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Modern models of nonlinear dynamo saturation in celestial bodies (specifically, on the Sun) are largely based on the consideration of the balance of magnetic helicity. This physical variable has also a topological meaning: it is associated with the linking coefficient of magnetic tubes. In addition to magnetic helicity, magnetohydrodynamics has a number of topological integrals of motion (the so-called higher helicity moments). We have compared these invariants with magnetic helicity properties and concluded that they can hardly serve as nonlinear constraints on dynamo action. [ABSTRACT FROM AUTHOR]

The solar activity cycle is successfully modeled by the flux transport dynamo, in which the meridional circulation of the Sun plays an important role. Most of the kinematic dynamo simulations assume a one-cell structure of the meridional circulation within the convection zone, with the equatorward return flow at its bottom. In view of the recent claims that the return flow occurs at a much shallower depth, we explore whether a meridional circulation with such a shallow return flow can still retain the attractive features of the flux transport dynamo (such as a proper butterfly diagram, the proper phase relation between the toroidal and poloidal fields). We consider additional cells of the meridional circulation below the shallow return flow—both the case of multiple cells radially stacked above one another and the case of more complicated cell patterns. As long as there is an equatorward flow in low latitudes at the bottom of the convection zone, we find that the solar behavior is approximately reproduced. However, if there is either no flow or a poleward flow at the bottom of the convection zone, then we cannot reproduce solar behavior. On making the turbulent diffusivity low, we still find periodic behavior, although the period of the cycle becomes unrealistically large. In addition, with a low diffusivity, we do not get the observed correlation between the polar field at the sunspot minimum and the strength of the next cycle, which is reproduced when diffusivity is high. On introducing radially downward pumping, we get a more reasonable period and more solar-like behavior even with low diffusivity. [ABSTRACT FROM AUTHOR]

A dynamic system for the Parker dynamo including meridional circulation that is applicable to astrophysical objects is constructed. The meridional circulation is able to control the regimes for the generation of magnetic fields. If the meridional flows are weak, regimes with steady oscillations, dynamo bursts, fluctuations, and chaotic components are possible. When the meridional circulation is strengthened, the range of dynamo numbers required for fluctuations and dynamo bursts is reduced, and gradually vanishes; at the same time, the range required for oscillations is increased and raised to higher dynamo numbers. The latitude-time distributions of the toroidal and poloidal magnetic fields for steady oscillations are presented. [ABSTRACT FROM AUTHOR]

ABSTRACT Models of rotationally driven dynamos in stellar radiative zones have suggested that magnetohydrodynamic transport of angular momentum and chemical composition can dominate over the otherwise purely hydrodynamic processes. A proper consideration of the interaction between rotation and magnetic fields is therefore essential. Previous studies have focused on a magnetic model where the magnetic field strength is derived as a function of the stellar structure and angular momentum distribution. We have adapted our one-dimensional stellar rotation code, rose, to model the poloidal and toroidal magnetic field strengths with a pair of time-dependent advection-diffusion equations coupled to the equations for the evolution of the angular momentum distribution and stellar structure. This produces a much more complete, though still reasonably simple, model for the magnetic field evolution. Our model reproduces well observed surface nitrogen enrichment of massive stars in the Large Magellanic Cloud (LMC). In particular it reproduces a population of slowly rotating nitrogen-enriched stars that cannot be explained by rotational mixing alone alongside the traditional rotationlly enriched stars. The model further predicts a strong mass-dependency for the dynamo-driven field. Above a threshold mass, the strength of the magnetic dynamo decreases abruptly and so we predict that more massive stars are much less likely to support a dynamo-driven field than less massive stars. [ABSTRACT FROM AUTHOR]

