Wave Calculations Research Articles

Effect of Exchange and Absorption Potential in the Distorted Wave Calculation of Electron Impact Excitation of Auto Ionizing State of Rubidium

A thesis is submitted in the partial fulfillment of the requirements for the award of the degree of Masters of Sciencein the School of Pure and Applied Sciences of Kenyatta University September, 2017

Extraction of gravitational-wave energy in higher dimensional numerical relativity using the Weyl tensor

Gravitational waves are one of the most important diagnostic tools in the analysis of strong-gravity dynamics and have been turned into an observational channel with LIGO’s detection of GW150914. Aside from their importance in astrophysics, black holes and compact matter distributions have also assumed a central role in many other branches of physics. These applications often involve spacetimes with D > 4 dimensions where the calculation of gravitational waves is more involved than in the four dimensional case, but has now become possible thanks to substantial progress in the theoretical study of general relativity in D > 4. Here, we develop a numerical implementation of the formalism by Godazgar and Reall []—based on projections of the Weyl tensor analogous to the Newman–Penrose scalars—that allows for the calculation of gravitational waves in higher dimensional spacetimes with rotational symmetry. We apply and test this method in black-hole head-on collisions from rest in D = 6 spacetime dimensions and find that a fraction of the Arnowitt–Deser–Misner mass is radiated away from the system, in excellent agreement with literature results based on the Kodama–Ishibashi perturbation technique. The method presented here complements the perturbative approach by automatically including contributions from all multipoles rather than computing the energy content of individual multipoles.

Numerical simulation of earthquakes impact on facilities by grid-characteristic method

Numerical modeling of dynamic wave processes in heterogeneous media allows to investigate the earthquake stability of different constructions. The aim of this work is to study the earthquakes’ impact on the ground buildings and underground facilities. The use of grid-characteristic method makes possible to take into account the physics of arising wave processes. The use of systems of hierarchical grids allows to perform a calculation of seismic waves directly from the earthquake source to the ground buildings and underground facilities. The arising area of cracks in this ground building (two-storied houses) at different times from different types of seismic waves is studied. Also the impact of earthquake on the underground facilities is considered. The dynamical arising of cracks and destruction into the underground facilities made from different types of reinforced concrete due to the impact of different types of seismic waves is investigated in this paper. The results demonstrate a possibility of investigation earthquake stability of underground facilities and living buildings using modeling of seismic waves’ propagation directly from the earthquake centers.

Transient calculation of pressure waves in a well induced by tubular expansion

Shell has developed a novel mono-diameter well concept for oil and gas wells as opposed to the traditional telescopic well design. A Mono- diameter well contains multiple casing sections with the same internal diameter. This is achieved by expansion of the casing sections concerned using an expansion cone. Since the well is drilled in stages and casings are inserted to support the open hole, an overlap section between two consecutive (expandable) casings exists which has to be expanded. When the cone enters the overlap section, the expansion force increases dramatically due to the expansion of two casings, cured cement and formation layers. When the cone finalizes the expansion of the overlap section it pops out, the expansion force vanishes and the cone accelerates upwards and it generates an empty volume to be filled by the well fluid (mud). As a result of this, fluid starts to flow through the drill pipe, around the cone and the fluid volume below the cone starts to decompress. This induces a surge pressure wave traveling upwards and a swab pressure wave in the expanded casing traveling downwards. If the pressure difference between outside and inside of the expanded casing exceeds the collapse rating of the casing, the casing will collapse which leads to the loss of the concerned well section. Repair of such a failure costs time and money, therefore this swab pressure must be well predicted to enable the installation process to be designed such that this collapse can be avoided. A model of fully coupled fluid-structure interaction between cone and the well fluid is built for calculating the swab pressure propagating downward and surge pressure propagating upward resulted from transient process occurring after cone pops out. This model has shown an effective tool for predicting the swabbing pressure in field deployments performed lately in Gulf of Mexico and according to its output the suitable cone is selected in order to avoid the casing collapse.

