By Albert R. Baswell

ISBN-10: 1604564547

ISBN-13: 9781604564549

ISBN-10: 1612098118

ISBN-13: 9781612098111

Advances in arithmetic learn provides unique study effects at the innovative of arithmetic examine. each one article has been conscientiously chosen in an try and current large examine effects throughout a vast spectrum.

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**Additional info for Advances in Mathematics Research **

**Example text**

Temperature Tx. The Method of Characteristics for the Numerical Solution… 21 Figure 16. Temperature Tz. 3. Vlasov-Maxwell Equations for Laser-Plasma Interaction Two systems of equations for 1D laser-plasma interaction will be discussed in this chapter. In the first one, presented in this section, we consider a linearly polarized electromagnetic wave [21]. This system is solved using a fractional step method and uses a cubic spline interpolation to solve for the advection term in the reduced one dimensional equations.

The normalized wave amplitude E 0 = E am e /(ω epw M e c) ≡ Vosc / c n / nc amplitude and nc the critical density. 00854265λ I 0 ) / n / nc . 032, and the intensity I0=100 (in units of 1014 W/cm2 ). 25 . Figure 17. Frequency spectrum of E+. 26 M. Shoucri Figure 18. Wavenumber spectrum of E+. We use again the same parameters as in [53]. 5(ω pe / c) . 4(ω pe / c) . 86(ω pe / c) . 5 . 265 , and N x = 5000 grid points in space, N v = 256 grid points in velocity space for electrons and 128 for ions.

Growth and saturation of the potential at the position x=3Lx /4. Figure 25. Contour plot of the potential at t=80. In this case k y < k ys , and the system is unstable [58,59]. 2058. 2 . (24) shows the growth and oscillation of the potential , monitored at the position x = 3Lx / 4; y = 0 . 124. (27-28) (dotted curves denote negative values). Note the very nice agreement of the theoretical and numerical results. The Method of Characteristics for the Numerical Solution… Figure 26. Contour plot of the potential at t=120.

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