We build a hydrodynamic model for computing and understanding the Sun's large-scale high-latitude flows. including Coriolis forces, turbulent diffusion of momentum, and gyroscopic pumping. Side boundaries of the spherical "polar cap," our computational domain, are located at latitudes ≥ 60°. Implementing observed low-latitude flows as side boundary conditions, we solve the flow equations for a Cartesian analog of the polar cap. The key parameter that determines whether there are nodes in the high-latitude meridional flow is ε = 2Ωnπ H²/v, where Ω is the interior rotation rate, n is the radial wave-number of the meridional flow, H is the depth of the convection zone, and v is the turbulent viscosity. The smaller the ε (larger turbulent viscosity), the fewer the number of nodes in high latitudes. For all latitudes within the polar cap, we find three nodes for v = 1012 cm² s-1, two for 1013, and one or none for 1015 or higher. For v near 1014 our model exhibits "node merging": as the meridional flow speed is increased, two nodes cancel each other, leaving no nodes. On the other hand, for fixed flow speed at the boundary, as v is increased the poleward-most node migrates to the pole and disappears, ultimately for high enough v leaving no nodes. These results suggest that primary poleward surface meridional flow can extend from 60° to the pole either by node merging or by node migration and disappearance. [ABSTRACT FROM AUTHOR]

We use a truncated dynamo model and observations of the sunspot number to infer cycle-to-cycle variations of several dynamo parameters. A correlation study between model parameters and solar cycle observables (period, amplitude, and rising time) is done, and our results are compared with the results of other authors. Using the strongest correlations found, we determined a series of relationships that can be used for prediction purposes. This technique indicates that solar cycle 24 will have a sunspot maximum of approximately 84 around June of 2013. In the context of the used model, most of the variability found in the solar cycle can be attributed to changes in the strength of the meridional circulation. The results also point to a common origin for the source of variation of the meridional flow and differential rotation and/or the α-effect. [ABSTRACT FROM AUTHOR]

The unexpected development of cycle 24 emphasizes the need for a better way to model future solar activity. In this article, we analyze the accumulation of spotless days during individual cycles from 1798 - 2010. The analysis shows that spotless days do not disappear abruptly in the transition toward an active Sun. A comparison with past cycles indicates that the ongoing accumulation of spotless days is comparable to that of cycle 5 near the Dalton minimum and to that of cycles 12, 14, and 15. It also suggests that the ongoing cycle has as much as 20±8 spotless days left, from July 2010, before it reaches the next solar maximum. The last spotless day is predicted to be in December 2012, with an uncertainty of 11 months. This trend may serve as input to the solar dynamo theories. [ABSTRACT FROM AUTHOR]

Abstract: Campanelli et al. (2009) have recently shown that electromagnetic fluctuations in Lorentz violation theories Colladay and Kostelecky (1998) along differential rotation may induce galactic dynamo amplification of magnetic fields from primordial seeds. In this Letter, instead of using the Maxwell–Chern–Simmons–Lagrangian used in their paper, one adopts the Lagrangean of the type , where represent the torsion modes, without dynamical curvature. This so-called Minkowski–Cartan spacetime torsion modes, allows us to handle QED vacuum in any Ricci scalar electrodynamics Lagrangean. It is shown that axial-torsion modes electrodynamics allows us to obtain a slow decay of magnetic fields. Thus primordial seed fields are amplified from differential rotation and protogalaxy turbulence as galactic dynamo action. This is mainly due to the fact that the collapse of the protogalaxy induces a strong suppression of the magnetic field decay. Magnetic field anisotropies are also considered. To resume, photon-torsion axial coupling in the quantum electrodynamics (QED) framework in Riemann flat contortioned spacetime may induce galactic dynamos. Fourier space transformation are used to compute electrodynamic equations. [ABSTRACT FROM AUTHOR]

Two systems of Lorenz-type equations modelling solar magnetic activity are studied: Firstly a low order dynamic system in which the toroidal and poloidal fields are represented by x- and y-coordinates respectively, and the hydrodynamical information is given by the z coordinate. Secondly a complex generalization of the three ordinary differential equations studied by Lorenz. By studying the Poincaré map we give numerical evidence that the flow has an attractor with fractal structure. The period is defined as the time needed for a point on a hyperplane to return to the hyperplane again. The periods are distributed in an interval. For large values of the Dynamo number there is a long tail toward long periods and other interesting comet-like features. These general relations found for periods can further be physically interpreted with improved helioseismic estimates of the parameters used by the dynamical systems. Solar Dynamic Observatory is expected to offer such improved measurements. [ABSTRACT FROM AUTHOR]

