Seeing the future: Predictive control in neural models of ocular accommodation.

Ocular accommodation is the process of adjusting the eye's crystalline lens so as to bring the retinal image into sharp focus. The major stimulus to accommodation is therefore retinal defocus, and in essence, the job of accommodative control is to send a signal to the ciliary muscle which will minimize the magnitude of defocus. In this article, we first provide a tutorial introduction to control theory to aid vision scientists without this background. We then present a unified model of accommodative control that explains properties of the accommodative response for a wide range of accommodative stimuli. Following previous work, we conclude that most aspects of accommodation are well explained by dual integral control, with a "fast" or "phasic" integrator enabling response to rapid changes in demand, which hands over control to a "slow" or "tonic" integrator which maintains the response to steady demand. Control is complicated by the sensorimotor latencies within the system, which delay both information about defocus and the accommodation changes made in response, and by the sluggish response of the motor plant. These can be overcome by incorporating a Smith predictor, whereby the system predicts the delayed sensory consequences of its own motor actions. For the first time, we show that critically-damped dual integral control with a Smith predictor accounts for adaptation effects as well as for the gain and phase for sinusoidal oscillations in demand. In addition, we propose a novel proportional-control signal to account for the power spectrum of accommodative microfluctuations during steady fixation, which may be important in hunting for optimal focus, and for the nonlinear resonance observed for low-amplitude, high-frequency input. Complete Matlab/Simulink code implementing the model is provided at https://doi.org/10.25405/data.ncl.14945550.

A scalable model of fluid flow, substrate removal and current production in microbial fuel cells.

Mathematical modelling can reduce the cost and time required to design complex systems, and is being increasingly used in microbial electrochemical technologies (METs). To be of value such models must be complex enough to reproduce important behaviour of MET, yet simple enough to provide insight into underlying causes of this behaviour. Ideally, models must also be scalable to future industrial applications, rather than limited to describing existing laboratory experiments. We present a scalable model for simulating both fluid flow and bioelectrochemical processes in microbial fuel cells (MFCs), benchmarking against an experimental pilot-scale bioreactor. The model describes substrate transport through a two-dimensional fluid domain, and biofilm growth on anode surfaces. Electron transfer is achieved by an intracellular redox mediator. We find significant spatial variations in both substrate concentration and current density. Simple changes to the reactor layout can greatly improve the overall efficiency, measured in terms of substrate removal and total current generated.

Magnetic field evolution in magnetar crusts through three-dimensional simulations.

Current models of magnetars require extremely strong magnetic fields to explain their observed quiescent and bursting emission, implying that the field strength within the star's outer crust is orders of magnitude larger than the dipole component inferred from spin-down measurements. This presents a serious challenge to theories of magnetic field generation in a proto-neutron star. Here, we present detailed modeling of the evolution of the magnetic field in the crust of a neutron star through 3D simulations. We find that, in the plausible scenario of equipartition of energy between global-scale poloidal and toroidal magnetic components, magnetic instabilities transfer energy to nonaxisymmetric, kilometer-sized magnetic features, in which the local field strength can greatly exceed that of the global-scale field. These intense small-scale magnetic features can induce high-energy bursts through local crust yielding, and the localized enhancement of Ohmic heating can power the star's persistent emission. Thus, the observed diversity in magnetar behavior can be explained with mixed poloidal-toroidal fields of comparable energies.

Effect of metallic walls on dynamos generated by laminar boundary-driven flow in a spherical domain.

We present a numerical study of dynamo action in a conducting fluid encased in a metallic spherical shell. Motions in the fluid are driven by differential rotation of the outer metallic shell, which we refer to as "the wall." The two hemispheres of the wall are held in counter-rotation, producing a steady, axisymmetric interior flow consisting of differential rotation and a two-cell meridional circulation with radial inflow in the equatorial plane. From previous studies, this type of flow is known to maintain a stationary equatorial dipole by dynamo action if the magnetic Reynolds number is larger than about 300 and if the outer boundary is electrically insulating. We vary independently the thickness, electrical conductivity, and magnetic permeability of the wall to determine their effect on the dynamo action. The main results are the following: (a) Increasing the conductivity of the wall hinders the dynamo by allowing eddy currents within the wall, which are induced by the relative motion of the equatorial dipole field and the wall. This processes can be viewed as a skin effect or, equivalently, as the tearing apart of the dipole by the differential rotation of the wall, to which the field lines are anchored by high conductivity. (b) Increasing the magnetic permeability of the wall favors dynamo action by constraining the magnetic field lines in the fluid to be normal to the wall, thereby decoupling the fluid from any induction in the wall. (c) Decreasing the wall thickness limits the amplitude of the eddy currents, and is therefore favorable for dynamo action, provided that the wall is thinner than the skin depth. We explicitly demonstrate these effects of the wall properties on the dynamo field by deriving an effective boundary condition in the limit of vanishing wall thickness.