Plane-wave Representation Research Articles

Relaxation-time model for the post-Newtonian Boltzmann equation

The non-equilibrium contributions to the post-Newtonian hydrodynamic equations are determined from a relaxation-time model of the post-Newtonian Boltzmann equation. The Chapman- Enskog method is used to calculate the non-equilibrium distribution function. The components of the energy–momentum tensor are found from the knowledge of the non-equilibrium and the post-Newtonian equilibrium Maxwell–Jüttner distribution functions. The linearized field equations for the mass, momentum and internal energy densities coupled with the three Poisson equations of the post-Newtonian approximation are investigated by considering a plane wave representation of the fields. The constitutive equations for the viscous stress and heat flux vector are obtained and it is shown that the transport coefficients of shear viscosity and heat conductivity do depend on the Newtonian gravitational potential.

Plane wave analysis of the second post-Newtonian hydrodynamic equations

The second post-Newtonian hydrodynamic equations are analyzed within the framework of a plane wave solution. The hydrodynamic equations for the mass and momentum density are coupled with six Poisson equations for the Newtonian and post-Newtonian gravitational potentials. Perturbations of the basic fields and gravitational potentials from a background state by assuming plane wave representations lead to a dispersion relation where the Jeans instability condition emerges. The influence of the first and second post-Newtonian approximations on the Jeans mass is determined. It was shown that the relative difference of the first post-Newtonian and the Newtonian Jeans masses is negative while the one of the second post-Newtonian approximation is positive. The two contributions imply a smaller mass needed for an overdensity to initiate the gravitational collapse than the one given by the Newtonian theory.

A convolutional plane wave model for sound field reconstruction

Spatial sound field interpolation relies on suitable models to conform to available measurements and predict the sound field in the domain of interest. A suitable model can be difficult to determine when the spatial domain of interest is large compared to the wavelength or when spherical and planar wavefronts are present or the sound field is complex, as in the near-field. To span such complex sound fields, the global reconstruction task can be partitioned into local subdomain problems. Previous studies have shown that partitioning approaches rely on sufficient measurements within each domain due to the higher number of model coefficients. This study proposes a joint analysis of all of the local subdomains while enforcing self-similarity between neighbouring partitions. More specifically, the coefficients of local plane wave representations are sought to have spatially smooth magnitudes. A convolutional model of the sound field in terms of plane wave filters is formulated and the inverse reconstruction problem is solved via the alternating direction method of multipliers. The experiments on simulated and measured sound fields suggest that the proposed method retains the flexibility of local models to conform to complex sound fields and also preserves the global structure to reconstruct from fewer measurements.

ASM and finite beam description of the excited leaky Lamb wave fields in a fluid-immersed plate

An angular spectrum method (ASM) full-wave description of stress and energy density in a fluid-immersed plate for the optimization of leaky Lamb wave applications is presented. It models the case when leaky Lamb waves are generated by an external finite transmitter in the immersion fluid, and can calculate the associated stress, energy density, and other field variables within the plate. The normal component of the stress tensor and the energy density are compared against calculations in COMSOL with good agreement, but with some differences due to the two methods. The spatial field of the stress is analyzed using the angular spectrum (plane wave) representation of the stress, which is also used as a reference to exemplify the discrepancies between a pure plane wave approach in leaky Lamb wave applications and the spatial fields that accounts for diffraction and dispersion effects. Comments on the insight that the spatial fields within the plate may provide towards NDT/SHM applications are also given, along with a discussion on why the derivation and implementation of the ASM model is valuable when compared against a benchmarked, ready-to-use software such as COMSOL.