More than half a century ago, Bullard suggested that the Earth's dynamo might be driven by the motions created in the Earth's core by the luni-solar precession. The precessionally forced motion of the mantle drives core flow through viscous forces and also, because of the electrical conductivity of the deep mantle, through magnetic forces. Both these couplings are thought to be insignificant in comparison with the topographical coupling created by the oblateness of the core-mantle interface. Because of technical difficulties in studying dynamo action in non-spherical bodies of electrically conducting fluid, this is the first serious attempt to study dynamo action by topographically forced flows. It describes the novel numerical methods that were employed, the tests that were devised to validate these methods, and the successful outcome of those tests. Some preliminary results for these dynamos are presented. It is shown that, in some parameter ranges, the magnetic field produced by the dynamos enhances the vigor of the precessional motions. [ABSTRACT FROM AUTHOR]

Solutions of the induction equation with a purely toroidal magnetic field in a spherical conductor are of special interest since they disclose the possibility of a dynamo operating in a celestial body which remains invisible to an external observer. A necessary condition for such solutions to exist are flow fields and conductivity distributions constrained in such a way that no poloidal field can arise. Otherwise these quantities are assumed to be arbitrary; we allow, in particular, non-radial conductivity variations in order to facilitate dynamo action. This article presents evidence that such solutions do not exist: based on a solution of the constraint a nonlinear evolution equation for the toroidal scalar T is derived. It is proved that sufficiently regular solutions of this equation cannot increase (in time) in the norm [image omitted], where R is the radius of the spherical conductor. Steady solutions are likewise excluded. [ABSTRACT FROM AUTHOR]

Experimental results are reported on the magnetohydrodynamic interaction between oscillating flows in adjoining channels of the Karlsruhe dynamo test facility. In the experiment, designed to simulate the Roberts–Busse kinematic dynamo model, a time periodic perturbation has been imposed on the axial channel flows, while the flow rates in the other two helical channel systems were supplied at constant power level. It has been observed that the onset of dynamo action is shifted slightly to lower mean flow rates. A temporal analysis shows distinct correlations between the evolving magnetic field and the different kinds of forced flows in the channels. From the beginning the environmental magnetic field adjusts to fluctuations of the axial channel flow. The fluctuations of the magnetic field increase owing to dynamo action in a transition range and induce quasiperiodic fluctuations on the flow in the helical channels by acting Lorentz forces. In the high supercritical range the fluctuations are dampened. [ABSTRACT FROM AUTHOR]

Photospheric ephemeral regions (EPRs) cover the Sun like a magnetic carpet. From this, we update the Babcock – Leighton solar dynamo. Rather than sunspot fields appearing in the photosphere de novo from eruptions originating in the deep interior, we consider that sunspots form directly in the photosphere by a rapid accumulation of like-sign field from EPRs. This would only occur during special circumstances: locations and times when the temperature structure is highly superadiabatic and contains a large subsurface horizontal magnetic field (only present in the Sun’s lower latitudes). When these conditions are met, superadiabatic percolation occurs, wherein an inflow and downflow of gas scours the surface of EPRs to form active regions. When these conditions are not met, magnetic elements undergo normal percolation, wherein magnetic elements move about the photosphere in Brownian-type motions. Cellular automata (CA) models are developed that allow these processes to be calculated and thereby both small-scale and large-scale models of magnetic motions can be obtained. The small-scale model is compared with active region development and Hinode observations. The large-scale CA model offers a solar dynamo, which suggests that fields from decaying bipolar magnetic regions (BMRs) drift on the photosphere driven by subsurface magnetic forces. These models are related to observations and are shown to support Waldmeier’s findings of an inverse relationship between solar cycle length and cycle size. Evidence for significant amounts of deep magnetic activity could disprove the model presented here, but recent helioseismic observations of “butterfly patterns” at depth are likely just a reflection of surface activity. Their existence seems to support the contention made here that the field and flow separate, allowing cool, relatively field-free downdrafts to descend with little field into the nether worlds of the solar interior. There they heat by compression to form a hot solar-type Santa Ana wind deep below active regions. [ABSTRACT FROM AUTHOR]

