Instantaneous Source Research Articles

Вариационные алгоритмы идентификации мощности импульсного источника загрязнения в модели переноса примеси

To solve the problems of monitoring the environmental situation it is necessary to create computer systems that allow assessing the state of the environment. Such systems should allow for rapid assessment of the effects of pollution in the areas under investigation, especially in the areas of traditional shipping lanes and intensive construction of various communications. To solve such problems, it is necessary to have mathematical models and methods for solving inverse problems, when the input parameters of the model are determined using the measurement data due to their rapid assimilation. Variational algorithms for assimilation of incoming information are based on iterative minimization of the quadratic prediction quality function that characterizes deviations of the solution obtained from the used model from the measurement data. In this case, the mathematical model is a constraint on the variation of input parameters while minimizing the forecast quality functional. In this paper we propose the use of such procedures for the assimilation of data distributed in space and time. Based on the passive impurity transfer model, various approaches are considered to solve the problem of identifying the power of a point instantaneous source of pollution from time and space distributed measurement data. In this paper, we consider a variational method for identifying the power of a point instantaneous source of pollution based on solving adjoint  problems and the problem in variations. The proposed algorithm is obtained for the case when the measurement data is received at different times. In addition, the method of estimation and the variational method of filtering linear systems of equations are considered for searching for the required values. The initial values of the power of the pollution source are determined in the result of solving the redefined system of equations. The result obtained is consistent with all available information about the impurity concentration. The considered algorithms for identifying the power of the pollution source in relation to the passive impurity transfer model can be used to solve various environmental problems when studying the impact of anthropogenic pollution sources.

Thermo-viscoelastic interaction under dual-phase-lag model with memory-dependent derivative

This article deals with the thermo-viscoelastic interaction in a two-dimensional homogeneous, isotropic, infinite space subjected to an instantaneous heat source. The problem is considered in the domain of dual-phase-lag (DPL) model of generalized thermo-viscoelasticity with memory-dependent derivative (MDD). The joint Laplace–Fourier transform is used as mathematical tool to obtain vector matrix differential equation and it is then solved by utilizing eigenvalue approach. Numerical estimation of displacements, stresses, and temperature are figured for a certain material by utilizing Bellman method and Gaussian quadrature formula. At last, the impact of space variable, time, kernel function, time-delay, and phase-lag parameters on the thermophysical quantities is analyzed graphically.

Inverse estimation of finite-duration source release mass in river pollution accidents based on adjoint equation method.

Obtaining the pollutant release mass at a timely manner is crucial in emergency response for river pollution accidents. However, compared to the instantaneous source, release mass estimation of finite-duration source has been rarely studied. In addition, few studies involve the influence of partial observation data and observation data with different levels of noise on inversion results. Based on the adjoint equation method (AEM), this study developed a new release mass estimation model to make up the above deficiencies. In this model, one-dimensional physical transport advection-dispersion equation was used as governing equation to describe pollutant transport and the finite-duration sources and instantaneous sources were both considered. Two synthetic experiments and two field experiments were used to evaluate this model. In synthetic experiments, detailed analysis of the influence of observation errors and incomplete concentration data due to equipment failure was conducted. Results indicate that the effect of observation errors on the inverse estimation results was within the relative error of 12%; the incomplete concentration data could also be used to obtain inverse estimation results. The two field experiments gave confidence to the application of this model in release mass estimation in actual pollution accidents with a relative error within 10%. These findings will assist in the decision-making for dealing with actual river pollution accidents.

Theory and Solutions of Heat Pulse Method for Determining Soil Thermal Properties

Information on thermal properties of soil is of paramount importance for environmental and earth science, and engineering. The heat pulse (HP) method has become the key technology for accurate determination of soil thermal properties and a variety of other physical properties (e.g., water content, bulk density, and water flux) in both laboratory and field environments. The HP method is a transient method that is commonly based on the analytical solutions to the radial heat flow equation when a line-heat source is applied. Over the past few decades, great endeavors have been devoted to advance the HP method. For example, the evolution and development in probe design, data logging equipment, data interpretation and computing capability has remarkably improved the accuracy and ease of use for determining soil thermal properties. However, there is a lack of study collating and synthesizing the development of the theory/solutions to obtain thermal properties of soil using the HP method. In this paper, we review the fundamental theories and solutions of the HP method, including differences and similarities of theories and applications between instantaneous line heat source (ILHS) and short-duration line heat-source (SLHS), between dual-probe heat-pulse (DPHP) and single-probe heat-pulse (SPHP) methods, and between the non-linear model fit (NMF) method and single point (SPM) method for data interpretation. In addition, the numerical solutions and semi-analytical solutions are also presented to provide heat pulse users information for selecting the best-fit method to meet their goals.

