A quasi-one-dimensional steady-state Poisson-Nernst-Planck model with Bikerman's local hard-sphere potential for ionic flows of two oppositely charged ion species through a membrane channel is analyzed. Of particular interest is the qualitative properties of ionic flows in terms of individual fluxes without the assumption of electroneutrality conditions, which is more realistic to study ionic flow properties of interest. This is the novelty of this work. Our result shows that i) boundary concentrations and relative size of ion species play critical roles in characterizing ion size effects on individual fluxes; ii) the first order approximation J k1 = D k J k1 in ion volume of individual fluxes J k = D k J k is linear in boundary potential, furthermore, the signs of ∂ V J k1 and ∂ 2 V λ J k1 , which play key roles in characterizing ion size effects on ionic flows can be both negative depending further on boundary concentrations while they are always positive and independent of boundary concentrations under electroneutrality conditions (see Corollaries 3.2-3.3, Theorems 3.4-3.5 and Proposition 3.7). Numerical simulations are performed to identify some critical potentials defined in (2). We believe our results will provide useful insights for numerical and even experimental studies of ionic flows through membrane channels.

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Predictive Adaptive Optics (AO) control is a promising technology for AO applications in high-disturbance and low-signal environments such as directed energy, optical communication, and astronomical seeing. Predictive AO utilizes future state predictions of an optical wavefront propagated through a turbulent medium to drive correction, thereby mitigating the limits imposed by inherent latency in the AO system. In this work, we present a novel Artificial Neural Network (ANN) approach for embedding the flow dynamics for a range of Airborne Aero-Optics Laboratory (AAOL) datasets into a single turbulent flow prediction model. As the angle of the laser beam through the hemispherical AAOL turret changes, flow characteristics vary greatly according to statistics such as mean advection speed, direction, and scale, as well as the presence of different turbulent structures and shock waves. As a result, a predictive model trained on a single look angle and flow condition will likely have poor performance when conditions change, for instance, by slewing the turret look angle during AO operation. In our approach, this limitation is mitigated by introducing the model to flow data from a range of look angles during training. We analyze this combined model’s ability to forecast turbulent wavefronts from look angles included in the training set to establish baseline model performance. We then consider performance on measured AAOL wavefront sensor data from holdout look angles entirely excluded from the training wavefront data to demonstrate the generalization capability of the resulting model, and consider the implications for ANN-based AO correction for dynamic, high-speed, turbulent flows.

In this work, we characterize the capability of artificial neural network predictive models for generalizable turbulence forecasting, particularly for use in predictive adaptive optics (AO) applications. Predictive AO control, which utilizes future state predictions of an optical wavefront propagated through a turbulent medium to drive correction, is a promising technology for optical propagation in high-disturbance and low-signal environments. The dynamics describing the evolution of turbulent flow can vary greatly. Accordingly, a generalizable approach to turbulence forecasting has key benefits in allowing for prediction across a range of conditions, thus enabling continuous predictive AO operation in dynamic environments and having reduced sensitivity to changes in conditions. We present a model for generalizable turbulence forecasting, which demonstrated consistent high performance over a range of compressible flow conditions outside those included in the training sample, with only a minimal increase in prediction error compared with a hypothetical baseline model, which assumes perfect a priori characterization. These results demonstrate a clear ability to extract useful dynamics from a limited domain of turbulent conditions and apply these appropriately for forecasting, which could inform future design of predictive AO systems.