1,416 research outputs found
Anisotropic fluxes and nonlocal interactions in MHD turbulence
We investigate the locality or nonlocality of the energy transfer and of the
spectral interactions involved in the cascade for decaying magnetohydrodynamic
(MHD) flows in the presence of a uniform magnetic field at various
intensities. The results are based on a detailed analysis of three-dimensional
numerical flows at moderate Reynold numbers. The energy transfer functions, as
well as the global and partial fluxes, are examined by means of different
geometrical wavenumber shells. On the one hand, the transfer functions of the
two conserved Els\"asser energies and are found local in both the
directions parallel (-direction) and perpendicular (-direction)
to the magnetic guide-field, whatever the -strength. On the other
hand, from the flux analysis, the interactions between the two
counterpropagating Els\"asser waves become nonlocal. Indeed, as the -intensity is increased, local interactions are strongly decreased and the
interactions with small modes dominate the cascade. Most of the energy
flux in the -direction is due to modes in the plane at , while
the weaker cascade in the -direction is due to the modes with .
The stronger magnetized flows tends thus to get closer to the weak turbulence
limit where the three-wave resonant interactions are dominating. Hence, the
transition from the strong to the weak turbulence regime occurs by reducing the
number of effective modes in the energy cascade.Comment: Submitted to PR
A weak turbulence theory for incompressible magnetohydrodynamics
We derive a weak turbulence formalism for incompressible magnetohydrodynamics. Three-wave interactions lead to a system of kinetic equations for the spectral densities of energy and helicity. The kinetic equations conserve energy in all wavevector planes normal to the applied magnetic field B0ê[parallel R: parallel]. Numerically and analytically, we find energy spectra E± [similar] kn±[bot bottom], such that n+ + n− = −4, where E± are the spectra of the Elsässer variables z± = v ± b in the two-dimensional case (k[parallel R: parallel] = 0). The constants of the spectra are computed exactly and found to depend on the amount of correlation between the velocity and the magnetic field. Comparison with several numerical simulations and models is also made
Performance analysis of knock detectors
This paper examines performance of the knock detection technique typically used in engine control systems, and the margin for possible improvement. We introduce a knock signal model and obtain an analytical result for the associated receiver operating characteristic of the standard knock detector. To show the improvement potential, we derive the theoretical upper bound of performance. A special case with unknown model parameters is also considered. Numerical results stimulate the research of improved detectors
On the von Karman-Howarth equations for Hall MHD flows
The von Karman-Howarth equations are derived for three-dimensional (3D) Hall
magnetohydrodynamics (MHD) in the case of an homogeneous and isotropic
turbulence. From these equations, we derive exact scaling laws for the
third-order correlation tensors. We show how these relations are compatible
with previous heuristic and numerical results. These multi-scale laws provide a
relevant tool to investigate the non-linear nature of the high frequency
magnetic field fluctuations in the solar wind or, more generally, in any plasma
where the Hall effect is important.Comment: 11 page
Tangent bundle geometry from dynamics: application to the Kepler problem
In this paper we consider a manifold with a dynamical vector field and
inquire about the possible tangent bundle structures which would turn the
starting vector field into a second order one. The analysis is restricted to
manifolds which are diffeomorphic with affine spaces. In particular, we
consider the problem in connection with conformal vector fields of second order
and apply the procedure to vector fields conformally related with the harmonic
oscillator (f-oscillators) . We select one which covers the vector field
describing the Kepler problem.Comment: 17 pages, 2 figure
Long-time properties of MHD turbulence and the role of symmetries
We investigate long-time properties of three-dimensional MHD turbulence in
the absence of forcing and examine in particular the role played by the
quadratic invariants of the system and by the symmetries of the initial
configurations. We observe that, when sufficient accuracy is used, initial
conditions with a high degree of symmetries, as in the absence of helicity, do
not travel through parameter space over time whereas by perturbing these
solutions either explicitly or implicitly using for example single precision
for long times, the flows depart from their original behavior and can become
either strongly helical, or have a strong alignment between the velocity and
the magnetic field. When the symmetries are broken, the flows evolve towards
different end states, as predicted by statistical arguments for non-dissipative
systems with the addition of an energy minimization principle, as already
analyzed in \cite{stribling_90} for random initial conditions using a moderate
number of Fourier modes. Furthermore, the alignment properties of these flows,
between velocity, vorticity, magnetic potential, induction and current,
correspond to the dominance of two main regimes, one helically dominated and
one in quasi-equipartition of kinetic and magnetic energy. We also contrast the
scaling of the ratio of magnetic energy to kinetic energy as a function of
wavenumber to the ratio of eddy turn-over time to Alfv\'en time as a function
of wavenumber. We find that the former ratio is constant with an approximate
equipartition for scales smaller than the largest scale of the flow whereas the
ratio of time scales increases with increasing wavenumber.Comment: 14 pages, 6 figure
Tensorial dynamics on the space of quantum states
A geometric description of the space of states of a finite-dimensional
quantum system and of the Markovian evolution associated with the
Kossakowski-Lindblad operator is presented. This geometric setting is based on
two composition laws on the space of observables defined by a pair of
contravariant tensor fields. The first one is a Poisson tensor field that
encodes the commutator product and allows us to develop a Hamiltonian
mechanics. The other tensor field is symmetric, encodes the Jordan product and
provides the variances and covariances of measures associated with the
observables. This tensorial formulation of quantum systems is able to describe,
in a natural way, the Markovian dynamical evolution as a vector field on the
space of states. Therefore, it is possible to consider dynamical effects on
non-linear physical quantities, such as entropies, purity and concurrence. In
particular, in this work the tensorial formulation is used to consider the
dynamical evolution of the symmetric and skew-symmetric tensors and to read off
the corresponding limits as giving rise to a contraction of the initial Jordan
and Lie products.Comment: 31 pages, 2 figures. Minor correction
Comment on "Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction" [J. Chem. Phys. 137, 22A530 (2012)]
In spite of the relevance of the proposal introduced in the recent work A.
Abedi, N. T. Maitra and E. K. U. Gross, J. Chem. Phys. 137, 22A530, 2012, there
is an important ingredient which is missing. Namely, the proof that the norms
of the electronic and nuclear wavefunctions which are the solutions to the
nonlinear equations of motion are preserved by the evolution. To prove the
conservation of these norms is precisely the objective of this Comment.Comment: 2 pages, published versio
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