Antenna to Core: A New Approach to RF Modelling

A new technique for the calculation of RF waves in toroidal geometry enables the simultaneous incorporation of antenna geometry, plasma facing components (PFCs), the scrape off-layer (SOL) and core propagation [Shiraiwa et al, “HIS-TORIC: Extending core ICRF wave simulation to include realistic SOL plasmas”, Nucl. Fusion in press 10 (2017)]. The calculation of antenna coupling has been traditionally performed separately from those of core propagation whereas this method allows them to be combined permitting the modelling of such phenomena as waves reflected from plasma-vacuum boundary or cyclotron resonances back to the antenna. Calculations with this technique also naturally capture wave propagation in the SOL and its interactions with non-conforming PFCs permitting self-consistent calculation of core absorption and edge power loss.

Standing Wave Calculation by Acoustic Simulation Tool

Standing Wave Calculation by Acoustic Simulation Tool

The effect of vacancies and the substitution of p-block atoms on single-layer buckled germanium selenide

This paper investigates the effect of point defects of both hole (Ge, Se) and substitution doping of p-block elements, in single-layer b-GeSe, based on first principles plane wave calculations within spin-polarized density functional theory.

Two-dimensional crystal CuS—electronic and structural properties

Covellite is a metallic layered mineral with rather strong interlayer interaction. Recently, synthesis of covellite nanosheets of 3.2 nm thickness was reported (Du et al 2012 Nat. Commun. 3 1177), which raises the question: ‘What is the thinnest possible covellite nanosheet?’ Based on density functional/plane waves calculations, we have shown that graphene-like structure CuS (1L–CuS) is unstable but can be stabilized on a support. Here, however, we demonstrate that the three layered CuS (3L–CuS) with thickness of 0.773 nm (including the atomic radius of the outer plans atoms) is predicted to be intrinsically stable, as confirmed by phonon analysis and Born–Oppenheimer molecular dynamics simulations, with 3L–CuS about 0.15 eV per CuS less stable than the bulk. Interestingly, the electronic band structure shows metallic character with four bands crossing the Fermi level. The nature of chemical bonding is confirmed by a detailed topological analysis of the electron density.

Multiple low-energy excitation states in FeNi disks observed by broadband ferromagnetic resonance measurement

Magnetization excitation in micron sized FeNi disks with different diameters is studied by broadband ferromagnetic resonance (FMR) measurement. Except the main FMR peak, additional adsorption peaks with lower energies are observed. Both micromagnetic simulation and quantum spin wave calculation confirm that the low-energy excitation states are attributed to backward volume magnetostatic (BVM) spin waves. The size dependence of the low-energy states is systematically studied in 50-nm-thick Py disks with diameters larger than 500 nm, and the linewidth of the first BVM state is found to be obviously smaller than that of the FMR absorption peak. Through a quantitative comparison with experimental results, the quantum spin wave calculation is proven to be a reliable method to get the susceptibility and is much faster than the classical micromagnetic simulations.

Adsorption of alkali and alkaline earth metal atoms and dimers on monolayer germanium carbide

First-principles plane wave calculations have been performed to study the adsorption of alkali and alkaline earth metals on monolayer germanium carbide (GeC). We found that the favourable adsorption sites on GeC sheet for single alkali and alkaline earth adatoms are generally different from graphene or germanene. Among them, Mg, Na and their dimers have weakly bounded to GeC due to their closed valence electron shells, so they may have high mobility on GeC. Two different levels of adatom coverage ( and ) have been investigated and we concluded that different electronic structures and magnetic moments for both coverages owing to alkali and alkaline earth atoms have long range electrostatic interactions. Lithium atom prefers to adsorbed on hollow site similar to other group-IV monolayers and the adsorption results in metallisation of GeC instead of semiconducting behaviour. Na and K adsorption can induce 1 total magnetic moment on GeC structures and they have shown semiconductor property which may have potential use in spintronic devices. We also showed that alkali or alkaline earth metal atoms can form dimer on GeC sheet. Calculated adsorption energies suggest that clustering of alkali and alkaline earth atoms is energetically favourable. All dimer adsorbed GeC systems have nonmagnetic semiconductor property with varying band gaps from 0.391 to 1.311 eV which are very suitable values for various device applications.