Using a one-dimensional -dynamo model appropriate to galaxies, we study the possibility of dynamo action driven by a stochastic α-effect and shear. To determine the field evolution, one needs to examine a large number of different realizations of the stochastic component of α. The net growth or decay of the field depends not only on the dynamo parameters but also on the particular realization, the correlation time of the stochastic α compared to turbulent diffusion time-scale and the time over which the system is evolved. For dynamos where both a coherent and fluctuating α are present, the stochasticity of α can help alleviate catastrophic dynamo quenching, even in the absence of helicity fluxes. One can obtain final field strengths up to a fraction ∼0.01 of the equipartition field for dynamo numbers , while fields comparable to require much larger degree of α-fluctuations or shear. This type of dynamo may be particularly useful for amplifying fields in the central regions of disc galaxies. [ABSTRACT FROM AUTHOR]

Transport of angular momentum is one of the thrust areas of astrophysical flows. Instabilities and hence the turbulence generated by it have been invoked to understand its role in angular momentum transport in hydrodynamic and magnetohydrodynamic regime. Investigation of an unexplored region described by the parameter space being the epicyclic frequency, resulted in a powerful magnetohydrodynamic instability. The growth rate of this instability is rather large and is found to depend on the wavenumber. [ABSTRACT FROM AUTHOR]

Using direct simulations, weakly non-linear theory and non-linear mean-field theory, it is shown that the quenched velocity field of a saturated non-linear dynamo can itself act as a kinematic dynamo. The flow is driven by a forcing function that would produce a Roberts flow in the absence of a magnetic field. This result confirms an analogous finding by Cattaneo & Tobias for the more complicated case of turbulent convection, suggesting that this may be a common property of non-linear dynamos; see also the talk given online at the Kavli Institute for Theoretical Physics ( ). It is argued that this property can be used to test non-linear mean-field dynamo theories. [ABSTRACT FROM AUTHOR]

Turbulent fluctuations in the velocity and magnetic fields of electrically conducting fluids have been experimentally shown to be capable of inducing large-scale magnetic fields. Here, simulations of the Madison Dynamo Experiment are used to qualitatively reproduce these experimental results. Due to the high magnetic Prandtl number of the simulations, Pm=0.08 vs Pm∼10-5 for liquid sodium, the simulations do not identically reproduce the fluctuation levels of the experiment’s magnetic and velocity fields. Nonetheless, the simulations reproduce the qualitative behavior of the fluctuation-induced large-scale magnetic field as a function of applied field magnitude and magnetic Reynolds number. The scaling of the induced dipole moment as a function of Reynolds number is also presented, demonstrating that the nature of the fluctuations in the simulations changes after a critical value of the Reynolds number is crossed, resulting in a change in the direction of the induced dipole moment. Experimental conditions using corotating impellers are presented, demonstrating that the induced dipole moment may be dependent on the shear layer present in the counter-rotating case. Measurements of velocity field fluctuations are examined to determine the possibility of an inhomogeneous turbulent resistivity. [ABSTRACT FROM AUTHOR]

The study of laminar flows with simple streamlines in conducting fluids that might support kinematic dynamo action has a long history. Early successful examples include the Gailitis (1970) dynamo, which has two meridional rolls. We show here that a single meridional roll, considered as a limit of a modified Gailitis-like dynamo, can also support kinematic dynamo action in a deep spherical shell. This flow has a claim to be the simplest such flow possible. [ABSTRACT FROM AUTHOR]

Using numerical simulations at moderate magnetic Reynolds numbers up to 220, it is shown that in the kinematic regime, isotropic helical turbulence leads to an α-effect and a turbulent diffusivity whose values are independent of the magnetic Reynolds number, Rm, provided Rm exceeds unity. These turbulent coefficients are also consistent with expectations from the first-order smoothing approximation. For small values of Rm, α and turbulent diffusivity are proportional to Rm. Over finite time-intervals, meaningful values of α and turbulent diffusivity can be obtained even when there is small-scale dynamo action that produces strong magnetic fluctuations. This suggests that the fields generated by the small-scale dynamo do not make a correlated contribution to the mean electromotive force. [ABSTRACT FROM AUTHOR]

