We develop an Eulerian-Lagrangian localized adjoint method (ELLAM) to solve two-dimensional advection-diffusion equations with all combinations of inflow and outflow Dirichlet, Neumann, and flux boundary conditions. The ELLAM formalism provides a systematic framework for implementation of general boundary conditions, leading to mass-conservative numerical schemes. The computational advantages of the ELLAM approximation have been demonstrated for a number of one-dimensional transport systems; practical implementations of ELLAM schemes in multiple spatial dimensions that require careful algorithm development are discussed in detail in this paper. Extensive numerical results are presented to compare the ELLAM scheme with many widely used numerical methods and to demonstrate the strength of the ELLAM scheme.

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The range of physiological adaptations possessed by marine animals allowing them to successfully operate in the marine environment is a plentiful source of inspiration for the designers of Autonomous Underwater Vehicles. This chapter compares the total energetic cost of straight line swimming for both marine animals and AUVs, using cost of transport (COT) as a comparative metric. COT is a normalised measure of the energetic cost of transporting the animal's or vehicle's mass over a unit distance. It includes non propulsion power requirements as well as considering the energy lost by actuators and mechanical couplings and energy lost in the wake. Comparisons presented in this chapter show that marine animals typically have higher optimum COT than engineered systems of equivalent size. However parallels may be drawn, for example, to increase range both marine animals and AUVs appear to favour reducing non-propulsion power costs and travelling slowly to ensure operating at the minimum COT.

Evidence suggests that electroencephalographic (EEG) activity extends far beyond the traditional frequency range. Much of the prior study of >120 Hz EEG is in epileptic brains. In the current work, we measured EEG activity in the range of 200 to 2000 Hz, in the brains of healthy, spontaneously behaving rats. Both arrhythmic (1/f-type) and rhythmic (band) activities were identified and their properties shown to depend on EEG-defined stage of sleep/wakefulness. The inverse power law exponent of 1/f-type noise is shown to decrease from 3.08 in REM and 2.58 in NonREM to a value of 1.99 in the Waking state. Such a trend represents a transition from long- to short-term memory processes when examined in terms of the corresponding Hurst index. In addition, treating the 1/f-type activity as baseline noise reveals the presence of two, newly identified, high frequency EEG bands. The first band (ψ) is centered between 260–280 Hz; the second, and stronger, band is a broad peak in the 400–500 Hz range (termed ω). Both of these peaks display lognormal distributions. The functional significance of these frequency bands is supported by the variation in the strength of the peaks with EEG-defined sleep/wakefulness.

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