52 research outputs found
Double-diffusive convection in a rotating cylindrical annulus with conical caps
Double-diffusive convection driven by both thermal and compositional buoyancy
in a rotating cylindrical annulus with conical caps is considered with the aim
to establish whether a small fraction of compositional buoyancy added to the
thermal buoyancy (or vice versa) can significantly reduce the critical Rayleigh
number and amplify convection in planetary cores. It is shown that the neutral
surface describing the onset of convection in the double-buoyancy case is
essentially different from that of the well-studied purely thermal case, and
does indeed allow the possibility of low-Rayleigh number convection. In
particular, isolated islands of instability are formed by an additional
"double-diffusive" eigenmode in certain regions of the parameter space.
However, the amplitude of such low-Rayleigh number convection is relatively
weak. At similar flow amplitudes purely compositional and double-diffusive
cases are characterized by a stronger time dependence compared to purely
thermal cases, and by a prograde mean zonal flow near the inner cylindrical
surface. Implications of the results for planetary core convection are briefly
discussed.Comment: Accepted for publication in Physics of the Earth and Planetary
Interiors on 20 April 201
How far can minimal models explain the solar cycle?
A physically consistent model of magnetic field generation by convection in a
rotating spherical shell with a minimum of parameters is applied to the Sun.
Despite its unrealistic features the model exhibits a number of properties
resembling those observed on the Sun. The model suggests that the large scale
solar dynamo is dominated by a non-axisymmetric component of the magnetic
field.Comment: Accepted for publication in the Astrophysical Journal on 2012/01/3
Magneto-inertial convection in rotating fluid spheres
The onset of convection in the form of magneto-inertial waves in a rotating
fluid sphere permeated by a constant axial electric current is studied through
a perturbation analysis. Explicit expressions for the dependence of the
Rayleigh number on the azimuthal wavenumber are derived in the limit of high
thermal diffusivity. Results for the cases of thermally infinitely conducting
and of nearly thermally insulating boundaries are obtained.Comment: 10 pages, 5 figures, to be submitted for publicatio
Asymptotic properties of mathematical models of excitability
We analyse small parameters in selected models of biological excitability,
including Hodgkin-Huxley (1952) model of nerve axon, Noble (1962) model of
heart Purkinje fibres, and Courtemanche et al. (1998) model of human atrial
cells. Some of the small parameters are responsible for differences in the
characteristic timescales of dynamic variables, as in the traditional singular
perturbation approaches. Others appear in a way which makes the standard
approaches inapplicable. We apply this analysis to study the behaviour of
fronts of excitation waves in spatially-extended cardiac models. Suppressing
the excitability of the tissue leads to a decrease in the propagation speed,
but only to a certain limit; further suppression blocks active propagation and
leads to a passive diffusive spread of voltage. Such a dissipation may happen
if a front propagates into a tissue recovering after a previous wave, e.g.
re-entry. A dissipated front does not recover even when the excitability
restores. This has no analogy in FitzHugh-Nagumo model and its variants, where
fronts can stop and then start again. In two spatial dimensions, dissipation
accounts for break-ups and self-termination of re-entrant waves in excitable
media with Courtemanche et al. (1998) kinetics.Comment: 15 pages, 8 figures, to appear in Phil Trans Roy Soc London
Non-symmetric magnetohydrostatic equilibria:a multigrid approach
Aims. Linear magnetohydrostatic (MHS) models of solar magnetic fields balance plasma pressure gradients, gravity and Lorentz forces where the current density is composed of a linear force-free component and a cross-field component that depends on gravitational stratification. In this paper, we investigate an efficient numerical procedure for calculating such equilibria.Methods. The MHS equations are reduced to two scalar elliptic equations – one on the lower boundary and the other within the interior of the computational domain. The normal component of the magnetic field is prescribed on the lower boundary and a multigrid method is applied on both this boundary and within the domain to find the poloidal scalar potential. Once solved to a desired accuracy, the magnetic field, plasma pressure and density are found using a finite difference method.Results. We investigate the effects of the cross-field currents on the linear MHS equilibria. Force-free and non-force-free examples are given to demonstrate the numerical scheme and an analysis of speed-up due to parallelization on a graphics processing unit (GPU) is presented. It is shown that speed-ups of ×30 are readily achievable
Asymptotics of conduction velocity restitution in models of electrical excitation in the heart.
Copyright © Springer 2011Journal ArticleThe original publication is available at www.springerlink.com - http://link.springer.com/article/10.1007/s11538-010-9523-6We extend a non-Tikhonov asymptotic embedding, proposed earlier, for calculation of conduction velocity restitution curves in ionic models of cardiac excitability. Conduction velocity restitution is the simplest non-trivial spatially extended problem in excitable media, and in the case of cardiac tissue it is an important tool for prediction of cardiac arrhythmias and fibrillation. An idealized conduction velocity restitution curve requires solving a non-linear eigenvalue problem with periodic boundary conditions, which in the cardiac case is very stiff and calls for the use of asymptotic methods. We compare asymptotics of restitution curves in four examples, two generic excitable media models, and two ionic cardiac models. The generic models include the classical FitzHugh-Nagumo model and its variation by Barkley. They are treated with standard singular perturbation techniques. The ionic models include a simplified "caricature" of Noble (J. Physiol. Lond. 160:317-352, 1962) model and Beeler and Reuter (J. Physiol. Lond. 268:177-210, 1977) model, which lead to non-Tikhonov problems where known asymptotic results do not apply. The Caricature Noble model is considered with particular care to demonstrate the well-posedness of the corresponding boundary-value problem. The developed method for calculation of conduction velocity restitution is then applied to the Beeler-Reuter model. We discuss new mathematical features appearing in cardiac ionic models and possible applications of the developed method
Bistability and hysteresis of dipolar dynamos generated by turbulent convection in rotating spherical shells
Bistability and hysteresis of magnetohydrodynamic dipolar dynamos generated by turbulent convection in rotating spherical fluid shells is demonstrated. Hysteresis appears as a transition between two distinct regimes of dipolar dynamos with rather different properties including a pronounced difference in the amplitude of the axisymmetric poloidal field component and in the form of the differential rotation. The bistability occurs from the onset of dynamo action up to about 9 times the critical value of the Rayleigh number for onset of convection and over a wide range of values of the ordinary and the magnetic Prandtl numbers including the value unity
Planetary dynamos
The theory of planetary dynamos and its applications to observed phenomena of
planetary magnetism are outlined. It is generally accepted that convection
flows driven by thermal or compositional buoyancy are the most likely source
for the sustenance of global planetary magnetic fields. While the existence of
dynamos in electrically conducting fluid planetary cores provides constraints
on properties of the latter, the lack of knowledge about time dependences of
the magnetic fields and about their toroidal components together with the
restricted parameter regions accessible to theory have prevented so far a full
understanding of the phenomena of planetary magnetism
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