Degenerate Variational Integrators for Magnetic Field Line Flow and Guiding Center Trajectories

Symplectic integrators offer many advantages for the numerical solution of Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two of the central Hamiltonian systems encountered in plasma physics --- the flow of magnetic field lines and the guiding center motion of magnetized charged particles --- resist symplectic integration by conventional means because the dynamics are most naturally formulated in non-canonical coordinates, i.e., coordinates lacking the familiar $(q, p)$ partitioning. Recent efforts made progress toward non-canonical symplectic integration of these systems by appealing to the variational integration framework; however, those integrators were multistep methods and later found to be numerically unstable due to parasitic mode instabilities. This work eliminates the multistep character and, therefore, the parasitic mode instabilities via an adaptation of the variational integration formalism that we deem ``degenerate variational integration''. Both the magnetic field line and guiding center Lagrangians are degenerate in the sense that their resultant Euler-Lagrange equations are systems of first-order ODEs. We show that retaining the same degree of degeneracy when constructing a discrete Lagrangian yields one-step variational integrators preserving a non-canonical symplectic structure on the original Hamiltonian phase space. The advantages of the new algorithms are demonstrated via numerical examples, demonstrating superior stability compared to existing variational integrators for these systems and superior qualitative behavior compared to non-conservative algorithms

Economic Analysis of Knowledge: The History of Thought and the Central Themes

Following the development of knowledge economies, there has been a rapid expansion of economic analysis of knowledge, both in the context of technological knowledge in particular and the decision theory in general. This paper surveys this literature by identifying the main themes and contributions and outlines the future prospects of the discipline. The wide scope of knowledge related questions in terms of applicability and alternative approaches has led to the fragmentation of research. Nevertheless, one can identify a continuing tradition which analyses various aspects of the generation, dissemination and use of knowledge in the economy

Three-dimensional Numerical Investigation of Electron Transport with Rotating Spoke in a Cylindrical Anode Layer Hall Plasma Accelerator

The oscillation behavior described in [Tang et. al, Phys. Plasmas 19, 073519 (2012)] di ers too greatly from previous experimental and numerical studies to claim observation of the same phenomenon. Most signi cantly, the rotation velocity in [Tang et. al, Phys. Plasmas 19, 073519 (2012)] is three orders of magnitude larger than that of typical \rotating spoke" phenomena. Several physical and numerical considerations are presented to more accurately understand the numerical results of [Tang et. al, Phys. Plasmas 19, 073519 (2012)] in light of previous studies

‘It was the last time we’d start the summer that way’: Space, race, and coming of age in Colson Whitehead’s Sag Harbor

This article argues that Colson Whitehead’s much understudied coming of age novel Sag Harbor makes an important intervention into the history of the coming of age genre. Sag Harbor is the story of upper-middle class Black boy Benji Cooper, now an adult, narrating a summer he spent at the majority Black beach town of Sag Harbor when he was fifteen years old. Through a series of extended comparative readings to canonical works of coming of age – James Baldwin’s If Beale Street Could Talk (1974) and Jeffrey Eugenides’ The Virgin Suicides (1993) – I argue that such narratives are often dependent on the freedom whiteness grants to move unimpeded through the world. Benji is only able to follow a ‘traditional’ coming of age narrative because his class gives him access to a space – Sag Harbor – which is not structured by an overdetermining white gaze. Thus, by aligning Benji with ‘traditional’ coming of age narratives, Whitehead intervenes in the history of Black coming of age literature, which depicts coming of age for Black youth as learning the limits of Blackness in a society built around whiteness