Structural performance of a submerged bottom-mounted compound porous cylinder on the water wave interaction in the presence of a porous sea-bed

Scattering problem of a submerged bottom-mounted compound porous cylinder located on a porous sea-bed is theoretically investigated under the assumption of linear potential flow theory. The compound cylinder is comprised of an impermeable inner cylinder and a porous outer cylinder. The boundary conditions on the porous boundaries follow Darcy's law by assuming fine pores in the porous structure. The whole fluid region is split into three bounded and unbounded sub-regions, within which the individual velocity potentials are found by using the eigenfunction expansion technique. Furthermore, utilization of the matching conditions along the boundaries of individual successive regions leads to a semi-analytical solution of the proposed problem. The impact of the non-dimensional porous-effect parameter of the cylindrical wall, the draft ratio, radius ratio, and the sea-bed porosity on wave loads and free-surface elevation are studied. In addition, the wave power dissipation for the system is calculated by integrating the power absorbed by the outer cylinder porous wall via direct method. Also, the far-field scattering coefficients are obtained with the help of asymptotic forms of Hankel functions in the plane wave representation form. Numerical results for the far-field scattering coefficient and power dissipation are investigated for various parameters. The theoretical model is verified by comparing it with the results of the conventional analytical work and experimental work. The results show that suitable consideration of porosity and structure parameters enhances the efficiency of the proposed compound cylinder in mitigating wave impact. Furthermore, the hydrodynamic wave load acting on the inner and outer cylinders can be reduced by the suitable positioning of the annular spacing of the system, which will provide explicit information for the purpose of engineering design in offshore and coastal regions.

A Fully Polarimetric Multilevel Fast Spectral Domain Algorithm for 3-D Imaging With Irregular Sample Locations

A fully polarimetric frequency-wavenumber domain algorithm for 3-D imaging using the synthetic aperture radar technique with irregular sample locations is introduced. At its core, the algorithm works with a multilevel plane-wave representation and relies on some of the concepts of the multilevel fast multipole method (MLFMM). By utilizing a recursive segmentation scheme, the presented algorithm efficiently handles irregular observation locations, which can vary along all three dimensions in space. The basic idea is to divide the observation region into subdomains of decreasing size, until the calculation of the spectral domain representation of the observation data in the individual subdomains by a discrete Fourier transform (DFT) without further acceleration is feasible. The overall uniformly sampled spectral representation of the observation data is then obtained by hierarchical aggregation of the subdomain spectra. The probe influence is fully compensated by the combined processing of several polarizations and solving small linear systems of equations related to the frequency-wavenumber samples on the coarsest level. The focused image is finally computed by fast Fourier transforms (FFTs). This approach, as opposed to conventional coherent back-projection algorithms (BPAs), allows for a fully polarimetric description of the scattering object and achieves good efficiency without loss of accuracy. To show the effectiveness of the algorithm, imaging results obtained from numerical simulations as well as from the evaluation of measured field data are presented and discussed.

Spatial Characterization of Electromagnetic Random Channels

The majority of stochastic channel models rely on the electromagnetic far-field assumption, which allows to decompose the channel in terms of plane waves. The far-field assumption breaks down in future applications that push towards the electromagnetic near-field region, such as those where the use of electromagnetically large antenna arrays is envisioned. Motivated by this consideration, we show how physical principles can be used to derive a plane-wave scalar channel model that is also valid in the reactive near-field region. Precisely, we show that narrowband wave propagation through a three-dimensional scattered medium can be generally modeled as a linear and space-variant system. We first review the physics principles that lead to a closed-form deterministic plane-wave representation of the channel impulse response. This serves as a basis for deriving a stochastic representation of the channel in terms of statistically independent Gaussian random coefficients for spatially stationary random propagation environments. The very desirable property of spatial stationarity can always be retained in the radiative near-field region by excluding reactive propagation mechanisms confined in close proximity to the source. Remarkably, the provided stochastic representation is directly connected to the Fourier spectral representation of a general stationary spatial random field.

Measuring Shared Electrons in Extended Molecular Systems: Covalent Bonds from Plane-Wave Representation of Wave Function.

