Eikonal Approximation for Coupled Equations for Multichannel Scattering

A new dynamical theory has been developed based on Yoshioka's coupled equations for describing inelastic electron scattering in thin crystals. Compared to existing theories, the primary advantage of this theory is that the incoherent summation of the diffracted intensities contributed by electrons after exciting vast numbers of different excited states has been evaluated before any numerical calculation. An additional advantage is that the phase correlations of atomic vibrations are considered, so that full lattice dynamics can be combined in the phonon scattering calculation. The new theory has been proven to be equivalent to the inelastic multislice theory, and has been applied to calculate energy-filtered diffraction patterns and images formed by phonon, single electron and valence scattered electrons.A calculated diffraction pattern of elastic and phonon scattered electrons for a parallel incident beam case is in agreement with the one observed (Fig. 1), showing thermal diffuse scattering (TDS) streaks and Kikuchi pattern.

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COUPLED EQUATIONS OF MODULATED PHOTOTHERMAL EFFECTS, HYPOTHESES AND SOLUTIONS

Le Journal de Physique Colloques ◽

10.1051/jphyscol:1983601 ◽

1983 ◽

Vol 44 (C6) ◽

pp. C6-3-C6-8 ◽

Cited By ~ 5

Author(s):

F. Lepoutre

Keyword(s):

Coupled Equations ◽

Photothermal Effects

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Ciliary Flow of Casson Nanofluid with the Influence of MHD having Carbon Nanotubes

Current Nanoscience ◽

10.2174/1573413716999201015090335 ◽

2020 ◽

Vol 16 ◽

Author(s):

Adel Alblawi ◽

Saba Keyani ◽

S. Nadeem ◽

Alibek Issakhov ◽

Ibrahim M. Alarifi

Keyword(s):

Carbon Nanotubes ◽

Velocity Profile ◽

Pressure Gradient ◽

Volume Fraction ◽

Solid Volume Fraction ◽

Pressure Rise ◽

Shear Stresses ◽

Left Wall ◽

Coupled Equations ◽

The Right

Objective: In this paper, we consider a model that describes the ciliary beating in the form of metachronal waves along with the effects of Magnetohydrodynamic fluid over a curved channel with slip effects. This work aims at evaluating the effect of Magnetohydrodynamic (MHD) on the steady two dimensional (2-D) mixed convection flow induced in carbon nanotubes. The work is done for both the single wall nanotube and multiple wall nanotube. The right wall and the left wall possess a metachronal wave that is travelling along the outer boundary of the channel. Methods: The wavelength is considered as very large for cilia induced MHD flow. The governing linear coupled equations are simplified by considering the approximations of long wavelength and small Reynolds number. Exact solutions are obtained for temperature and velocity profile. The analytical expressions for the pressure gradient and wall shear stresses are obtained. Term for pressure rise is obtained by applying Numerical integration method. Results: Numerical results of velocity profile are mentioned in a table form, for various values of solid volume fraction, curvature, Hartmann number [M] and Casson fluid parameter [ζ]. Final section of this paper is devoted to discussing the graphical results of temperature, pressure gradient, pressure rise, shear stresses and stream functions. Conclusion: Velocity profile near the right wall of the channel decreases when we add nanoparticles into our base fluid, whereas an opposite behaviour is depicted near the left wall due to ciliated tips whereas the temperature is an increasing function of B and ߛ and decreasing function of ߶.

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Novel semi-analytical optoelectronic modeling based on homogenization theory for realistic plasmonic polymer solar cells

Scientific Reports ◽

10.1038/s41598-021-82525-5 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Zahra Arefinia ◽

Dip Prakash Samajdar

Keyword(s):

Solar Cells ◽

Active Layer ◽

Analytical Modeling ◽

High Efficiency ◽

Polymer Solar Cells ◽

Scattered Light ◽

Homogenization Theory ◽

Computational Time ◽

Coupled Equations ◽

Long Time

AbstractNumerical-based simulations of plasmonic polymer solar cells (PSCs) incorporating a disordered array of non-uniform sized plasmonic nanoparticles (NPs) impose a prohibitively long-time and complex computational demand. To surmount this limitation, we present a novel semi-analytical modeling, which dramatically reduces computational time and resource consumption and yet is acceptably accurate. For this purpose, the optical modeling of active layer-incorporated plasmonic metal NPs, which is described by a homogenization theory based on a modified Maxwell–Garnett-Mie theory, is inputted in the electrical modeling based on the coupled equations of Poisson, continuity, and drift–diffusion. Besides, our modeling considers the effects of absorption in the non-active layers, interference induced by electrodes, and scattered light escaping from the PSC. The modeling results satisfactorily reproduce a series of experimental data for photovoltaic parameters of plasmonic PSCs, demonstrating the validity of our modeling approach. According to this, we implement the semi-analytical modeling to propose a new high-efficiency plasmonic PSC based on the PM6:Y6 PSC, having the highest reported power conversion efficiency (PCE) to date. The results show that the incorporation of plasmonic NPs into PM6:Y6 active layer leads to the PCE over 18%.

