Oscillatory mean-field dynamos with a spherically symmetric, isotropic helical turbulence parameterα

2003 ◽  
Vol 67 (2) ◽  
Author(s):  
Frank Stefani ◽  
Gunter Gerbeth
Keyword(s):  
Mean Field ◽  
Spherically Symmetric ◽  
Helical Turbulence

scholarly journals Dynamical Instabilities in Spherical Stellar Systems

1985 ◽  
Vol 113 ◽  
pp. 297-299
Author(s):  
Joshua Barnes
Keyword(s):  
Mass Distribution ◽  
Spherical Symmetry ◽  
Mean Field ◽  
The Other ◽  
Stellar Systems ◽  
Spherically Symmetric ◽  
Quadrupole Mode ◽  
Radial Forces ◽  
The Mean ◽  
Dynamical Instabilities

Equlibrium spherical stellar systems exhibiting instabilities on a dynamical timescale were first studied by Henon (1973), using a spherically symmetric N-body code. We have re-examined Henon's models using an improved code which includes non-radial forces to quadrupole order. In addition to the radial instability reported by Henon, two new non-radial instabilities are also observed. In one, found in models with highly circular orbits, the mass distribution exhibits quadrupole-mode oscillations. In the other, seen in models with highly radial orbits, the system spontaneously breaks spherical symmetry and settles into a tri-axial ellipsoid. These instabilities, which are driven by fluctuations of the mean field, offer some analogies to the well-known dynamical instabilities of a cold disk of stars. While our models are rather artificial, they indicate that dynamical instabilities may be more common in spherical systems than had been thought.

scholarly journals NEUTRON STAR CORES IN THE GENERAL RELATIVISTIC THOMAS-FERMI TREATMENT

2013 ◽  
Vol 23 ◽  
pp. 185-192
Author(s):  
RICCARDO BELVEDERE ◽  
JORGE A. RUEDA ◽  
REMO RUFFINI
Keyword(s):  
General Relativity ◽  
Neutron Stars ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Strong Interactions ◽  
Spherically Symmetric ◽  
The Core ◽  
General Relativistic ◽  
The Mean

We introduce a new set of equations to describe the equilibrium of the core of neutron stars, composed by self-gravitating degenerate neutrons, protons and electrons in β-equilibrium. We take into account strong, weak, electromagnetic and gravitational interactions within the framework of general relativity. We extend the conditions of equilibrium based on the constancy of the Klein potentials to the strongly interactive case. The strong interactions between nucleons are modeled through the exchange of the σ, ω and ρ virtual mesons. The equations are solved numerically in the case of zero temperatures and for a non-rotating spherically symmetric neutron stars in the mean-field approximation.

scholarly journals Active spheres induce Marangoni flows that drive collective dynamics

2021 ◽  
Vol 44 (2) ◽  
Author(s):  
Martin Wittmann ◽  
Mihail N. Popescu ◽  
Alvaro Domínguez ◽  
Juliane Simmchen
Keyword(s):  
Field Model ◽  
Collective Motion ◽  
Mean Field ◽  
Spherically Symmetric ◽  
Fluid Interface ◽  
Mean Field Model ◽  
Collective Dynamics ◽  
Active Particles ◽  
Oil Water ◽  
Marangoni Flows

Abstract For monolayers of chemically active particles at a fluid interface, collective dynamics is predicted to arise owing to activity-induced Marangoni flow even if the particles are not self-propelled. Here, we test this prediction by employing a monolayer of spherically symmetric active $$\hbox {TiO}_2$$ TiO 2 particles located at an oil–water interface with or without addition of a nonionic surfactant. Due to the spherical symmetry, an individual particle does not self-propel. However, the gradients produced by the photochemical fuel degradation give rise to long-ranged Marangoni flows. For the case in which surfactant is added to the system, we indeed observe the emergence of collective motion, with dynamics dependent on the particle coverage of the monolayer. The experimental observations are discussed within the framework of a simple theoretical mean-field model. Graphic abstract

scholarly journals The Solar Dynamo

1993 ◽  
Vol 157 ◽  
pp. 1-12
Author(s):  
D. Schmitt
Keyword(s):  
Magnetic Field ◽  
Solar Cycle ◽  
Magnetic Flux ◽  
Convection Zone ◽  
Mean Field ◽  
Solar Dynamo ◽  
Acoustic Oscillations ◽  
Model Calculations ◽  
Helical Turbulence ◽  
Magnetic Buoyancy

The generation of the solar magnetic field is generally ascribed to dynamo processes in the convection zone. The dynamo effects, differential rotation (ω–effect) and helical turbulence (α–effect) are explained, and the basic properties of the mean–field dynamo equations are discussed in close comparison with the observed solar cycle.Especially the question of the seat of the dynamo is addressed. Problems of a dynamo in the convection zone proper could be magnetic buoyancy, the nearly strict observance of the polarity rules and the migration pattern of the magnetic fields which are difficult to understand in the light of recent studies of the field structure in the convection zone and by observations of the solar acoustic oscillations. To overcome some of these problems it has been suggested that the solar dynamo operates in the thin overshoot region at the base of the convection zone instead. Some aspects of such an interface dynamo are discussed. As an alternative to the turbulent α–effect a dynamic α-effect based on magnetostrophic waves driven by a magnetic buoyancy instability of a magnetic flux layer is introduced. Model calculations for both pictures, a convection zone and an interface dynamo, are presented which use the internal rotation of the sun as deduced from helioseismology. Solutions with solar cycle behaviour are only obtained if the magnetic flux is bounded in the lower convection zone and the α–effect is concentrated near the equator.Another aspect briefly addressed is the nonlinear saturation of the magnetic field. The necessity of the dynamic nature of the dynamo processes is emphasized, and different processes, e.g. magnetic buoyancy and α-quenching, are mentioned.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

Mean field theory of n-layer unbinding

1993 ◽  
Vol 3 (3) ◽  
pp. 385-393 ◽  
Author(s):  
W. Helfrich
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field
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