Kramers-Kronig, Bode, and the meaning of zero

The implications of causality, as captured by the Kramers-Kronig relations between the real and imaginary parts of a linear response function, are familiar parts of the physics curriculum. In 1937, Bode derived a similar relation between the magnitude (response gain) and phase. Although the Kramers-Kronig relations are an equality, Bode's relation is effectively an inequality. This perhaps-surprising difference is explained using elementary examples and ultimately traces back to delays in the flow of information within the system formed by the physical object and measurement apparatus.Comment: 8 pages; American Journal of Physics, to appea

Estimating radar positions using unmanned air vehicle teams engaged in cooperative deception

Standard TDOA (time-difference of arrival) estimation techniques are modified and applied to locate networked enemy radars using a cooperative team of unmanned electronic combat air vehicles (ECAVs). The team is engaged in deceiving the radars, which limits where the ECAVs can fly and requires accurate radar positions to be known. Two TDOA measurements of radar pulses taken by two ECAV pairs are used to estimate the position of the middle radar. A nonlinear system model for estimation is formulated and used to perform simulations with "noisy" TDOAs; a linearized time-varying model for straight nominal ECAV trajectories is derived from the nonlinear model. The choice of optimal ECAV trajectories and an observer to minimize the variance of the middle radar position - using the linearized model is addressed. Application of a time-varying Kalman filter to the linearized system shows drastic improvement in reducing the variance of position estimates when compared to the original nonlinear system via simulations

Reactive control of autonomous drones

Aerial drones, ground robots, and aquatic rovers enable mobile applications that no other technology can realize with comparable flexibility and costs. In existing platforms, the low-level control enabling a drone's autonomous movement is currently realized in a time-triggered fashion, which simplifies implementations. In contrast, we conceive a notion of reactive control that supersedes the time-triggered approach by leveraging the characteristics of existing control logic and of the hardware it runs on. Using reactive control, control decisions are taken only upon recognizing the need to, based on observed changes in the navigation sensors. As a result, the rate of execution dynamically adapts to the circumstances. Compared to time-triggered control, this allows us to: i) attain more timely control decisions, ii) improve hardware utilization, iii) lessen the need to overprovision control rates. Based on 260+ hours of real-world experiments using three aerial drones, three different control logic, and three hardware platforms, we demonstrate, for example, up to 41% improvements in control accuracy and up to 22% improvements in flight time

Characterizing Interdisciplinarity of Researchers and Research Topics Using Web Search Engines

Researchers' networks have been subject to active modeling and analysis. Earlier literature mostly focused on citation or co-authorship networks reconstructed from annotated scientific publication databases, which have several limitations. Recently, general-purpose web search engines have also been utilized to collect information about social networks. Here we reconstructed, using web search engines, a network representing the relatedness of researchers to their peers as well as to various research topics. Relatedness between researchers and research topics was characterized by visibility boost-increase of a researcher's visibility by focusing on a particular topic. It was observed that researchers who had high visibility boosts by the same research topic tended to be close to each other in their network. We calculated correlations between visibility boosts by research topics and researchers' interdisciplinarity at individual level (diversity of topics related to the researcher) and at social level (his/her centrality in the researchers' network). We found that visibility boosts by certain research topics were positively correlated with researchers' individual-level interdisciplinarity despite their negative correlations with the general popularity of researchers. It was also found that visibility boosts by network-related topics had positive correlations with researchers' social-level interdisciplinarity. Research topics' correlations with researchers' individual- and social-level interdisciplinarities were found to be nearly independent from each other. These findings suggest that the notion of "interdisciplinarity" of a researcher should be understood as a multi-dimensional concept that should be evaluated using multiple assessment means.Comment: 20 pages, 7 figures. Accepted for publication in PLoS On

Modelling for Robust Feedback Control of Fluid Flows

This paper addresses the problem of obtaining low-order models of fluid flows for the purpose of designing robust feedback controllers. This is challenging since whilst many flows are governed by a set of nonlinear, partial differential-algebraic equations (the Navier-Stokes equations), the majority of established control theory assumes models of much greater simplicity, in that they are firstly: linear, secondly: described by ordinary differential equations, and thirdly: finite-dimensional. Linearisation, where appropriate, overcomes the first disparity, but attempts to reconcile the remaining two have proved difficult. This paper addresses these two problems as follows. Firstly, a numerical approach is used to project the governing equations onto a divergence-free basis, thus converting a system of differential-algebraic equations into one of ordinary differential equations. This dispenses with the need for analytical velocity-vorticity transformations, and thus simplifies the modelling of boundary sensing and actuation. Secondly, this paper presents a novel and straightforward approach for obtaining suitable low-order models of fluid flows, from which robust feedback controllers can be synthesised that provide~\emph{a~priori} guarantees of robust performance when connected to the (infinite-dimensional) linearised flow system. This approach overcomes many of the problems inherent in approaches that rely upon model-reduction. To illustrate these methods, a perturbation shear stress controller is designed and applied to plane channel flow, assuming arrays of wall mounted shear-stress sensors and transpiration actuators. DNS results demonstrate robust attenuation of the perturbation shear-stresses across a wide range of Reynolds numbers with a single, linear controller

Communicating with people living with dementia who are nonverbal: the creation of Adaptive Interaction

Loss of verbal language production makes people with dementia appear unreachable. We previously presented a case study applying nonverbal communication techniques with a lady with dementia who could no longer speak, which we termed Adaptive Interaction. The current small-n study examines the applicability of Adaptive Interaction as a general tool for uncovering the communication repertoires of non-verbal individuals living with dementia. Communicative responses of 30 interaction sessions were coded and analysed in two conditions: Standard (Baseline) and Adaptive Interaction (Intervention). All participants retained the ability to interact plus a unique communication repertoire comprising a variety of nonverbal components, spanning eye gaze, emotion expression, and movement. In comparison to Baseline sessions, Intervention sessions were characterised by more smiling, looking at ME and imitation behaviour from the people with dementia. These findings allude to the potential of Adaptive Interaction as the basis for interacting with people living with dementia who can no longer speak