Transient Solute Dispersion in Wetland Flows With Submerged Vegetation: An Analytical Study in Terms of Time‐Dependent Properties

AbstractPredicting the concentration distribution of solute transport in vegetated flows is significant for associated environmental applications in water resources. While a semianalytical study has been made for the steady dispersion with a continuous release (Rubol et al., 2016, https://doi.org/10.1002/2016WR018907), an in‐depth analytical investigation has yet to be performed for the more complicated case of transient dispersion due to an instantaneous release. In regard to the pioneering benchmark observation (Murphy et al., 2007, https://doi.org/10.1029/2006WR005229) of transient solute dispersion in a submerged vegetated flow for an instantaneous source release at the top of the canopy, an extensive analytical effort is paid in this work to derive the time‐dependent basic properties and to investigate the temporal evolution of concentration distribution. Obtained large‐time asymptotic dispersivities agree well with available experimental results (Murphy et al., 2007, https://doi.org/10.1029/2006WR005229), with higher significance ( , ) for correlation between analytical results and experimental data. Analytical solutions covering effects of dispersivity, skewness, and kurtosis of detailed concentration distribution are compared satisfactorily with numerical results obtained by the random displacement method. The findings illuminate the applicability of this analytical approach in environmental risk assessment and water quality management.

Determination of Dynamic Dispersion Coefficient for Solid Particles Flowing in a Fracture With Consideration of Gravity Effect

Abstract A robust and pragmatic method has been developed and validated to analytically determine dynamic dispersion coefficients for particles flowing in a parallel-plate fracture, in which gravity settling has been considered due to its significant impact on particle flowing behavior. More specifically, a two-dimensional (2D) advection–diffusion equation together with the initial and boundary conditions has been formulated to describe the flow behavior of finite-sized particles on the basis of coupling the Poiseuille flow with vertical settling. Meanwhile, three types of instantaneous source conditions (i.e., point source, uniform line source, and volumetric line source) have been considered. Explicit expressions, which can directly and time-efficiently calculate dynamic dispersion coefficient, have been derived through the moment analysis and the Green’s function method. By performing the simulation based on the random walk particle tracking (RWPT) algorithm, the newly developed model has been verified to determine particle dispersion coefficients agreeing well with those obtained from the RWPT simulations. It is found that the point source is the most sensitive to gravity effect among different source conditions, while the volumetric line source is affected more than the uniform line source. For particle size larger than its critical value, an increased particle size leads to a decreased asymptotical dispersion coefficient for all the source conditions due to the significant gravity effect, while gravity positively affects the dispersion coefficient at early times for the point source condition. In addition, average flow velocity positively affects the dispersion coefficient for all the source conditions, while the associated gravity effect is influenced only at early times for the point source condition.

A novel mixing matrix estimation algorithm in instantaneous underdetermined blind source separation

Due to the lack of sufficient prior information, how to estimate the mixing matrix in multiple underdetermined blind source separation (UBSS) models is a difficult problem. This study proposes an algorithm, which is used for the estimation of mixing matrix in instantaneous UBSS. Firstly, we propose an efficient single-source-points detection criterion with the transformation for the mixed signal vector, which is used as the basis for the clustering process. There are some shortcomings in the classical clustering algorithms, including the dependence on input parameters, restrictions on the data dimension, the requirement of the prior knowledge of the source signals and high complexity. To overcome these drawbacks, the modified density peaks clustering algorithm is used for the estimation of the initial clustering centers to adapt to different circumstances. Based on the idea of mean clustering, the single source points near each initial cluster center are processed, respectively, and the final estimation results of the mixing matrix are obtained. A variety of simulation experiments demonstrate the universality and validity of the proposed algorithm. The proposed method also has excellent performance even under the circumstance of low signal-to-noise ratio.

