Identification of the Coordinates of Impulse Pollution Sources in Anisotropic Environments using Numerical Quasiconformal Mapping Methods

The process of filtration in a single-connected curvilinear domain bounded by streamlines and equipotential lines is considered, provided that the medium under study is piecewise homogeneous. It is assumed that certain unknown curves act as impulse sources of pollution. It is assumed that their propagation occurs only due to the convective component, without significantly affecting the filtration background. It is proposed to use the method of characteristics for solving the convection equation to identify the coordinates of pollution sources. In this case, quasipotentials at the fluid inlet and outlet at the boundary of the domain, coordinates of the points of pollution detection, and the time of its movement downstream can serve as a priori data. The general algorithm involves the adaptation of the numerical quasiconformal mapping method to build a hydrodynamic mesh, according to which the coordinates of pollution sources are identified. Numerical experiments were carried out and analysed. In particular, it is emphasised that with a sufficient mesh division, the maximum discrepancies between the a priori known data and the calculated data are small compared to the size of the studied domain. This indicates the effectiveness of the developed algorithm for identifying pollution sources in the case of a piecewise homogeneous environment. As an additional measure to reduce the magnitude of the uncertainties, it is proposed to use more accurate approximation schemes for specific expressions. On the other hand, there is an increase in computational complexity compared to the case of a continuous setting of the filtration coefficient. Given the relatively high accuracy of the calculations, it seems advisable to further develop an described approach to larger-scale in comparison with point sources of pollution and to spatial case. Taking into account the sensitivity of the solutions to the discontinuity of the filtration coefficient values, it is also worthwhile to introduce additional conditions at the contact of homogeneous media in the future.

<h3>Abstract</h3> This paper presents a physics-based, multifrequency, strong scintillation simulator that requires only two input parameters: the <i>S</i>₄ index and decorrelation time <i>τ</i>₀. This simulator is developed based on the two-component power-law phase screen model, which is specified by five parameters and suitable for representation of strong equatorial scintillation. By setting three of the model parameters to representative values, numerical mappings from the user input parameter set (<i>S</i>₄ and <i>τ</i>₀) to the remaining model parameter subset of two parameters can be established through numerical evaluation. The numerical mappings are then used to drive the scintillation model to generate time series of scintillation amplitude and phase. A large group of strong scintillation data (with <i>S</i>₄ &gt; 0.6) from two equatorial sites are processed to obtain the representative values of the three model default parameters and to validate the numerical parameter mappings. A MATLAB implementation of the scintillation simulator has been made available.

This paper shows how the geometry of the region affects the conditioning and the accuracy of numerical conformal mapping methods for simply connected regions, especially Fourier series methods. Both explicit examples of popular test cases and more general estimates are discussed. The severe ill conditioning that is known as the crowding phenomenon is discussed and its effect on a conformally transplanted boundary value problem is illustrated. Remarks on various numerical methods are included.

An improved inverse method was presented recently for the estimation of the location and the rate of an unknown point stationary source of passive atmospheric pollutant in a complex urban geometry. The inverse method was incorporated in the well-established and updated version of the ADREA-HF Computational Fluid Dynamics code. The key improvement of the proposed inverse method implementation lies in a two-step segregated approach combining a correlation and cost functions. At first only the source coordinates are analyzed using a correlation function of measured and calculated concentrations. In the second step the source rate is identified by minimizing a quadratic cost function. The validation of the new algorithm is performed by simulating the MUST wind tunnel experiment. Overall, we observed significant improvement, compared to previous implementations, on reconstructing the source information (location and rate).

The exceptional speed in increase of genomic data at public databases requires advanced computational tools to perform quick gene analysis. The tools can be devised with the aid of genomic signal processing. The pivotal task in genomic signal processing is numerical mapping. In numerical mapping, the string of nucleotides is transformed into discrete numerical sequence by assigning optimum mathematical descriptor to a nucleotide. The descriptor must be compatible with the further stages of genomic application in order to achieve high efficiency. In this work, a simple numerical mapping method is proposed in which the optimum descriptor value is obtained by applying Gray code concept. The proposed method is evaluated on benchmark databases HRM195 and ASP67 for an identification of protein coding region application. The proposed method exhibits improved exon prediction efficiency in terms of performance accuracy and equal error rate when compared with similar methods.

We present a fast and accurate numerical method for constructing incompressible, inviscid and irrotational flows in two-dimensional coastal domains, which are unbounded multiply connected domains above an infinitely long coastline boundary. In the numerical method, we utilize a numerical conformal mapping method based on a boundary integral equation with the generalized Neumann kernel in order to construct conformal mappings from coastal domains onto four of Koebe’s canonical domains. The numerical method is fast and accurate, since it just requires \(O((m+1)n\ln n)\) operations and it converges with \(O(e^{-cn})\) for coastal domains of connectivity \(m+1\), where \(n\) is the number of nodes in discretizing each smooth boundary component and \(c\) is a positive constant. With some examples, we also show that it is applicable to arbitrary coastal domains with high connectivity and complex geometry.

