Theoretical analysis of flux amplification by soft magnetic material in a putative biological magnetic-field receptor

Birds are endowed with a magnetic sense that allows them to detectEarth’s magnetic field and to use it for orientation. Physiological andbehavioral experiments have shown the upper beak to host amagnetoreceptor. Putative magnetoreceptive structures in the beak arenerve terminals that each contain a dozen or so of micrometer-sizedclusters of superparamagnetic nanocrystals made of magnetite/maghemiteand numerous electron-opaque platelets filled with a so farunidentified, amorphous ferric iron compound. The platelets typicallyform chainlike structures, which have been proposed to function asmagnetic flux focusers for detecting the intensity of the geomagneticfield. Here, we test that proposition from first principles and developan unconstrained model to determine the equilibrium distribution ofmagnetization along a linear chain of platelets which we assume tobehave magnetically soft and to have no magnetic remanence. Ouranalysis, which is valid for arbitrary values of the intrinsic magneticsusceptibility chi, shows that chi needs to be much greater than unityto amplify the external field by two orders of magnitude in a chain ofplatelets. However, the high amplification is confined to the centralregion of the chain and subsides quadratically toward the ends of thechain. For large values of chi, the possibility opens up of realizingmagnetoreceptor mechanisms on the basis of attraction forces betweenadjacent platelets in a linear chain. The force in the central region ofthe chain may amount to several pN, which would be sufficient to convertmagnetic input energy into mechanical output energy. The strikingfeature of an ensemble of platelets is its ability to organize intotightly spaced chains under the action of an external field of givenstrength. We discuss how this property can be exploited for amagnetoreception mechanism

Critical Dynamics of Self-Organizing Eulerian Walkers

The model of self-organizing Eulerian walkers is numerically investigated on the square lattice. The critical exponents for the distribution of a number of steps ($\tau_l$) and visited sites ($\tau_s$) characterizing the process of transformation from one recurrent configuration to another are calculated using the finite-size scaling analysis. Two different kinds of dynamical rules are considered. The results of simulations show that both the versions of the model belong to the same class of universality with the critical exponents $\tau_l=\tau_s=1.75\pm 0.1$.Comment: 3 pages, 4 Postscript figures, RevTeX, additional information available at http://thsun1.jinr.dubna.su/~shche

Distribution of sizes of erased loops of loop-erased random walks in two and three dimensions

We show that in the loop-erased random walk problem, the exponent characterizing probability distribution of areas of erased loops is superuniversal. In d-dimensions, the probability that the erased loop has an area A varies as A^{-2} for large A, independent of d, for 2 <= d <= 4. We estimate the exponents characterizing the distribution of perimeters and areas of erased loops in d = 2 and 3 by large-scale Monte Carlo simulations. Our estimate of the fractal dimension z in two-dimensions is consistent with the known exact value 5/4. In three-dimensions, we get z = 1.6183 +- 0.0004. The exponent for the distribution of durations of avalanche in the three-dimensional abelian sandpile model is determined from this by using scaling relations.Comment: 25 pages, 1 table, 8 figure

Reversals in nature and the nature of reversals

The asymmetric shape of reversals of the Earth's magnetic field indicates a possible connection with relaxation oscillations as they were early discussed by van der Pol. A simple mean-field dynamo model with a spherically symmetric $\alpha$ coefficient is analysed with view on this similarity, and a comparison of the time series and the phase space trajectories with those of paleomagnetic measurements is carried out. For highly supercritical dynamos a very good agreement with the data is achieved. Deviations of numerical reversal sequences from Poisson statistics are analysed and compared with paleomagnetic data. The role of the inner core is discussed in a spectral theoretical context and arguments and numerical evidence is compiled that the growth of the inner core might be important for the long term changes of the reversal rate and the occurrence of superchrons.Comment: 24 pages, 12 figure

Radiative Models of Sagittarius A* and M87 from Relativistic MHD Simulations

Ongoing millimeter VLBI observations with the Event Horizon Telescope allow unprecedented study of the innermost portion of black hole accretion flows. Interpreting the observations requires relativistic, time-dependent physical modeling. We discuss the comparison of radiative transfer calculations from general relativistic MHD simulations of Sagittarius A* and M87 with current and future mm-VLBI observations. This comparison allows estimates of the viewing geometry and physical conditions of the Sgr A* accretion flow. The viewing geometry for M87 is already constrained from observations of its large-scale jet, but, unlike Sgr A*, there is no consensus for its millimeter emission geometry or electron population. Despite this uncertainty, as long as the emission region is compact, robust predictions for the size of its jet launching region can be made. For both sources, the black hole shadow may be detected with future observations including ALMA and/or the LMT, which would constitute the first direct evidence for a black hole event horizon.Comment: 8 pages, 2 figures, submitted to the proceedings of AHAR 2011: The Central Kiloparse

