Fixed Point Source Research Articles

Uniqueness Results for Some Inverse Electromagnetic Scattering Problems with Phaseless Far-Field Data

Consider three electromagnetic scattering models, namely, electromagnetic scattering by an elastic body, by a chiral medium, and by a cylinder at oblique incidence. We are concerned with the corresponding inverse problems of determining the locations and shapes of the scatterers from phaseless far-field patterns. There are certain essential differences from the usual inverse electromagnetic scattering problems, and some fundamental conclusions need to be proved. First, we show that the phaseless far-field data are invariant under the translation of the scatterers and prove the reciprocity relations of the scattering data. Then, we justify the unique determination of the scatterers by utilizing the reference ball approach and the superpositions of a fixed point source and plane waves as the incident fields. The proofs are based on the reciprocity relations, Green’s formulas, and the analyses of the wave fields in the reference ball.

Development of a moving point source model for shipping emission dispersion modeling in EPISODE–CityChem v1.3

Abstract. This paper demonstrates the development of a moving point source (MPS) model for simulating the atmospheric dispersion of pollutants emitted from ships under movement. The new model is integrated into the chemistry transport model EPISODE–CityChem v1.3. In the new model, ship parameters, especially speed and direction, are included to simulate the instantaneous ship positions and then the emission dispersion at different simulation time. The model was first applied to shipping emission dispersion modeling under simplified conditions, and the instantaneous and hourly averaged emission concentrations predicted by the MPS model and the commonly used line source (LS) and fixed point source (FPS) models were compared. The instantaneous calculations were quite different due to the different ways to treat the moving emission sources by different models. However, for the hourly averaged concentrations, the differences became smaller, especially for a large number of ships. The new model was applied to a real configuration from the seas around Singapore that included hundreds of ships, and their dispersion was simulated over a period of a few hours. The simulated results were compared to measured values at different locations, and it was found that reasonable emission concentrations were predicted by the moving point source model.

Bayesian identification of oil spill source parameters from image contours

Oil spills at sea pose a serious threat to coastal environments. Identifying oil pollution sources could help to investigate unreported spills, and satellite imagery can be an effective tool for this purpose. We present a Bayesian approach to estimate the source parameters of a spill from contours of oil slicks detected by remotely sensed images. Five parameters of interest are estimated: the 2D coordinates of the source of release, the time and duration of the spill, and the quantity of oil released. Two synthetic experiments of a spill released from a fixed point source are investigated, where a contour is fully observed in the first case, while two contours are partially observed at two different times in the second. In both experiments, the proposed method is able to provide good estimates of the parameters along with a level of confidence reflected by the uncertainties within.

Coherent interferometric imaging in a random flow

This paper is concerned with the development of imaging methods to localize sources or reflectors in inhomogeneous moving media with acoustic waves that have travelled through them. A typical example is the localization of broadband acoustic sources in a turbulent jet flow for aeroacoustic applications. The proposed algorithms are extensions of Kirchhoff migration (KM) and coherent interferometry (CINT) which have been considered for smooth and randomly inhomogeneous quiescent media so far. They are constructed starting from the linearized Euler equations for the acoustic perturbations about a stationary ambient flow. A model problem for the propagation of acoustic waves generated by a fixed point source in an ambient flow with constant velocity is addressed. Based on this result imaging functions are proposed to modify the existing KM and CINT functions to account for the ambient flow velocity. They are subsequently tested and compared by numerical simulations in various configurations, including a synthetic turbulent jet representative of the main features encountered in actual jet flows.

Exact closed-form solutions for Lamb’s problem—II: a moving point load

SUMMARYIn this paper, we report on an exact closed-form solution for the displacement in an elastic homogeneous half-space elicited by a downward vertical point source moving with constant velocity over the surface of the medium. The problem considered here is an extension to Lamb’s problem. Starting with the integral solutions of Bakker et al., we followed the method developed by Feng and Zhang, which focuses on the displacement triggered by a fixed point source observed on the free surface, to obtain the final solution in terms of elementary algebraic functions as well as elliptic integrals of the first, second and third kind. Our closed-form results agree perfectly with the numerical results of Bakker et al., which confirms the correctness of our formulae. The solution obtained in this paper may lay a solid foundation for further consideration of the response of an actual physical moving load, such as a high-speed rail train.

