Thermodynamics of MHD flows with axial symmetry

We present strategies based upon extremization principles, in the case of the axisymmetric equations of magnetohydrodynamics (MHD). We study the equilibrium shape by using a minimum energy principle under the constraints of the MHD axisymmetric equations. We also propose a numerical algorithm based on a maximum energy dissipation principle to compute in a consistent way the equilibrium states. Then, we develop the statistical mechanics of such flows and recover the same equilibrium states giving a justification of the minimum energy principle. We find that fluctuations obey a Gaussian shape and we make the link between the conservation of the Casimirs on the coarse-grained scale and the process of energy dissipation

Thirty years of change in the fynbos vegetation of the Cape of Good Hope Nature Reserve, South Africa

This study used permanently marked 50 m: sites, surveyed at a 30 year interval, to provide a descriptive account of the temporal change in the fynbos vegetation of the Cape of Good Hope Nature Reserve. South Africa. Management records were used to examine the role of post-fire age. fire frequency and intensity, as well as biotic interactions (competition from overstorey proteoids and alien plants) in influencing vegetation composition over this time period. The mean similarity in species composition of sites between surveys was 62%, indicating an average of nearly 40% turnover in species over the 30 year period. The main causes of this change included differences resulting from different stages in the post-fire succession as well as the impact of differential fire regimes (especially frequency effects). Competition from serotinous Proteaceae. which proved highly mobile after fire, as well as invasive Australian acacias also impacted on the composition of the vegetation over time. The study demonstrated that fynbos communities are temporally dynamic and that the changes over time in species composition are caused by a variety of processes. The study also provided evidence for the role of temporal diversity in contributing to the high species diversity in fynbos systems

Plasma waves driven by gravitational waves in an expanding universe

In a Friedmann-Robertson-Walker (FRW) cosmological model with zero spatial curvature, we consider the interaction of the gravitational waves with the plasma in the presence of a weak magnetic field. Using the relativistic hydromagnetic equations it is verified that large amplitude magnetosonic waves are excited, assuming that both, the gravitational field and the weak magnetic field do not break the homogeneity and isotropy of the considered FRW spacetime.Comment: 14 page

Observation of a Turbulence-Induced Large Scale Magnetic Field

An axisymmetric magnetic field is applied to a spherical, turbulent flow of liquid sodium. An induced magnetic dipole moment is measured which cannot be generated by the interaction of the axisymmetric mean flow with the applied field, indicating the presence of a turbulent electromotive force. It is shown that the induced dipole moment should vanish for any axisymmetric laminar flow. Also observed is the production of toroidal magnetic field from applied poloidal magnetic field (the omega-effect). Its potential role in the production of the induced dipole is discussed.Comment: 5 pages, 4 figures Revisions to accomodate peer-reviewer concerns; changes to main text including simplification of a proof, Fig. 2 updated, and minor typos and clarifications; Added refrences. Resubmitted to Phys. Rev. Let

Fractal-like Distributions over the Rational Numbers in High-throughput Biological and Clinical Data

Recent developments in extracting and processing biological and clinical data are allowing quantitative approaches to studying living systems. High-throughput sequencing, expression profiles, proteomics, and electronic health records are some examples of such technologies. Extracting meaningful information from those technologies requires careful analysis of the large volumes of data they produce. In this note, we present a set of distributions that commonly appear in the analysis of such data. These distributions present some interesting features: they are discontinuous in the rational numbers, but continuous in the irrational numbers, and possess a certain self-similar (fractal-like) structure. The first set of examples which we present here are drawn from a high-throughput sequencing experiment. Here, the self-similar distributions appear as part of the evaluation of the error rate of the sequencing technology and the identification of tumorogenic genomic alterations. The other examples are obtained from risk factor evaluation and analysis of relative disease prevalence and co-mordbidity as these appear in electronic clinical data. The distributions are also relevant to identification of subclonal populations in tumors and the study of the evolution of infectious diseases, and more precisely the study of quasi-species and intrahost diversity of viral populations

Dust-driven Dynamos in Accretion Disks

Magnetically driven astrophysical jets are related to accretion and involve toroidal magnetic field pressure inflating poloidal magnetic field flux surfaces. Examination of particle motion in combined gravitational and magnetic fields shows that these astrophysical jet toroidal and poloidal magnetic fields can be powered by the gravitational energy liberated by accreting dust grains that have become positively charged by emitting photo-electrons. Because a dust grain experiences magnetic forces after becoming charged, but not before, charging can cause irreversible trapping of the grain so dust accretion is a consequence of charging. Furthermore, charging causes canonical angular momentum to replace mechanical angular momentum as the relevant constant of the motion. The resulting effective potential has three distinct classes of accreting particles distinguished by canonical angular momentum, namely (i) "cyclotron-orbit", (ii) "Speiser-orbit", and (iii) "zero canonical angular momentum" particles. Electrons and ions are of class (i) but depending on mass and initial orbit inclination, dust grains can be of any class. Light-weight dust grains develop class (i) orbits such that the grains are confined to nested poloidal flux surfaces, whereas grains with a critical weight such that they experience comparable gravitational and magnetic forces can develop class (ii) or class (iii) orbits, respectively producing poloidal and toroidal field dynamos.Comment: 70 pages, 16 figure