Spontaneous decays of magneto-elastic excitations in non-collinear antiferromagnet (Y,Lu)MnO3

Magnons and phonons are fundamental quasiparticles in a solid and can be coupled together to form a hybrid quasi-particle. However, detailed experimental studies on the underlying Hamiltonian of this particle are rare for actual materials. Moreover, the anharmonicity of such magnetoelastic excitations remains largely unexplored, although it is essential for a proper understanding of their diverse thermodynamic behaviour and intrinsic zero-temperature decay. Here we show that in non-collinear antiferromagnets, a strong magnon–phonon coupling can significantly enhance the anharmonicity, resulting in the creation of magnetoelastic excitations and their spontaneous decay. By measuring the spin waves over the full Brillouin zone and carrying out anharmonic spin wave calculations using a Hamiltonian with an explicit magnon–phonon coupling, we have identified a hybrid magnetoelastic mode in (Y,Lu)MnO3 and quantified its decay rate and the exchange-striction coupling term required to produce it.

One-step simulation of thermoacoustic waves in two-dimensional enclosures

Abstract This paper reports on a one-step simulation study of the generation and propagation of thermoacoustic waves in a two-dimensional enclosure using a finite-difference lattice-Boltzmann-type method (FDLBM) with a single relaxation time and one equilibrium particle distribution function (EPDF), and a direct aeroacoustic simulation (DAS) technique that solves the primitive Navier–Stokes (N–S) equations. Conventional expansion of the EPDF is not adopted; instead, it is expanded in terms of the particle velocity alone, and the expansion coefficients are determined by requiring the FDLBM to fully recover the N–S equations. The expansion coefficients are found to depend on the flow and thermal properties and their nonlinear interactions. Thus formulated, physical boundary conditions can be specified for the FDLBM. This EPDF has been validated against simple aeroacoustic problems and good agreement with DAS results is obtained. In this paper, the EPDF is further validated against three thermoacoustic cases: 1) a sudden increase of temperature on the left vertical wall of the enclosure; 2) a sudden increase of temperature on the left vertical wall coupled by a sudden decrease of temperature on the right vertical wall in the enclosure; 3) a gradually heated up left vertical wall of the enclosure. Comparisons with DAS simulations show that FDLBM and DAS give essentially identical results; hence, the validity and extent of the EPDF is ascertained for the calculation of these thermoacoustic waves. The FDLBM results are also compared with known theoretical and numerical results. These known solutions are found to be less accurate compared to the FDLBM results. The discrepancy could be attributed to the partially linearized equations solved in the theoretical analysis, and the inadequacy of the numerical scheme to replicate the nonlinear effects accurately in the generation and propagation of thermoacoustic waves.

Enthalpies of Formation of Equiatomic Binary Hafnium Transition Metal Compounds HfM (M=Co, Ir, Os, Pt, Rh, Ru)

In order to investigate Hafnium transition metal alloys HfM (M= Co, Ir, Os,Pt, Rh, Ru) phase diagrams in the region of 50/50% atomic ratio, we performed ab initio Full-Potential Linearized Augmented Plane Waves calculations of the enthalpies of formation of HfM compounds at B2 (CsCl) structure type. The obtained enthalpies of formation are discussed and compared to some of the existing models and available experimental data.