We present a simple semi-analytical model of non-linear, mean field galactic dynamos and use it to study the effects of various magnetic helicity fluxes. The dynamo equations are reduced using the ‘no- z’ approximation to a non-linear system of ordinary differential equations in time; we demonstrate that the model reproduces accurately earlier results, including those where non-linear behaviour is driven by a magnetic helicity flux. We discuss the implications and interplay of two types of magnetic helicity flux, one produced by advection (e.g. due to the galactic fountain or wind) and the other, arising from anisotropy of turbulence as suggested by Vishniac & Cho. We argue that the latter is significant if the galactic differential rotation is strong enough: in our model, for in terms of the corresponding turbulent magnetic Reynolds number. We confirm that the intensity of gas outflow from the galactic disc optimal for the dynamo action is close to that expected for normal spiral galaxies. The steady-state strength of the large-scale magnetic field supported by the helicity advection is still weaker than that corresponding to equipartition with the turbulent energy. However, the Vishniac–Cho helicity flux can boost magnetic field further to achieve energy equipartition with turbulence. For stronger outflows that may occur in starburst galaxies, the Vishniac–Cho flux can be essential for the dynamo action. However, this mechanism requires a large-scale magnetic field of at least to be launched, so that it has to be preceded by a conventional dynamo assisted by the advection of magnetic helicity by the fountain or wind. [ABSTRACT FROM AUTHOR]

We discuss the current status of solar dynamo theory and describe the dynamo model developed by our group. The toroidal magnetic field is generated in the tachocline by the strong differential rotation and rises to the solar surface due to magnetic buoyancy to create active regions. The decay of these active regions at the surface gives rise to the poloidal magnetic field by the Babcock-Leighton mechanism. This poloidal field is advected by the meridional circulation first to high latitudes and then down below to the tachocline. Dynamo models based on these ideas match different aspects of observational data reasonably well. [ABSTRACT FROM AUTHOR]

The Archontis dynamo was the first stationary dynamo discovered which saturates with almost equal magnetic and kinetic energies in the limit of large Reynolds numbers. In this paper we present two further examples, one based on a series of numerical calculations and the other on the analytic rotor dynamos of Herzenberg. The forcing and flow in these new examples lack some of the symmetries of the Archontis dynamo are therefore more generic. The saturation mechanism is thus not a unique property of the Archontis dynamo. For the numerical solutions, we also have investigated the structure and stability of the flow and field near the stagnation points and those streamlines which enter and leave them. These structures play an important part in the operation of the dynamo mechanism, and the way they interact with one another is mirrored in the analytic example based on the Herzenberg rotors. [ABSTRACT FROM AUTHOR]

The present article considers dynamo action in flows driven by Ekman and Taylor–Couette instabilities. The system comprises a rotating, horizontal plane layer of electrically conducting fluid. The top of the layer is at rest, while the base has a given velocity that drives a net shear across the layer. The fluid flow in the system is parameterised by a Reynolds number Re, the square root of the Taylor number t, and the angle???between the rotation vector and the vertical. When the rotation vector has a vertical component,???? p/2, then in the limit of large t, the shear takes the form of an thin Ekman layer localised at the bottom boundary. This may be subject to a hydrodynamic Ekman instability which for moderate Re generates steady cat's eyes in a co-moving frame. The flow gives dynamo action, amplifying magnetic fields in the form of sheets concentrated on hyperbolic points and their unstable manifolds. At greater Re, the cat's eyes become three-dimensional, and time-dependent amplifying fields with a more irregular structure. In nonlinear regimes the magnetic field and fluid flow show a relaxation oscillation for moderate Re, and for higher values, oscillatory fluid flows sustain tubes of magnetic field. When the rotation vector is entirely horizontal, ??=p /2, the shear driven is uniform across the layer. This can become subject to a primary Taylor–Couette instability driving a cellular flow, and with a further increase of Re, there is a secondary bifurcation to steady, wavy rolls. This flow supports a dynamo and its properties are studied in kinematic and nonlinear regimes. [ABSTRACT FROM AUTHOR]

