Energy dynamics in a simulation of LAPD turbulence

Energy dynamics calculations in a 3D fluid simulation of drift wave turbulence in the linear Large Plasma Device (LAPD) [W. Gekelman et al., Rev. Sci. Inst. 62, 2875 (1991)] illuminate processes that drive and dissipate the turbulence. These calculations reveal that a nonlinear instability dominates the injection of energy into the turbulence by overtaking the linear drift wave instability that dominates when fluctuations about the equilibrium are small. The nonlinear instability drives flute-like ($k_\parallel = 0$) density fluctuations using free energy from the background density gradient. Through nonlinear axial wavenumber transfer to $k_\parallel \ne 0$ fluctuations, the nonlinear instability accesses the adiabatic response, which provides the requisite energy transfer channel from density to potential fluctuations as well as the phase shift that causes instability. The turbulence characteristics in the simulations agree remarkably well with experiment. When the nonlinear instability is artificially removed from the system through suppressing $k_\parallel=0$ modes, the turbulence develops a coherent frequency spectrum which is inconsistent with experimental data

Quasi-Adiabatic Continuation in Gapped Spin and Fermion Systems: Goldstone's Theorem and Flux Periodicity

We apply the technique of quasi-adiabatic continuation to study systems with continuous symmetries. We first derive a general form of Goldstone's theorem applicable to gapped nonrelativistic systems with continuous symmetries. We then show that for a fermionic system with a spin gap, it is possible to insert $\pi$-flux into a cylinder with only exponentially small change in the energy of the system, a scenario which covers several physically interesting cases such as an s-wave superconductor or a resonating valence bond state.Comment: 19 pages, 2 figures, final version in press at JSTA

Topological entropy of realistic quantum Hall wave functions

The entanglement entropy of the incompressible states of a realistic quantum Hall system are studied by direct diagonalization. The subdominant term to the area law, the topological entanglement entropy, which is believed to carry information about topologic order in the ground state, was extracted for filling factors 1/3, 1/5 and 5/2. The results for 1/3 and 1/5 are consistent with the topological entanglement entropy for the Laughlin wave function. The 5/2 state exhibits a topological entanglement entropy consistent with the Moore-Read wave function.Comment: 6 pages, 6 figures; improved computations and graphics; added reference

Structure and Response in the World Trade Network

We examine how the structure of the world trade network has been shaped by globalization and recessions over the last 40 years. We show that by treating the world trade network as an evolving system, theory predicts the trade network is more sensitive to evolutionary shocks and recovers more slowly from them now than it did 40 years ago, due to structural changes in the world trade network induced by globalization. We also show that recession-induced change to the world trade network leads to an \emph{increased} hierarchical structure of the global trade network for a few years after the recession.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

Soil Moisture Workshop

The Soil Moisture Workshop was held at the United States Department of Agriculture National Agricultural Library in Beltsville, Maryland on January 17-19, 1978. The objectives of the Workshop were to evaluate the state of the art of remote sensing of soil moisture; examine the needs of potential users; and make recommendations concerning the future of soil moisture research and development. To accomplish these objectives, small working groups were organized in advance of the Workshop to prepare position papers. These papers served as the basis for this report

Polaron Excitations in Doped C60: Effects of Disorders

Effects on C$_{60}$ by thermal fluctuations of phonons, misalignment of C$_{60}$ molecules in a crystal, and other intercalated impurities (remaining C$_{70}$, oxygens, and so on) are simulated by disorder potentials. The Su-Schrieffer-Heeger--type electron-phonon model for doped C$_{60}$ is solved with gaussian bond disorders and also with site disorders. Sample average is performed over sufficient number of disorder configurations. The distributions of bond lengths and electron densities are shown as functions of the disorder strength and the additional electron number. Stability of polaron excitations as well as dimerization patterns is studied. Polarons and dimerizations in lightly doped cases (C$_{60}^{-1,-2}$) are relatively stable against disorders, indicated by peak structures in distribution functions. In more heavily doped cases, the several peaks merge into a single peak, showing the breakdown of polaron structures as well as the decrease of the dimerization strength. Possibility of the observation of polaronic lattice distortions and electron structures in doped C$_{60}$ is discussed.Comment: Note: This manusript was accepted for publication in Physical Review B. Figures will be sent to you via snail (conventional) mai

Analysis of plasma instabilities and verification of the BOUT code for the Large Plasma Device

The properties of linear instabilities in the Large Plasma Device [W. Gekelman et al., Rev. Sci. Inst., 62, 2875 (1991)] are studied both through analytic calculations and solving numerically a system of linearized collisional plasma fluid equations using the 3D fluid code BOUT [M. Umansky et al., Contrib. Plasma Phys. 180, 887 (2009)], which has been successfully modified to treat cylindrical geometry. Instability drive from plasma pressure gradients and flows is considered, focusing on resistive drift waves, the Kelvin-Helmholtz and rotational interchange instabilities. A general linear dispersion relation for partially ionized collisional plasmas including these modes is derived and analyzed. For LAPD relevant profiles including strongly driven flows it is found that all three modes can have comparable growth rates and frequencies. Detailed comparison with solutions of the analytic dispersion relation demonstrates that BOUT accurately reproduces all characteristics of linear modes in this system.Comment: Published in Physics of Plasmas, 17, 102107 (2010

Quantifying Model Complexity via Functional Decomposition for Better Post-Hoc Interpretability

Post-hoc model-agnostic interpretation methods such as partial dependence plots can be employed to interpret complex machine learning models. While these interpretation methods can be applied regardless of model complexity, they can produce misleading and verbose results if the model is too complex, especially w.r.t. feature interactions. To quantify the complexity of arbitrary machine learning models, we propose model-agnostic complexity measures based on functional decomposition: number of features used, interaction strength and main effect complexity. We show that post-hoc interpretation of models that minimize the three measures is more reliable and compact. Furthermore, we demonstrate the application of these measures in a multi-objective optimization approach which simultaneously minimizes loss and complexity

Modification of turbulent transport with continuous variation of flow shear in the Large Plasma Device

Continuous control over azimuthal flow and shear in the edge of the Large Plasma Device (LAPD) has been achieved using a biasable limiter which has allowed a careful study of the effect of flow shear on pressure-gradient-driven turbulence and transport in LAPD. LAPD rotates spontaneously in the ion diamagnetic direction (IDD); positive limiter bias first reduces, then minimizes (producing a near-zero shear state), and finally reverses the flow into the electron diamagnetic direction (EDD). Degradation of particle confinement is observed in the minimum shearing state and reduction in turbulent particle flux is observed with increasing shearing in both flow directions. Near-complete suppression of turbulent particle flux is observed for shearing rates comparable to the turbulent autocorrelation rate measured in the minimum shear state. Turbulent flux suppression is dominated by amplitude reduction in low-frequency ($<10$kHz) density fluctuations. An increase in fluctuations for the highest shearing states is observed with the emergence of a coherent mode which does not lead to net particle transport. The variations of density fluctuations are fit well with power-laws and compare favorably to simple models of shear suppression of transport.Comment: 10 pages, 5 figures; Submitted to Phys. Rev. Let