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.

Intermittently-visual tracking experiments reveal the roles of error-correction and predictive mechanisms in the human visual-motor control system

Prediction mechanism is necessary for human visual motion to compensate a delay of sensory-motor system. In a previous study, “proactive control” was discussed as one example of predictive function of human beings, in which motion of hands preceded the virtual moving target in visual tracking experiments. To study the roles of the positional-error correction mechanism and the prediction mechanism, we carried out an intermittently-visual tracking experiment where a circular orbit is segmented into the target-visible regions and the target-invisible regions. Main results found in this research were following. A rhythmic component appeared in the tracer velocity when the target velocity was relatively high. The period of the rhythm in the brain obtained from environmental stimuli is shortened more than 10%. The shortening of the period of rhythm in the brain accelerates the hand motion as soon as the visual information is cut-off, and causes the precedence of hand motion to the target motion. Although the precedence of the hand in the blind region is reset by the environmental information when the target enters the visible region, the hand motion precedes the target in average when the predictive mechanism dominates the error-corrective mechanism.

Transition from an anti-phase error-correction-mode to a synchronization mode in the mutual hand tracking

Proactive motion in hand tracking and in finger bending, in which the body motion occurs prior to the reference signal, was reported by the preceding researchers when the target signals were shown to the subjects at relatively high speed or high frequencies. These phenomena indicate that the human sensory-motor system tends to choose an anticipatory mode rather than a reactive mode, when the target motion is relatively fast. The present research was undertaken to study what kind of mode appears in the sensory-motor system when two persons were asked to track the hand position of the partner with each other at various mean tracking frequency. The experimental results showed a transition from a mutual error-correction mode to a synchronization mode occurred in the same region of the tracking frequency with that of the transition from a reactive error-correction mode to a proactive anticipatory mode in the mechanical target tracking experiments. Present research indicated that synchronization of body motion occurred only when both of the pair subjects operated in a proactive anticipatory mode. We also presented mathematical models to explain the behavior of the error-correction mode and the synchronization mode.

A new algorithm for tracking people in a pervasive mining environment

This paper analyze and study a pervasive computing system in a mining environment to track people based on RFID (radio frequency identification) technology. In first instance, we explain the RFID fundamentals and the LANDMARC (location identification based on dynamic active RFID calibration) algorithm, then we present the proposed algorithm combining LANDMARC and trilateration technique to collect the coordinates of the people inside the mine, next we generalize a pervasive computing system that can be implemented in mining, and finally we show the results and conclusions.

Efficient calculation of two-dimensional periodic and waveguide acoustic Green’s functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

Acoustic scattering by an inhomogeneous layer on a rigid plate

The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R2 is considered. The density is assumed to be unity in the media: within the layer the sound speed is assumed to be an arbitrary bounded measurable function. The problem is modelled by the reduced wave equation with variable wavenumber in the layer and a Neumann condition on the plate. To formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate. Under additional assumptions on the wavenumber in the layer, uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established. General results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data.

Efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane

This paper is concerned with the problem of propagation from a monofrequency coherent line source above a plane of homogeneous surface impedance. The solution of this problem occurs in the kernel of certain boundary integral equation formulations of acoustic propagation above an impedance boundary, and the discussion of the paper is motivated by this application. The paper starts by deriving representations, as Laplace-type integrals, of the solution and its first partial derivatives. The evaluation of these integral representations by Gauss-Laguerre quadrature is discussed, and theoretical bounds on the truncation error are obtained. Specific approximations are proposed which are shown to be accurate except in the very near field, for all angles of incidence and a wide range of values of surface impedance. The paper finishes with derivations of partial results and analogous Laplace-type integral representations for the case of a point source.

Are greenhouse gas signals of Northern Hemisphere winter extra-tropical cyclone activity dependent on the identification and tracking algorithm?

For Northern Hemisphere extra-tropical cyclone activity, the dependency of a potential anthropogenic climate change signal on the identification method applied is analysed. This study investigates the impact of the used algorithm on the changing signal, not the robustness of the climate change signal itself. Using one single transient AOGCM simulation as standard input for eleven state-of-the-art identification methods, the patterns of model simulated present day climatologies are found to be close to those computed from re-analysis, independent of the method applied. Although differences in the total number of cyclones identified exist, the climate change signals (IPCC SRES A1B) in the model run considered are largely similar between methods for all cyclones. Taking into account all tracks, decreasing numbers are found in the Mediterranean, the Arctic in the Barents and Greenland Seas, the mid-latitude Pacific and North America. Changing patterns are even more similar, if only the most severe systems are considered: the methods reveal a coherent statistically significant increase in frequency over the eastern North Atlantic and North Pacific. We found that the differences between the methods considered are largely due to the different role of weaker systems in the specific methods.

IMILAST: a community effort to intercompare extratropical cyclone detection and tracking algorithms

The variability of results from different automated methods of detection and tracking of extratropical cyclones is assessed in order to identify uncertainties related to the choice of method. Fifteen international teams applied their own algorithms to the same dataset—the period 1989–2009 of interim European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERAInterim) data. This experiment is part of the community project Intercomparison of Mid Latitude Storm Diagnostics (IMILAST; see www.proclim.ch/imilast/index.html). The spread of results for cyclone frequency, intensity, life cycle, and track location is presented to illustrate the impact of using different methods. Globally, methods agree well for geographical distribution in large oceanic regions, interannual variability of cyclone numbers, geographical patterns of strong trends, and distribution shape for many life cycle characteristics. In contrast, the largest disparities exist for the total numbers of cyclones, the detection of weak cyclones, and distribution in some densely populated regions. Consistency between methods is better for strong cyclones than for shallow ones. Two case studies of relatively large, intense cyclones reveal that the identification of the most intense part of the life cycle of these events is robust between methods, but considerable differences exist during the development and the dissolution phases.

