scholarly journals NLSE for quantum plasmas with the radiation damping

2016 ◽  
Vol 30 (13) ◽  
pp. 1650180 ◽  
Author(s):  
Pavel A. Andreev
Keyword(s):  
Wave Function ◽  
Schrodinger Equation ◽  
Relativistic Effects ◽  
Second Order ◽  
Radiation Damping ◽  
Third Order ◽  
Langmuir Waves ◽  
The Third ◽  
Quantum Plasmas ◽  
Quantum Hydrodynamic

We consider contribution of the radiation damping in the quantum hydrodynamic (QHD) equations for spinless particles. We discuss possibility of obtaining corresponding nonlinear Schrödinger equation (NLSE) for the macroscopic wave function. We compare contribution of the radiation damping with weakly (or semi-) relativistic effects appearing in the second-order on [Formula: see text]. The radiation damping appears in the third-order on [Formula: see text]. So it might be smaller than weakly relativistic effects, but it gives damping of the Langmuir waves which can be considerable.

scholarly journals B-splines Algorithms for Solving Fredholm Linear Integro-Differential Equations

2004 ◽  
Vol 1 (2) ◽  
pp. 340-346
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Spline Function ◽  
Cubic Spline ◽  
Second Order ◽  
Third Order ◽  
B Spline ◽  
Numerical Examples ◽  
B Splines ◽  
The Third ◽  
New Procedures

Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

A Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion

1988 ◽  
Vol 32 (02) ◽  
pp. 83-91
Author(s):  
X. M. Wang ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Model ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Potential Flow Model ◽  
Good Agreement

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.

WENO-TVD schemes for hyperbolic conservation laws

Analysis ◽  
2007 ◽  
Vol 27 (1) ◽  
Author(s):  
Yousef Hashem Zahran
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Building Blocks ◽  
Second Order ◽  
Third Order ◽  
Weno Schemes ◽  
Hyperbolic Conservation ◽  
Systematic Assessment ◽  
The Third ◽  
Seventh Order

The purpose of this paper is twofold. Firstly we carry out a modification of the finite volume WENO (weighted essentially non-oscillatory) scheme of Titarev and Toro [14] and [15].This modification is done by using two fluxes as building blocks in spatially fifth order WENO schemes instead of the second order TVD flux proposed by Titarev and Toro [14] and [15]. These fluxes are the second order TVD flux [19] and the third order TVD flux [20].Secondly, we propose to use these fluxes as a building block in spatially seventh order WENO schemes. The numerical solution is advanced in time by the third order TVD Runge–Kutta method. A way to extend these schemes to general systems of nonlinear hyperbolic conservation laws, in one and two dimension is presented. Systematic assessment of the proposed schemes shows substantial gains in accuracy and better resolution of discontinuities, particularly for problems involving long time evolution containing both smooth and non-smooth features.

Contigious hyperquadrics of coequipped hyperbands sHm

2019 ◽  
pp. 126-132
Author(s):  
Yu. Popov
Keyword(s):  
Projective Space ◽  
Second Order ◽  
Third Order ◽  
Base Surface ◽  
The Third ◽  
Two Parameter ◽  
Order Contact

We consider hyperquadrics that are internally connected to coequipped hyperbands in the projective space. Specifically, a hyperquadric Qn1 tangent to a hyperplane at the point is called a contiguous hyper quadric of a hyperband if it has a second-order contact with the base surface of the hyperband. In a the third order differential neighborhood of the forming element of the hyperband, two two-parameter bundles of fields of adjoining hyperquadrics are internally invariantly joined, their equations are given in a dot frame. The set of hyperquadrics such that the plane and the plane of Cartan are conjugate with respect to hyperquadric Qn1 is considered. The condition is shown under which the normal of the 2nd kind and the Cartan plane are conjugate with respect to the hyperquadric Qn1 . In addition, the following theorem is proved: normalization of a coequipped regular hyperband has a semi-internal equipment if and only if its normals of the first and second kind are polarly conjugate with respect to the hyperquadric.