Improvement of Instantaneous Point Source Model for Simulating Radionuclide Diffusion in Oceans under Nuclear Power Plant Accidents

Simulation methods have become an important tool to reveal radionuclide migration during accidental radionuclide releases and predict influences of accidents on the marine environment. The instantaneous point source model is a useful method to simulate the large-scale radionuclide diffusion in marine areas. However, the simulation accuracy of this method requires improvement as it didn’t take radionuclide decay into account. In this study, an improved instantaneous point source model considering radionuclide decay was proposed on the basis of the original model. Furthermore, the instantaneous point source model and the improved version were used to simulate the concentrations of 131I and 137Cs following the Fukushima Dai-ichi nuclear power plant accident. The results showed that the relative error of 131I concentrations decreased from 136.03% to 37.59% when using the improved model; and improvements in relative errors for 137Cs concentrations were not apparent as the simualtion period was much shorter than its half-life period. Therefore, the improved model can accurately simulate the diffusion process for radionuclides following an accident and provides an efficient decision support tool for risk assessment managers and for use in safety guarantees of nuclear power plants during siting and operational phases.

ANALYTICAL SOLUTION OF A NON - HOMOGENEOUS ONE - DIMENSIONAL ADVECTION DIFFUSION EQUATION WITH TEMPORALLY VARYING COEFFICIENTS .

Advection Diffusion Equation is a partial differential equation that describes the transport of pollutants in rivers. Its coefficients (dispersion and velocity) can be constant, dependent on space or time or both space and time. This study presents an analytical solution of a one dimensional non - homogeneous advection diffusion equation with temporally dependent coefficients, describing one dimensional pollutant transport in a section of a river. Temporal dependence is accounted for by considering a temporally dependent dispersion coefficient along an unsteady flow assuming that dispersion is proportional to the velocity. Transformations are used to convert the time dependent coefficients to constant coefficients and to eliminate the advection term. Analytical solution is obtained using Fourier transform method considering an instantaneous point source. Numerical results are presented. The findings show that concentration monotonically decreases with increasing distance and increasing time.

Convolutive Blind Source Separation for Communication Signals Based on the Sliding Z-Transform

Convolutive blind source separation (CBSS) is one of the main branches in the field of intelligent signal processing. Inspired by the thought of sliding discrete Fourier transform (DFT), an idea of the sliding Z-transform is introduced in the present study. Based on the sliding Z-transform, a method called the sliding Z-transform for CBSS (ZCBSS) is applied to CBSS for communication signals with the same or different frequency. It is found that the deduced algorithm can accomplish the separation task without setting any preset parameter and directly recover time-domain sources from the convolutive mixtures with the help of robust instantaneous blind source separation algorithms. Simulations are carried out accordingly, and it is concluded that the proposed approach is effective in terms of both separation performance and signal de-noising.

Blind Source Separation Algorithm for Chaotic Masking Multipath Signals Based on Spectral Peak Search Counter Permutation

Since voice communication is the main method of information transmission, it is important to ensure the safety and efficiency of voice communication. In this paper, a more complex multipath channel model in a wireless environment is considered, and chaotic masking technology is used to ensure the security of voice signal transmission. Based on this, a multipath blind source separation algorithm based on cross-correlation permutation of spectral peak search counters is proposed. First, chaotic masking is performed between multiple voice signals and chaotic signal, and an impulse response filter is used to simulate the multipath transmission process. Next, the short-time Fourier transform is employed to convert the observation signal into a frequency-domain signal. Then, the joint approximate diagonalization of eigen-matrix algorithm is used to perform linear instantaneous blind source separation at each frequency. And to solve the permutation uncertainty problem in the frequency domain method, a cross-correlation permutation algorithm based on a spectral peak search counter is proposed. Finally, the permuted signal is transformed back to the time domain to get the estimated source signal by the inverse short-time Fourier transform. And simulation experiments show that the algorithm greatly reduces the calculation amount of the autocorrelation coefficient in the traditional permutation algorithm. Moreover, the permutation algorithm has stability and accuracy, and provides a solution for the secure transmission and effective separation of voice signals in multipath transmission channels.