Alkyl Spacer Length and Protonation Induced Changes in Crystalline Psychoactive Arylpiperazine Derivatives: Single-Crystal X-ray, Solid-State NMR, and Computational Studies

A series of new long-chain arylpiperazine derivatives with a flexible alkyl spacer were synthesized. A controversy concerning the role of the spacer, whether it participates actively in binding to 5-HT1A and D2 receptors or it acts as a distance arm, encouraged us to investigate how the molecular and crystal structure changes with the increased length of the alkyl linker (from four CH2 units to six). In this study both the basic active compounds as well as their hydrochlorides were studied. Single crystal X-ray structure analysis with a combination of 13C, 15N solid state NMR spectroscopy supported by gauge-including projector-augmented wave calculations of chemical shielding was used. These studies were aimed to examine, elucidate, and compare molecular conformations and to point out the most important intermolecular interactions leading to large supramolecular synthons formed in crystals of both bases and hydrochlorides.

Spectral element method for elastic and acoustic waves in frequency domain

Numerical techniques in time domain are widespread in seismic and acoustic modeling. In some applications, however, frequency-domain techniques can be advantageous over the time-domain approach when narrow band results are desired, especially if multiple sources can be handled more conveniently in the frequency domain. Moreover, the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain. In this paper, we present a spectral-element method (SEM) in frequency domain to simulate elastic and acoustic waves in anisotropic, heterogeneous, and lossy media. The SEM is based upon the finite-element framework and has exponential convergence because of the use of GLL basis functions. The anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems. Compared with the conventional finite-element method, the number of unknowns in the SEM is significantly reduced, and higher order accuracy is obtained due to its spectral accuracy. To account for the acoustic-solid interaction, the domain decomposition method (DDM) based upon the discontinuous Galerkin spectral-element method is proposed. Numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain.

Six Decades of Spiral Density Wave Theory

The theory of spiral density waves had its origin approximately six decades ago in an attempt to reconcile the winding dilemma of material spiral arms in flattened disk galaxies. We begin with the earliest calculations of linear and nonlinear spiral density waves in disk galaxies, in which the hypothesis of quasi-stationary spiral structure (QSSS) plays a central role. The earliest success was the prediction of the nonlinear compression of the interstellar medium and its embedded magnetic field; the earliest failure, seemingly, was not detecting color gradients associated with the migration of OB stars whose formation is triggered downstream from the spiral shock front. We give the reasons for this apparent failure with an update on the current status of the problem of OB star formation, including its relationship to the feathering substructure of galactic spiral arms. Infrared images can show two-armed, grand design spirals, even when the optical and UV images show flocculent structures. We suggest how the nonlinear response of the interstellar gas, coupled with overlapping subharmonic resonances, might introduce chaotic behavior in the dynamics of the interstellar medium and Population I objects, even though the underlying forces to which they are subject are regular. We then move to a discussion of resonantly forced spiral density waves in a planetary ring and their relationship to the ideas of disk truncation, and the shepherding of narrow rings by satellites orbiting nearby. The back reaction of the rings on the satellites led to the prediction of planet migration in protoplanetary disks, which has had widespread application in the exploding data sets concerning hot Jupiters and extrasolar planetary systems. We then return to the issue of global normal modes in the stellar disk of spiral galaxies and its relationship to the QSSS hypothesis, where the central theoretical concepts involve waves with negative and positive surface densities of energy and angular momentum in the regions interior and exterior, respectively, to the corotation circle; the consequent transmission and overreflection of propagating spiral density waves incident on the corotation circle; and the role of feedback from the central regions.

A new level set numerical wave tank with improved density interpolation for complex wave hydrodynamics

A new three-dimensional numerical wave tank is developed for the calculation of wave propagation and wave hydrodynamics by solving the incompressible Navier–Stokes equations. The free surface is modeled with the level set method based on a two-phase flow approximation, allowing for the simulation of complex phenomena such as wave breaking. The convection terms of the momentum and the level set equations are discretized with the finite difference version of the fifth-order WENO scheme. Time stepping is handled with the third-order TVD Runge–Kutta scheme. The equations are solved on a staggered Cartesian grid, with a ghost cell immersed boundary method for the treatment of irregular cells. Waves are generated at the inlet and dissipated at the numerical beach with the relaxation method. The choice of the numerical grid and discretization methods leads to excellent accuracy and stability for the challenging calculation of free surface waves. The performance of the numerical model is validated and verified through several benchmark cases: solitary wave interaction with a rectangular abutment, wave forces on a vertical cylinder, wave propagation over a submerged bar and plunging breaking waves on a sloping bed.