Sensitivities of a cyclone detection and tracking algorithm: individual tracks and climatology

Northern Hemisphere cyclone activity is assessed by applying an algorithm for the detection and tracking of synoptic scale cyclones to mean sea level pressure data. The method, originally developed for the Southern Hemisphere, is adapted for application in the Northern Hemisphere winter season. NCEP-Reanalysis data from 1958/59 to 1997/98 are used as input. The sensitivities of the results to particular parameters of the algorithm are discussed for both case studies and from a climatological point of view. Results show that the choice of settings is of major relevance especially for the tracking of smaller scale and fast moving systems. With an appropriate setting the algorithm is capable of automatically tracking different types of cyclones at the same time: Both fast moving and developing systems over the large ocean basins and smaller scale cyclones over the Mediterranean basin can be assessed. The climatology of cyclone variables, e.g., cyclone track density, cyclone counts, intensification rates, propagation speeds and areas of cyclogenesis and -lysis gives detailed information on typical cyclone life cycles for different regions. The lowering of the spatial and temporal resolution of the input data from full resolution T62/06h to T42/12h decreases the cyclone track density and cyclone counts. Reducing the temporal resolution alone contributes to a decline in the number of fast moving systems, which is relevant for the cyclone track density. Lowering spatial resolution alone mainly reduces the number of weak cyclones.

Tracking the momentum flux of a CME and quantifying its influence on geomagnetically induced currents at Earth

We investigate a coronal mass ejection (CME) propagating toward Earth on 29 March 2011. This event is specifically chosen for its predominately northward directed magnetic field, so that the influence from the momentum flux onto Earth can be isolated. We focus our study on understanding how a small Earth-directed segment propagates. Mass images are created from the white-light cameras onboard STEREO which are also converted into mass height-time maps (mass J-maps). The mass tracks on these J-maps correspond to the sheath region between the CME and its associated shock front as detected by in situ measurements at L1. A time series of mass measurements from the STEREO COR-2A instrument is made along the Earth propagation direction. Qualitatively, this mass time series shows a remarkable resemblance to the L1 in situ density series. The in situ measurements are used as inputs into a three-dimensional (3-D) magnetospheric space weather simulation from the Community Coordinated Modeling Center. These simulations display a sudden compression of the magnetosphere from the large momentum flux at the leading edge of the CME, and predictions are made for the time derivative of the magnetic field (dB/dt) on the ground. The predicted dB/dt values were then compared with the observations from specific equatorially located ground stations and showed notable similarity. This study of the momentum of a CME from the Sun down to its influence on magnetic ground stations on Earth is presented as a preliminary proof of concept, such that future attempts may try to use remote sensing to create density and velocity time series as inputs to magnetospheric simulations.

Automated identification and tracking of polar-cap plasma patches at solar minimum

A method of automatically identifying and tracking polar-cap plasma patches, utilising data inversion and feature-tracking methods, is presented. A well-established and widely used 4-D ionospheric imaging algorithm, the Multi-Instrument Data Assimilation System (MIDAS), inverts slant total electron content (TEC) data from ground-based Global Navigation Satellite System (GNSS) receivers to produce images of the free electron distribution in the polar-cap ionosphere. These are integrated to form vertical TEC maps. A flexible feature-tracking algorithm, TRACK, previously used extensively in meteorological storm-tracking studies is used to identify and track maxima in the resulting 2-D data fields. Various criteria are used to discriminate between genuine patches and "false-positive" maxima such as the continuously moving day-side maximum, which results from the Earth's rotation rather than plasma motion. Results for a 12-month period at solar minimum, when extensive validation data are available, are presented. The method identifies 71 separate structures consistent with patch motion during this time. The limitations of solar minimum and the consequent small number of patches make climatological inferences difficult, but the feasibility of the method for patches larger than approximately 500 km in scale is demonstrated and a larger study incorporating other parts of the solar cycle is warranted. Possible further optimisation of discrimination criteria, particularly regarding the definition of a patch in terms of its plasma concentration enhancement over the surrounding background, may improve results.

The role of soil microbes in the global carbon cycle: tracking the below-ground microbial processing of plant-derived carbon for manipulating carbon dynamics in agricultural systems.

It is well known that atmospheric concentrations of carbon dioxide (CO2) (and other greenhouse gases) have increased markedly as a result of human activity since the industrial revolution. It is perhaps less appreciated that natural and managed soils are an important source and sink for atmospheric CO2 and that, primarily as a result of the activities of soil microorganisms, there is a soil-derived respiratory flux of CO2 to the atmosphere that overshadows by tenfold the annual CO2 flux from fossil fuel emissions. Therefore small changes in the soil carbon cycle could have large impacts on atmospheric CO2 concentrations. Here we discuss the role of soil microbes in the global carbon cycle and review the main methods that have been used to identify the microorganisms responsible for the processing of plant photosynthetic carbon inputs to soil. We discuss whether application of these techniques can provide the information required to underpin the management of agro-ecosystems for carbon sequestration and increased agricultural sustainability. We conclude that, although crucial in enabling the identification of plant-derived carbon-utilising microbes, current technologies lack the high-throughput ability to quantitatively apportion carbon use by phylogentic groups and its use efficiency and destination within the microbial metabolome. It is this information that is required to inform rational manipulation of the plant–soil system to favour organisms or physiologies most important for promoting soil carbon storage in agricultural soil.