The Painleve test for a system of coupled equations from nonlinear birefringence

2018 ◽  
Vol 12 (1) ◽  
pp. 27-36
Author(s):  
Tat Leung Yee
Keyword(s):  
Painlevé Test ◽  
Coupled Equations ◽  
Nonlinear Birefringence

Towards quantitative simulations of inelastic electron diffraction patterns and images

1992 ◽  
Vol 50 (2) ◽  
pp. 1170-1171
Author(s):  
Z. L. Wang
Keyword(s):  
Phonon Scattering ◽  
Incident Beam ◽  
Dynamical Theory ◽  
Inelastic Electron ◽  
Additional Advantage ◽  
Coupled Equations ◽  
Atomic Vibrations ◽  
Diffraction Patterns ◽  
Primary Advantage ◽  
The One

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.

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

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 ߶.

scholarly journals Singularity analysis and analytic solutions for the Benney–Gjevik equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Genly Leon ◽  
P. G. L. Leach
Keyword(s):  
Evolution Equations ◽  
Singularity Analysis ◽  
Analytic Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Painlevé Test ◽  
Wave Solutions ◽  
Algebraic Solutions

Abstract We apply the Painlevé test for the Benney and the Benney–Gjevik equations, which describe waves in falling liquids. We prove that these two nonlinear 1 + 1 evolution equations pass the singularity test for the travelling-wave solutions. The algebraic solutions in terms of Laurent expansions are presented.

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

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%.

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

Particles ◽  
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.

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

1984 ◽  
Vol 139 ◽  
pp. 105-130 ◽  
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.

scholarly journals Research on Coupled Dynamic Model of Tracked Vehicles and Its Solving Method

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Yuliang Li ◽  
Chong Tang
Keyword(s):  
Dynamic Performance ◽  
Tractive Force ◽  
Actual Structure ◽  
Discrete Method ◽  
Tracked Vehicles ◽  
Coupled Equations ◽  
Calculation Results ◽  
Dynamic Software ◽  
Multi Body ◽  
Body Dynamic

In order to conveniently analyze the dynamic performance of tracked vehicles, mathematic models are established based on the actual structure of vehicles and terrain mechanics when they are moving on the soft random terrain. A discrete method is adopted to solve the coupled equations to calculate the acceleration of the vehicle’s mass center and tractive force of driving sprocket. Computation results output by the model presented in this paper are compared with results given by the model, which has the same parameters, built in the multi-body dynamic software. It shows that the steady state calculation results are basically consistent, while the model presented in this paper is more convenient to be used in the optimization of structure parameters of tracked vehicles.

Theory of a Time Domain Boundary Element Development for the Dynamic Analysis of Coupled Multiphase Porous Media

2017 ◽  
Vol 08 (03n04) ◽  
pp. 1750007
Author(s):  
Pooneh Maghoul ◽  
Behrouz Gatmiri
Keyword(s):  
Boundary Element ◽  
Time Domain ◽  
Unsaturated Soils ◽  
Water Pressure ◽  
Domain Boundary ◽  
Fundamental Solutions ◽  
Element Formulation ◽  
Inertia Effects ◽  
Coupled Equations ◽  
The Time Domain

This paper presents an advanced formulation of the time-domain two-dimensional (2D) boundary element method (BEM) for an elastic, homogeneous unsaturated soil subjected to dynamic loadings. Unlike the usual time-domain BEM, the present formulation applies a convolution quadrature which requires only the Laplace-domain instead of the time-domain fundamental solutions. The coupled equations governing the dynamic behavior of unsaturated soils ignoring contributions of the inertia effects of the fluids (water and air) are derived based on the poromechanics theory within the framework of a suction-based mathematical model. In this formulation, the solid skeleton displacements [Formula: see text], water pressure [Formula: see text] and air pressure [Formula: see text] are presumed to be independent variables. The fundamental solutions in Laplace transformed-domain for such a dynamic [Formula: see text] theory have been obtained previously by authors. Then, the BE formulation in time is derived after regularization by partial integrations and time and spatial discretizations. Thereafter, the BE formulation is implemented in a 2D boundary element code (PORO-BEM) for the numerical solution. To verify the accuracy of this implementation, the displacement response obtained by the boundary element formulation is verified by comparison with the elastodynamics problem.

Sign in / Sign up

Export Citation Format

Share Document