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An integer-fractal mobile-immobile (MIM) model for reactive solute transport in a heterogeneous porous media is investigated, where the transport in the mobile zone is given by an advection-dispersion equation, and the diffusion in the immobile zone is described by a time fractional differential equation. A finite difference scheme is put forward to solve the MIM model, and convergence and stability of the scheme are proved based on the spectrum estimation of the coefficient matrix. An inverse problem of identifying the fractional order and the degradation coefficient is considered with the measured data in the mobile zone, and uniqueness of the inverse problem is proved by the method of Laplace transform. Numerical inversions with noisy data are presented to demonstrate a numerical stability of the inverse problem. [ABSTRACT FROM AUTHOR]

This article deals with an inverse problem of determining two space-time-dependent sources in an integerfractional mobile-immobile two-region solute transport system by additional Dirichlet-Neumann data. The unique existence of a solution to the forward problem is obtained by the method of Laplace transform, and a dynamical system connecting the known data with the unknown sources is established by variational method and boundary homogenization. The dynamical system is discretized to a linear system at a given time in a homogenous polynomial space, and the sources are reconstructed by alternative iterations and Tikhonov regularization. Numerical examples are presented to illustrate the validity of the inversion algorithm. [ABSTRACT FROM AUTHOR]

Copyright of Clean Coal Technology is the property of Clean Coal Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Zhengzhou University (Natural Science Edition) is the property of Journal of Zhengzhou University (Natural Science Edition) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Modeling several physical events leads to the Bagley–Torvik equation (BTE). In this study, we have taken into account the BTE, including the Caputo–Fabrizio and Atangana–Baleanu derivatives. It becomes challenging to find the analytical solution to these kinds of problems using standard methods in many circumstances. Therefore, to arrive at the required outcome, numerical techniques are used. The Laplace transform is a promising method that has been utilized in the literature to address a variety of issues that come up when modeling real-world data. For complicated functions, the Laplace transform approach can make the analytical inversion of the Laplace transform excessively laborious. As a result, numerical techniques are utilized to invert the Laplace transform. The numerical inverse Laplace transform is generally an ill-posed problem. Numerous numerical techniques for inverting the Laplace transform have been developed as a result of this challenge. In this article, we use the Weeks method, which is one of the most efficient numerical methods for inverting the Laplace transform. In our proposed methodology, first the BTE is transformed into an algebraic equation using Laplace transform. Then the reduced equation solved the Laplace domain. Finally, the Weeks method is used to convert the obtained solution from the Laplace domain into the real domain. Three test problems with Caputo–Fabrizio and Atangana–Baleanu derivatives are considered to demonstrate the accuracy, effectiveness, and feasibility of the proposed numerical method.

A partially enclosed fault reservoir is a common reservoir type. The partially enclosed faults caused by low-order faults lead to different fluid flow and distribution laws of remaining oil between partially enclosed fault reservoirs and completely enclosed reservoirs. Through the existing technology， it is difficult to quantitatively describe the evolution law of the dominant flow channel in the deep part of the reservoir in the whole process of water flooding， which affects the efficient development of this kind of reservoir. Therefore， the physical model of a partially enclosed fault reservoir was designed and fabricated， and the water flooding experiment was carried out. The numerical inversion model was established according to the model parameters and experimental results. The dominant flow channel was quantitatively characterized based on the standardized flow rate algorithm. Then， the numerical inversion model was used to compare with the evolution law of the dominant flow channels in fault-free reservoirs and reveal the evolution law of the dominant flow channel in the physical model of the partially enclosed fault reservoir. The results show that the accumulative oil yield and the oil production rate of the production well in the fault-occluded area were low. The reduction of the flow area in the fault discontinuity led to the earliest breakthrough in the production well. Although the production wells on the other side of the fault had close oil production in the early stage， the blocking effect of the fault on injection water led to a higher flow diversion rate and the highest oil production rate in the late stage in the strongly fault-occluded area. During the anhydrous oil production period， a dominant flow area played a positive role in oil displacement， which developed into a spindle-shaped dominant flow channel at the bottom of the reservoir through vertical equilibrium distribution and “finger-shaped” distribution. After water production in each well， a dominant flow channel was formed from the injection well to the bottom of the production well， except for the strongly fault-occluded area. With the increase in injection volume， this channel developed in the vertical direction and around the production well and played a negative role in oil displacement. Compared with fault-free reservoirs， partially enclosed faults made the development of dominant flow channels lag in strongly fault-occluded areas and difficult water sweep in strongly fault-occluded areas， resulting in significant differences in the distribution of remaining oil in each area， and the remaining oil is concentrated in the upper part of the strongly fault-occluded area and near the faults in strongly fault-occluded areas.

Copyright of Petroleum Geology & Recovery Efficiency is the property of Petroleum Geology & Recovery Efficiency and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This article deals with a fractional mobile-immobile solute transport system in porous media and an inverse problem of identifying the fractional orders by the additional measurements at one interior point. The unique existence of a solution to the forward problem is obtained based on the inverse Laplace transform, and the uniqueness of the inverse problem is proved in the real space of Laplace transform by the maximum principle. Numerical inversions with noisy data are presented to support the uniqueness result of the inverse problem. [ABSTRACT FROM AUTHOR]

The Tsallis q-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It belongs to the q-distribution family, which is characterized by a non-additive entropy. Due to their versatility and practicality, q-Gaussians are a natural choice for modeling input quantities in measurement models. This paper presents the characteristic function of a linear combination of independent q-Gaussian random variables and proposes a numerical method for its inversion. The proposed technique makes it possible to determine the exact probability distribution of the output quantity in linear measurement models, with the input quantities modeled as independent q-Gaussian random variables. It provides an alternative computational procedure to the Monte Carlo method for uncertainty analysis through the propagation of distributions.