In the study of materials and macromolecules by first-principle methods, the bond order is a useful tool to represent molecules, bulk materials and interfaces in terms of simple chemical concepts. Despite the availability of several methods to compute the bond order, most applications have been limited to small systems because a high spatial resolution of the wave function and an all-electron representation of the electron density are typically required. Both limitations are critical for large-scale atomistic calculations, even within approximate density-functional theory (DFT) approaches. In this work, we describe our methodology to quickly compute delocalization indices for all atomic pairs, while keeping the same representation of the wave function used in most compute-intensive DFT calculations on high-performance computing equipment. We describe our implementation into a post-processing tool, designed to work with Quantum ESPRESSO, a popular open-source DFT package. In this way, we recover a description in terms of covalent bonds from a representation of wave function containing no explicit information about atomic types and positions.

Surface wave scattering by multiple flexible fishing cage system

A study of the wave dynamics around a multiple cylindrical fishing cage system is carried out under the assumption of linear water wave theory and small-amplitude wave response. The Fourier–Bessel series expansion of the velocity potential is derived for the regions enclosed under the open-water and cage systems and the immediate vicinity. The scattering between the cages is accounted for by employing Graf's addition theorem. The porous flexible cage system is modeled using Darcy's law and the three-dimensional membrane equation. The edges of the cages are moored along their circumferences to balance its position. The unknown coefficients in the potentials are obtained by employing the matched eigenfunction method. In addition, the far-field scattering coefficients for the entire system are obtained by expanding the Bessel and Hankel functions in the plane wave representation form. Numerical results for the hydrodynamic forces, scattering coefficients, and power dissipation are investigated for various cage and wave parameters. The time simulation for the wave scattering from the cage system is investigated. The study reveals that wave loading on the cage system can be significantly reduced by the appropriate spatial arrangement, membrane tension, and porous-effect parameter. Moreover, the far-field results suggest that the cage system can also be used as a breakwater.

RESEARCH OF THERMOMETRIC MATERIAL Er1-xScxNiSb. I. MODELLING OF PERFORMANCES

Automated The results of modeling performances of the semiconductor solid solution Er1-xScxNiSb are presented, which can be a promising thermometric material for the manufacture of sensitive elements of thermoelectric and electroresistive thermocouples. Fullprof Suite software was used to model the crystallographic characteristics of the Er1-xScxNiSb thermometric material. Modeling of the electronic structure of Er1-xScxNiSb was performed by Coring-Kon-Rostocker methods in the approximation of coherent potential and local density using the exchange-correlation potential Moruzzi-Janak-Williams and Linear Muffin-Tin Orbital in the framework of DFT density functional theory. The Brillouin zone was divided into 1000 k-points, which were used to model energetic performances by calculating DOS. The width of the energy window was 22 eV and was chosen to capture all semi-core states of p-elements. Full potential (FP) was used in the representation of the linear MT orbital in the representation of plane waves. The accuracy of calculating the position of the Fermi level was εF ± 6 meV. To verify the existence of a continuous solid solution, Er1-xScxNiSb substitution, the change in the values of the period of the unit cell a (x) was calculated within the framework of the DFT density functional theory in the range x = 0–1.0. It is presented that the calculated and experimentally obtained dependences of the period of the unit cell a(x) Er1-xScxNiSb are almost parallel, which confirms the correctness of the used tools and the obtained modeling results. To research the possibility of obtaining thermometric material Er1-xScxNiSb in the form of a continuous solid solution was performed modeling of thermodynamic calculations in the approximation of harmonic oscillations of atoms in the theory of DFT density functional for a hypothetical solid solution Er1-xScxNiSb, x = 0–1.0. It is shown that the change in the values of free energy ΔG(x) (Helmholtz potential) passes through the minimum at the concentration x≈0.1 for all temperatures of possible homogenizing annealing of the samples, indicating the solubility limit of Sc atoms in the structure of the ErNiSb compound. The presence of this minimum indicates that the substitution of Er atoms for Sc atoms in the ErNiSb compound is energetically advantageous only up to the concentration of impurity atoms Sc, x≈0.1. At higher concentrations of Sc atoms, x> 0.10, stratification occurs (spinoidal phase decay). It is shown that modeling of the mixing entropy behavior S even at a hypothetical temperature T = 4000 K shows the absence of complete solubility of Sc atoms in Er1-xScxNiSb. To model the energetic and kinetic performances of the semiconductor thermometric material Er1-xScxNiSb, particularly the behavior of the Fermi level F e , bandgap width g e the distribution of the density of electronic states (DOS) and the behavior of its electrical resistance ρ(x, T) is calculated for an ordered variant of the structure in which the Er atoms in position 4a are replaced by Sc atoms. It is shown that the ErNiSb compound is a semiconductor of the electronic conductivity type, in which the Fermi level is located near the level of the conduction band C e . The modeling showed that at higher concentrations of Sc atoms, the number of generated acceptors exceeds the concentration of uncontrolled donors, and the concentration of free holes exceeds the concentration of electrons. Under these conditions, the Fermi level F e approaches, and then the level of the valence band Er1- xScxNiSb crosses: the dielectric-metal conductivity transition occurs. The experiment should change the sign of the thermo-emf coefficient α(x, T) Er1-xScxNiSb from negative to positive, and the intersection of the Fermi level F e and the valence band changes the conductivity from activating to metallic: on the dependences ln(ρ(1/T)) the activation sites disappear, and the values of resistivity ρ increase with temperature.

