameter nozzle throat for a downstream pressure of ∼ 0.1 Torr. The cycle average magnitude of the double layer potential is ∆ΦDL = 77 V and the electron temperature at the high potential edge of the double layer is kBTe = 2.64eV, yielding a strength of ∆ΦDL/(kBTe) ∼ 30. The double layer is 1.2 mm wide which corresponds to ∼ 90 Debye lengths. The axial electric field of the double layer accelerates ions along the nozzle to a maximum drift velocity of 17 km s−1, about 3.3 times the ion sound speed, and their kinetic energy is transferred to neutrals by ion-neutral charge exchange col- lisions. The ion transit time τi through the potential structure spontaneously forming at the nozzle throat is about 5 times the radiofrequency excitation period τRF. These findings are discussed in the broader context of double layer physics and the dynamics of their formation as well as in the context of electrothermal thruster optimisation in which neutral propellant heating via ion-neutral charge exchange collisions is the main source of thrust.

Millimeter-wave spectroscopy of HDC=CH.

Rotational transitions of the mono(β)-deuterated vinyl radical, HDC=CH, produced in a supersonic jet expansion by the ArF excimer laser photolysis, were observed by millimeter-wave spectroscopy. The b-type rotational transitions together with the weak a-type transitions were observed only for the lower component of the tunneling doublet, and no tunneling-rotation transitions connecting the lower and upper components were observed, suggesting that state mixing between the two components is negligibly small. The derived molecular constants such as the A rotational constant, Fermi contact interaction constants, and magnetic dipolar interaction constants indicate that the carrier of the observed spectrum is the trans-form of HDC=CH isomers, where the α-proton is located on the opposite side of the β-deuteron. The present conclusion of the trans-form of HDC=CH was also supported by the ab initio calculation in the CCSD(T)/cc-pVTZ level since the trans-form is calculated to be located by 30.04 cm-1 lower than the cis-form due to the difference in the zero point energy. As a result, the tunneling components in the ground state of HDC=CH behave as two different isomers localized at the trans- and cis-wells of the asymmetric double minimum potential. Observed hyperfine constants for HDC=CH were compared with those for H2C=CH to be consistent with each other.

About Three Dimensional Jump Boundary Value Problems for the Laplacian

The conditions of well-posed solvability of searched function and its normal derivative three dimensional jump problem for the Laplacian and equivalent to them integral equation system for the sum of the simple and double layer potentials are determined in the Hilbert space, element of which as well as their normal derivatives have the jump through boundary surface.

An algebraic approach to calculate Franck–Condon factors

An algebraic approach based on unitary algebras to calculate Franck–Condon factors (FCF’s) is presented. The method is based on the unitary group approach, which consists in adding a scalar boson to the $$\nu $$-D harmonic oscillator space, taking advantage of the transformation brackets connecting the energy, coordinate and momentum representations. In this scheme the solutions are given in terms of an expansion of harmonic oscillator functions. In this way the overlaps are expressed in terms of simple scalar product of the eigenvectors. As a benchmark to illustrate our approach the case of two 1D-Morse potentials is presented. Discussions concerned with both non-Condon contributions and the harmonic limit are included. FCF’s involving the 1D-Morse and asymmetric double Morse potentials are also considered. As an application, the FCF’s involving the S–S stretching in the $$\hbox {S}_2\hbox {O}$$ molecule are described in terms of two Morse potentials.

Optical solitons and stability analysis with coupled nonlinear schrodinger’s equations having double external potentials

We consider coupled nonlinear Schrodinger equation (CNLSE) of the Gross-Pitaevskii-type, with linear mixing and nonlinear cross-phase modulation. Motivated by the study of matter waves in Bose-Einstein condensates and multicomponent (vectorial) nonlinear optical systems, we investigate the eigenvalue problem of the CNLSE with double external potentials in a self-defocusig Kerr medium. For this system, we obtain different kinds of wave structures induced by two injected beams, of physical relevance in nonlinear optics and Bose-Einstein condensation. Exact solutions are found by the extended unified method. The linear stability of these solutions is analyzed through the formulation of an eigenvalue problem. The spectral problem is constructed by perturbing the frequency of stationary solutions and by linearizing the resulting equations near the stationary (or steady) states. Our study may simulate experimental work on multiple injected laser beams in a medium with Kerr-type nonlinearity.