The Meuse/Haute‐Marne Underground Research Laboratory provides the location for the experiment designed to investigate the induced fracture network around open or sealed galleries and drifts. The objective of this study is to investigate and reconstruct the hydraulic properties and the geometry of the induced fracture network to improve the insights and validate the conceptual model of the induced fracture network due to the stress redistribution during tunnel excavations. Within the presented study, the cross‐hole responses of the pneumatic tests were analyzed in the first step with an equivalent porous media—3D travel time‐based tomographic approach. In the next step selected 2D profiles of the 3D model domain were inverted using a discrete fracture network inversion approach. The database of the tomographic analysis is based on 18 gas injection tests and 151 pressure interferences, which were recorded between nine closely spaced boreholes. The travel time‐based inversion approach allowed for the reconstruction of the 3D gas diffusivity distribution between nine boreholes with high‐resolution. The applied discrete fracture network inversion approach is based on a transdimensional Markov Chain Monte Carlo (MCMC) methodology and it operates with reversible model updates (jumps) that change the problem dimensions, that is, the number, length and position of fractures within the model domain after each iteration step. The synthesis of the results between the reconstructed 3D diffusivity tomogram and the 2D fracture tomograms improved the insights into the spatial geometry of the induced fracture network around galleries. Key Points: Excavation‐induced fractures were reconstructed using the pneumatic interference testsEquivalent porous media and discrete fracture network approaches were used to invert the pressure responsesThe results provide information about fracture connectivity, hydraulic properties, and the geometry of the dominant structures [ABSTRACT FROM AUTHOR]

This article deals with numerical solution and identification of the fractal orders for the generalized nonlocal elastic model. Based on the collocation-finite difference scheme for the forward operator, a regularized method is proposed for solving of the forward problem with the aid of Tikhonov regularization. This method is non-iterative and independent of preconditioning of the coefficient matrix, which gives a simple and direct approach to numerical solution of the nonlocal elastic model. The identification problem of determining the fractal orders is solved by using the optimal perturbation algorithm with additional observations at some measurable points. The inversion solutions with noisy data give good approximations to the exact orders demonstrating the validity of the numerical algorithms. [ABSTRACT FROM AUTHOR]

Thermal diffusivity is a parameter of fundamental importance in heat transfer studies of solids. This parameter can be determined from the transient Fourier heat conduction equation using different techniques. In this research, a new algorithm based on Talbot's method was proposed to determine the thermal diffusivity using a one-dimensional Fourier heat conduction equation. Furthermore, a free and open-source program was developed to perform the calculations. Experimental data in heating and cooling conditions of ham were used to test the programming. It was found that n and ω are strongly related and affect the results. The developed program in Scilab using Talbot's method, the Levenberg-Marquardt algorithm of optimization (lsqrolve routine), n = 100 and ω = 1.8 obtained r2 of 0.999 and 0.998; thermal diffusivities of 0.98 × 10−7 m2/s and 1.13 × 10−7 m2/s with the time required to run the programming from 0.6 to 1.1 s. [ABSTRACT FROM AUTHOR]

Differential equations of fractional order arising in engineering and other sciences describe nature sufficiently in terms of symmetry properties. In this article, a numerical method based on Laplace transform and numerical inverse Laplace transform for the numerical modeling of differential equations of fractional order is developed. The analytic inversion can be very difficult for complex forms of the transform function. Therefore, numerical methods are used for the inversion of the Laplace transform. In general, the numerical inverse Laplace transform is an ill-posed problem. This difficulty has led to various numerical methods for the inversion of the Laplace transform. In this work, the Weeks method is utilized for the numerical inversion of the Laplace transform. In our proposed numerical method, first, the fractional-order differential equation is converted to an algebraic equation using Laplace transform. Then, the transformed equation is solved in Laplace space using algebraic techniques. Finally, the Weeks method is utilized for the inversion of the Laplace transform. Weeks method is one of the most efficient numerical methods for the computation of the inverse Laplace transform. We have considered five test problems for validation of the proposed numerical method. Based on the comparison between analytical results and the Weeks method results, the reliability and effectiveness of the Weeks method for fractional-order differential equations was confirmed. [ABSTRACT FROM AUTHOR]

The Tsallis q-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It belongs to the q-distribution family, which is characterized by a non-additive entropy. Due to their versatility and practicality, q-Gaussians are a natural choice for modeling input quantities in measurement models. This paper presents the characteristic function of a linear combination of independent q-Gaussian random variables and proposes a numerical method for its inversion. The proposed technique makes it possible to determine the exact probability distribution of the output quantity in linear measurement models, with the input quantities modeled as independent q-Gaussian random variables. It provides an alternative computational procedure to the Monte Carlo method for uncertainty analysis through the propagation of distributions. [ABSTRACT FROM AUTHOR]

Transient excavation unloading of in situ stress affects the stability of surrounding rock in the deep tunnel engineering. This paper focuses on the dynamic responses triggered by the transient unloading of a non-hydrostatic geo-stress field in deep-buried engineering. With resort to the integral transformation, the frequency-domain responses of stress, displacement and velocity components induced by the transient unloading are obtained under a non-hydrostatic in situ stress. Based on the numerical inversion of the Laplace transformation, the corresponding time-domain theoretical results are determined. Agreement of the current solutions with the existing results and the numerical simulations verifies the proposed scheme in this paper. The elastic analytical results indicate that the influence of unloading path on the stress redistribution is characterized by the unloading rate. The higher the unloading rate is, the larger the stress magnitude is. The smaller the unloading time is, the more remarkable vibration is. The elasto-plastic dynamic numerical responses are investigated on the basis of a self-developed code, elasto-plastic cellular automaton (EPCA), which is a module of CASRock. The numerical results demonstrate that the transient excavation unloading results in the stress redistribution and concentration of surrounding rock mass, inducing damage for the case of exceeding the capacity of rock mass. For the small lateral pressure coefficient (less than 0.25), the tensile-shear failure is the major damage mechanism of surrounding rock, while the shear failure is the major damage mechanism for the large lateral pressure coefficient. The analytical and numerical results can provide theoretical basis for the support and reinforcement of underground tunnel. [ABSTRACT FROM AUTHOR]