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Gravitational and Electromagnetic Perturbations of a Charged Black Hole in a General Gauge Condition

Particles ◽

10.3390/particles4020012 ◽

2021 ◽

Vol 4 (2) ◽

pp. 106-128

Author(s):

Claudia Moreno ◽

Juan Carlos Degollado ◽

Darío Núñez ◽

Carlos Rodríguez-Leal

Keyword(s):

Black Hole ◽

Scalar Function ◽

Gauge Condition ◽

Fluid Distribution ◽

Electromagnetic Signal ◽

Charged Fluid ◽

Coupled Equations ◽

Electromagnetic Signals ◽

Limiting Case ◽

Weyl Scalar

We derive a set of coupled equations for the gravitational and electromagnetic perturbation in the Reissner–Nordström geometry using the Newman–Penrose formalism. We show that the information of the physical gravitational signal is contained in the Weyl scalar function Ψ4, as is well known, but for the electromagnetic signal, the information is encoded in the function χ, which relates the perturbations of the radiative Maxwell scalars φ2 and the Weyl scalar Ψ3. In deriving the perturbation equations, we do not impose any gauge condition and as a limiting case, our analysis contains previously obtained results, for instance, those from Chandrashekhar’s book. In our analysis, we also include the sources for the perturbations and focus on a dust-like charged fluid distribution falling radially into the black hole. Finally, by writing the functions on the basis of spin-weighted spherical harmonics and the Reissner–Nordström spacetime in Kerr–Schild type coordinates, a hyperbolic system of coupled partial differential equations is presented and numerically solved. In this way, we completely solve a system that generates a gravitational signal as well as an electromagnetic/gravitational one, which sets the basis to find correlations between them and thus facilitates gravitational wave detection via electromagnetic signals.

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Calculation of charge form factor of elastic electron scattering based on Skyrme force and relativistic eikonal approximation

International Journal of Modern Physics E ◽

10.1142/s0218301319500150 ◽

2019 ◽

Vol 28 (03) ◽

pp. 1950015

Author(s):

Xiaoyong Guo ◽

Zaijun Wang ◽

Tianjing Li ◽

Jian Liu

Keyword(s):

Electron Scattering ◽

Mean Field ◽

Form Factors ◽

Eikonal Approximation ◽

Skyrme Force ◽

Elastic Electron ◽

Elastic Electron Scattering ◽

Charge Form ◽

Relativistic Treatment ◽

Rmf Model

We construct a scheme to calculate the charge form factors for the elastic electron scattering. Our calculation is based on the relativistic eikonal approximation and the Skyrme–Hartree–Fock equation. To perform our calculation and benchmark the results, eight model nuclei with available experimental data: [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] are considered. For the comparison, the charge form factors calculated by the relativistic mean-field (RMF) model are also provided. Parameter set SLy5 is utilized for the Skyrme force, and the set NL3 is applied for the RMF model. It has been confirmed that combining of a nonrelativistic treatment for the target nucleus with a relativistic treatment for the incident electron may work better to reach highly descriptive and predictive results similar to the pure relativistic treatment. The results of this work are also useful for future experiments to test different inputs of densities for a specific nucleus.

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Laminar condensation on a moving drop. Part 1. Singular perturbation technique

Journal of Fluid Mechanics ◽

10.1017/s0022112084000288 ◽

1984 ◽

Vol 139 ◽

pp. 105-130 ◽

Cited By ~ 27

Author(s):

J. N. Chung ◽

P. S. Ayyaswamy ◽

S. S. Sadhal

Keyword(s):

Singular Perturbation ◽

Perturbation Technique ◽

Continuous Phase ◽

Transport Processes ◽

Forced Flow ◽

Saturated Steam ◽

Singular Perturbation Technique ◽

Spherical Drop ◽

Coupled Equations ◽

Induced Velocity

In this paper, laminar condensation on a spherical drop in a forced flow is investigated. The drop experiences a strong, radial, condensation-induced velocity while undergoing slow translation. In view of the high condensation velocity, the flow field, although the drop experiences slow translation, is not in the Stokes-flow regime. The drop environment is assumed to consist of a mixture of saturated steam (condensable) and air (non-condensable). The study has been carried out in two different ways. In Part 1 the continuous phase is treated as quasi-steady and the governing equations for this phase are solved through a singular perturbation technique. The transient heat-up of the drop interior is solved by the series-truncation numerical method. The solution for the total problem is obtained by matching the results for the continuous and dispersed phases. In Part 2 both the phases are treated as fully transient and the entire set of coupled equations are solved by numerical means. Validity of the quasi-steady assumption of Part 1 is discussed. Effects due to the presence of the non-condensable component and of the drop surface temperature on transport processes are discussed in both parts. A significant contribution of the present study is the inclusion of the roles played by both the viscous and the inertial effects in the problem treatment.

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