Generation of intense negative ion beams

An electron gun is used with a mirror electrostatic field to produce zero or near zero velocity electrons by forming a turning point in their trajectories. A gas capable of attaching zero or near zero velocity is introduced at this turning point, and negative ions are produced by the attachment or dissociative attachment process. Operation may be continuous or pulsed. Ions thus formed are extracted by a simple lens system and suitable biasing of grids

High-Order Shock Capturing for Computational Aeroacoustics

Jet noise is not only an annoyance to passengers and communities near airports, it is a major contributor to hearing loss in veterans who served on aircraft carriers, as well as a significant limiting factor for the growth of commercial airlines. High-fidelity large eddy simulation (LES) is an important tool for analyzing and predicting jet noise; however the utilized non-dissipative high order finite difference schemes produce instabilities at shock waves. Schemes for capturing shock waves, however, are more dissipative and do a poor job preserving turbulent structures and acoustic waves. To maximize the strengths of both approaches, hybrid methods utilize shock capturing locally where the flow is discontinuous and traditional LES methods over the remaining regions. In this study, a sixth-order compact scheme is hybridized with a weighted essentially non-oscillatory (WENO) method for local shock-capturing. Furthermore, improvements are made to the dissipative and dispersive qualities of WENO. Optimized bandwidth resolution and reduced nonlinearity are found to improve resolution of flow structures passing through shocks on standard test problems. Additionally, proper detection of shock waves is critical to overall performance of hybrid schemes, so several approaches are examined. Superior efficiency and accuracy are obtained through careful selection of shock wave detectors

Learning Bilinear Models of Actuated Koopman Generators from Partially-Observed Trajectories

Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature learning, state estimation, and control. It has become well known that the Koopman generators for control-affine systems also have affine dependence on the input, leading to convenient finite-dimensional bilinear approximations of the dynamics. Yet there are still two main obstacles that limit the scope of current approaches for approximating the Koopman generators of systems with actuation. First, the performance of existing methods depends heavily on the choice of basis functions over which the Koopman generator is to be approximated; and there is currently no universal way to choose them for systems that are not measure preserving. Secondly, if we do not observe the full state, then it becomes necessary to account for the dependence of the output time series on the sequence of supplied inputs when constructing observables to approximate Koopman operators. To address these issues, we write the dynamics of observables governed by the Koopman generator as a bilinear hidden Markov model, and determine the model parameters using the expectation-maximization (EM) algorithm. The E-step involves a standard Kalman filter and smoother, while the M-step resembles control-affine dynamic mode decomposition for the generator. We demonstrate the performance of this method on three examples, including recovery of a finite-dimensional Koopman-invariant subspace for an actuated system with a slow manifold; estimation of Koopman eigenfunctions for the unforced Duffing equation; and model-predictive control of a fluidic pinball system based only on noisy observations of lift and drag

Effects of an active visuomotor steering task on covert attention

In complex dynamic tasks such as driving it is essential to be aware of potentially important targets in peripheral vision. While eye tracking methods in various driving tasks have provided much information about drivers’ gaze strategies, these methods only inform about overt attention and provide limited grounds to assess hypotheses concerning covert attention. We adapted the Posner cue paradigm to a dynamic steering task in a driving simulator. The participants were instructed to report the presence of peripheral targets while their gaze was fixed to the road. We aimed to see whether and how the active steering task and complex visual stimulus might affect directing covert attention to the visual periphery. In a control condition, the detection task was performed without a visual scene and active steering. Detection performance in bends was better in the control task compared to corresponding performance in the steering task, indicating that active steering and the complex visual scene affected the ability to distribute covert attention. Lower targets were discriminated slower than targets at the level of the fixation circle in both conditions. We did not observe higher discriminability for on-road targets. The results may be accounted for by either bottom-up optic flow biasing of attention, or top-down saccade planning.Peer reviewe

Model Reduction for Nonlinear Systems by Balanced Truncation of State and Gradient Covariance

Data-driven reduced-order models often fail to make accurate forecasts of high-dimensional nonlinear dynamical systems that are sensitive along coordinates with low-variance because such coordinates are often truncated, e.g., by proper orthogonal decomposition, kernel principal component analysis, and autoencoders. Such systems are encountered frequently in shear-dominated fluid flows where non-normality plays a significant role in the growth of disturbances. In order to address these issues, we employ ideas from active subspaces to find low-dimensional systems of coordinates for model reduction that balance adjoint-based information about the system's sensitivity with the variance of states along trajectories. The resulting method, which we refer to as covariance balancing reduction using adjoint snapshots (CoBRAS), is analogous to balanced truncation with state and adjoint-based gradient covariance matrices replacing the system Gramians and obeying the same key transformation laws. Here, the extracted coordinates are associated with an oblique projection that can be used to construct Petrov-Galerkin reduced-order models. We provide an efficient snapshot-based computational method analogous to balanced proper orthogonal decomposition. This also leads to the observation that the reduced coordinates can be computed relying on inner products of state and gradient samples alone, allowing us to find rich nonlinear coordinates by replacing the inner product with a kernel function. In these coordinates, reduced-order models can be learned using regression. We demonstrate these techniques and compare to a variety of other methods on a simple, yet challenging three-dimensional system and a nonlinear axisymmetric jet flow simulation with $10^5$ state variables

Analysis of amplification mechanisms and cross-frequency interactions in nonlinear flows via the harmonic resolvent

We propose a framework that elucidates the input-output characteristics of flows with complex dynamics arising from nonlinear interactions between different time scales. More specifically, we consider a periodically time-varying base flow, and perform a frequency-domain analysis of periodic perturbations about this base flow; the response of these perturbations is governed by the harmonic resolvent, which is a linear operator similar to the harmonic transfer function introduced by Wereley (1991). This approach makes it possible to explicitly capture the triadic interactions that are responsible for the energy transfer between different time scales in the flow. For instance, perturbations at frequency $\alpha$ are coupled with perturbations at frequency $\omega$ through the base flow at frequency $\omega-\alpha$. We draw a connection with resolvent analsyis, which is a special case of the harmonic resolvent when evaluated about a steady base flow. We show that the left and right singular vectors of the harmonic resolvent are the optimal response and forcing modes, which can be understood as full spatio-temporal signals that reveal space-time amplification characteristics of the flow. We illustrate the method on examples, including a three-dimensional system of ordinary differential equations and the flow over an airfoil at near-stall angle of attack