Measurement reduction in variational quantum algorithms

Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in a Hamiltonian. The number of terms can become overwhelmingly large for problems at the scale of NISQ hardware that may soon be available. We approach this problem from the perspective of contextuality, and use unitary partitioning (developed independently by Izmaylov et al. [J. Chem. Theory Comput. 16, 190 (2020)]) to define variational quantum eigensolver procedures in which additional unitary operations are appended to the ansatz preparation to reduce the number of terms. This approach may be scaled to use all coherent resources available after ansatz preparation. We also study the use of asymmetric qubitization to implement the additional coherent operations with lower circuit depth. We investigate this technique for lattice Hamiltonians, random Pauli Hamiltonians, and electronic structure Hamiltonians. Using this technique, we find a constant factor speedup for lattice and random Pauli Hamiltonians. For electronic structure Hamiltonians, we prove that linear term reduction with respect to the number of orbitals, which has been previously observed in numerical studies, is always achievable. For systems represented on 10--30 qubits, we find that there is a reduction in the number of terms by approximately an order of magnitude. Applied to the plane-wave dual basis representation of fermionic Hamiltonians, however, unitary partitioning offers only a constant factor reduction. Finally, we show that noncontextual Hamiltonians may be reduced to effective commuting Hamiltonians using unitary partitioning.

Mathematical interpretation of seismic wave scattering and refraction on tunnel structures of circular cross-section

Mathematical interpretation of the elastic wave diffraction in circular cylinder coordinates is in the focus of this paper. Firstly, some of the most important properties of Bessel functions, pertinent to the elastic wave scattering problem, have been introduced. Afterwards, basic equations, upon which the method of wave function expansions is established, are given for cylindrical coordinates and for plane-wave representation. In addition, steady-state solutions for the cases of a single cavity and a single tunnel are presented, with respect to the wave scattering and refraction phenomena, considering both incident plane harmonic compressional and shear waves. The last part of the work is dealing with the translational addition theorems having an important role in the problems of diffraction of waves on a pair of circular cylinders.

