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  • 1.
    Gaite, José A.
    et al.
    Inst. de Matemat./Fis. Fundamental, CSIC.
    Zorzano, María Paz
    Centro de Astrobiología, CSIC-INTA.
    Nonlinear spherical gravitational downfall of gas onto a solid ball: Analytic and numerical results2003In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 183, no 1-2, p. 102-116Article in journal (Refereed)
    Abstract [en]

    The process of downfall of initially homogeneous gas onto a solid ball due to the ball's gravity (relevant in astrophysical situations) is studied with a combination of analytic and numerical methods. The initial explicit solution soon becomes discontinuous and gives rise to a shock wave. Afterwards, there is a crossover between two intermediate asymptotic similarity regimes, where the shock wave propagates outwards according to two self-similar laws, initially accelerating and eventually decelerating and vanishing, leading to a static state. The numerical study allows one to investigate in detail this dynamical problem and its time evolution, verifying and complementing the analytic results on the initial solution, intermediate self-similar laws and static long-term solution.

  • 2.
    Wyller, John
    et al.
    Luleå tekniska universitet.
    Flå, Tor
    Department of Mathematics, University of Tromsö.
    Mjølhus, Einar
    Department of Mathematics, University of Tromsö.
    The effect of resonant particles on Alfvén solitons1989In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 39, no 2, p. 405-422Article in journal (Refereed)
    Abstract [en]

    The derivative nonlinear Schrödinger equation is treated. A perturbation theory for the evolution of an Alfvén soliton is given. This leads to a phase portrait of the changes in the soliton parameters. The phase curves are circles. Energy dissipation is estimated. Numerical calculations are given and results compared.

  • 3.
    Zorzano, María Paz
    et al.
    Deutsches Elektronen-Synchrotron (DESY).
    Mais, Helmut
    Deutsches Elektronen-Synchrotron (DESY).
    Vázquez, Luiz
    Dpto. de Matematica Aplicada, Escuela Superior de Informatica, Universidad Complutense de Madrid .
    Numerical solution for Fokker-Planck equations in accelerators1998In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 113, no 2-4, p. 379-381Article in journal (Refereed)
    Abstract [en]

    We present a finite difference scheme to solve numerically the type of Fokker-Planck equations describing the stochastic dynamics of a particle in a storage ring.

  • 4.
    Zorzano, María Paz
    et al.
    Centro de Astrobiología, CSIC/INTA, NASA Astrobiology Institute.
    Vázquez, Luiz
    Departamento de Matemáatica Aplicada, Facultad de Inform´atica, Universidad Complutense de Madrid.
    Emergence of synchronous oscillations in neural networks excited by noise2003In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 179, no 1-2, p. 105-114Article in journal (Refereed)
    Abstract [en]

    The presence of noise in nonlinear dynamical systems can play a constructive role, increasing the degree of order and coherence or evoking improvements in the performance of the system. An example of this positive influence in a biological system is the impulse transmission in neurons and the synchronization of a neural network. Integrating numerically the Fokker-Planck (FP) equation we show a self-induced synchronized oscillation. Such an oscillatory state appears in a neural network coupled with a feedback term, when this system is excited by noise and the noise strength is within a certain range

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