Optimal kinematic control of an autonomous underwater vehicle

This note investigates the motion control of an autonomous underwater vehicle (AUV). The AUV is modeled as a nonholonomic system as any lateral motion of a conventional, slender AUV is quickly damped out. The problem is formulated as an optimal kinematic control problem on the Euclidean Group of Motions SE(3), where the cost function to be minimized is equal to the integral of a quadratic function of the velocity components. An application of the Maximum Principle to this optimal control problem yields the appropriate Hamiltonian and the corresponding vector fields give the necessary conditions for optimality. For a special case of the cost function, the necessary conditions for optimality can be characterized more easily and we proceed to investigate its solutions. Finally, it is shown that a particular set of optimal motions trace helical paths. Throughout this note we highlight a particular case where the quadratic cost function is weighted in such a way that it equates to the Lagrangian (kinetic energy) of the AUV. For this case, the regular extremal curves are constrained to equate to the AUV's components of momentum and the resulting vector fields are the d'Alembert-Lagrange equations in Hamiltonian form.

Ocean acoustic models for low frequency propagation in 2D and 3D environments

In this paper we are mainly concerned with the development of efficient computer models capable of accurately predicting the propagation of low-to-middle frequency sound in the sea, in axially symmetric (2D) and in fully 3D environments. The major physical features of the problem, i.e. a variable bottom topography, elastic properties of the subbottom structure, volume attenuation and other range inhomogeneities are efficiently treated. The computer models presented are based on normal mode solutions of the Helmholtz equation on the one hand, and on various types of numerical schemes for parabolic approximations of the Helmholtz equation on the other. A new coupled mode code is introduced to model sound propagation in range-dependent ocean environments with variable bottom topography, where the effects of an elastic bottom, of volume attenuation, surface and bottom roughness are taken into account. New computer models based on finite difference and finite element techniques for the numerical solution of parabolic approximations are also presented. They include an efficient modeling of the bottom influence via impedance boundary conditions, they cover wide angle propagation, elastic bottom effects, variable bottom topography and reverberation effects. All the models are validated on several benchmark problems and versus experimental data. Results thus obtained were compared with analogous results from standard codes in the literature.

Acoustic trapped modes in a three-dimensional waveguide of slowly varying cross section

In this paper we develop an asymptotic scheme to approximate the trapped mode solutions to the time harmonic wave equation in a three-dimensional waveguide with a smooth but otherwise arbitrarily shaped cross section and a single, slowly varying `bulge', symmetric in the longitudinal direction. Extending the work in Biggs (2012), we first employ a WKBJ-type ansatz to identify the possible quasi-mode solutions which propagate only in the thicker region, and hence find a finite cut-on region of oscillatory behaviour and asymptotic decay elsewhere. The WKBJ expansions are used to identify a turning point between the cut-on and cut-on regions. We note that the expansions are nonuniform in an interior layer centred on this point, and we use the method of matched asymptotic expansions to connect the cut-on and cut-on regions within this layer. The behaviour of the expansions within the interior layer then motivates the construction of a uniformly valid asymptotic expansion. Finally, we use this expansion and the symmetry of the waveguide around the longitudinal centre, x = 0, to extract trapped mode wavenumbers, which are compared with those found using a numerical scheme and seen to be extremely accurate, even to relatively large values of the small parameter.

The role of spectral- and temporal-envelope room-acoustic cues in auditory selective attention

Listeners can attend to one of several simultaneous messages by tracking one speaker’s voice characteristics. Using differences in the location of sounds in a room, we ask how well cues arising from spatial position compete with these characteristics. Listeners decided which of two simultaneous target words belonged in an attended “context” phrase when it was played simultaneously with a different “distracter” context. Talker difference was in competition with position difference, so the response indicates which cue‐type the listener was tracking. Spatial position was found to override talker difference in dichotic conditions when the talkers are similar (male). The salience of cues associated with differences in sounds, bearings decreased with distance between listener and sources. These cues are more effective binaurally. However, there appear to be other cues that increase in salience with distance between sounds. This increase is more prominent in diotic conditions, indicating that these cues are largely monaural. Distances between spectra calculated using a gammatone filterbank (with ERB‐spaced CFs) of the room’s impulse responses at different locations were computed, and comparison with listeners’ responses suggested some slight monaural loudness cues, but also monaural “timbre” cues arising from the temporal‐ and spectral‐envelope differences in the speech from different locations.

