On the mean field dynamo with Hall effect

We study in the present paper how Hall effect modifies the quenching process of the electromotive force (e.m.f.) in Mean Field Dynamo (MFD) theories. We write down the evolution equations for the e.m.f. and for the large and small scale magnetic helicity, treat Hall effect as a perturbation and integrate the resulting equations assuming boundary conditions such that the total divergencies vanish. For force-free large scale magnetic fields, Hall effect acts by coupling the small scale velocity and magnetic fields. For the range of parameters considered, the overall effect is a stronger quenching of the e.m.f. than in standard MHD and a damping of the inverse cascade of magnetic helicity. In astrophysical environments characterized by the parameters considered here, Hall effect would produce an earlier quenching of the e.m.f. and consequently a weaker large scale magnetic field.Comment: 8 pages, 4 figures. Accepted by A&

Asymptotics of capture zone distributions in a fragmentation-based model of submonolayer deposition

We consider the asymptotics of the distribution of the capture zones associated with the islands nucleated during submonolayer deposition onto a one-dimensional substrate. We use a convolution of the distribution of inter-island gaps, the asymptotics of which is known for a class of nucleation models, to derive the asymptotics for the capture zones. The results are in broad agreement with published Monte Carlo simulation data (O'Neill et al., 2012) [13]

Accretion Disks and Dynamos: Toward a Unified Mean Field Theory

Conversion of gravitational energy into radiation in accretion discs and the origin of large scale magnetic fields in astrophysical rotators have often been distinct topics of research. In semi-analytic work on both problems it has been useful to presume large scale symmetries, necessarily resulting in mean field theories. MHD turbulence makes the underlying systems locally asymmetric and nonlinear. Synergy between theory and simulations should aim for the development of practical mean field models that capture essential physics and can be used for observational modeling. Mean field dynamo (MFD) theory and alpha-viscosity accretion theory exemplify such ongoing pursuits. 21st century MFD theory has more nonlinear predictive power compared to 20th century MFD theory, whereas accretion theory is still in a 20th century state. In fact, insights from MFD theory are applicable to accretion theory and the two are artificially separated pieces of what should be a single theory. I discuss pieces of progress that provide clues toward a unified theory. A key concept is that large scale magnetic fields can be sustained via local or global magnetic helicity fluxes or via relaxation of small scale magnetic fluctuations, without the kinetic helicity driver of 20th century textbooks. These concepts may help explain the formation of large scale fields that supply non-local angular momentum transport via coronae and jets in a unified theory of accretion and dynamos. In diagnosing the role of helicities and helicity fluxes in disk simulations, each disk hemisphere should be studied separately to avoid being misled by cancelation that occurs as a result of reflection asymmetry. The fraction of helical field energy in disks is expected to be small compared to the total field in each hemisphere as a result of shear, but can still be essential for large scale dynamo action.Comment: For the Proceedings of the Third International Conference and Advanced School "Turbulent Mixing and Beyond," TMB-2011 held on 21 - 28 August 2011 at the Abdus Salam International Centre for Theoretical Physics, Trieste, http://users.ictp.it/~tmb/index2011.html Italy, To Appear in Physica Scripta (corrected small items to match version in print

Molecular gyroscopes and biological effects of weak ELF magnetic fields

Extremely-low-frequency magnetic fields are known to affect biological systems. In many cases, biological effects display `windows' in biologically effective parameters of the magnetic fields: most dramatic is the fact that relatively intense magnetic fields sometimes do not cause appreciable effect, while smaller fields of the order of 10--100 $\mu$T do. Linear resonant physical processes do not explain frequency windows in this case. Amplitude window phenomena suggest a nonlinear physical mechanism. Such a nonlinear mechanism has been proposed recently to explain those `windows'. It considers quantum-interference effects on protein-bound substrate ions. Magnetic fields cause an interference of ion quantum states and change the probability of ion-protein dissociation. This ion-interference mechanism predicts specific magnetic-field frequency and amplitude windows within which biological effects occur. It agrees with a lot of experiments. However, according to the mechanism, the lifetime $\Gamma^{-1}$ of ion quantum states within a protein cavity should be of unrealistic value, more than 0.01 s for frequency band 10--100 Hz. In this paper, a biophysical mechanism has been proposed that (i) retains the attractive features of the ion interference mechanism and (ii) uses the principles of gyroscopic motion and removes the necessity to postulate large lifetimes. The mechanism considers dynamics of the density matrix of the molecular groups, which are attached to the walls of protein cavities by two covalent bonds, i.e., molecular gyroscopes. Numerical computations have shown almost free rotations of the molecular gyros. The relaxation time due to van der Waals forces was about 0.01 s for the cavity size of 28 angstr\"{o}ms.Comment: 10 pages, 7 figure

Finite-Size Scaling in the Energy-Entropy Plane for the 2D +- J Ising Spin Glass

For $L \times L$ square lattices with $L \le 20$ the 2D Ising spin glass with +1 and -1 bonds is found to have a strong correlation between the energy and the entropy of its ground states. A fit to the data gives the result that each additional broken bond in the ground state of a particular sample of random bonds increases the ground state degeneracy by approximately a factor of 10/3. For $x = 0.5$ (where $x$ is the fraction of negative bonds), over this range of $L$, the characteristic entropy defined by the energy-entropy correlation scales with size as $L^{1.78(2)}$. Anomalous scaling is not found for the characteristic energy, which essentially scales as $L^2$. When $x= 0.25$, a crossover to $L^2$ scaling of the entropy is seen near $L = 12$. The results found here suggest a natural mechanism for the unusual behavior of the low temperature specific heat of this model, and illustrate the dangers of extrapolating from small $L$.Comment: 9 pages, two-column format; to appear in J. Statistical Physic

Jet Deflection via Cross winds: Laboratory Astrophysical Studies

We present new data from High Energy Density (HED) laboratory experiments designed to explore the interaction of a heavy hypersonic radiative jet with a cross wind. The jets are generated with the MAGPIE pulsed power machine where converging conical plasma flows are produced from a cylindrically symmetric array of inclined wires. Radiative hypersonic jets emerge from the convergence point. The cross wind is generated by ablation of a plastic foil via soft-X-rays from the plasma convergence region. Our experiments show that the jets are deflected by the action of the cross wind with the angle of deflection dependent on the proximity of the foil. Shocks within the jet beam are apparent in the data. Analysis of the data shows that the interaction of the jet and cross wind is collisional and therefore in the hydro-dynamic regime. MHD plasma code simulations of the experiments are able to recover the deflection behaviour seen in the experiments. We consider the astrophysical relevance of these experiments applying published models of jet deflection developed for AGN and YSOs. Fitting the observed jet deflections to quadratic trajectories predicted by these models allows us to recover a set of plasma parameters consistent with the data. We also present results of 3-D numerical simulations of jet deflection using a new astrophysical Adaptive Mesh Refinement code. These simulations show highly structured shocks occurring within the beam similar to what was observed in the experimentsComment: Submitted to ApJ. For a version with figures go to http://web.pas.rochester.edu/~afrank/labastro/CW/Jet-Wind-Frank.pd