In this work, a 2D axisymmetric problem for an infinite body is considered. An infinite cylinder composed of a different material and containing a variable heat source lies inside the body. The medium is assumed to be initially quiescent. The theory used is that of thermoelasticity due to Green–Lindsay. The solution is obtained by exponential Fourier and Laplace transform techniques. The inversion process is carried out numerically. Numerical results are computed for the temperature, stress distributions, and displacement and shown graphically. [ABSTRACT FROM AUTHOR]

In order to study the soil–water characteristic curve and soil–water movement in the unsaturated zone of the humid plain area and investigate its influence on the regional water cycle process, this study conducted a long series of hydrometeorological data monitoring on the whole process of precipitation, evaporation, soil water content, pore water pressure and depth of groundwater level at the Jintan field hydrological test in the plain area of the Taihu Basin, China. Based on the collected data, the soil water dynamic at different depths was analyzed, and the results showed that the soil water fluctuated most frequently and drastically at a soil horizon depth of 0–40 cm, with an obvious soil moisture wetting and drying cycle. The van Genuchten model (VG model) was used to describe the soil–water characteristic curve, and the parameters of the VG model were obtained by numerical inversion of field monitoring data using numerical code (HYDRUS-1D). The obtained parameters were used to simulate soil water movement in each soil horizon for six precipitation events and were compared with the simulation results of laboratory data. The study shows that the soil water simulation based on field data is better, which verifies the accuracy and reliability of the VG model obtained from field observation and provides a reliable theoretical basis for soil water movement and the calculation of runoff yield in the plain area of the Taihu Basin. [ABSTRACT FROM AUTHOR]

Aggregate loss is the total loss suffered by an insured in a certain period. The aggregate loss depends on the claim frequency and the amount of the claim each time the insured makes a claim. The distribution of aggregate losses must be known to calculate motor vehicle insurance premiums. In general, there are two methods that can be used in determining the distribution of aggregate losses, namely exact and numerical. When an exact solution is difficult to find, numerical methods such as Monte Carlo, Panjer Recursion, and Fast Fourier Transform can be used. This research will discuss the determination of the distribution of aggregate losses through the numerical inverse of the characteristic function using the trapezoidal quadrature rule, on the data of motor vehicle insurance category 7 in Indonesia. The estimated cumulative distribution function for the largest aggregate loss is 0.999993. When x=0, it means that if someone does not file a claim, the estimated value of the cumulative distribution function is 0.9293. This value is close to the percentage of the number of insured, which is 0.9241.

The problem of computing the distribution of quadratic forms in normal variables has a long tradition in the statistical literature. Well-established numerical algorithms that deal with this task rely on the inversion of Fourier transforms or series representations. In this article, the Mellin transform is proposed as a tool to compute both the density and the cumulative distribution functions of a positive definite quadratic form: an outline of the numerical algorithm is presented, providing details on the error analysis. The algorithm's characteristics allow us to propose an efficient way to compute the random variables' quantiles. From the theoretical point of view, the analytic properties of the Mellin transform are exploited to provide a novel representation of the distribution of the ratio of independent quadratic forms as a mixture of beta random variables of the second kind. Moreover, algorithms are proposed for computations related to ratios of both independent and dependent quadratic forms. The methods are tested and compared to popular numerical algorithms in terms of computational times and accuracy. The R package QF implementing all the proposed algorithms is also made available. for this article are available online. [ABSTRACT FROM AUTHOR]

Geohazard is one of the major factors threating the safe operation of oil and gas pipelines. However, due to the inspection accuracy of equipment and the discreteness of inspection data, the pipeline safety cannot be analyzed quantitatively with a single monitoring and inspection technology. Thus, it is urgent to study the Digital Twin mechanism model for the structural safety of pipelines in combination with the multi-source monitoring and inspection data, so as to realize the intelligent perception and prediction of pipeline safety in geohazard areas. Herein, the process to establish a Digital Twin mechanism model for the structural safety of pipelines in geohazard areas was put forward. Meanwhile, by building a parameterized finite element model of pipelines in geohazard areas, a stress-strain database of the pipeline was established with consideration to the range of the variable parameters affecting the stress-strain distribution of pipelines, and then the highly nonlinear relationship between the variable parameters and the stress-strain state of the pipelines was fitted by BP neural network. In addition, combined with the real monitoring data of pipeline stress and strain, a mechanism model capable of accurately inverting the real stress and strain distribution along the pipeline was constructed with the particle swarm optimization algorithm. Moreover, the accuracy of the model was verified by an application case. Therefore, the research results could be applied to the quantitative safety assessment of the pipelines in geohazard areas, and core support could be provided for the construction of Digital Twin of pipelines.

The electrodynamics of geological media investigates the interrelations of resistivity logging signals and properties of fluid-containing rocks and creates innovative well logging technologies. Its development is inextricably linked with modern techniques for mathematical modeling and quantitative interpretation of high-precision data. In order to increase the information content of galvanic and electromagnetic logging, we have developed algorithms and software for numerical simulation and inversion of field data. In our study of the Cretaceous and Jurassic deposits of West Siberia, a quantitative interpretation of high-frequency electromagnetic and lateral logging signals was carried out. To create geoelectric models, we interpreted the field resistivity logging data by an unconventional quantitative technique based on their joint numerical inversion and estimations of the vertical resistivity of permeable deposits. Another line of our research was aimed at a scientific substantiation of a new technology for mapping and spatial tracking of lateral heterogeneities and oil-promising zones in the Bazhenov Formation. The aim was achieved by using the TEM sounding data on a spatially distributed system of directional and horizontal wells.

