3,593 research outputs found
Apparent suppression of turbulent magnetic dynamo action by a dc magnetic field
Numerical studies of the effect of a dc magnetic field on dynamo action
(development of magnetic fields with large spatial scales), due to
helically-driven magnetohydrodynamic turbulence, are reported. The apparent
effect of the dc magnetic field is to suppress the dynamo action, above a
relatively low threshold. However, the possibility that the suppression results
from an improper combination of rectangular triply spatially-periodic boundary
conditions and a uniform dc magnetic field is addressed: heretofore a common
and convenient computational convention in turbulence investigations. Physical
reasons for the observed suppression are suggested. Other geometries and
boundary conditions are offered for which the dynamo action is expected not to
be suppressed by the presence of a dc magnetic field component.Comment: To appear in Physics of Plasma
Dissociation in a polymerization model of homochirality
A fully self-contained model of homochirality is presented that contains the
effects of both polymerization and dissociation. The dissociation fragments are
assumed to replenish the substrate from which new monomers can grow and undergo
new polymerization. The mean length of isotactic polymers is found to grow
slowly with the normalized total number of corresponding building blocks.
Alternatively, if one assumes that the dissociation fragments themselves can
polymerize further, then this corresponds to a strong source of short polymers,
and an unrealistically short average length of only 3. By contrast, without
dissociation, isotactic polymers becomes infinitely long.Comment: 16 pages, 6 figures, submitted to Orig. Life Evol. Biosp
Compact Drawings of 1-Planar Graphs with Right-Angle Crossings and Few Bends
We study the following classes of beyond-planar graphs: 1-planar, IC-planar,
and NIC-planar graphs. These are the graphs that admit a 1-planar, IC-planar,
and NIC-planar drawing, respectively. A drawing of a graph is 1-planar if every
edge is crossed at most once. A 1-planar drawing is IC-planar if no two pairs
of crossing edges share a vertex. A 1-planar drawing is NIC-planar if no two
pairs of crossing edges share two vertices. We study the relations of these
beyond-planar graph classes (beyond-planar graphs is a collective term for the
primary attempts to generalize the planar graphs) to right-angle crossing (RAC)
graphs that admit compact drawings on the grid with few bends. We present four
drawing algorithms that preserve the given embeddings. First, we show that
every -vertex NIC-planar graph admits a NIC-planar RAC drawing with at most
one bend per edge on a grid of size . Then, we show that
every -vertex 1-planar graph admits a 1-planar RAC drawing with at most two
bends per edge on a grid of size . Finally, we make two
known algorithms embedding-preserving; for drawing 1-planar RAC graphs with at
most one bend per edge and for drawing IC-planar RAC graphs straight-line
Chirality Selection in Open Flow Systems and in Polymerization
As an attempt to understand the homochirality of organic molecules in life, a
chemical reaction model is proposed where the production of chiral monomers
from achiral substrate is catalyzed by the polymers of the same enatiomeric
type. This system has to be open because in a closed system the enhanced
production of chiral monomers by enzymes is compensated by the associated
enhancement in back reaction, and the chiral symmetry is conserved. Open flow
without cross inhibition is shown to lead to the chirality selection in a
general model. In polymerization, the influx of substrate from the ambience and
the efflux of chiral products for purposes other than the catalyst production
make the system necessarily open. The chiral symmetry is found to be broken if
the influx of substrate lies within a finite interval. As the efficiency of the
enzyme increases, the maximum value of the enantiomeric excess approaches unity
so that the chirality selection becomes complete.Comment: 8 pages, 4 figure
Simulations of galactic dynamos
We review our current understanding of galactic dynamo theory, paying
particular attention to numerical simulations both of the mean-field equations
and the original three-dimensional equations relevant to describing the
magnetic field evolution for a turbulent flow. We emphasize the theoretical
difficulties in explaining non-axisymmetric magnetic fields in galaxies and
discuss the observational basis for such results in terms of rotation measure
analysis. Next, we discuss nonlinear theory, the role of magnetic helicity
conservation and magnetic helicity fluxes. This leads to the possibility that
galactic magnetic fields may be bi-helical, with opposite signs of helicity and
large and small length scales. We discuss their observational signatures and
close by discussing the possibilities of explaining the origin of primordial
magnetic fields.Comment: 28 pages, 15 figure, to appear in Lecture Notes in Physics "Magnetic
fields in diffuse media", Eds. E. de Gouveia Dal Pino and A. Lazaria
Pixel and Voxel Representations of Graphs
We study contact representations for graphs, which we call pixel
representations in 2D and voxel representations in 3D. Our representations are
based on the unit square grid whose cells we call pixels in 2D and voxels in
3D. Two pixels are adjacent if they share an edge, two voxels if they share a
face. We call a connected set of pixels or voxels a blob. Given a graph, we
represent its vertices by disjoint blobs such that two blobs contain adjacent
pixels or voxels if and only if the corresponding vertices are adjacent. We are
interested in the size of a representation, which is the number of pixels or
voxels it consists of.
We first show that finding minimum-size representations is NP-complete. Then,
we bound representation sizes needed for certain graph classes. In 2D, we show
that, for -outerplanar graphs with vertices, pixels are
always sufficient and sometimes necessary. In particular, outerplanar graphs
can be represented with a linear number of pixels, whereas general planar
graphs sometimes need a quadratic number. In 3D, voxels are
always sufficient and sometimes necessary for any -vertex graph. We improve
this bound to for graphs of treewidth and to
for graphs of genus . In particular, planar graphs
admit representations with voxels
Astrophysical turbulence modeling
The role of turbulence in various astrophysical settings is reviewed. Among
the differences to laboratory and atmospheric turbulence we highlight the
ubiquitous presence of magnetic fields that are generally produced and
maintained by dynamo action. The extreme temperature and density contrasts and
stratifications are emphasized in connection with turbulence in the
interstellar medium and in stars with outer convection zones, respectively. In
many cases turbulence plays an essential role in facilitating enhanced
transport of mass, momentum, energy, and magnetic fields in terms of the
corresponding coarse-grained mean fields. Those transport properties are
usually strongly modified by anisotropies and often completely new effects
emerge in such a description that have no correspondence in terms of the
original (non coarse-grained) fields.Comment: 88 pages, 26 figures, published in Reports on Progress in Physic
Current status of turbulent dynamo theory: From large-scale to small-scale dynamos
Several recent advances in turbulent dynamo theory are reviewed. High
resolution simulations of small-scale and large-scale dynamo action in periodic
domains are compared with each other and contrasted with similar results at low
magnetic Prandtl numbers. It is argued that all the different cases show
similarities at intermediate length scales. On the other hand, in the presence
of helicity of the turbulence, power develops on large scales, which is not
present in non-helical small-scale turbulent dynamos. At small length scales,
differences occur in connection with the dissipation cutoff scales associated
with the respective value of the magnetic Prandtl number. These differences are
found to be independent of whether or not there is large-scale dynamo action.
However, large-scale dynamos in homogeneous systems are shown to suffer from
resistive slow-down even at intermediate length scales. The results from
simulations are connected to mean field theory and its applications. Recent
work on helicity fluxes to alleviate large-scale dynamo quenching, shear
dynamos, nonlocal effects and magnetic structures from strong density
stratification are highlighted. Several insights which arise from analytic
considerations of small-scale dynamos are discussed.Comment: 36 pages, 11 figures, Spa. Sci. Rev., submitted to the special issue
"Magnetism in the Universe" (ed. A. Balogh
- …