Third-order pseudostate calculation of excitation–ionization by protons and antiprotons

1996 ◽  
Vol 74 (7-8) ◽  
pp. 554-558 ◽  
Author(s):  
Jack C. Straton ◽  
J. Wang ◽  
J. H. McGuire ◽  
L. Nagy
Keyword(s):  
Cross Section ◽  
Significant Contribution ◽  
Order Term ◽  
Second Order ◽  
Third Order ◽  
Double Excitation ◽  
Closure Approximation ◽  
The Third ◽  
Experimental Factor ◽  
Electron Process

Techniques the authors developed to include correlation in the double-excitation of atoms are applied to a second two-electron process, excitation–ionization by proton versus antiproton impact. The second-order cross section, in the closure approximation and using pseudostates for the unbound electron, reproduces only a small percentage of the experimental factor of 2 difference for positively versus negatively charged projectiles. Inclusion of a portion of the third-order term yields a significant contribution near 0.5 MeV.

Photoproduction of Gravitational Radiation in Static Electromagnetic Fields. Radiative Corrections

1975 ◽  
Vol 53 (20) ◽  
pp. 2315-2320 ◽  
Author(s):  
G. Papini ◽  
S. -R. Valluri
Keyword(s):  
Cross Section ◽  
Gravitational Radiation ◽  
Low Energy ◽  
Radiative Corrections ◽  
Third Order ◽  
The Third ◽  
Relativistic Approximation ◽  
Effective Lagrangian ◽  
Charge Renormalization ◽  
Made In

The radiative corrections of second and third order for the process of photoproduction of gravitons in Coulomb and magnetic dipole fields have been calculated.All divergences have been removed either by charge renormalization or regularization. No approximations have been made in the calculation of the second order cross section. In the third order calculation only the extreme relativistic approximation is given. The forms of the effective Lagrangian, corresponding to the low energy approximations have been determined.

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.

An Numeric Method on the Third Order Term of KDV Equation

2011 ◽  
Vol 135-136 ◽  
pp. 253-255
Author(s):  
Yi Min Tian
Keyword(s):  
Difference Scheme ◽  
Kdv Equation ◽  
Order Term ◽  
Boundary Value ◽  
Difference Schemes ◽  
Boundary Values ◽  
Implicit Difference Scheme ◽  
Third Order ◽  
The Third ◽  
Numeric Experiment

Numeric scheme and numeric result was in this paper. First, We proposes a kind of explicit - implicit difference scheme to solve the initial and boundary value questions of the third order term of KDV equation here,and so we can solve the problem that the additional boundary values must be given first for present difference schemes when we try to realize the calculation by then., second, numeric experiment results was given ay the end of this article.

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.

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