Massive Rarita-Schwinger field in de Sitter space

We present a covariant quantization of the "massive" spin-${\frac{3}{2}}$ Rarita-Schwinger field in de Sitter (dS) spacetime. The dS group representation theory and its Wigner interpretation combined with the Wightman-G$\mbox{\"{a}}$rding axiomatic and analyticity requirements in the complexified pseudo-Riemanian manifold constitute the basis of the quantization scheme, while the whole procedure is carried out in terms of coordinate-independent dS plane waves. We make explicit the correspondence between unitary irreducible representations (UIRs) of the dS group and the field theory in dS spacetime: by "massive" is meant a field that carries a particular principal series representation of the dS group. We drive the plane-wave representation of the dS massive Rarita-Schwinger field in a manifestly dS-invariant manner. We show that it exactly reduces to its Minkowskian counterpart when the curvature tends to zero as far as the analyticity domain conveniently chosen. We then present the Wightman two-point function fulfilling the minimal requirements of local anticommutativity, covariance, and normal analyticity. The Hilbert space structure and the unsmeared field operator are also defined. The analyticity properties of the waves and the two-point function that we discuss in this paper allow for a detailed study of the Hilbert space of the theory, and give rise to the thermal physical interpretation.

Optical excitations of chlorophyll a and b monomers and dimers.

A necessary first step in the development of technologies such as artificial photosynthesis is understanding the photoexcitation process within the basic building blocks of naturally occurring light harvesting complexes (LHCs). The most important of these building blocks in biological LHCs such as LHC II from green plants are the chlorophyll a (Chl a) and chlorophyll b (Chl b) chromophores dispersed throughout the protein matrix. However, efforts to describe such systems are still hampered by the lack of computationally efficient and accurate methods that are able to describe optical absorption in large biomolecules. In this work, we employ a highly efficient linear combination of atomic orbitals (LCAOs) to represent the Kohn-Sham (KS) wave functions at the density functional theory (DFT) level and perform time-dependent density functional theory (TDDFT) calculations in either the reciprocal space and frequency domain (LCAO-TDDFT-k-ω) or real space and time domain (LCAO-TDDFT-r-t) of the optical absorption spectra of Chl a and b monomers and dimers. We find that our LCAO-TDDFT-k-ω and LCAO-TDDFT-r-t calculations reproduce results obtained with a plane-wave (PW) representation of the KS wave functions (PW-TDDFT-k-ω) but with a significant reduction in computational effort. Moreover, by applying the Gritsenko, van Leeuwen, van Lenthe, and Baerends solid and correlation derivative discontinuity correction Δx to the KS eigenenergies, with both LCAO-TDDFT-k-ω and LCAO-TDDFT-r-t methods, we are able to semiquantitatively reproduce the experimentally measured photoinduced dissociation results. This work opens the path to first principles calculations of optical excitations in macromolecular systems.

The transmission of structured light fields in uniaxial crystals employing the Laguerre-Gaussian mode spectrum.

In the plane-wave angular-spectrum representation, we derive the analytical expressions for any order Laguerre-Gaussian beams propagating along the optical axis of uniaxial crystals. We further prove the orthogonality of propagating modes inside the uniaxial crystals, and investigate the energy efficiency as well as the behavior of spin-orbital coupling. Based on the analytical solutions, we propose a scheme for the transmission of structured light fields through the uniaxial crystals, which firstly decomposes the input fields into LG spectrum and then superposes all OAM components inside crystals to obtain the propagating optical fields. We use the trefoil image as an example to demonstrate the effectiveness of our scheme. The evolution of optical fields and spectra of trefoil image are also studied.

Scalable atomistic simulations of quantum electron transport using empirical pseudopotentials