Perturbation treatment of the Hartree–Fock equations for the ground states of the boron-like ions

1969 ◽  
Vol 47 (7) ◽  
pp. 699-705 ◽  
Author(s):  
C. S. Sharma ◽  
R. G. Wilson
Keyword(s):  
Ground State ◽  
Atomic System ◽  
Ground States ◽  
Great Accuracy ◽  
Second Order ◽  
Expectation Values ◽  
Third Order ◽  
First Order ◽  
Hartree Fock ◽  
The Third

The first-order Hartree–Fock and unrestricted Hartree–Fock equations for the ground state of a five electron atomic system are solved exactly. The solutions are used to evaluate the corresponding second-order energies exactly and the third-order energies with great accuracy. The first-order terms in the expectation values of 1/r, r, r2, and δ(r) are also calculated.

A perturbation calculation of properties of the 2 pπ state of HeH 2+

1957 ◽  
Vol 240 (1221) ◽  
pp. 274-283 ◽  
Keyword(s):  
Dipole Moment ◽  
Total Energy ◽  
Second Order ◽  
Wave Functions ◽  
Quadrupole Moments ◽  
Perturbation Calculation ◽  
Third Order ◽  
The Third ◽  
Fifth Order ◽  
Kinetic And Potential Energies

A perturbation calculation, valid in the limit of large separations, of various properties of the 2 pπ state of HeH 2+ is carried out. The total energy and the kinetic and potential energies are calculated to the fifth order, the dipole moment to the third order and the quadrupole moments to the second order and the results compared with those obtained using exact and variationally determined two-centre wave functions. Some results are also given for the 2 pπ u and 3 dπ g states of H + 2 and the influence of nuclear symmetry at large separations is briefly discussed.

scholarly journals Analysis on the Performance of a Second-order and a Third-order RLC Circuit of PRBS Generator

2021 ◽  
Vol 1 (1) ◽  
pp. 1-10
Author(s):  
Ahmad’ ‘Athif Mohd Faudzi ◽  
Na Zhang
Keyword(s):  
System Identification ◽  
Black Box ◽  
Second Order ◽  
Order Model ◽  
Complex Signals ◽  
Third Order ◽  
The Third ◽  
Rlc Circuit ◽  
Best Fit ◽  
Sample Time

A pseudo-binary random signal (PRBS) has been widely utilized for system identification in complex signals to develop an experimental approach. PRBS generator is a circuit that generates pseudo-random numbers. This work aims to analyze the best fit value of the PRBS generator with second-order and third-order under-damped black-box RLC circuit of the estimated model. The procedures conducting here can be divided into three parts. First, to design two black boxes using the RLC circuit representing a critically under-damped second-order and third-order system. PRBS generated with maximum-length sequence (MLS) equals 127 bits by using seven shift registers. Second, simulate the PRBS generator using MATLAB software and validate the estimated model from the simulation using the System Identification Tool in MATLAB. Next, connecting hardware RLC circuit and reading input and output signals using an oscilloscope. Finally, 2500 samples of captured data were used for estimation. Then, analyze and compare the best fit of the simulation and experiment with second-order and third-order under-damped black-box RLC circuit. Furthermore, analyze and compare best fit using different sample time. The results showed that the best fit of the second-order model with under-damped black-box RLC circuit was autoregressive with the exogenous term (ARX) 211, where the best fit of the simulation was 99.88%, and the best fit of the experiment was 96.04%. And the results showed that the best fit of the third-order model with an under-damped black-box RLC circuit was ARX 331, where the best fit of the simulation was 99%, and the best fit of the experiment was 94.28%. It was concluded that the best fit value of the second-order was better than the third order. What’s more, the results showed that when the select range is the same, the bigger the sample time, the better the best fit.

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