The permeable pavement is a compensatory drainage technique for urban waters that aims to control runoff and to ensure ideal hydrological conditions. This work had as main objectives to evaluate the infiltration capacity of a permeable pavement (PP) at real scale, through analytical and numerical modeling. It relies on water infiltration experiments and related modeling for the hydrodynamic characterization of the coating layer (saturated hydraulic conductivity, Ks, and sorptivity, S). A large panel of analytical and numerical models was considered, and several estimates were obtained. Then, the criteria for the evaluation of the maintenance requirement of the permeable pavements were computed for all the Ks-estimates considering the NCRS standards (assessment of permeability levels). The results indicated nice fits and accurate estimates for both the saturated hydraulic conductivity and the sorptivity. However, the Ks-estimates depended on the considered model and led to contrasting results in terms of classification. For 8 of the 9 models, the value of the Ks-estimate leads to the classification of “Group A” of the NCRS soil classification, meaning a very permeable material. In contrasts, the last method (numerical inverse modeling) classified the permeable pavement as “Group D”, i.e., soils with low permeability. Those results show the importance of the selection of characterization methods regarding the assessment of the hydrological classification of permeable pavements.

Based on the characteristics of injection-production units in fractured-vuggy carbonate reservoirs, nine groups of experiments were designed and performed to analyze the interference characteristics and their influencing factors during water flooding. Based on percolation theory, an inversion model for simulating waterflooding interferences was proposed to study the influence laws of different factors on interference characteristics. The results show that well spacing, permeability ratio, cave size, and cave location all affect the interference characteristics of water flooding. When the cave is located in high permeability fractures, or in the small well spacing direction, or close to the producer in an injection-production unit, the effects of water flooding are much better. When the large cave is located in the high-permeability or small well spacing direction, the well in the direction with lower permeability or smaller well spacing will see water breakthrough earlier. When the cave is in the higher permeability direction and the reserves between the water injector and producer differ greatly, the conductivity differences in different injection-production directions are favorable for water flooding. When the injection-production well pattern is constructed or recombined, it's better to make the reserves of caves in different injection-production directions proportional to permeability, and inversely proportional to the well spacing. The well close to the cave should be a producer, and the well far from the cave should be an injector. Different ratios of cave reserves to fracture reserves correspond to different optimal well spacings and optimal permeability ratios. Moreover, both optimal well spacing and optimal permeability ratio increase as the ratio of cave reserves to fracture reserves increases.

The present manuscript investigates the role being played by various laser short heating sources in a conduction process of a metallic substrate. The Cattaneo heat conduction model is considered in favour of its finiteness of conduction speed. The analytical solutions for the temperature fields are determined via the application of the Laplace integral transform. Finally, we sought a numerical Laplace inversion scheme where the analytical inversion failed and graphically examined the significance of the heating parameters on the temperature fields. [ABSTRACT FROM AUTHOR]

This article investigates the numerical inversion of the Laplace Transform by the Rational-Talbot method and analyzes the influence on the variation of the free parameter N established by the technique when applied to certain functions. The set of elementary functions, for which the method is tested, has exponential and oscillatory characteristics. Based on the results obtained, it was concluded that the Rational-Talbot method is e cient for the inversion of decreasing exponential functions. At the same time, to perform the inversion process effectively for trigonometric forms, the algorithm requires a greater amount of terms in the sum. For higher values of N, the technique works well. In fact, this is observed in inverting the functions transform, that combine trigonometric and polynomial factors. The method numerical results have a good precision for the treatment of decreasing exponential functions when multiplied by trigonometric functions.

In many inference problems, the evaluation of complex and costly models is often required. In this context, Bayesian methods have become very popular in several fields over the last years, in order to obtain parameter inversion, model selection, or uncertainty quantification. Bayesian inference requires the approximation of complicated integrals involving (often costly) posterior distributions. Generally, this approximation is obtained by means of Monte–Carlo (MC) methods. In order to reduce the computational cost of the corresponding technique, surrogate models (also called emulators) are often employed. Another alternative approach is the so-called approximate Bayesian computation (ABC) scheme. ABC does not require the evaluation of the costly model but the ability to simulate artificial data according to that model. Moreover, in ABC, the choice of a suitable distance between real and artificial data is also required. In this work, we introduce a novel approach where the expensive model is evaluated only in some well-chosen samples. The selection of these nodes is based on the so-called compressed MC scheme. We provide theoretical results supporting the novel algorithms and give empirical evidence of the performance of the proposed method in several numerical experiments. Two of them are real-world applications in astronomy and satellite remote sensing. (Corresponding author: Luca Martino.) [ABSTRACT FROM AUTHOR]

Unsteady free convection flows of an incompressible differential type fluid over an infinite vertical plate with fractional thermal transport are studied. Modern definitions of the fractional derivatives in the sense of Atangana–Baleanu (ABC) and Caputo Fabrizio (CF) are used in the constitutive equations for the thermal flux. Exact solutions in both cases of the (ABC) and (CF) derivatives for the dimensionless temperature and velocity fields are established by using the Laplace transform technique. Solutions for the ordinary case and some well-known results from the literature are recovered as a limiting case. Expressions for Nusselt number and Skin friction coefficient are also determined. The influence of the pertinent parameters on temperature and velocity fields are discussed graphically. A comparison of ordinary model, and (ABC) and (CF) models are also depicted. It is found that memory of the physical aspects of the problem is well explained by fractional order (ABC) and (CF) models as compared to ordinary one. Further it is noted that the (ABC) model is the best fit to explain the memory effect of the temperature and velocity fields. [ABSTRACT FROM AUTHOR]

