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Mean Field (mean + field)

Distribution by Scientific Domains

Physics and Astronomy	57%
Earth and Environmental Science	28%

Terms modified by Mean Field

mean field approximation

mean field theory

Selected Abstracts

Reduction of quantum fluctuations by anisotropy fields in Heisenberg ferro- and antiferromagnets

ANNALEN DER PHYSIK, Issue 10-11 2009
B. Vogt
Abstract The physical properties of quantum systems, which are described by the anisotropic Heisenberg model, are influenced by thermal as well as by quantum fluctuations. Such a quantum Heisenberg system can be profoundly changed towards a classical system by tuning two parameters, namely the total spin and the anisotropy field: Large easy-axis anisotropy fields, which drive the system towards the classical Ising model, as well as large spin quantum numbers suppress the quantum fluctuations and lead to a classical limit. We elucidate the incipience of this reduction of quantum fluctuations. In order to illustrate the resulting effects we determine the critical temperatures for ferro- and antiferromagnets and the ground state sublattice magnetization for antiferromagnets. The outcome depends on the dimension, the spin quantum number and the anisotropy field and is studied for a widespread range of these parameters. We compare the results obtained by: Classical Mean Field, Quantum Mean Field, Linear Spin Wave and Random Phase Approximation. Our findings are confirmed and quantitatively improved by numerical Quantum Monte Carlo simulations. The differences between the ferromagnet and antiferromagnet are investigated. We finally find a comprehensive picture of the classical trends and elucidate the suppression of quantum fluctuations in anisotropic spin systems. In particular, we find that the quantum fluctuations are extraordinarily sensitive to the presence of small anisotropy fields. This sensitivity can be quantified by introducing an "anisotropy susceptibility". [source]

Reduction of quantum fluctuations by anisotropy fields in Heisenberg ferro- and antiferromagnets

Effective elastic properties of randomly fractured soils: 3D numerical experiments

GEOPHYSICAL PROSPECTING, Issue 3 2004
Erik H. Saenger
ABSTRACT This paper is concerned with numerical tests of several rock physical relationships. The focus is on effective velocities and scattering attenuation in 3D fractured media. We apply the so-called rotated staggered finite-difference grid (RSG) technique for numerical experiments. Using this modified grid, it is possible to simulate the propagation of elastic waves in a 3D medium containing cracks, pores or free surfaces without applying explicit boundary conditions and without averaging the elastic moduli. We simulate the propagation of plane waves through a set of randomly cracked 3D media. In these numerical experiments we vary the number and the distribution of cracks. The synthetic results are compared with several (most popular) theories predicting the effective elastic properties of fractured materials. We find that, for randomly distributed and randomly orientated non-intersecting thin penny-shaped dry cracks, the numerical simulations of P- and S-wave velocities are in good agreement with the predictions of the self-consistent approximation. We observe similar results for fluid-filled cracks. The standard Gassmann equation cannot be applied to our 3D fractured media, although we have very low porosity in our models. This is explained by the absence of a connected porosity. There is only a slight difference in effective velocities between the cases of intersecting and non-intersecting cracks. This can be clearly demonstrated up to a crack density that is close to the connectivity percolation threshold. For crack densities beyond this threshold, we observe that the differential effective-medium (DEM) theory gives the best fit with numerical results for intersecting cracks. Additionally, it is shown that the scattering attenuation coefficient (of the mean field) predicted by the classical Hudson approach is in excellent agreement with our numerical results. [source]

The VMFCI method: A flexible tool for solving the molecular vibration problem

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 5 2006
P. Cassam-Chenaï
Abstract The present article introduces a general variational scheme to find approximate solutions of the spectral problem for the molecular vibration Hamiltonian. It is called the "vibrational mean field configuration interaction" (VMFCI) method, and consists in performing vibrational configuration interactions (VCI) for selected modes in the mean field of the others. The same partition of modes can be iterated until self-consistency, generalizing the vibrational self-consistent field (VSCF) method. As in contracted-mode methods, a hierarchy of partitions can be built to ultimately contract all the modes together. So, the VMFCI method extends the traditional variational approaches and can be included in existing vibrational codes based on the latter approaches. The flexibility and efficiency of this new method are demonstrated on several molecules of atmospheric interest. © 2006 Wiley Periodicals, Inc. J Comput Chem 27: 627,640, 2006 [source]

A novel type of intermittency in a non-linear dynamo in a compressible flow

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2009
Erico L. Rempel
ABSTRACT The transition to an intermittent mean-field dynamo is studied using numerical simulations of magnetohydrodynamic turbulence driven by a helical forcing. The low-Prandtl number regime is investigated by keeping the kinematic viscosity fixed while the magnetic diffusivity is varied. Just below the critical parameter for the onset of dynamo action, a transient mean field with low magnetic energy is observed. After the transition to a sustained dynamo, the system is shown to evolve through different types of intermittency until a large-scale coherent field with small-scale turbulent fluctuations is formed. Prior to this coherent field stage, a new type of intermittency is detected, where the magnetic field randomly alternates between phases of coherent and incoherent large-scale spatial structures. The relevance of these findings to the understanding of the physics of mean-field dynamo and the physical mechanisms behind intermittent behaviour observed in stellar magnetic field variability are discussed. [source]

Coronal activity from dynamos in astrophysical rotators

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 3 2000
Eric G. Blackman
We show that a steady mean-field dynamo in astrophysical rotators leads to an outflow of relative magnetic helicity and thus magnetic energy available for particle and wind acceleration in a corona. The connection between energy and magnetic helicity arises because mean-field generation is linked to an inverse cascade of magnetic helicity. To maintain a steady state in large magnetic Reynolds number rotators, there must then be an escape of relative magnetic helicity associated with the mean field, accompanied by an equal and opposite contribution from the fluctuating field. From the helicity flow, a lower limit on the magnetic energy deposited in the corona can be estimated. Steady coronal activity including the dissipation of magnetic energy, and formation of multi-scale helical structures therefore necessarily accompanies an internal dynamo. This highlights the importance of boundary conditions which allow this to occur for non-linear astrophysical dynamo simulations. Our theoretical estimate of the power delivered by a mean-field dynamo is consistent with that inferred from observations to be delivered to the solar corona, the Galactic corona, and Seyfert 1 AGN coronae. [source]

The cumulus-capped boundary layer.

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 618 2006
I: Modelling transports in the cloud layer
Abstract Scalar-flux budgets have been obtained from large-eddy simulations (LESs) of the cumulus-capped boundary layer. Parametrizations of the terms in the budgets are discussed, and two parametrizations for the transport term in the cloud layer are proposed. It is shown that these lead to two models for scalar transports by shallow cumulus convection. One is equivalent to the subsidence detrainment form of convective tendencies obtained from mass-flux parametrizations of cumulus convection. The second is a flux-gradient relationship that is similar in form to the non-local parametrizations of turbulent transports in the dry-convective boundary layer. Using the fluxes of liquid-water potential temperature and total water content from the LES, it is shown that both models are reasonable diagnostic relations between fluxes and the vertical gradients of the mean fields. The LESs used in this study are for steady-state convection and it is possible to treat the fluxes of conserved thermodynamic variables as independent, and ignore the effects of condensation. It is argued that a parametrization of cumulus transports in a model of the cumulus-capped boundary layer should also include an explicit representation of condensation. A simple parametrization of the liquid-water flux in terms of conserved variables is also derived. © Crown Copyright, 2006 [source]