Green's function for three‐dimensional elastic wave equation with a moving point source on the free surface with applications

ABSTRACTHigh‐speed train seismology has come into being recently. This new kind of seismology uses a high‐speed train as a repeatable moving seismic source. Therefore, Green's function for a moving source is needed to make theoretical studies of the high‐speed train seismology. Green's function for three‐dimensional elastic wave equation with a moving point source on the free surface is derived. It involves a line integral of the Green's function for a fixed point source with different positions and corresponding time delays. We give a rigorous mathematical proof of this Green's function. According to the principle of linear superposition, we have also obtained the Green's function for a group of moving sources which can be regarded as a model of a traveling high‐speed train. Based on a temporal convolution, an analytical formula for other moving sources is also given. In terms of a moving Gaussian source, we deal with the issue of numerical calculations of the analytical formula. Applications to modelling of a traveling high‐speed train are presented. We have considered both the land case and the bridge case for a traveling high‐speed train. The theoretical seismograms show different waveform features for these two cases.

Solute transport in a semi-infinite homogeneous aquifer with a fixed point source concentration

This study derives an analytical solution of the advection–dispersion (AD) equation commonly used to describe the transport of pollutants in a semi-infinite homogeneous aquifer. When an extra constant source term is added to the AD equation, it changes the solution of the equation. The AD equation is solved analytically using Laplace transform. Also, the equation is solved numerically using an explicit finite difference method and its stability condition is presented with the aid of matrix method. For the solution of the AD equation the following considerations are made: (1) The dispersion and velocity are considered as time-dependent; (2) dispersion is expressed as directly proportional to the square of velocity; (3) there is also diffusion; (4) there is some initial concentration and the aquifer domain is, therefore, not pollutant-free; (5) There is a time-dependent exponentially decreasing input source; and (6) the concentration gradient is assumed to be zero at the exit boundary. It is found that the contaminant concentration decreases with time contrary to what happens when the extra term is not included.

In‐place query driven big data platform: Applications to post processing of environmental monitoring

SummaryThis paper describes the use of an experimental big data platform for applications of environmental monitoring associated with visualization of global climate forecast data and air quality model simulation and response. Environmental monitoring in general requires both capabilities of model simulation for forecast, and data processing for visualization and analyses. The in‐place query driven big data platform, based on concepts of Query Driven Visualization and shared‐nothing distributed database, thus is developed for the need. The system architecture of this experimental big data platform entails one master data node and 17 slave data nodes, while the system links to the National Center for High‐performance Computing supercomputer, Advanced Large‐scale Parallel Supercluster, and storage pool. For software implementation, the openSUSE operating system and MariaDB database are installed on all nodes. The master data node is responsible for metadata management and information integration and the 17 slave data nodes for distributed database and parallel model simulation, data visualization, and analyses. The application of global climate data visualization (Outgoing Longwave Radiation or OLR, temperature, rainfall, etc.) in the platform serves first to partition Network Common Data Form file data into shared‐nothing distributed databases for partial visualization in slave data nodes, then integrated into whole visualization in the master node through Message Passing Interface communication.For the application of air quality management, we first accessed Taiwan Environmental Protection Administration (EPA) observed data in the master node. EPA observed data are replicated to distributed databases in slave nodes; and the air pollution model, Gaussian plume trajectory model, is replicated in all slave nodes for model simulation, which produces output data and associated image files in the local file system. The master node is able to collect whole image files through the remote shared file system for display of the results. We can see the approach of data I/O access in 2 applications, due to individual problem features, each application is unique. Examples of benchmark cases reveal strong performance in accelerating computing speed and reducing the I/O operational time. It is found that the platform is able to accelerate climate data visualization processes, help research scientists gain the deep insights into data, and explore the potential phenomena and features, such as formation of Typhoon eddies. In air quality management applications, the platform is used to perform the air pollution model Gaussian plume trajectory model. Backward trajectory simulation of PM2.5 concentrations is used to identify the 30+ point source's contribution on 73 EPA monitor stations (receptors) in Taiwan. A user‐friendly, web‐service based big data presentation uses the heterogeneous observed and forecast pollutant data in space and time. The results support for air quality decision‐making and emergency response. The limitation of data size for applications in the platform, the current users and future development of the platform, and the linkage of PRAGMA collaboration are also described in the paper.

Research of Ammonia Concentration Distribution Simulation in Road Transportation Leakage Based on the Gaussian Model

The leakage of liquid ammonia during road transportation is chosen as the research object in this paper, and then the model of toxic gas diffusion after leakage accident is established; MATLAB is used to achieve the accident simulation and risk analysis of continuous leakage from moving and fixed point source. On the basis of different harm to human body of different concentrations of ammonia and the spread concentration curve of the ammonia, the dangerous area is divided into five zones: mild zone, moderate zone, severe zone, dead zone and instantaneous dead zone; according to the comparison between leakage diffusion processes from moving and fixed point source, following conclusions can be reached: during the leakage, area of dangerous zones increased and after the leakage, dangerous zone areas first increased and then decreased; the peak ammonia concentration from fixed source is higher than that from moving point source, whereas influence area of the former is smaller than the latter. This method can quickly simulate the scope and severity of leakage accident in road transportation and provide references for the emergency rescue after accidents.

