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ABSTRACTNonlinear propagation of dust-ion-acoustic shock waves in an unmagnetized, collisionless four-component quantum plasma containing electrons, positrons, ions and negatively charged dust grains affected by dust charge variations and viscosity of ions is studied using quantum hydrodynamic model. Considering dust charge variation give rise to calculating of charging currents of the plasma particles. These currents have been calculated with orbit limited motion theory and using Fermi-distribution functions or Boltzmann–Maxwell distribution depending on quantum or classical particles, respectively. The basic characteristics of quantum dust-ion-acoustic shock waves are investigated by deriving Korteweg–de Vries–Burgers equation under the reductive perturbation method. Depending on the relative values of the dispersive and dissipative coefficients, oscillatory and monotonic shock waves can propagate in the plasma model. The effect of chemical potential and density of dust particles on the shock wave’s height and thickness is investigated. In addition, the critical value of H (Hc) is calculated and it is shown that for R?>?0 compressive shock waves and for R?<?0 rarefactive ones can exist. The present study is applicable to researchers on quantum nonlinear structures in dense astrophysical objects and ultra-small micro- and nano-electronic devices. 相似文献
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S. Pishbin 《Numerical Algorithms》2016,73(2):305-322
The υ-smoothing property of a one-dimensional Volterra integral operator and some projectors (Liang and Brumer, SIAM J. Numer. Anal. 51, 2238–2259 (2013)) are extended for two-dimensional integral-algebraic equations (TIAEs). Using these concepts, we decompose the given general TIAEs into mixed systems of two-dimensional Volterra integral equations (TVIEs) consisting of second- and first-kind TVIEs. Numerical technique based on the Chebyshev polynomial collocation methods is presented for the solution of the mixed TVIE system. Global convergence results are established and the performance of the numerical scheme is illustrated by means of some test problems. 相似文献
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This paper is concerned with obtaining the approximate solution of a class of semi-explicit Integral Algebraic Equations (IAEs) of index-2. A Jacobi collocation method including the matrix-vector multiplication representation is proposed for the IAEs of index-2. A rigorous analysis of error bound in weighted L2 norm is also provided which theoretically justifies the spectral rate of convergence while the kernels and the source functions are sufficiently smooth. Results of several numerical experiments are presented which support the theoretical results. 相似文献
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Numerical Algorithms - In this paper, we consider product integration method based on orthogonal polynomials to solve mixed system of Volterra integral equations of the first and second kind with... 相似文献
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