The relevance of the research is caused by the need to develop basic algorithms for processing and inversion of data from a new multi-coil multi-frequency multi-mode electromagnetic tool with toroidal coils designed for studying the electrical macroanisotropy of rocks, determining the saturation of reservoirs, identifying thinly bedded sandy-argillaceous oil-saturated intervals and fracture zones. The main aim of the research is to develop basic algorithms for processing and inversion of data from the new electromagnetic tool with toroidal coils for studying the macroanisotropic properties of reservoirs with complex geological structure (thinly bedded, fractured). Objects of the researches are the signals of the new electromagnetic tool with toroidal coils. Methods: finite-difference numerical simulation and comparative analysis of signals of the new electromagnetic tool with toroidal coils. Results. The authors have developed the basic algorithms for processing and inversion of data of the new electromagnetic tool with toroidal coils, among which: the algorithms of transforming the signals into the apparent resistivity and electrical anisotropy coefficient, selection of contrasting geoelectric boundaries, as well as software for numerical inversion with determination of the parameters of isotropic and anisotropic formations, taking into account the host medium. The computational algorithms are combined into a single computer program for quantitative interpretation of data from the new electromagnetic tool with toroidal coils. The algorithms are tested on noisy synthetic data. We have shown their efficiency when processing practical data from petroleum boreholes in the Volga-Ural oil and gas province. The investigations demonstrate that the new electromagnetic tool with toroidal coils has a high potential for use in geological sections of complex structure (thin-bedded, fractured).

Application of the exact statistical inference frequently leads to non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by their characteristic functions, as is the case for the null distribution of the Bartlett's test statistic. However, analytical inversion of the characteristic function, if possible, frequently leads to complicated expressions for computing the distribution function and the corresponding quantiles. An efficient alternative is the well-known method based on numerical inversion of the characteristic functions, which is, however, ignored in popular statistical software packages. In this paper, we present the explicit characteristic function of the corrected Bartlett's test statistic together with the computationally fast and efficient implementation of the approach based on numerical inversion of this characteristic function, suggested for evaluating the exact null distribution used for testing homogeneity of variances in several normal populations, with possibly unequal sample sizes. [ABSTRACT FROM AUTHOR]

Based on the characteristics of injection-production units in fractured-vuggy carbonate reservoirs, nine groups of experiments were designed and performed to analyze the interference characteristics and their influencing factors during water flooding. Based on percolation theory, an inversion model for simulating waterflooding interferences was proposed to study the influence laws of different factors on interference characteristics. The results show that well spacing, permeability ratio, cave size, and cave location all affect the interference characteristics of water flooding. When the cave is located in high permeability fractures, or in the small well spacing direction, or close to the producer in an injection-production unit, the effects of water flooding are much better. When the large cave is located in the high-permeability or small well spacing direction, the well in the direction with lower permeability or smaller well spacing will see water breakthrough earlier. When the cave is in the higher permeability direction and the reserves between the water injector and producer differ greatly, the conductivity differences in different injection-production directions are favorable for water flooding. When the injection-production well pattern is constructed or recombined, it's better to make the reserves of caves in different injection-production directions proportional to permeability, and inversely proportional to the well spacing. The well close to the cave should be a producer, and the well far from the cave should be an injector. Different ratios of cave reserves to fracture reserves correspond to different optimal well spacings and optimal permeability ratios. Moreover, both optimal well spacing and optimal permeability ratio increase as the ratio of cave reserves to fracture reserves increases. [ABSTRACT FROM AUTHOR]

In this paper, we present a new method to determine the pore-size distribution (PSD) in a porous medium. This innovative technique uses the rheological properties of non-Newtonian yield stress fluids flowing through the porous sample. In a first approach, the capillary bundle model will be used. The PSD is obtained from the measurement of the total flow rate of fluid as a function of the imposed pressure gradient magnitude. The mathematical processing of the experimental data, which depends on the type of yield stress fluid, provides an overview of the pore size distribution of the porous material. The technique proposed here was successfully tested analytically and numerically for usual pore size distributions such as the Gaussian mono and multimodal distributions. The study was conducted for yield stress fluids obeying the classical Bingham model and extended to the more realistic Herschel-Bulkley model. Unlike other complex methods, expensive and sometimes toxic, this technique presents a lower cost, requires simple measurements and is easy to interpret. This new method could become in the future an alternative, non-toxic and cheap method for the characterization of porous materials. [ABSTRACT FROM AUTHOR]

Suggested is a non-parametric method and algorithm for estimating the probability distribution of a stochastic sum of independent identically distributed continuous random variables, based on combining and numerically inverting the associated empirical characteristic function (CF) derived from the observed data. This is motivated by classical problems in financial risk management, actuarial science, and hydrological modelling. This approach can be naturally generalized to more complex semi-parametric modelling and estimating approaches, e.g., by incorporating the generalized Pareto distribution fit for modelling heavy tails of the considered continuous random variables, or by considering the weighted mixture of the parametric CFs (used to incorporate the expert knowledge) and the empirical CFs (used to incorporate the knowledge based on the observed or historical data). The suggested numerical approach is based on combination of the Gil-Pelaez inversion formulae for deriving the probability distribution (PDF and CDF) from the associated CF and the trapezoidal quadrature rule used for the required numerical integration. The presented non-parametric estimation method is related to the bootstrap estimation approach, and thus, it shares similar properties. Applicability of the proposed estimation procedure is illustrated by estimating the aggregate loss distribution from the well-known Danish fire losses data. [ABSTRACT FROM AUTHOR]

