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 $n$-vertex NIC-planar graph admits a NIC-planar RAC drawing with at most one bend per edge on a grid of size $O(n) \times O(n)$. Then, we show that every $n$-vertex 1-planar graph admits a 1-planar RAC drawing with at most two bends per edge on a grid of size $O(n^3) \times O(n^3)$. 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 $W^\pm$ and $W^\pm$ 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 $TeV$ scale could in principle be observable at the Tevatron with $10^6$ $W^\pm$ decays.Comment: 15 pgs with standard LATEX, 7 ps figures embedded with eps