Nonlinear structures: soliton, shocklike and explosive waves in quantum semiconductor plasma

2021 ◽  
Author(s):  
Haifa Al-Yousef
Keyword(s):  
Analytical Procedure ◽  
Integration Method ◽  
Fluid Model ◽  
Three Dimensional ◽  
Semiconductor Plasma ◽  
Direct Integration Method ◽  
Solution Methods ◽  
Gradient Forces ◽  
Quantum Semiconductor ◽  
Nonlinear Solutions

Abstract The properties and conditions for the appearance of some nonlinear waves in a three-dimensional semiconductor plasma are discussed, by studying the described plasma fluid system with quantum gradient forces and degraded pressures. Our analytical procedure is built on the reductive perturbation theory to obtain the Kadomtsev-Petvashvili equation for the fluid model and solving it using the direct integration method and the Bäcklund transform. Through different solution methods we got different nonlinear solutions describing different pulse profiles such as soliton, kink and explosive pulses. This model can be used to identify the potential disturbances in a semiconductor plasma.

scholarly journals Direct integration method in three-dimensional elasticity and thermoelasticity problems for inhomogeneous transversely isotropic solids: governing equations in terms of stresses

2019 ◽  
pp. 102-105
Author(s):  
R. M. Kushnir ◽  
Y. V. Tokovyy ◽  
D. S. Boiko
Keyword(s):  
Stress Tensor ◽  
Integral Equations ◽  
Integration Method ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Solution Technique ◽  
Direct Integration ◽  
Governing Equations ◽  
Direct Integration Method

An efficient technique for thermoelastic analysis of inhomogeneous anisotropic solids is suggested within the framework of three-dimensional formulation. By making use of the direct integration method, a system of governing equations is derived in order to solve three-dimensional problems of elasticity and thermoelasticity for transversely isotropic inhomogeneous solids with elastic and thermo-physical properties represented by differentiable functions of the variable in the direction that is transversal to the plane of isotropy. By implementing the relevant separation of variables, the obtained equations can be uncoupled and reduced to second-kind integral equations for individual stress-tensor components and the total stress, which represents the trace of the stress tensor. The latter equations can be attempted by any of the numerical, analyticalnumerical, or analytical means available for the solution of the second-kind integral equations. In order to construct the solutions in an explicit form, an advanced solution technique can be developed on the basis of the resolvent-kernel method implying the series representation by the recurring kernels, computed iteratively by the original kernel of an integral equation.

scholarly journals Simulation and measurement of air quality in the traffic congestion area

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Shin Yu ◽  
Chang Tang Chang ◽  
Chih Ming Ma
Keyword(s):  
Air Quality ◽  
Traffic Congestion ◽  
Traffic Management ◽  
Reference Model ◽  
Dispersion Model ◽  
Fluid Model ◽  
Three Dimensional ◽  
Vehicle Speed ◽  
Management Plans ◽  
Dimensional Distribution

AbstractThe traffic congestion in the Hsuehshan tunnel and at the Toucheng interchange has led to traffic-related air pollution with increasing concern. To ensure the authenticity of our simulation, the concentration of the last 150 m in Hsuehshan tunnel was simulated using the computational fluid dynamics fluid model. The air quality at the Toucheng interchange along a 2 km length highway was simulated using the California Line Source Dispersion Model. The differences in air quality between rush hours and normal traffic conditions were also investigated. An unmanned aerial vehicle (UAV) with installed PM2.5 sensors was developed to obtain the three-dimensional distribution of pollutants. On different roads, during the weekend, the concentrations of pollutants such as SOx, CO, NO, and PM2.5 were observed to be in the range of 0.003–0.008, 7.5–15, 1.5–2.5 ppm, and 40–80 μg m− 3, respectively. On weekdays, the vehicle speed and the natural wind were 60 km h− 1 and 2.0 m s− 1, respectively. On weekdays, the SOx, CO, NO, and PM2.5 concentrations were found to be in the range of 0.002–0.003, 3–9, 0.7–1.8 ppm, and 35–50 μg m− 3, respectively. The UAV was used to verify that the PM2.5 concentrations of vertical changes at heights of 9.0, 7.0, 5.0, and 3.0 m were 45–48, 30–35, 25–30, and 50–52 μg m− 3, respectively. In addition, the predicted PM2.5 concentrations were 40–45, 25–30, 45–48, and 45–50 μg m− 3 on weekdays. These results provide a reference model for environmental impact assessments of long tunnels and traffic jam-prone areas. These models and data are useful for transportation planners in the context of creating traffic management plans.