Identification of depth location of a radiation source by measurement from only one direction using a Compton camera

A scintillation simulator is an important tool for the scientific, engineering, and GNSS applications community to study the physical mechanism and effects of scintillation and to develop advanced receiver technologies that can mitigate these effects. For users focused on the latter objective, it is desirable that the simulator be not only capable of capturing realistic scintillation effects, but also convenient and intuitive to configure and use. This paper presents a physics-based, multi-frequency, strong scintillation simulator that requires only two input parameters: the expected scintillation index S_4 and the intensity decorrelation time tau_0 . This simulator is developed based on the two-component power-law phase screen model, which is specified by five parameters and suitable for representation of strong equatorial scintillation. In this paper, by defaulting three of the model parameters to representative values, numerical mappings from the user input parameter set S_4 and tau_0 to the remaining model parameter subset of two parameters, U_0 and rho_F/V_eff , can be established through numerical evaluation. Therefore, the scintillation simulation model can be controlled by user-specified expected S_4 and tau_0. To obtain the representative values for the three default model parameters and to validate the numerical mappings for strong equatorial scintillation scenario, we first apply the irregularity estimation method (IPE) to a large group of strong scintillation data (with S_4 > 0.6) from two equatorial sites to establish the profiles of the model parameters. The representative values for the three default model parameters are then determined based on their respective profiles. Based on the estimates of U_0 and rho_F/V_eff and S_4 and tau_0 obtained from this multi-site real scintillation data set, we validated that the numerical mappings are generally accurate to represent the case in the observed strong equatorial scintillation. In addition, this paper also presents the evaluation results of the IPE method in terms of triple-frequency consistency using real scintillation data set with triple-frequency scintillation. Finally, a MATLAB implementation of the scintillation simulator has been made available.

The main strategies for soil pollution apportionment: A review of the numerical methods

Conformal mapping technique is important in theoretical analysis and numerical computation for the fields of stress and displacement. In general, a unlined tunnel with arbitrary shape has no analytical solution for conformal mapping. Therefore, the study of numerical method for conformal mapping has great significance. The basic functions of numerical conformal mapping are given based on Symm’s method in this paper. Furthermore, the inverse mapping functions were deduced according to the relationships between the boundary nodes in physical and mapped plane. Compared to the other numerical methods, the presented method has some advantages such that, it is simple in concept to be understood, and can give the mapping function without iteration process. The method can be used to the forward and inverse numerical conformal mappings for multiple underground unlined tunnels with arbitrary shapes in finite and infinite domains. With the help of method of fundamental solutions (MFS), the interpolation equations were proposed for multiple underground unlined tunnels with arbitrary shapes. Finally, several numerical examples for the groups of U-shaped and rectangle tunnels have been given to verify the effectiveness of this method. The numerical results can convergent to real cases, which show that the proposed method has the properties of good accuracy and strong adaptability.

Recently, digital signal processing has been widely applied in the study of genomics. One of the genomic studies is identification of protein-coding regions. Where is a protein coded? How much is encoded? Where are growth and development regulated? The answer to these questions is possible by DNA sequences that can be classified as the exon and intron. In signal processing application, numerical signals are used due to symbolic signal nature of DNA sequence; yet, it must be converted from symbolic sequence to numeric sequence prior the analysis in data preprocessing. The bases in a DNA sequence are represented with four letters A, G, C and T. Each letter corresponds to a numeric value. In the literature, several numerical mapping techniques exist. In this paper, a novel numerical mapping approach has been proposed for converting string to numerical values. Each codon is mapped by improved fractional derivative of Shannon equation in this approach. For exon regions prediction, three methods have been used. These methods are singular value decomposition (SVD), discrete Fourier transform (DFT) and short-time Fourier transform (STFT). The performance of the proposed mapping technique has been evaluated based on the above-mentioned three classification methods. The proposed novel technique has showed more success in the identification of protein-coding regions as compared to the predominant existing mapping techniques SVD, DFT and STFT methods.

Sensitivity Enhancement of DWT Based Algorithm for Detection of CpG Islands in DNA Sequences

An approach to solving the problem of image reconstruction based on applied quasipotential tomographic data in the three-dimensional case is developed. It is based on the synthesis of spatial analogues of numerical quasiconformal mapping methods and algorithm for identifying the parameters of local bursts of homogeneous materials using similar methods on the plane. The peculiarity of the corresponding algorithm is taking into account (for each of the appropriate injections) the presence of only equipotential lines (with given values of the flow function or distributions of local velocities on them) and flow lines (with known potential distributions on them) at the domain boundary. Numerical experiments of simulative restoration of the environment structure are carried out.

Although the basic theory for the methods of numerical mapping has been published [ Jones and Gallet, 1962a] , some essential procedures used in the Numerical Map Program have not been justified in scientific liter- ature. In particular, the problem of the "stability" of the geographic representation in areas where no stations are available appears to be solved by a method of "screen points", which has been extensively applied and tested. While the method is described in section 2.2, further justi- fication and illustrations will be given in a subsequent paper.

In this paper, we present a method to improve the accuracy of the charge simulation method for numerical conformal mapping. The method constructs the constraint equation by using the charge simulation method. The charges and the conformal radius are computed by using the Runge‐Kutta method based on the dynamic system of the constraint equation. By using this method, we can obtain new approximated conformal mapping function and improve the accuracy of numerical conformal mapping compared to the charge simulation method for numerical conformal mapping proposed by Amano. Furthermore, the corresponding numerical results are shown to illustrate the performance of the proposed method.