The deep permeable sandy and pebble strata are closely related to the surrounding surface water in the middle reaches of the Hanjiang River, and the depth of the ground water is shallow so that it caused great difficulty to dewater of the strata during the foundation pit excavation. Considering the specific characteristics of the permeable sandy and pebble strata around Hanjiang River, we take the foundation pit of pipe joint prefabrication dry dock with axis method in Xiangyang East- West Axis Road Project as an example to carry out well group dewatering test and numerical simulation calculation. The influence radius of dewatering, water output of single well, water level recovery rate and other parameters are determined by field dewatering test. On this basis, using the unsteady flow analysis method and three-dimensional seepage numerical model, the comprehensive permeability coefficient of the formation is 64.5 m/d, and the permeability coefficient of each layer is 12 m/d for the upper sand layer, 102.5 m/d for the middle pebble mixed with round gravel, and 25.4 m/d for the lower pebble, which can provide reference for the design scheme of axis dry dock foundation pit dewatering. [ABSTRACT FROM AUTHOR]

In this work, a three-dimensional (3D) model of the generalized thermoelasticity with fractional order strain is constructed. The resulting non-dimensional governing equations together with the Laplace and double Fourier transform techniques have been applied to a 3D half-space subjected to thermal shock and traction free surface. The inverses of double Fourier transforms, and Laplace transforms have been obtained numerically by using a complex inversion formula of the transform with the techniques of the Fourier expansion. Numerical results for the strain, thermal stress, displacement, and temperature are represented graphically based on various values of the strain fractional order parameter to stand on its effect on the thermo-mechanical waves. The fractional order parameter of the strain has significant effects on the mechanical waves while it has a limited effect on the thermal waves. [ABSTRACT FROM AUTHOR]

Abstract In the light of the idealization of the outer boundary conditions (infinite, constant pressure and closed) of the conventional homogeneous reservoir model, the paper introduces the elastic outer boundary conditions and establishes the percolation model of homogeneous reservoir. By combining Laplace transforms with the Similarity Construction Method, the solutions of the percolation model of homogeneous reservoir can be obtained in Laplace space. The solutions are inverted into real space with the Stehfest numerical inversion method. In addition, the characteristic curves are drawn, and the impacts of the variation of the main parameters on the curves are analyzed. The results show that the conventional three kinds of outer boundary conditions are actually three special cases of elastic outer boundary. The pressure curve under the elastic outer boundary is between the pressure curve of the constant pressure outer boundary and the closed outer boundary, and the curves above exhibit affine similarities. In this paper, the elastic outer boundary condition is introduced not only to enlarge the range of data interpretation, but also to reflect the real situation of the outer boundary of oil and gas reservoir (Strict closed and constant pressure boundaries rarely exist in real reservoirs). The similarity construction theory greatly simplifies the complicated process of solving the model, which will have a profound influence on the development of the well test analysis software in the future. Highlights • We propose a generalized elastic outer boundary condition. • The characteristic curves have affine similarities. • Using the Similarity Construction Method can simplify the solution of the model. • The similarity construction theory provides a new idea for well test software. [ABSTRACT FROM AUTHOR]

Ｆｒａｃｔｕｒｅｄ ｖｕｇｇｙ ｒｅｓｅｒｖｏｉｒｓ ｃｏｎｓｉｓｔ ｏｆ ｍａｔｒｉｘ， ｆｒａｃｔｕｒｅｓ ａｎｄ ｖｕｇｓ． Ｒｅｓｅａｒｃｈｅｒｓ ｕｓｕａｌｌｙ ｔｒｅａｔ ｔｈｅ ｍａｔｒｉｘ⁃ｆｒａｃｔｕｒｅ⁃ｖｕｇ ｉｎｔｅｒａｃｔｉｏｎ ａｓ ｉｎｔｅｒ⁃ｐｏｒｏｓｉｔｙ ｆｌｏｗ ｄｕｅ ｔｏ ｔｈｅｉｒ ｃｏｍｐｌｅｘ ｐｏｒｅ ｓｙｓｔｅｍ ａｎｄ ｆｌｏｗ ｍｅｃｈａｎｉｓｍ． Ｉｎ ｆａｃｔ， ｖｕｇｓ ｐｌａｙ ａｎ ｉｍｐｏｒｔａｎｔ ｒｏｌｅ ｉｎ ｆｒａｃｔｕｒｅｄ ｖｕｇｇｙ ｒｅｓｅｒｖｏｉｒｓ ａｎｄ ｃａｎ’ｔ ｂｅ ｓｉｍｐｌｉｆｉｅｄ ｔｏ ｏｎｅ ｈｏｍｏｇｅｎｅｏｕｓ ｍｅｄｉｕｍ． Ｔｈｅ ｉｄｅａ ｔｈａｔ ｐｒｅｓｓｕｒｅ ｓｐｒｅａｄｉｎｇ ｉｎ ｖｕｇｓ ｉｓ ｉｎ ｆｏｒｍ ｏｆ ｗａｖｅ， ｗｈｉｃｈ ｉｓ ｓｉｍｉｌａｒ ｔｏ ｐｒｅｓｓｕｒｅ ｄｅｃｌｉｎｅ， ｗａｓ ｐｒｏｐｏｓｅｄ． Ｂａｓｅｄ ｏｎ ｔｈａｔ， ａｎ ａｎａｌｙｔｉｃａｌ ｗｅｌｌ ｔｅｓｔ ｍｏｄｅｌ ｆｏｒ ｆｒａｃｔｕｒｅｄ ｖｕｇｇｙ ｒｅｓｅｒｖｏｉｒｓ ｃｏｍｂｉｎｅｄ ｗｉｔｈ ｓｅｅｐａｇｅ ｅｑｕａｔｉｏｎｓ ｆｏｒ ｏｕｔｅｒ ｆｏｒｍａｔｉｏｎ ｗａｓ ｐｒｅｓｅｎｔｅｄ． Ｔｈｅｎ ｔｈｅ ｌｏｇ⁃ｌｏｇ ｔｙｐｅ ｃｕｒｖｅｓ ｏｆ ｔｈｅ ｗｅｌｌｂｏｒｅ ｐｒｅｓｓｕｒｅ ａｎｄ ｉｔｓ ｄｅｒｉｖａｔｉｖｅ ｗｅｒｅ ｏｂ⁃ ｔａｉｎｅｄ ｔｈｒｏｕｇｈ ｔｈｅ Ｌａｐｌａｃｅ ｔｒａｎｓｆｏｒｍ ａｎｄ ｎｕｍｅｒｉｃａｌ ｉｎｖｅｒｓｉｏｎ． Ｔｈｅ ｒｅｓｕｌｔｓ ｓｈｏｗ ｔｈａｔ， ｔｈｅ ｐｒｅｓ⁃ ｓｕｒｅ ｃｕｒｖｅ ｆｏｒｍｓ ｗｅｒｅ ｉｎｆｌｕｅｎｃｅｄ ｂｙ ｄｉｍｅｎｓｉｏｎｌｅｓｓ ｐａｒａｍｅｔｅｒｓ ｒｅｌａｔｅｄ ｔｏ ｆｌｏｗ ａｎｄ ｗａｖｅ ｐｒｏｐａ⁃ ｇａｔｉｏｎ， ａｌｓｏ ｂｙ ｄｉｍｅｎｓｉｏｎｌｅｓｓ ｐａｒａｍｅｔｅｒｓ ｒｅｌａｔｅｄ ｔｏ ｔｈｅ ｏｕｔｅｒ ｆｏｒｍａｔｉｏｎ． Ｓｅｎｓｉｔｉｖｉｔｙ ａｎａｌｙｓｉｓ ｏｆ ｔｈｅｓｅ ｐａｒａｍｅｔｅｒｓ ｗｅｒｅ ｄｏｎｅ． Ｌａｓｔｌｙ， ａ ｆｉｅｌｄ ｅｘａｍｐｌｅ ｗａｓ ｄｅｍｏｎｓｔｒａｔｅｄ ｔｏ ｖａｌｉｄａｔｅ ｔｈｅ ａｃｃｕｒａｃｙ ｏｆ ｔｈｅ ｐｒｏｐｏｓｅｄ ｍｏｄｅｌ， ｗｈｉｃｈ ｍａｔｃｈｅｄ ｔｈｅ ｒｅａｌ ｇｅｏｌｏｇｉｃａｌ ｄａｔａ ｗｅｌｌ. [ABSTRACT FROM AUTHOR]