Room-acoustic factors in attentional tracking

In a “busy” auditory environment listeners can selectively attend to one of several simultaneous messages by tracking one listener's voice characteristics. Here we ask how well other cues compete for attention with such characteristics, using variations in the spatial position of sound sources in a (virtual) seminar room. Listeners decided which of two simultaneous target words belonged in an attended “context” phrase when it was played with a simultaneous “distracter” context that had a different wording. Talker difference was in competition with a position difference, so that the target‐word chosen indicates which cue‐type the listener was tracking. The main findings are that room‐acoustic factors provide some tracking cues, whose salience increases with distance separation. This increase is more prominent in diotic conditions, indicating that these cues are largely monaural. The room‐acoustic factors might therefore be the spectral‐ and temporal‐envelope effects of reverberation on the timbre of speech. By contrast, the salience of cues associated with differences in sounds' bearings tends to decrease with distance, and these cues are more effective in dichotic conditions. In other conditions, where a distance and a bearing difference cooperate, they can completely override a talker difference at various distances.

Design and fabrication of infrared filters for remote sounding instrumentation

Cooled infrared filters have been used in pressure modulation and filter radiometry to measure the dynamics, temperature distribution and concentrations of atmospheric elements in various satellite radiometers. Invariably such instruments use precision infrared bandpass filters and coatings for spectral selction, often operating at cryogenic temperatures. More recent developments in the use of spectrally-selective cooled detectors in focal plane arrays have simplified the optical layout and reduced the component count of radiometers but have placed additional demands on both the spectral and physical performance requirements of the filters. This paper describes and contrasts the more traditional radiometers using discrete detectors with those which use focal plane detector array technology, with particular emphasis on the function of the filters and coatings in the two cases. Additionally we discuss the spectral techniques and materials used to fabricate infrared coatings and filters for use in space optics, and give examples of their application in the fabrication of some demanding long wavelength dichroics and filters. We also discuss the effects of the space environment on the stability and durability of high performance infrared filters and materials exposed to low Earth orbit for 69 months on the NASA Long Duration Exposure Facility (LDEF).

A new frequency-uniform coercive boundary integral equation for acoustic scattering

A new boundary integral operator is introduced for the solution of the soundsoft acoustic scattering problem, i.e., for the exterior problem for the Helmholtz equation with Dirichlet boundary conditions. We prove that this integral operator is coercive in L2(Γ) (where Γ is the surface of the scatterer) for all Lipschitz star-shaped domains. Moreover, the coercivity is uniform in the wavenumber k = ω/c, where ω is the frequency and c is the speed of sound. The new boundary integral operator, which we call the “star-combined” potential operator, is a slight modification of the standard combined potential operator, and is shown to be as easy to implement as the standard one. Additionally, to the authors' knowledge, it is the only second-kind integral operator for which convergence of the Galerkin method in L2(Γ) is proved without smoothness assumptions on Γ except that it is Lipschitz. The coercivity of the star-combined operator implies frequency-explicit error bounds for the Galerkin method for any approximation space. In particular, these error estimates apply to several hybrid asymptoticnumerical methods developed recently that provide robust approximations in the high-frequency case. The proof of coercivity of the star-combined operator critically relies on an identity first introduced by Morawetz and Ludwig in 1968, supplemented further by more recent harmonic analysis techniques for Lipschitz domains.

Wave trapping in a two-dimensional sound-soft or sound-hard acoustic waveguide of slowly-varying width

In this paper we derive novel approximations to trapped waves in a two-dimensional acoustic waveguide whose walls vary slowly along the guide, and at which either Dirichlet (sound-soft) or Neumann (sound-hard) conditions are imposed. The guide contains a single smoothly bulging region of arbitrary amplitude, but is otherwise straight, and the modes are trapped within this localised increase in width. Using a similar approach to that in Rienstra (2003), a WKBJ-type expansion yields an approximate expression for the modes which can be present, which display either propagating or evanescent behaviour; matched asymptotic expansions are then used to derive connection formulae which bridge the gap across the cut-off between propagating and evanescent solutions in a tapering waveguide. A uniform expansion is then determined, and it is shown that appropriate zeros of this expansion correspond to trapped mode wavenumbers; the trapped modes themselves are then approximated by the uniform expansion. Numerical results determined via a standard iterative method are then compared to results of the full linear problem calculated using a spectral method, and the two are shown to be in excellent agreement, even when $\epsilon$, the parameter characterising the slow variations of the guide’s walls, is relatively large.

Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering

In this article we describe recent progress on the design, analysis and implementation of hybrid numerical-asymptotic boundary integral methods for boundary value problems for the Helmholtz equation that model time harmonic acoustic wave scattering in domains exterior to impenetrable obstacles. These hybrid methods combine conventional piecewise polynomial approximations with high-frequency asymptotics to build basis functions suitable for representing the oscillatory solutions. They have the potential to solve scattering problems accurately in a computation time that is (almost) independent of frequency and this has been realized for many model problems. The design and analysis of this class of methods requires new results on the analysis and numerical analysis of highly oscillatory boundary integral operators and on the high-frequency asymptotics of scattering problems. The implementation requires the development of appropriate quadrature rules for highly oscillatory integrals. This article contains a historical account of the development of this currently very active field, a detailed account of recent progress and, in addition, a number of original research results on the design, analysis and implementation of these methods.

Wernicke’s aphasia reflects a combination of acoustic-phonological and semantic control deficits: A case-series comparison of Wernicke’s aphasia, semantic dementia and semantic aphasia

Wernicke’s aphasia (WA) is the classical neurological model of comprehension impairment and, as a result, the posterior temporal lobe is assumed to be critical to semantic cognition. This conclusion is potentially confused by (a) the existence of patient groups with semantic impairment following damage to other brain regions (semantic dementia and semantic aphasia) and (b) an ongoing debate about the underlying causes of comprehension impairment in WA. By directly comparing these three patient groups for the first time, we demonstrate that the comprehension impairment in Wernicke’s aphasia is best accounted for by dual deficits in acoustic-phonological analysis (associated with pSTG) and semantic cognition (associated with pMTG and angular gyrus). The WA group were impaired on both nonverbal and verbal comprehension assessments consistent with a generalised semantic impairment. This semantic deficit was most similar in nature to that of the semantic aphasia group suggestive of a disruption to semantic control processes. In addition, only the WA group showed a strong effect of input modality on comprehension, with accuracy decreasing considerably as acoustic-phonological requirements increased. These results deviate from traditional accounts which emphasise a single impairment and, instead, implicate two deficits underlying the comprehension disorder in WA.

Detection of mutations in Salmonella enterica gyrA, gyrB, parC and parE genes by denaturing high performance liquid chromatography (DHPLC) using standard HPLC instrumentation

Aims: Quinolone antibiotics are the agents of choice for treating systemic Salmonella infections. Resistance to quinolones is usually mediated by mutations in the DNA gyrase gene gyrA. Here we report the evaluation of standard HPLC equipment for the detection of mutations (single nucleotide polymorphisms; SNPs) in gyrA, gyrB, parC and parE by denaturing high performance liquid chromatography (DHPLC). Methods: A panel of Salmonella strains was assembled which comprised those with known different mutations in gyrA (n = 8) and fluoroquinolone-susceptible and -resistant strains (n = 50) that had not been tested for mutations in gyrA. Additionally, antibiotic-susceptible strains of serotypes other than Salmonella enterica serovar Typhimurium strains were examined for serotype-specific mutations in gyrB (n = 4), parC (n = 6) and parE (n = 1). Wild-type (WT) control DNA was prepared from Salmonella Typhimurium NCTC 74. The DNA of respective strains was amplified by PCR using Optimase (R) proofreading DNA polymerase. Duplex DNA samples were analysed using an Agilent A1100 HPLC system with a Varian Helix (TM) DNA column. Sequencing was used to validate mutations detected by DHPLC in the strains with unknown mutations. Results: Using this HPLC system, mutations in gyrA, gyrB, parC and parE were readily detected by comparison with control chromatograms. Sequencing confirmed the gyrA predicted mutations as detected by DHPLC in the unknown strains and also confirmed serotype-associated sequence changes in non-Typhimurium serotypes. Conclusions: The results demonstrated that a non-specialist standard HPLC machine fitted with a generally available column can be used to detect SNPs in gyrA, gyrB, parC and parE genes by DHPLC. Wider applications should be possible.

Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes

We extend the a priori error analysis of Trefftz-discontinuous Galerkin methods for time-harmonic wave propagation problems developed in previous papers to acoustic scattering problems and locally refined meshes. To this aim, we prove refined regularity and stability results with explicit dependence of the stability constant on the wave number for non convex domains with non connected boundaries. Moreover, we devise a new choice of numerical flux parameters for which we can prove L2-error estimates in the case of locally refined meshes near the scatterer. This is the setting needed to develop a complete hp-convergence analysis.