Bright and dark optical solitons for the generalized variable coefficients nonlinear Schrödinger equation

2020 ◽  
Vol 21 (7-8) ◽  
pp. 675-681
Author(s):  
Rehab M. El-Shiekh ◽  
Mahmoud Gaballah
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Integration Method ◽  
Variable Coefficients ◽  
Nonlinear Schrodinger Equation ◽  
Equation Method ◽  
Direct Integration ◽  
Wave Solutions ◽  
Direct Integration Method

AbstractIn this paper, the generalized nonlinear Schrödinger equation with variable coefficients (gvcNLSE) arising in optical fiber is solved by using two different techniques the trail equation method and direct integration method. Many different new types of wave solutions like Jacobi, periodic and soliton wave solutions are obtained. From this study we have concluded that the direct integration method is more easy and straightforward than the trail equation method. As an application in optic fibers the propagation of the frequency modulated optical soliton is discussed and we have deduced that it's propagation shape is affected with the different values of both the amplification increment and the group velocity (GVD).

scholarly journals Precise Integration Method for Solving Noncooperative LQ Differential Game

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Hai-Jun Peng ◽  
Sheng Zhang ◽  
Zhi-Gang Wu ◽  
Biao-Song Chen
Keyword(s):  
Differential Equation ◽  
Differential Game ◽  
Integration Method ◽  
Transformation Method ◽  
Linear Quadratic ◽  
Riccati Differential Equation ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Direct Integration Method ◽  
Two Parameters

The key of solving the noncooperative linear quadratic (LQ) differential game is to solve the coupled matrix Riccati differential equation. The precise integration method based on the adaptive choosing of the two parameters is expanded from the traditional symmetric Riccati differential equation to the coupled asymmetric Riccati differential equation in this paper. The proposed expanded precise integration method can overcome the difficulty of the singularity point and the ill-conditioned matrix in the solving of coupled asymmetric Riccati differential equation. The numerical examples show that the expanded precise integration method gives more stable and accurate numerical results than the “direct integration method” and the “linear transformation method”.

scholarly journals A three-dimensional steady state thermal fluid model of jumbo ingot casting during electron beam re-melting of Ti–6Al–4V

2014 ◽  
Vol 38 (14) ◽  
pp. 3607-3623 ◽  
Author(s):  
X. Zhao ◽  
C. Reilly ◽  
L. Yao ◽  
D.M. Maijer ◽  
S.L. Cockcroft ◽  
...  
Keyword(s):  
Electron Beam ◽  
Steady State ◽  
Fluid Model ◽  
Three Dimensional ◽  
Ingot Casting

scholarly journals Choice and Limits of a Fluid Model for the Numerical Study in Dynamic Fluid Structure Interaction Problems

2003 ◽  
Author(s):  
Jean Franc¸ois Sigrist ◽  
Christian Laine ◽  
Dominique Lemoine ◽  
Bernard Peseux
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Model ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Linear Solution ◽  
Fluid Structure ◽  
Design Engineers ◽  
Inviscid Incompressible Fluid ◽  
Basic Fluid

This paper is related to the study of a nuclear propulsion reactor prototype for the French Navy. This prototype is built on ground and is to be dimensioned toward seismic loading. The dynamic analysis takes the coupled fluid structure analysis into account. The basic fluid models used by design engineers are inviscid incompressible or compressible. The fluid can be described in a bidimensional by slice or a three-dimensional approach. A numerical study is carried out on a generic problem for the linear FSI dynamic problem. The results of this study are presented and discussed. As a conclusion, the three-dimensional inviscid incompressible fluid appears to be the best compromise between the description of physical phenomena and the cost of modeling. The geometry of the reactor is such that large displacements of the structure in the fluid can occur. Therefore, the linearity hypothesis might not be longer valid. The case of large amplitude imposed oscillating motion of a cylinder in a confined fluid is numerically studied. A CFD code is used to investigate the fluid behavior solving the NAVIER-STOKES equations. The forces induced on the cylinder by the fluid are computed and compared to the linear solution. The limit of the linear model can then be exhibited.

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