On magnetic field generation in Kolmogorov turbulence

We analyze the initial, kinematic stage of magnetic field evolution in an isotropic and homogeneous turbulent conducting fluid with a rough velocity field, v(l) ~ l^alpha, alpha<1. We propose that in the limit of small magnetic Prandtl number, i.e. when ohmic resistivity is much larger than viscosity, the smaller the roughness exponent, alpha, the larger the magnetic Reynolds number that is needed to excite magnetic fluctuations. This implies that numerical or experimental investigations of magnetohydrodynamic turbulence with small Prandtl numbers need to achieve extremely high resolution in order to describe magnetic phenomena adequately.Comment: 4 pages, revised, new material adde

Ullemar's formula for the Jacobian of the complex moment mapping

The complex moment sequence m(P) is assigned to a univalent polynomial P by the Cauchy transform of the P(D), where D is the unit disk. We establish the representation of the Jacobian det dm(P) in terms of roots of the derivative P'. Combining this result with the special decomposition for the Hurwitz determinants, we prove a formula for the Jacobian which was previously conjectured by C. Ullemar. As a consequence, we show that the boundary of the class of all locally univalent polynomials in $U$ is contained in the union of three irreducible algebraic surfaces.Comment: 14 pages, submitted for "Complex Variables. Theory and Application

Numerical simulations of current generation and dynamo excitation in a mechanically-forced, turbulent flow

The role of turbulence in current generation and self-excitation of magnetic fields has been studied in the geometry of a mechanically driven, spherical dynamo experiment, using a three dimensional numerical computation. A simple impeller model drives a flow which can generate a growing magnetic field, depending upon the magnetic Reynolds number, Rm, and the fluid Reynolds number. When the flow is laminar, the dynamo transition is governed by a simple threshold in Rm, above which a growing magnetic eigenmode is observed. The eigenmode is primarily a dipole field tranverse to axis of symmetry of the flow. In saturation the Lorentz force slows the flow such that the magnetic eigenmode becomes marginally stable. For turbulent flow, the dynamo eigenmode is suppressed. The mechanism of suppression is due to a combination of a time varying large-scale field and the presence of fluctuation driven currents which effectively enhance the magnetic diffusivity. For higher Rm a dynamo reappears, however the structure of the magnetic field is often different from the laminar dynamo; it is dominated by a dipolar magnetic field which is aligned with the axis of symmetry of the mean-flow, apparently generated by fluctuation-driven currents. The fluctuation-driven currents have been studied by applying a weak magnetic field to laminar and turbulent flows. The magnetic fields generated by the fluctuations are significant: a dipole moment aligned with the symmetry axis of the mean-flow is generated similar to those observed in the experiment, and both toroidal and poloidal flux expulsion are observed.Comment: 14 pages, 14 figure

Stellar Hydrodynamics in Radiative Regions

We present an analysis of the response of a radiative region to waves generated by a convective region of the star; this wave treatment of the classical problem of ``overshooting'' gives extra mixing relative to the treatment traditionally used in stellar evolutionary codes. The interface between convectively stable and unstable regions is dynamic and nonspherical, so that the nonturbulent material is driven into motion, even in the absence of ``penetrative overshoot.'' These motions may be described by the theory of nonspherical stellar pulsations, and are related to motion measured by helioseismology. Multi-dimensional numerical simulations of convective flow show puzzling features which we explain by this simplified physical model. Gravity waves generated at the interface are dissipated, resulting in slow circulation and mixing seen outside the formal convection zone. The approach may be extended to deal with rotation and composition gradients. Tests of this description in the stellar evolution code TYCHO produce carbon stars on the asymptotic giant branch (AGB), an isochrone age for the Hyades and three young clusters with lithium depletion ages from brown dwarfs, and lithium and beryllium depletion consistent with observations of the Hyades and Pleiades, all without tuning parameters. The insight into the different contributions of rotational and hydrodynamic mixing processes could have important implications for realistic simulation of supernovae and other questions in stellar evolution.Comment: 27 pages, 5 figures, accepted to the Astrophysical Journa