A reference radiance-meter system for thermodynamic temperature measurements

This paper presents the work carried out to evaluate the radiometric performance of a radiance-meter system which has been built at the LNE-Cnam to determine the thermodynamic temperature of high-temperature fixed points. The work comes as an integral part of the ‘implementing the new Kelvin’ (INK) project in which nine National Metrology Institutes (NMIs) strive to assign the thermodynamic temperatures to the melting curve of high-temperature fixed points with the lowest possible uncertainty. The method used in this research is based on the radiance approach. It exploits a system based on a laser-illuminated integrating sphere source whose radiance is absolutely measured by a trap detector through a well-defined geometry. The trap detector is calibrated traceable to the LNE-Cnam’s cryogenic radiometer. Once the radiance of the sphere is defined, a single grating-based spectroradiometer is used to measure the radiance of the fixed point source at the laser wavelength through direct comparison with the sphere radiance. This allows the thermodynamic temperature of the fixed point to be determined using Planck’s radiation law. The work provides a thorough evaluation of the system along with a detailed study of all related systematic effects and their corresponding uncertainties.

Estimation method to identify scalar point source in turbulent flow based on Taylor’s diffusion theory

We introduce a new approach to diffusion-source estimation for quick identification of the unknown source, based on Taylor’s diffusion theory for turbulent transport of passive scalar from a fixed point source. In order to evaluate the method, we used planar laser-induced fluorescence to measure the concentration field of fluorescent dye in water flowing in a channel. We considered two kinds of datasets: basis data and observed data. The former is used to determine the basis functions characterizing the streamwise dependence of variances for three statistics: the mean concentration, root-mean-square (RMS) of fluctuations in the concentration, and RMS of the temporal gradient of the fluctuating concentration. Consistent with Taylor’s theory, we found that the lateral distribution of each statistic was basically Gaussian, and their standard deviations increased as a function of the square root of the distance from the emitted point. Based on these facts, a basis function can be formulated and expected to be valid for estimation of unknown sources. Source estimation was performed with the observed data, which corresponded to limited available information about the concentration from an unknown point source. We confirmed a good prediction accuracy of the proposed method with an averaged bias as small as the turbulent integral scale. Better precision was achieved by employing several statistics simultaneously. In this case, the standard deviation of the estimated source position was assessed at 14 % of the mean distance between the source and measurement points, after 100 source-estimate trials with different datasets. The methodology tested in this paper is expected to be applicable more general and complex environmental diffusion issues involving anisotropic turbulent dispersion, and space–time variable mainstream systems; but its versatility in such systems is currently under investigation.

A Kirchhoff approximation-based numerical method to compute multiple acoustic scattering of a moving source

Within the scope of a study of external noise propagation from moving ground vehicles, a numerical method is developed to compute the acoustic field emitted by a moving source in the presence of scattering objects such as roads, buildings or noise-shields. This method is developed with the purpose of being used in a vehicle design process and therefore it must have a low computational cost, which requires a certain number of approximations. The case of a fixed point source is studied first then the effect of a movement of the source is taken into account through the introduction of a retarded time. The acoustic source is assumed to be represented by one or many harmonic monopoles of possibly different frequency moving with a constant speed in a quiescent flow field. Scattering from nearby perfectly reflecting objects is computed through a Kirchhoff–Helmholtz integral equation applying the Kirchhoff approximation. A ray-surface intersection algorithm to compute shadow areas is proposed. The method is validated against analytical solutions and experimental results for a fixed source, and against a higher-order finite difference time-domain method for the multiple scattering of a moving source. Results are good and show that this method can potentially be used to predict urban noise.

Theory of microbe motion in a poisoned environment

The motility of a microorganism which tries to avoid a poisoned environment by chemotaxis is studied within a simple model which couples its velocity to the concentration field of the poison. The latter is time independent but inhomogeneous in space. The presence of the poison is assumed to irreversibly reduce the propulsion speed. The model is solved analytically for different couplings of the total poison dose experienced by the microbe to the propulsion mechanism. In a stationary poison field resulting from a constant emission of a fixed point source, we find a power law for the distance traveled by the microbe as a function of time with a nonuniversal exponent which depends on the coupling in the model. With an inverted sign in the couplings, the acceleration of microbe motion induced by a food field can also be described.