Several decades since the work E. P. Velikhov, Zh. Éksp. Teor. Fiz. 36,1398 (1959) [Sov. Phys. JETP 9,995 (1959)] [1] concerning magnetorotational instability was published, great astrophysical interest has been manifested in the mechanism of generating a magnetic field in a rotating well-conducting medium in view of difficulties in the development of the theory of anomalous matter transfer in accretion discs both upon the formation of stars and planets from gaseous conglomerations and upon the formation of a galactic core with a black hole at the center {S. A. Balbus and J. F. Hawley, Astrophys. J. 376,214 (1991) [2] and G. Ruediger and R. Hollerbach, TheMagneticUniverse (Wiley–VCH, Weinheim, 2004) [3]}. Attempts to experimentally observe the magnetorotational instability were successful only for spherical geometry in experiments initially devoted to the verification of geomagnetic dynamo theory {D. R. Sisan etal., Phys. Rev. Lett. 93,114502 (2004) [4]}. In experiments with liquid sodium in the complete absence of temperature gradients and, therefore, convection, which is very important for the conventional theory of the geomagnetic dynamo, the generation of the magnetic field was obtained due to the development of the magnetorotational instability, which is usually ignored when developing the theory of the origin of the Earth’s magnetic field. The results obtained in this work enable one to develop a theory of geomagnetic dynamo that is primarily based on the magnetorotational instability, which provides a new insight into not only the origin of the Earth’s magnetic field but its evolution in time. © 2005 Pleiades Publishing, Inc. [ABSTRACT FROM AUTHOR]

Abstract: The current understanding of astrophysical magnetic fields is reviewed, focusing on their generation and maintenance by turbulence. In the astrophysical context this generation is usually explained by a self-excited dynamo, which involves flows that can amplify a weak ‘seed’ magnetic field exponentially fast. Particular emphasis is placed on the nonlinear saturation of the dynamo. Analytic and numerical results are discussed both for small scale dynamos, which are completely isotropic, and for large scale dynamos, where some form of parity breaking is crucial. Central to the discussion of large scale dynamos is the so-called alpha effect which explains the generation of a mean field if the turbulence lacks mirror symmetry, i.e. if the flow has kinetic helicity. Large scale dynamos produce small scale helical fields as a waste product that quench the large scale dynamo and hence the alpha effect. With this in mind, the microscopic theory of the alpha effect is revisited in full detail and recent results for the loss of helical magnetic fields are reviewed. [Copyright &y& Elsevier]

The growth of magnetic field is considered in the stretch–fold–shear map in the limit of weak diffusion. Numerical results are given for insulating, perfectly conducting and periodic boundary conditions. The resulting eigenvalue branches and magnetic fields are related to eigenvalue branches for perfect dynamo action, obtained for zero diffusion using a complex variable formulation. The effect of diffusion on these perfect dynamo modes depends on their structure, growth rate and the diffusive boundary conditions employed. In some cases, the effect of diffusion is a small perturbation, giving a correction going to zero in the limit of weak diffusion, with a scaling exponent given analytically. In other cases weak diffusion can entirely destroy a perfect dynamo branch. Diffusive boundary layers can also generate entirely new branches. These different cases are elucidated, and within the framework of the asymptotic approximations used (which do not constitute a rigorous proof), it is seen that for all three boundary conditions employed, the stretch–fold–shear map is a fast dynamo. [ABSTRACT FROM AUTHOR]

It is shown that the α2-dynamo of magnetohydrodynamics, the hydrodynamic Squire equation as well as an interpolation model of PT-symmetric quantum mechanics are closely related as spectral problems in Krein spaces. For the α2-dynamo and the PT-symmetric model the strong similarities are demonstrated with the help of a 2×2 operator matrix representation, whereas the Squire equation is reinterpreted as a rescaled and Wick-rotated PT-symmetric problem. Based on recent results on the Squire equation the spectrum of the PT-symmetric interpolation model is analyzed in detail and the Herbst limit is described as spectral singularity. [ABSTRACT FROM AUTHOR]