The simulation of charge transport in ultra-scaled electronic devices requires the knowledge of the atomic configuration and the associated potential. Such “atomistic” device simulation is most commonly handled using a tight-binding approach based on a basis-set of localized orbitals. Here, in contrast to this widely-used tight-binding approach, we formulate the problem using a highly accurate plane-wave representation of the atomic (pseudo)-potentials. We develop a new approach that separately deals with the intrinsic Hamiltonian, containing the potential due to the atomic configuration, and the extrinsic Hamiltonian, related to the external potential. We realize efficient performance by implementing a finite-element like partition-of-unity approach combining linear shape functions with Bloch-wave enhancement functions. We match the performance of previous tight-binding approaches, while retaining the benefits of a plane wave based model. We present the details of our model and its implementation in a full-fledged self-consistent ballistic quantum transport solver. We demonstrate our implementation by simulating the electronic transport and device characteristics of a graphene nanoribbon transistor containing more than 2000 atoms. We analyze the accuracy, numerical efficiency and scalability of our approach. We are able to speed up calculations by a factor of 100 compared to previous methods based on plane waves and envelope functions. Furthermore, our reduced basis-set results in a significant reduction of the required memory budget, which enables devices with thousands of atoms to be simulated on a personal computer.

Near zone scattering and extinction properties of a left handed material cylinder buried in a semi infinite medium with rough interface

ABSTRACTA solution utilizing the spectral plane wave representation of fields (SPRF) combined with the extended boundary condition method (EBCM) is presented to study the scattering and extinction properties of a left handed material cylinder buried in a semi infinite medium with a rough interface. The EBCM is used to evaluate the field transmitted through the interface, which excites the cylinder. The SPRF is used to study the interaction of scattered field from the cylinder with the rough interface. The effect of the negative permittivity and permeability of the cylinder on the far zone scattered field is observed. Further, the near zone scattered field is investigated, which is very helpful to characterize the scenario in which object detection is a challenging task. It is also observed that the electrical size is an important factor affecting the near zone scattered field since the extinction cross section depends upon size.

Scattered field from a PEMC cylinder buried below rough interface using extended boundary condition method

Use of extended boundary condition method (EBCM) and spectral plane wave representation of fields (SPRF) has been done to evaluate the rough surface scattering and the interactions between the perfect electromagnetic conductor (PEMC) cylinder and the rough surface. Expressions of cylindrical waves in terms of plane waves are written in order to calculate the successive reflections and transmission of initial scattered field. First, results obtained by perturbation method and EBCM are compared. Moreover, far zone, near zone and back scattered fields are reported for size and admittance M of the cylinder. Parameter describing the rough surface is also varied to observe the co as well as cross polarized scattered fields. It is observed that the scattering pattern is quite complicated due to many geometrical and physical parameters involved. The effect of parameters on the scattering pattern cannot be described in terms of increase or decrease of the field. Utilizing the formulation, the special case of flat interface and PEC/PMC cylinder can readily be obtained both for transverse magnetic (TM) and transverse electric (TE) polarization states.

Sampling Rules for an Inhomogeneous Plane-Wave Representation of Scattered Fields

Inhomogeneous plane waves (IPWs) based on a linear contour deformation provide an accurate and concise field representation for scattering problems in which source and observation domains are visible within a limited angular sector. Given an error level, we derive closed-form expressions for the truncation limit, the sampling step, and the contour slope that minimize the number of plane waves. A relation is drawn between the required number of plane waves and the degrees of freedom of the field, defined as the minimum number of orthonormal basis functions that represents scattered fields. The sampling rules are then applied to an efficient evaluation of the physical optics radiation integral.

Talbot effect with a grating of period 1 μm

Under coherent plane wave illumination, the classical Talbot effect yields exact replica of the periodic input pattern in planes periodically distributed in the free propagation direction (paraxial regime). But when the period of the object is comparable with the wavelength, the Talbot phenomenon is considered to enter its non-paraxial regime(non-paraxial Talbot effect). In this contribution an experimental and theoretical report of this phenomenon is presented at non-paraxial regime with a amplitude grating of period 1μm, using a plane wave with wavelength of 616nm. The experimental self-images are registered by a confocal microscope and these self-images are contrasted with those obtained by the theory of diffraction in representation of plane waves. Contrary to what was expected, the remarkable results obtained is that it does not present quasi-self-images phenomenon and a detailed discussion of this behavior is included.