5,478 research outputs found
Trigonometric time integrators for the Zakharov system
The main challenge in the analysis of numerical schemes for the Zakharov
system originates from the presence of derivatives in the nonlinearity. In this
paper a new trigonometric time-integration scheme for the Zakharov system is
constructed and convergence is proved. The time-step restriction is independent
from a spatial discretization. Numerical experiments confirm the findings
A time-splitting spectral scheme for the Maxwell-Dirac system
We present a time-splitting spectral scheme for the Maxwell-Dirac system and
similar time-splitting methods for the corresponding asymptotic problems in the
semi-classical and the non-relativistic regimes. The scheme for the
Maxwell-Dirac system conserves the Lorentz gauge condition, is unconditionally
stable and highly efficient as our numerical examples show. In particular we
focus in our examples on the creation of positronic modes in the semi-classical
regime and on the electron-positron interaction in the non-relativistic regime.
Furthermore, in the non-relativistic regime, our numerical method exhibits
uniform convergence in the small parameter \dt, which is the ratio of the
characteristic speed and the speed of light.Comment: 29 pages, 119 figure
Jet color chemistry and anomalous baryon production in -collisions
We study anomalous high- baryon production in -collisions due to
formation of the two parton collinear system in the anti-sextet color
state for quark jets and system in the decuplet/anti-decuplet color states
for gluon jets. Fragmentation of these states, which are absent for
-collisions, after escaping from the quark-gluon plasma leads to baryon
production. Our qualitative estimates show that this mechanism can be
potentially important at RHIC and LHC energies.Comment: 20 pages, 4 figures, Eur.Phys.J. versio
The Structure of Global Attractors for Dissipative Zakharov Systems with Forcing on the Torus
The Zakharov system was originally proposed to study the propagation of
Langmuir waves in an ionized plasma. In this paper, motivated by earlier work
of the first and third authors, we numerically and analytically investigate the
dynamics of the dissipative Zakharov system on the torus in 1 dimension. We
find an interesting family of stable periodic orbits and fixed points, and
explore bifurcations of those points as we take weaker and weaker dissipation.Comment: 16 pages, 7 figure
A Parameterized multi-step Newton method for solving systems of nonlinear equations
We construct a novel multi-step iterative method for solving systems of nonlinear equations by introducing a parameter. to generalize the multi-step Newton method while keeping its order of convergence and computational cost. By an appropriate selection of theta, the new method can both have faster convergence and have larger radius of convergence. The new iterative method only requires one Jacobian inversion per iteration, and therefore, can be efficiently implemented using Krylov subspace methods. The new method can be used to solve nonlinear systems of partial differential equations, such as complex generalized Zakharov systems of partial differential equations, by transforming them into systems of nonlinear equations by discretizing approaches in both spatial and temporal independent variables such as, for instance, the Chebyshev pseudo-spectral discretizing method. Quite extensive tests show that the new method can have significantly faster convergence and significantly larger radius of convergence than the multi-step Newton method.Peer ReviewedPostprint (author's final draft
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