Observation of explosive collisionless reconnection in 3D nonlinear gyrofluid simulations

The nonlinear dynamics of collisionless reconnecting modes is investigated, in the framework of a three-dimensional gyrofluid model. This is the relevant regime of high-temperature plasmas, where reconnection is made possible by electron inertia and has higher growth rates than resistive reconnection. The presence of a strong guide field is assumed, in a background slab model, with Dirichlet boundary conditions in the direction of nonuniformity. Values of ion sound gyro-radius and electron collisionless skin depth much smaller than the current layer width are considered. Strong acceleration of growth is found at the onset to nonlinearity, while at all times the energy functional is well conserved. Nonlinear growth rates more than one order of magnitude higher than linear growth rates are observed when entering into the small-$\Delta'$ regime

A notion of rectifiability modeled on Carnot groups

We introduce a notion of rectifiability modeled on Carnot groups. Precisely, we say that a subset E of a Carnot group M and N is a subgroup of M, we say E is N-rectifiable if it is the Lipschitz image of a positive measure subset of N. First, we discuss the implications of N-rectifiability, where N is a Carnot group (not merely a subgroup of a Carnot group), which include N-approximability and the existence of approximate tangent cones isometric to N almost everywhere in E. Second, we prove that, under a stronger condition concerning the existence of approximate tangent cones isomorphic to N almost everywhere in a set E, that E is N-rectifiable. Third, we investigate the rectifiability properties of level sets of C^1_N functions, where N is a Carnot group. We show that for almost every real number t and almost every noncharacteristic point x in a level set of f, there exists a subgroup T_x of H and r >0 so that f^{-1}(t) intersected with B_H(x,r) is T_x-approximable at x and an approximate tangent cone isomorphic to T_x at x.Comment: 27 page

Dynamical Alignment in Three Species Tokamak Edge Turbulence

Three dimensional computations of self consistent three species gyrofluid turbulence are carried out for tokamak edge conditions. Profiles as well as disturbances in dependent variables are followed, running the dynamical system to transport equilibrium. The third species density shows a significant correlation with that of the electrons, regardless of initial conditions and drive mechanisms. For decaying systems the densities evolve toward each other. Companion tests with a simple two dimensional drift wave model show this persists even if the third species is a passively advected test field. Similarity in the transport character of electrons and the trace species does not imply that the electrons themselves have a test particle transport character.Comment: RevTeX 4, 21 pages, 15 figures, submitted to Physics of Plasma

Who Is a “Veteran”?—Basic Eligibility for Veterans’ Benefits

The U.S. Department of Veterans Affairs (VA) offers a broad range of benefits to veterans of the U.S. Armed Forces and to certain members of their families. Among these benefits are various types of financial assistance, including monthly cash payments to disabled veterans, health care, education, and housing. Certain criteria must be met to be eligible to receive any of the benefits administered by the VA. This report focuses on basic eligibility and entitlement requirements for former servicemembers for benefits administered by the VA. Certain VA benefits are available to current servicemembers, and the eligibility requirements for those benefits are not a component of this report. The VA uses a two-step process to evaluate claims for benefits. First, the claimant must demonstrate eligibility for veterans’ benefits in general. That is, the claimant must prove that he or she is a bona fide veteran and verify certain related matters. Second, the veteran must prove entitlement to the particular benefit being sought

Engaging the Digitally Engaged Student: Comparing Technology-Mediated Communication Use and Effects on Student Learning

The role of communication technologies in the learning process is both a dynamic and complex issue. Yet, we know surprisingly little about how the use of specific communication technologies may influence classroom performance, key learning outcomes, and other measures of course satisfaction. The research reported here attempts to add to our knowledge about the role of communication in the technology enhanced classroom (TEC) education and in technology-enhanced online (TEO) education through a direct comparison of two courses. Our findings indicate additional support for “The No Significant Difference Phenomenon.” Furthermore, we found that prior experiences lead students to gravitate towards their preferred learning environments, and that basic website elements are required in any learning environment to enhance student outcomes. Finally, we found that when used appropriately, the benefits of communication technology use in education outweigh many of the drawbacks

Gyrokinetic Field Theory as a Gauge Transform or: gyrokinetic theory without Lie transforms

Gyrokinetic theory is a basis for treating magnetised plasma dynamics slower than particle gyrofrequencies where the scale of the background is larger than relevant gyroradii. The energy of field perturbations can be comparable to the thermal energy but smaller than the energy of the background magnetic field. Properly applied, it is a low-frequency gauge transform rather than a treatment of particle orbits, and more a representation in terms of gyrocenters rather than particles than an approximation. By making all transformations and approximations in the field/particle Lagrangian one preserves exact energetic consistency so that time symmetry ensures energy conservation and spatial axisymmetry ensures toroidal angular momentum conservation. This method draws on earlier experience with drift kinetic models while showing the independence of gyrokinetic representation from particularities of Lie transforms or specific ordering limits, and that the essentials of low-frequency magnetohydrodynamics, including the equilibrium, are recovered. It gives a useful basis for total-f electromagnetic gyrokinetic computation. Various versions of the representation based upon choice of parallel velocity space coordinate are illustrated.Comment: 33 pages, no figure