• Semi-analytic methods are used to solve 3D DPL problems. • Compared with FEM, the semi-analytic method has higher computational efficiency. • The phase lag of heat flow and the phase lag of temperature gradient have influence on the temperature response speed and the formation of temperature field. With the development of picosecond laser technology, the dual-phase-lagging (DPL) model is more suitable to describe the heat transfer problem with micro-scale effect and micro-time effect. In this paper, a three-dimensional dual-phase-lagging heat transfer model for picosecond laser processing is established. Then Fourier transform (FT) and Laplace transform (LT) are used to derive the frequency response functions (FRFs) of the problem in the frequency domain, and the inverse Laplace transform (ILT) and discrete-convolution fast Fourier transform (DC-FFT) algorithm are used to solve the temperature field. The calculation accuracy of this method is verified and the effect of phase lag constants on temperature field is studied. The results show that the semi-analytical method has a high accuracy for solving the dual-phase-lagging heat conduction model, and the phase lag of heat flux will affect the heating rate in the heating stage, and the phase lag of temperature gradient will delay the formation of temperature field. The effect of phase lag constants on temperature-time history is investigated and the related phenomena are explained by using the two-step heat transfer theory. This semi-analytical method provides a new approach to solve the problem of three-dimensional dual-phase-lagging heat transfer. [ABSTRACT FROM AUTHOR]

In this paper, a three-dimensional solution of the steady-state advection-diffusion equation is obtained applying the Generalized Integral Advection Diffusion Multilayer Technique (GIADMT), considering non-local closure for turbulent flow. Two different parameterizations were considering for the countergradient term and different methods of numerical inversion for inverse Laplace transform. The results were compared with the experimental data of Copenhagen experiment by an evaluation of statistical indices to analyse the solution of the equation through the methods of numerical inversion. Differents parameterizations for the vertical turbulent eddy diffusivity and wind profile were utilized. The results show a good agreement with the experiment and the methods of numerical inversion for inverse Laplace transform show same efficacy.

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Lévy processes have become very popular in many applications in finance, physics and beyond. The Student-Lévy process is one interesting special case where increments are heavy-tailed and, for 1-increments, Student t distributed. Although theoretically available, there is a lack of path simulation techniques in the literature due to its complicated form. In this paper we address this issue using series representations with the inverse Lévy measure method and the rejection method and prove upper bounds for the mean squared approximation error. In the numerical section we discuss a numerical inversion scheme to find the inverse Lévy measure efficiently. We extend the existing numerical inverse Lévy measure method to incorporate explosive Lévy tail measures. Monte Carlo studies verify the error bounds and the effectiveness of the simulation routine. As a side result we obtain series representations of the so called inverse gamma subordinator which are used to generate paths in this model. [ABSTRACT FROM AUTHOR]

The paper presents a computationally efficient method for modeling and simulating distributed systems with lossy transmission line (TL) including multiconductor ones, by a less conventional method. The method is devised based on 1D and 2D Laplace transforms, which facilitates the possibility of incorporating fractional-order elements and frequency-dependent parameters. This process is made possible due to the development of effective numerical inverse Laplace transforms (NILTs) of one and two variables, 1D NILT and 2D NILT. In the paper, it is shown that in high frequency operating systems, the frequency dependencies of the system ought to be included in the model. Additionally, it is shown that incorporating fractional-order elements in the modeling of the distributed parameter systems compensates for losses along the wires, provides higher degrees of flexibility for optimization and produces more accurate and authentic modelling of such systems. The simulations are performed in the Matlab environment and are effectively algorithmized. [ABSTRACT FROM AUTHOR]