Band structure calculation of SH waves in nanoscale multilayered piezoelectric phononic crystals using radial basis function method with consideration of nonlocal interface effects

In this paper, the radial basis function (RBF) collocation method based on the nonlocal Eringen piezoelectricity theory is developed to compute the band structures of nanoscale multilayered piezoelectric phononic crystals taking account of nonlocal interface effects. Detailed calculations are performed for anti-plane transverse waves propagating obliquely or vertically in the system. The correctness of the present method is verified by comparing the numerical results with those obtained by applying the transfer matrix method in the case of nonlocal perfect interfaces. The effects of nonlocal interface imperfections are considered by comparing with the nonlocal perfect interfaces. In addition, the influences of the piezoelectric constant, the nanoscale size, the impedance ratio and the incidence angle on the cut-off frequency and band structures are investigated and discussed in detail. Numerical results show that the nonlocal interface discontinuity has more obvious effect on the low-frequency band structures at the microscopic scale than at the macroscopic scale. Furthermore, at the macroscopic scale, the nonlocal interface imperfection has an obvious effect on the high frequency waves, but the effect on the low frequency waves is not obvious, and the nonlocal interface imperfection has no effect on the cut-off frequency at the microscopic scale.

High-temperature superconductivity at high pressures for H3SixP1−x, H3PxS1−x, and H3ClxS1−x

Recent experimental and computational works have established the occurrence of superconducting temperatures, Tc, near 200K when the pressure is close to 200GPa in hydrogen-based sulfur compounds. In this work we investigate the effects of phosphorus and chlorine substitutions of sulfur on Tc, as well as the effect of hydrogen vacancies. In addition, we explore the superconductivity-relevant parameters in the H3SixP1−x system.In executing this work we used the virtual crystal approximation and performed a systematic set of linearized augmented plane wave calculations (LAPW) for many different concentrations of the sulfur component. From the densities of states and the scattering phase shifts at the Fermi level, we calculated electron-ion matrix elements and estimated the electron-phonon coupling constants for different concentrations, as well as Tc. We find that the highest value of Tc=197K corresponds to a phosphorus concentration of x=0.15, or 8.85 valence electrons in a H3P0.15S0.85 alloy. From a detailed analysis of the results given by a Gaspari–Gyorffy (GG) determination of the Hopfield parameter, we identify the role of each term in the GG equation that produce the maximum Tc. In addition, we present a non-orthogonal tight-binding parameterization of the band structure of H3S which fits very well with the LAPW results.

Scaling of collision strengths for highly-excited states of ions of the H- and He-like sequences

Emission lines from highly-excited states (n >= 5) of H- and He-like ions have been detected in astrophysical sources and fusion plasmas. For such excited states, R-matrix or distorted wave calculations for electron-impact excitation are very limited, due to the large size of the atomic basis set needed to describe them. Calculations for n >= 6 are also not generally available. We study the behaviour of the electron-impact excitation collision strengths and effective collision strengths for the most important transitions used to model electron collision dominated astrophysical plasmas, solar, for example. We investigate the dependence on the relevant parameters: the principal quantum number n or the nuclear charge Z. We also estimate the importance of coupling to highly-excited states and the continuum by comparing the results of different sized calculations. We provide analytic formulae to calculate the electron-impact excitation collision strengths and effective collision strengths to highly-excited states (n >= 8) of H- and He-like ions. These extrapolated effective collision strengths can be used to interpret astrophysical and fusion plasma via collisional-radiative modelling.