A time-space Hausdorff derivative model for anomalous transport in porous media

Abstract This paper presents a time-space Hausdorff derivative model for depicting solute transport in aquifers or water flow in heterogeneous porous media. In this model, the time and space Hausdorff derivatives are defined on non-Euclidean fractal metrics with power law scaling transform which, respectively, connect the temporal and spatial complexity during transport. The Hausdorff derivative model can be transformed to an advection-dispersion equation with time- and space-dependent dispersion and convection coefficients. This model is a fractal partial differential equation (PDE) defined on a fractal space and differs from the fractional PDE which is derived for non-local transport of particles on a non-fractal Euclidean space. As an example of applications of this model, an explicit solution with a constant diffusion coefficient and flow velocity subject to an instantaneous source is derived and fitted to the breakthrough curves of tritium as a tracer in porous media. These results are compared with those of a scale-dependent dispersion model and a time-scale dependent dispersion model. Overall, it is found that the fractal PDE based on the Hausdorff derivatives better captures the early arrival and heavy tail in the scaled breakthrough curves for variable transport distances. The estimated parameters in the fractal Hausrdorff model represent clear mechanisms such as linear relationships between the orders of Hausdorff derivatives and the transport distance. The mathematical formulation is applicable to both solute transport and water flow in porous media.

Convolutional neural network for single-sensor acoustic localization of a transiting broadband source in very shallow water

When a broadband source of radiated noise transits past a fixed hydrophone, a Lloyd's mirror constructive/destructive interference pattern can be observed in the output spectrogram. By taking the spectrum of a (log) spectrum, the power cepstrum detects the periodic structure of the Lloyd's mirror fringe pattern by generating a sequence of pulses located at the fundamental quefrency and its multiples. The fundamental quefrency, which is the reciprocal of the frequency difference between adjacent destructive interference fringes, equates to the multipath delay time. An experiment is conducted where a motorboat transits past a hydrophone located about 1 m above the seafloor in very shallow water (20 m deep). The hydrophone has a frequency bandwidth of 90 kHz, and its output is sampled at 250 kHz. A cepstrogram database is compiled from multiple vessel transits, and its cepstrum-based feature vectors (along with ground-truth range data) form the input to train a convolutional neural network (CNN) so that it can predict the source range relative to the hydrophone for other ("unseen") vessel transits. The CNN provides an accurate prediction of the instantaneous source range even when the range estimate from conventional multipath passive ranging is biased, which occurs at low grazing angles (<12°).

On The Limiting Laws of Buoyant Convective Jets and Thermals from Local Sources of a Heat Releasing Impurity

By using the methods of scale analysis, dimensional analysis, and of the symmetry of differential equations, the dynamics of buoyant convective jets connected with stationary, local sources of a weightless heat-releasing impurity in a neutrally stratified medium is investigated. An example of such an impurity is an aerosol that absorbs solar radiation in the atmosphere (in particular, coal dust, and soot, which earlier was suggested to be used to actively affect certain atmospheric processes). An analog of Ya. B. Zel′dovich′s theory of convective jets for laminar and turbulent axisymmetric and plane jets has been obtained. The laws of motion of turbulent thermals connected with instantaneous sources of the impurity are given that follow from the considerations of dimensionality and similarity.

Application of fractal geometry to describe reservoirs with complex structures

Abstract This study provides basic instantaneous source functions for different source-reservoir geometries in infinite fractal reservoirs (FRs) and infinite slab FRs. The concept of fractal geometry (FG) has already been adopted to analyse and model well-reservoir systems with complex structures. All these complexities have been modelled through a partial differential equation called fractal diffusivity equation (FDE). In this paper, by use of the source/Green’s function technique, we analytically solve the FDE for different boundary conditions, i.e., different source-reservoir geometries. The wellbore pressure response for horizontal wells in an infinite slab FR (synthetic example) is derived and analysed to illustrate the applications of the provided analytical source solutions and how to use these solutions.

A numerical model with Stokes drift for pollutant transport within the surf zone on a plane beach

This study examines the effects of Stokes drift on pollutant transport within the surf zone on a plane beach both numerically and experimentally. Firstly, the numerical model is described. The wave-induced current is modeled using the concept of the radiation stress. The wave propagation model is based on the wave energy conservation equation. And the advective diffusion model including the Stokes drift is used to describe the pollutant transport in the surf zone. Model validation was achieved in this case versus an analytical solution for an instantaneous point source in a uniform horizontal flow. This study also describes a laboratory experiment on dye release in the surf zone over a plane beach. We examined the final inclination angle required by a continuously released pollutant plume to reach the shoreline under both cases, and transport velocities in the alongshore and cross-shore directions were estimated by linearly fitting the location of a dye-patch front at different time. Results show that this dye patch moved shoreward with an approximate speed of 0.05 m/s (0.017 m/s) between 10 s and 40 s and 0.001 m/s (0.011 m/s) after 40 s for Case 1 (2). This model was then used to simulate pollutant transport in the surf zone on a plane beach as reproduced in the current experiment. Comparisons between our dye transport experiment and numerical results were then also conducted; the data showed that the numerical results including Stokes drift agreed more closely with experimental results than those without it. The data showed that the pollutant was generally transported obviously shoreward in addition to its expected drift along the shore. We also suggest that Stokes drift plays an important role in pollutant movement in the surf zone, especially shoreward.

