3,635 research outputs found
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
Vorticity production and survival in viscous and magnetized cosmologies
We study the role of viscosity and the effects of a magnetic field on a
rotating, self-gravitating fluid, using Newtonian theory and adopting the ideal
magnetohydrodynamic approximation. Our results confirm that viscosity can
generate vorticity in inhomogeneous environments, while the magnetic tension
can produce vorticity even in the absence of fluid pressure and density
gradients. Linearizing our equations around an Einstein-de Sitter cosmology, we
find that viscosity adds to the diluting effect of the universal expansion.
Typically, however, the dissipative viscous effects are confined to relatively
small scales. We also identify the characteristic length bellow which the
viscous dissipation is strong and beyond which viscosity is essentially
negligible. In contrast, magnetism seems to favor cosmic rotation. The magnetic
presence is found to slow down the standard decay-rate of linear vortices, thus
leading to universes with more residual rotation than generally anticipated.Comment: Minor changes. References added and updated. Published versio
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
Active and Passive Fields in Turbulent Transport: the Role of Statistically Preserved Structures
We have recently proposed that the statistics of active fields (which affect
the velocity field itself) in well-developed turbulence are also dominated by
the Statistically Preserved Structures of auxiliary passive fields which are
advected by the same velocity field. The Statistically Preserved Structures are
eigenmodes of eigenvalue 1 of an appropriate propagator of the decaying
(unforced) passive field, or equivalently, the zero modes of a related
operator. In this paper we investigate further this surprising finding via two
examples, one akin to turbulent convection in which the temperature is the
active scalar, and the other akin to magneto-hydrodynamics in which the
magnetic field is the active vector. In the first example, all the even
correlation functions of the active and passive fields exhibit identical
scaling behavior. The second example appears at first sight to be a
counter-example: the statistical objects of the active and passive fields have
entirely different scaling exponents. We demonstrate nevertheless that the
Statistically Preserved Structures of the passive vector dominate again the
statistics of the active field, except that due to a dynamical conservation law
the amplitude of the leading zero mode cancels exactly. The active vector is
then dominated by the sub-leading zero mode of the passive vector. Our work
thus suggests that the statistical properties of active fields in turbulence
can be understood with the same generality as those of passive fields.Comment: 13 pages, 13 figures, submitted to Phys. Rev.
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
Statistical Description of a Magnetized Corona above a Turbulent Accretion Disk
We present a physics-based statistical theory of a force-free magnetic field
in the corona above a turbulent accretion disk. The field is represented by a
statistical ensemble of loops tied to the disk. Each loop evolves under several
physical processes: Keplerian shear, turbulent random walk of the disk
footpoints, and reconnection with other loops. To build a statistical
description, we introduce the distribution function of loops over their sizes
and construct a kinetic equation that governs its evolution. This loop kinetic
equation is formally analogous to Boltzmann's kinetic equation, with loop-loop
reconnection described by a binary collision integral. A dimensionless
parameter is introduced to scale the (unknown) overall rate of reconnection
relative to Keplerian shear. After solving for the loop distribution function
numerically, we calculate self-consistently the distribution of the mean
magnetic pressure and dissipation rate with height, and the equilibrium shapes
of loops of different sizes. We also compute the energy and torque associated
with a given loop, as well as the total magnetic energy and torque in the
corona. We explore the dependence of these quantities on the reconnection
parameter and find that they can be greatly enhanced if reconnection between
loops is suppressed.Comment: 22 pages, 15 figures. Submitted to the Astrophysical Journa
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
Looking for CP Violation in W Production and Decay
We describe CP violating observables in resonant and plus one
jet production at the Tevatron. We present simple examples of CP violating
effective operators, consistent with the symmetries of the Standard Model,
which would give rise to these observables. We find that CP violating effects
coming from new physics at the scale could in principle be observable at
the Tevatron with decays.Comment: 15 pgs with standard LATEX, 7 ps figures embedded with eps
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