1,529 research outputs found
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
Growth rate degeneracies in kinematic dynamos
We consider the classical problem of kinematic dynamo action in simple steady flows. Due to the adjointness of the induction operator, we show that the growth rate of the dynamo will be exactly the same for two types of magnetic boundary conditions: the magnetic field can be normal (infinite magnetic permeability, also called pseudovacuum) or tangent (perfect electrical conductor) to the boundaries of the domain. These boundary conditions correspond to well-defined physical limits often used in numerical models and relevant to laboratory experiments. The only constraint is for the velocity field u to be reversible, meaning there exists a transformation changing u into âu. We illustrate this surprising property using S2T2 type of flows in spherical geometry inspired by [Dudley and James, Proc. R. Soc. London A 425, 407 (1989)]. Using both types of boundary conditions, it is shown that the growth rates of the dynamos are identical, although the corresponding magnetic eigenmodes are drastically different
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
A Magnetically-Switched, Rotating Black Hole Model For the Production of Extragalactic Radio Jets and the Fanaroff and Riley Class Division
A model is presented in which both Fanaroff and Riley class I and II
extragalactic jets are produced by magnetized accretion disk coronae in the
ergospheres of rotating black holes. While the jets are produced in the
accretion disk itself, the output power still is an increasing function of the
black hole angular momentum. For high enough spin, the black hole triggers the
magnetic switch, producing highly-relativistic, kinetic-energy-dominated jets
instead of Poynting-flux-dominated ones for lower spin. The coronal mass
densities needed to trigger the switch at the observed FR break power are quite
small (), implying that the source of the jet material
may be either a pair plasma or very tenuous electron-proton corona, not the
main accretion disk itself.
The model explains the differences in morphology and Mach number between FR I
and II sources and the observed trend for massive galaxies to undergo the FR
I/II transition at higher radio power. It also is consistent with the energy
content of extended radio lobes and explains why, because of black hole
spindown, the space density of FR II sources should evolve more rapidly than
that of FR I sources.
If the present model is correct, then the ensemble average speed of
parsec-scale jets in sources distinguished by their FR I morphology (not
luminosity) should be distinctly slower than that for sources with FR II
morphology. The model also suggests the existence of a population of
high-redshift, sub-mJy FR I and II radio sources associated with spiral or
pre-spiral galaxies that flared once when their black holes were formed but
were never again re-kindled by mergers.Comment: 14 pages, 2 figures, final version to appear in Sept Ap
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
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
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 is contained in the union of
three irreducible algebraic surfaces.Comment: 14 pages, submitted for "Complex Variables. Theory and Application
Bounds on the Magnetic Fields in the Radiative Zone of the Sun
We discuss bounds on the strength of the magnetic fields that could be buried
in the radiative zone of the Sun. The field profiles and decay times are
computed for all axisymmetric toroidal Ohmic decay eigenmodes with lifetimes
exceeding the age of the Sun. The measurements of the solar oblateness yield a
bound <~ 7 MG on the strength of the field. A comparable bound is expected to
come from the analysis of the splitting of the solar oscillation frequencies.
The theoretical analysis of the double diffusive instability also yields a
similar bound. The oblateness measurements at their present level of
sensitivity are therefore not expected to measure a toroidal field
contribution.Comment: 15 pages, 6 figure
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