Optimal Spatial Deployment of CO2 Capture and Storage Given a Price on Carbon

Carbon dioxide capture and storage (CCS) links together technologies that separate carbon dioxide (CO2) from fixed point source emissions and transport it by pipeline to geologic reservoirs into which it is injected underground for long-term containment. Previously, models have been developed to minimize the cost of a CCS infrastructure network that captures a given amount of CO2. The CCS process can be costly, however, and large-scale implementation by industry will require government regulations and economic incentives. The incentives can price CO2 emissions through a tax or a cap-and-trade system. This paper extends the earlier mixed-integer linear programming model to endogenously determine the optimal quantity of CO2 to capture and optimize the various components of a CCS infrastructure network, given the price per tonne to emit CO2 into the atmosphere. The spatial decision support system first generates a candidate pipeline network and then minimizes the total cost of capturing, transporting, storing, or emitting CO2. To illustrate how the new model based on CO2 prices works, it is applied to a case study of CO2 sources, reservoirs, and candidate pipeline links and diameters in California.

A Normal Mode Solution for Low-Frequency Bottom-Refracted Wave Propagation

A normal mode solution for low-frequency bottom-sediment-refracted wave propagation is formulated for use with a normal mode method of solving the Helmholtz wave equation to describe the underwater sound field for a fixed point source in a plane multilayered medium. The approach utilizes a factorization of the Wronskian of Green's function which enables sediment reflecting and refracting modes to be summed independently. The sensitivity of propagation loss to the nature of mode interaction with the bottom is investigated for multiple frequencies in a sample environment, and results are compared to measurements of 100-Hz bottom returns in the Caribbean Basin.

The Research and Implementation of Illumination Technology in the 3D GIS Visualization

Building mountains as the basic model for illumination model in the system of 3DGIS visualization. The establishing of this model adopts the approach of the global illumination model combine with the local reflection model and also the combination of shading and shadow. Complete the drawing of the shadow in the global illumination model ,using the shadow algorithm of Ray tracing as the main algorithm for drawing shadow, take advantage of shadow volume algorithm as the additional algorithm for shadow; complete the drawing of the shading in the local reflection model ,using the Blinn proportion algorithm as the main algorithm. Select the single ideal fixed point source as the light source of the illumination model. The results of this experimental show that the approach of combination of global and local model is feasible, the selection of the shadow and shading algorithms are also can reference.

Full spectrum acoustic wave propagation prediction.

An overview of a normal mode solution to the Helmholtz wave equation to describe the underwater sound field for a fixed point source in a plane multilayered medium which utilizes Bessel functions of order 1/3 is presented. The mode functions are continuous across turning points of the separated depth‐dependent differential equation due to careful selection of the representations to be used for Bessel function arguments in various regions of the complex plane. A quotient involving vertical wave number and phase is seen to behave as a constant through turning points, enabling the mode amplitude functions to remain analytic, changing from oscillatory to exponential on traversing the turning point, thus enabling smooth incorporation of the continuous spectrum. The method also provides vertical directionality at all field points without post‐processing the complex acoustic field. Comparisons of model results to a limited number of measured data sets and benchmark propagation codes are presented. Derivation and verification of the solution for bottom‐interacting modes, including shear and compressional reflection and transmission for a layered bottom, as well as an extension into horizontally varying, shallow water environments are also discussed. Portions of this work have been published in the IEEE Journal of Oceanic Engineering.

A mode solution for sediment-refracted wave propagation.

An normal mode solution for low‐frequency bottom‐sediment refracted wave propagation is formulated for use with a normal mode method of solving the Helmholtz wave equation to describe the underwater sound field for a fixed point source in a plane multilayered medium. The approach utilizes a factorization of the Wronskian of the Green’s function which enables sediment reflecting and refracting modes to be summed independently. The sensitivity of propagation loss to the nature of mode interaction with the bottom is investigated for a sample environment and results are compared to measured data.

An Efficient Normal Mode Solution to Wave Propagation Prediction

In this paper, an overview of a normal mode method of solving the Helmholtz wave equation to describe the underwater sound field for a fixed-point source in a plane multilayered medium is presented. The mode functions are well-defined at all depths of the medium as they are continuous across turning points of the separated depth-dependent differential equation. Comparisons of model results to a limited number of measured data sets and benchmark propagation codes are presented.

A fixed-point algorithm for blind source separation with nonlinear autocorrelation

This paper addresses blind source separation (BSS) problem when source signals have the temporal structure with nonlinear autocorrelation. Using the temporal characteristics of sources, we develop an objective function based on the nonlinear autocorrelation of sources. Maximizing the objective function, we propose a fixed-point source separation algorithm. Furthermore, we give some mathematical properties of the algorithm. Computer simulations for sources with square temporal autocorrelation and the real-world applications in the analysis of the magnetoencephalographic recordings (MEG) illustrate the efficiency of the proposed approach. Thus, the presented BSS algorithm, which is based on the nonlinear measure of temporal autocorrelation, provides a novel statistical property to perform BSS.