The magnetohydrodynamic dynamo equation is derived within general relativity, using the covariantapproach, for a plasma with finite electrical conductivity. This formalism allows for a clear division and interpretation of plasma and gravitational effects, and we are not restricted to a particular space–time geometry. The results should be of interest in astrophysics and cosmology, and the formulation is well suited to gauge-invariant perturbation theory. Moreover, the dynamo equation is presented in some specific limits. In particular, we consider the interaction of gravitational waves with magnetic fields, and present results for the evolution of the linearly growing electromagnetic induction field, as well as the diffusive damping of these fields. [ABSTRACT FROM AUTHOR]

In this article we address the problem of magnetic field generation and front propagation in turbulent electrically conducting fluids, involving the velocity with finite correlations times and small magnetic diffusivity. We suggest an integro-differential dynamo equation which involves the non-local terms for both the dynamo source α -term and turbulent transport of the mean magnetic field. We derive a set of formulas which allows us to determine the rate of magnetic front propagation in galaxies valid for arbitrary memory kernels. We illustrate the general results through the use of the exponential correlation functions for memory kernels and 'no-z' approximation. We find that the memory effects have strong influence on for both the growth rate and propagation speed. We perform numerical simulations of exterior front speed, and find that the transport memory essentially decreases the propagation rate. [ABSTRACT FROM AUTHOR]

A simple nonlinear model which describes the 1 1-year solar cycle can be derived from the usual α - ω dynamo theory in the form of a Van der Pol equation. Solar activity displays also small- scale inter-cycle persistent stochastic oscillations with a Hurst exponent of the order of H ... 0.76 ± 0.01. The results obtained from the Van der Pol oscillator superimposed on a fractional Brownian motion which describes the stochastic fluctuations are presented. [ABSTRACT FROM AUTHOR]

Mean field dynamo theory is a leading candidate to explain the large scale magnetic fields of galaxies and stars. However, controversy arises over the extent of quenching by the backreaction of the growing field. Here boundary conditions and magnetic helicity flow are shown to play a role in determining whether the mean field dynamo action is fast, as required by astrophysical systems, or resistively limited (slow). Existing work suggesting that mean field dynamos are resistively limited include restrictive approximations such as stationarity and periodic boundary conditions that suppress magnetic helicity flow. Thus even though the backreaction is present, such studies cannot unambiguously reveal whether real astrophysical mean field dynamos are dynamically suppressed when the helicity flow is allowed. If the dynamo is sustained by an outflow of helicity from the system, then a magnetically active corona is expected. Open boundaries alone may not be sufficient for rapid dynamo action and the additional physics of buoyancy and outflows may be required. Possible simulation approaches to test some of the principles are briefly discussed. Some limitations of the"Zeldovich relation" are also addressed. [ABSTRACT FROM AUTHOR]

Mean-field galactic dynamo theory is the leading theory to explain the prevalence of regular magnetic fields in spiral galaxies, but its systematic comparison with observations is still incomplete and fragmentary. Here we compare predictions of mean-field dynamo models to observational data on magnetic pitch angle and the strength of the mean magnetic field. We demonstrate that a standard dynamo model produces pitch angles of the regular magnetic fields of nearby galaxies that are reasonably consistent with available data. The dynamo estimates of the magnetic field strength are generally within a factor of a few of the observational values. Reasonable agreement between theoretical and observed pitch angles generally requires the turbulent correlation time τ to be in the range of 10–, in agreement with standard estimates. Moreover, good agreement also requires that the ratio of the ionized gas scale height to root-mean-square turbulent velocity increases with radius. Our results thus widen the possibilities to constrain interstellar medium parameters using observations of magnetic fields. This work is a step toward systematic statistical tests of galactic dynamo theory. Such studies are becoming more and more feasible as larger data sets are acquired using current and up-and-coming instruments. [ABSTRACT FROM AUTHOR]

A spectacular phenomenon of intermittency, i.e. a progressive growth of higher statistical moments of a physical field excited by an instability in a random medium, attracted the attention of Zeldovich in the last years of his life. At that time, the mathematical aspects underlying the physical description of this phenomenon were still under development and relations between various findings in the field remained obscure. Contemporary results from the theory of the product of independent random matrices (the Furstenberg theory) allowed the elaboration of the phenomenon of intermittency in a systematic way. We consider applications of the Furstenberg theory to some problems in cosmology and dynamo theory. [ABSTRACT FROM PUBLISHER]