Probing photo-ionization: Experiments on positive streamers in pure gasses and mixtures

Positive streamers are thought to propagate by photo-ionization whose parameters depend on the nitrogen:oxygen ratio. Therefore we study streamers in nitrogen with 20%, 0.2% and 0.01% oxygen and in pure nitrogen, as well as in pure oxygen and argon. Our new experimental set-up guarantees contamination of the pure gases to be well below 1 ppm. Streamers in oxygen are difficult to measure as they emit considerably less light in the sensitivity range of our fast ICCD camera than the other gasses. Streamers in pure nitrogen and in all nitrogen/oxygen mixtures look generally similar, but become somewhat thinner and branch more with decreasing oxygen content. In pure nitrogen the streamers can branch so much that they resemble feathers. This feature is even more pronounced in pure argon, with approximately 10^2 hair tips/cm^3 in the feathers at 200 mbar; this density could be interpreted as the free electron density creating avalanches towards the streamer stem. It is remarkable that the streamer velocity is essentially the same for similar voltage and pressure in all nitrogen/oxygen mixtures as well as in pure nitrogen, while the oxygen concentration and therefore the photo-ionization lengths vary by more than five orders of magnitude. Streamers in argon have essentially the same velocity as well. The physical similarity of streamers at different pressures is confirmed in all gases; the minimal diameters are smaller than in earlier measurements.Comment: 28 pages, 14 figures. Major differences with v1: - appendix and spectra removed - subsection regarding effects of repetition frequency added - many more smaller change

The Galactic Center Black Hole Laboratory

The super-massive 4 million solar mass black hole Sagittarius~A* (SgrA*) shows flare emission from the millimeter to the X-ray domain. A detailed analysis of the infrared light curves allows us to address the accretion phenomenon in a statistical way. The analysis shows that the near-infrared flare amplitudes are dominated by a single state power law, with the low states in SgrA* limited by confusion through the unresolved stellar background. There are several dusty objects in the immediate vicinity of SgrA*. The source G2/DSO is one of them. Its nature is unclear. It may be comparable to similar stellar dusty sources in the region or may consist predominantly of gas and dust. In this case a particularly enhanced accretion activity onto SgrA* may be expected in the near future. Here the interpretation of recent data and ongoing observations are discussed.Comment: 30 pages - 7 figures - accepted for publication by Springer's "Fundamental Theories of Physics" series; summarizing GC contributions of 2 conferences: 'Equations of Motion in Relativistic Gravity' at the Physikzentrum Bad Honnef, Bad Honnef, Germany, (Feb. 17-23, 2013) and the COST MP0905 'The Galactic Center Black Hole Laboratory' Granada, Spain (Nov. 19 - 22, 2013

Self-similar solutions of viscous and resistive ADAFs with thermal conduction

We have studied the effects of thermal conduction on the structure of viscous and resistive advection-dominated accretion flows (ADAFs). The importance of thermal conduction on hot accretion flow is confirmed by observations of hot gas that surrounds Sgr A$^*$ and a few other nearby galactic nuclei. In this research, thermal conduction is studied by a saturated form of it, as is appropriated for weakly-collisional systems. It is assumed the viscosity and the magnetic diffusivity are due to turbulence and dissipation in the flow. The viscosity also is due to angular momentum transport. Here, the magnetic diffusivity and the kinematic viscosity are not constant and vary by position and $\alpha$-prescription is used for them. The govern equations on system have been solved by the steady self-similar method. The solutions show the radial velocity is highly subsonic and the rotational velocity behaves sub-Keplerian. The rotational velocity for a specific value of the thermal conduction coefficient becomes zero. This amount of conductivity strongly depends on magnetic pressure fraction, magnetic Prandtl number, and viscosity parameter. Comparison of energy transport by thermal conduction with the other energy mechanisms implies that thermal conduction can be a significant energy mechanism in resistive and magnetized ADAFs. This property is confirmed by non-ideal magnetohydrodynamics (MHD) simulations.Comment: 8 pages, 5 figures, accepted by Ap&S

Fatou flowers and parabolic curves

In this survey we collect the main results known up to now (July 2015) regarding possible generalizations to several complex variables of the classical Leau-Fatou flower theorem about holomorphic parabolic dynamics