The threshold pressure gradient (TPG) generally exists in the seepage process of low permeability reservoir. In view of characteristics of low permeability seepage, the mathematical model for the moving boundary of non-Darcy flow was established, and the formula for calculating the moving speed of the boundary was given. The Laplace transform and the infinite series method were used to obtain the model’s general solution, and the Stehfest numerical inversion was conducted. The characteristics of moving boundary problems. the boundary change and propagation were discussed and explained in detail, and the phenomenon of TPG extending outward was explicated. The TPG effects on the bottom pressure and the pressure derivative were calculated, and the Gringarten-Bourdet charts under different conditions were given. The results show that, the low pressure percolation model is significantly different from the Darcy seepage model. For low permeability cases, the pressure drop expands with time and the pressure distribution curve is of compact support. The study on the low permeability problem with moving boundary, considering the influence of the TPG and the moving boundary. provides a theoretical basis for the seepage mechanism and production performance, interpretation and numerical simulation of low permeability oil reservoirs. [ABSTRACT FROM AUTHOR]

This article deals with an inverse problem of determining the diffusion coefficients in 2D fractional diffusion equation with a Dirichlet boundary condition by the final observations at the final time. The forward problem is solved by the alternating direction implicit finite-difference scheme with the discrete of fractional derivative by shift Grünwald formula and a numerical text which is to prove its numerically stability and convergence is given. Furthermore, the homotopy regularization algorithm with the regularization parameter chosen by a Sigmoid-type function is introduced to solve the inversion problem numerically. Numerical inversions both with accurate data and noisy data are carried out for the unknown diffusion coefficients of constant and variable with polynomials, trigonometric and index functions. The reconstruction results show that the inversion algorithm is efficient for the inverse problem of determining diffusion coefficients in 2D space fractional diffusion equation, and the algorithm is also numerically stable for additional date having random noises. [ABSTRACT FROM AUTHOR]

This article deals with an inverse problem of determining the space-dependent diffusion coefficient and the source coefficient simultaneously in the multi-term time fractional diffusion equation (TFDE in short) using measurements at one inner point. From a view point of optimality, solving the inverse problem is transformed to minimize an error functional with the help of the solution operator from the unknown to the additional observation. The solution operator is nonlinear but it is of Lipschitz continuity by which existence of a minimum to the error functional is obtained using Sobolev embedding theorems. The homotopy regularization algorithm is introduced to solve the simultaneous inversion problem based on the minimization problem, and numerical examples are presented. The inversion solutions give good approximations to the exact solutions demonstrating that the homotopy regularization algorithm is efficient for the simultaneous inversion problem arising in the multi-term TFDE. [ABSTRACT FROM PUBLISHER]

This paper deals with an inverse problem of determining a space-dependent source coefficient in the 2D/3D advection-dispersion equation with final observations using the variational adjoint method. Data compatibility for the inverse problem is analyzed by which an admissible set for the unknowns is induced. With the aid of an adjoint problem, a bilinear functional based on the variational identity is set forth with which a norm for the unknown is well-defined under suitable conditions, and then a conditional Lipschitz stability for the inverse problem is established. Furthermore, numerical inversions with random noisy data are performed using the optimal perturbation algorithm, and the inversion solutions give good approximations to the exact solution as the noise level goes to small. [ABSTRACT FROM AUTHOR]

This paper deals with numerical solution for the space-time fractional diffusion equation with variable diffusion coefficient, and numerical inversion for the space-dependent diffusion coefficient by the homotopy regularization algorithm. An equivalent system to the forward problem is deduced by utilizing properties of the fractional derivatives, and an implicit finite difference scheme for solving the forward problem is set forth, and its stability and convergence are proved based on estimation to the spectrum radius of the coefficient matrix. The homotopy regularization algorithm is introduced to solve the inverse problem, and numerical inversions are performed with noisy data. The inversion solutions give good approximations to the exact solution as the noise level goes to small demonstrating a numerical stability of the inverse problem here. [ABSTRACT FROM PUBLISHER]

An infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. The two-dimensional coupled thermoelastodynamic PDEs are specified based on equations of motion and energy equation, which are uncoupled using Nowacki potential functions. The Laplace integral transform and Bessel-Fourier series are used to derive the solution for the potential functions, and then the displacements-, stresses- and temperature-potential relationships are used to determine the displacements, stresses and temperature fields. It is shown that the formulation presented here are identically collapsed on the solution existed in the literature for simpler case of axissymetric configuration. A numerical procedure is needed to evaluate the displacements, stresses and temperature at any point and any time. The numerical inversion method proposed by Durbin is applied to evaluate the inverse Laplace transforms of different functions involved in this paper. For numerical inversion, there exist many difficulties such as singular points in the integrand functions, infinite limit of the integral and the time step of integration. With a very precise attention, the desired functions have been numerically evaluated and shown that the boundary conditions have been satisfied very accurately. The numerical evaluations are graphically shown to make engineering sense for the problem involved in this paper for different case of boundary conditions. The results show the wave velocity and the time lack of receiving stress waves. The effect of temperature boundary conditions are shown to be somehow oscillatory, which is used in designing of such an elements.

We present a numerical approximate solution to Sobolev-type differential equation subject to nonlocal initial boundary conditions. A Laplace transform method is described for the solution of considered equation. Following Laplace transform of the original problem, an appropriate method of solving differential equations is used to solve the resultant time-independent modified equation and solution is inverted numerically back into the time domain. Numerical results are provided to show the accuracy of the proposed method.