An analysis of the fluctuations of the geomagnetic dipole

The time evolution of the strength of the Earth's virtual axial dipole moment (VADM) is analyzed by relating it to the Fokker-Planck equation, which describes a random walk with VADM-dependent drift and diffusion coefficients. We demonstrate first that our method is able to retrieve the correct shape of the drift and diffusion coefficients from a time series generated by a test model. Analysis of the Sint-2000 data shows that the geomagnetic dipole mode has a linear growth time of 13 to 33 kyr, and that the nonlinear quenching of the growth rate follows a quadratic function of the type [1-(x/x0)^2]. On theoretical grounds, the diffusive motion of the VADM is expected to be driven by multiplicative noise, and the corresponding diffusion coefficient to scale quadratically with dipole strength. However, analysis of the Sint-2000 VADM data reveals a diffusion which depends only very weakly on the dipole strength. This may indicate that the magnetic field quenches the amplitude of the turbulent velocity in the Earth's outer core.Comment: 11 pages, 6 figure

Fast plasma heating by anomalous and inertial resistivity effects

Fast plasma heating by anomalous and inertial resistivity effects is described. A small fraction of the plasma contains strong currents that run parallel to the magnetic field and are driven by an exponentiating electric field. The anomalous character of the current dissipation is caused by the excitation of electrostatic ion cyclotron and/or ion acoustic waves. The role of resistivity due to geometrical effects is considered. Through the use of a marginal stability analysis, equations for the average electron and ion temperatures are derived and numerically solved. The evolution of the plasma is described as a path in the drift velocity diagram, in which the drift velocity is plotted as a function of the electron to ion temperature ratio

Stochastic Analysis of Subcritical Amplification of Magnetic Energy in a Turbulent Dynamo

We present and analyze a simplified stochastic $\alpha \Omega -$dynamo model which is designed to assess the influence of additive and multiplicative noises, non-normality of dynamo equation, and nonlinearity of the $\alpha -$% effect and turbulent diffusivity, on the generation of a large-scale magnetic field in the subcritical case. Our model incorporates random fluctuations in the $\alpha -$parameter and additive noise arising from the small-scale fluctuations of magnetic and turbulent velocity fields. We show that the noise effects along with non-normality can lead to the stochastic amplification of the magnetic field even in the subcritical case. The criteria for the stochastic instability during the early kinematic stage are established and the critical value for the intensity of multiplicative noise due to $\alpha -$fluctuations is found. We obtain numerical solutions of non-linear stochastic differential equations and find the series of phase transitions induced by random fluctuations in the $\alpha -$parameter.Comment: 21pages,7 figure

Artificial Reverse Shoulder Arthroplasty Joint Project

This proposed project will be developing an artificial reverse shoulder arthroplasty joint that focuses on improvements to the Zimmer Biomet Comprehensive Reverse System by freating a unique feature, or features, to the humeral component that focuses on the prevention of dislocation by not limiting the range of motion of men from ages 45 to 65 years. The development of the this project will utilize the Food and Drug Administration (FDA) medical device design process. This project will involve a total of four Biomedical Engineering students from the University of Akron. Two students, Michael and Bailei, are in the Honors college while the other two are not

Helical rotating turbulence. Part II. Intermittency, scale invariance and structures

We study the intermittency properties of the energy and helicity cascades in two 1536^3 direct numerical simulations of helical rotating turbulence. Symmetric and anti-symmetric velocity increments are examined, as well as probability density functions of the velocity field and of the helicity density. It is found that the direct cascade of energy to small scales is scale invariant and non-intermittent, whereas the direct cascade of helicity is highly intermittent. Furthermore, the study of structure functions of different orders allows us to identify a recovery of isotropy of strong events at very small scales in the flow. Finally, we observe the juxtaposition in space of strong laminar and persistent helical columns next to time-varying vortex tangles, the former being associated with the self-similarity of energy and the latter with the intermittency of helicity.Comment: 11 pages, 10 figure

Statistical dynamo theory: Mode excitation

We compute statistical properties of the lowest-order multipole coefficients of the magnetic field generated by a dynamo of arbitrary shape. To this end we expand the field in a complete biorthogonal set of base functions, viz. B = sum_k a^k(t) b^k(r). We consider a linear problem and the statistical properties of the fluid flow are supposed to be given. The turbulent convection may have an arbitrary distribution of spatial scales. The time evolution of the expansion coefficients a^k(t) is governed by a stochastic differential equation from which we infer their averages , autocorrelation functions <a^k(t) a^{k*}(t+tau)>, and an equation for the cross correlations . The eigenfunctions of the dynamo equation (with eigenvalues lambda_k) turn out to be a preferred set in terms of which our results assume their simplest form. The magnetic field of the dynamo is shown to consist of transiently excited eigenmodes whose frequency and coherence time is given by Im(lambda_k) and -1/(Re lambda_k), respectively. The relative r.m.s. excitation level of the eigenmodes, and hence the distribution of magnetic energy over spatial scales, is determined by linear theory. An expression is derived for / in case the fundamental mode b^0 has a dominant amplitude, and we outline how this expression may be evaluated. It is estimated that / ~ 1/N where N is the number of convective cells in the dynamo. We show that the old problem of a short correlation time (or FOSA) has been partially eliminated. Finally we prove that for a simple statistically steady dynamo with finite resistivity all eigenvalues obey Re(lambda_k) < 0.Comment: 14 pages, 2 figures. Accepted for publication in Physical Review

Does the butterfly diagram indicate asolar flux-transport dynamo?

We address the question whether the properties of the observed latitude-time diagram of sunspot occurence (the butterfly diagram) provide evidence for the operation of a flux-transport dynamo, which explains the migration of the sunspot zones and the period of the solar cycle in terms of a deep equatorward meridional flow. We show that the properties of the butterfly diagram are equally well reproduced by a conventional dynamo model with migrating dynamo waves, but without transport of magnetic flux by a flow. These properties seem to be generic for an oscillatory and migratory field of dipole parity and thus do not permit an observational distinction between different dynamo approaches.Comment: 4 pages, 1 figur