Continuous time random walk model for non-uniform bed-load transport with heavy-tailed hop distances and waiting times

Bed-load transport along widely graded river-beds typically exhibits anomalous dynamics, whose efficient characterization may require parsimonious stochastic models with pre-defined statistics involving the waiting time and hop distance distributions for sediment particles. This study employs a continuous time random walk (CTRW) model to characterize bed-load particle motions on a widely graded gravel-bed with cluster microforms built in our lab. Flume experiments guide the selection of the Mittag-Leffler (M-L) function as the waiting time distribution function, and the Lévy α-stable density for the hop distance distribution function in the CTRW model. Monte Carlo simulations show that the resulting CTRW model can well capture the observed flume experimental data (with either a continuous or an instantaneous source) with coexisting super- and sub-dispersion behaviors in the bed-load transport process. Analyses further discover the dual impact of clusters on the dynamics of fine sediment particles. Some particles are more likely to be blocked or trapped by clusters, while others have a high probability to be accelerated by the flow accelerating belt between the clusters. Therefore, with proper statistical distributions and relevant parameters for sediment waiting times and hop distances, the CTRW model may efficiently capture the complex dynamics in sediment transport.

On the regularization problem with functions generalized

In physics and mathematics, there are idealized concepts exist, such as the density of a material point, the point density, the intensity of an instantaneous source, etc., These are necessary for real engineering and physical problems. Treating this type of concepts correctly is done with the theory of generalized functions, it´s properties are outside the framework of the properties of conventional functions. The concept of generalized function is a generalization of the conventional concept of function and encompasses functions that contain singular points. In order to mathematically treat this type of functions or functions, it is necessary to introduce regularization processes. In this article we analyze the process of regularization of singular functions with generalized functions and compare the integrity of the function before and after the regularization. Keywords: Generalized functions, distributions, regularization, information

Resonance of Nanoscale Beam due to Various Sources in Modified Couple Stress Thermoelastic Diffusion with Phase Lags

Abstract This paper deals with the study of thermoelastic thin beam in a modified couple stress with three-phase-lag thermoelastic diffusion model subjected to thermal and chemical potential sources. The governing equations are derived by using the Euler-Bernoulli beam assumption and eigenvalue approach. The Laplace transform technique is employed to obtain the expressions for displacements, lateral deflection, temperature change, axial stress and chemical potential. A particular type of instantaneous and distributed sources is taken to show the utility of the approach. The general algorithm of the inverse Laplace transform is developed to compute the results numerically. The numerical results are depicted graphically to show the effects of phase lags, with and without energy dissipation on the resulting quantities. Some special cases are given.

Inverse tracking of an airborne pollutant source location in a residential apartment by joint simulation of CFD and a multizone model

Prompt identification of an indoor air pollutant source location is important for the safety of building residents in gaseous contaminant leakage incidents. Using the computational fluid dynamics (CFD) method in such inverse modeling is time consuming, especially for naturally ventilated residential buildings, which have multiple rooms and require consideration both indoor and outdoor environments. This paper compares the results of the pollutant source location identification and the simulation time based on two different inverse modeling methods: the CFD method and joint modeling of the multizone and CFD methods, to discuss the consumption of the computing time, as well as the accuracy of the location identification result. An instantaneous airborne pollutant source is assumed in a typical residential apartment that utilizes natural ventilation. A CFD model with the computational domain of the whole apartment and surrounding environment is built, for which the adjoint probability method is applied to simulate the source location probability from limited sensor readings. Meanwhile, a multizone model of the apartment is built to simulate and identify the room in which the source is located using the adjoint probability method. The CFD method is applied to the identified room afterwards to identify the exact location of the source within that room. The joint simulation of CFD and the multizone model is verified by a scaled model experiment of the apartment. It is found that the joint simulation method can significantly reduce the computing time and provides a good alternative for real-time inverse tracking of the indoor airborne pollutant.