1,009 research outputs found
Homogeneous quantum electrodynamic turbulence
The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means
A Fourier collocation time domain method for numerically solving Maxwell's equations
A new method for solving Maxwell's equations in the time domain for arbitrary values of permittivity, conductivity, and permeability is presented. Spatial derivatives are found by a Fourier transform method and time integration is performed using a second order, semi-implicit procedure. Electric and magnetic fields are collocated on the same grid points, rather than on interleaved points, as in the Finite Difference Time Domain (FDTD) method. Numerical results are presented for the propagation of a 2-D Transverse Electromagnetic (TEM) mode out of a parallel plate waveguide and into a dielectric and conducting medium
Electromagnetic potential vectors and the Lagrangian of a charged particle
Maxwell's equations can be shown to imply the existence of two independent three-dimensional potential vectors. A comparison between the potential vectors and the electric and magnetic field vectors, using a spatial Fourier transformation, reveals six independent potential components but only four independent electromagnetic field components for each mode. Although the electromagnetic fields determined by Maxwell's equations give a complete description of all possible classical electromagnetic phenomena, potential vectors contains more information and allow for a description of such quantum mechanical phenomena as the Aharonov-Bohm effect. A new result is that a charged particle Lagrangian written in terms of potential vectors automatically contains a 'spontaneous symmetry breaking' potential
Nonlinear dynamics and control of a vibrating rectangular plate
The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined
On weak and strong magnetohydrodynamic turbulence
Recent numerical and observational studies contain conflicting reports on the
spectrum of magnetohydrodynamic turbulence. In an attempt to clarify the issue
we investigate anisotropic incompressible magnetohydrodynamic turbulence with a
strong guide field . We perform numerical simulations of the reduced MHD
equations in a special setting that allows us to elucidate the transition
between weak and strong turbulent regimes. Denote ,
characteristic field-parallel and field-perpendicular wavenumbers of the
fluctuations, and the fluctuating field at the scale . We find that when the critical balance condition, , is satisfied, the turbulence is strong, and the energy
spectrum is . As the width of
the spectrum increases, the turbulence rapidly becomes weaker, and in the limit
, the spectrum approaches
. The observed sensitivity of the spectrum
to the balance of linear and nonlinear interactions may explain the conflicting
numerical and observational findings where this balance condition is not well
controlled.Comment: 4 pages, 2 figure
Anisotrophy in MHD turbulence due to a mean magnetic field
The development of anisotropy in an initially isotropic spectrum is studied numerically for two-dimensional magnetohydrodynamic (MHD) turbulence. The anisotropy develops due to the combined effects of an externally imposed dc magnetic field and viscous and resistive dissipation at high wave numbers. The effect is most pronounced at high mechanical and magnetic Reynolds numbers. The anisotropy is greater at the higher wave numbers.;The statistical structure of two-dimensional MHD turbulence is also considered. It is shown that the three known rugged invariants of the isotropic case reduce to two for the anisotropic case. Randomness and ergodicity are also briefly discussed
Anisotropy in MHD turbulence due to a mean magnetic field
The development of anisotropy in an initially isotropic spectrum is studied numerically for two-dimensional magnetohydrodynamic turbulence. The anisotropy develops due to the combined effects of an externally imposed dc magnetic field and viscous and resistive dissipation at high wave numbers. The effect is most pronounced at high mechanical and magnetic Reynolds numbers. The anisotropy is greater at the higher wave numbers
The Statistical Mechanics of Ideal MHD Turbulence
Turbulence is a universal, nonlinear phenomenon found in all energetic fluid and plasma motion. In particular. understanding magneto hydrodynamic (MHD) turbulence and incorporating its effects in the computation and prediction of the flow of ionized gases in space, for example, are great challenges that must be met if such computations and predictions are to be meaningful. Although a general solution to the "problem of turbulence" does not exist in closed form, numerical integrations allow us to explore the phase space of solutions for both ideal and dissipative flows. For homogeneous, incompressible turbulence, Fourier methods are appropriate, and phase space is defined by the Fourier coefficients of the physical fields. In the case of ideal MHD flows, a fairly robust statistical mechanics has been developed, in which the symmetry and ergodic properties of phase space is understood. A discussion of these properties will illuminate our principal discovery: Coherent structure and randomness co-exist in ideal MHD turbulence. For dissipative flows, as opposed to ideal flows, progress beyond the dimensional analysis of Kolmogorov has been difficult. Here, some possible future directions that draw on the ideal results will also be discussed. Our conclusion will be that while ideal turbulence is now well understood, real turbulence still presents great challenges
The Anisotropy of MHD Alfv\'{e}nic Turbulence
We perform direct 3-dimensional numerical simulations for magnetohydrodynamic
(MHD) turbulence in a periodic box of size threaded by strong uniform
magnetic fields. We use a pseudo-spectral code with hyperviscosity and
hyperdiffusivity to solve the incompressible MHD equations. We analyze the
structure of the eddies as a function of scale. A straightforward calculation
of anisotropy in wavevector space shows that the anisotropy is scale-{\it
independent}. We discuss why this is {\it not} the true scaling law and how the
curvature of large-scale magnetic fields affects the power spectrum and leads
to the wrong conclusion. When we correct for this effect, we find that the
anisotropy of eddies depends on their size: smaller eddies are more elongated
than larger ones along {\it local} magnetic field lines. The results are
consistent with the scaling law proposed by Goldreich and Sridhar (1995, 1997). Here
(and ) are wavenumbers measured relative to
the local magnetic field direction. However, we see some systematic deviations
which may be a sign of limitations to the model, or our inability to fully
resolve the inertial range of turbulence in our simulations.Comment: 13 pages (11 NEW figures), ApJ, in press (Aug 10, 2000?
Energy spectra stemming from interactions of Alfven waves and turbulent eddies
We present a numerical analysis of an incompressible decaying
magnetohydrodynamic turbulence run on a grid of 1536^3 points. The Taylor
Reynolds number at the maximum of dissipation is ~1100, and the initial
condition is a superposition of large scale ABC flows and random noise at small
scales, with no uniform magnetic field. The initial kinetic and magnetic
energies are equal, with negligible correlation. The resulting energy spectrum
is a combination of two components, each moderately resolved. Isotropy obtains
in the large scales, with a spectral law compatible with the
Iroshnikov-Kraichnan theory stemming from the weakening of nonlinear
interactions due to Alfven waves; scaling of structure functions confirms the
non-Kolmogorovian nature of the flow in this range. At small scales, weak
turbulence emerges with a k_{\perp}^{-2} spectrum, the perpendicular direction
referring to the local quasi-uniform magnetic field.Comment: 4 pages, 4 figure
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