Inverse Coefficient Research Articles

Constrained modulus of fine-grained soils from in situ-based correlations and comparison with laboratory tests

The Constrained Modulus of soil is an important parameter to quantify compressibility of soils and calculate consolidation settlements, especially for clays. It is often expressed in terms of 1D constrained modulus, M or its inverse coefficient of volume change, mv. One method that has been suggested to assess M is from Cone Penetration Testing (CPTU) measurements through various correlations. Although, this is sometimes difficult, because of uncertainties regarding the appropriate stress, σ’v0, which are highly affected by the groundwater and bulk density γ, of soils. The usual method to measure M (or mv) is from oedometer tests in laboratory. Correlating in situ tests with laboratory tests results is crucial to increase the quality of soils strengths and stiffness information for design. However, most of the times it is a challenging process, which involves many uncertainties from different soils’ tests. This paper will look at comparison of CPTU derived M to oedometer tests taking into consideration various types of soils mostly from well-documented testbed sites where high quality in situ (CPTU for all sites and SDMT where available) and oedometer tests are carried out. The importance of CPTU measurements and site-specific correlations with laboratory tests to establish unique soil type coefficients for use in equations to derive CPTU-based M will be highlighted.

Sharp estimate for starlikeness related to a tangent domain

In the recent years, the study of the Hankel determinant problems have been widely investigated by many researchers. We were essentially motivated by the recent research going on with the Hankel determinant and other coefficient bounds problems. In this research article, we first considered the subclass of analytic starlike functions connected with the domain of the tangent function. We then derived the initial four sharp coefficient bounds, the sharp Fekete-Szegö inequality, and the sharp second and third order Hankel determinant for the defined class. Also, we derived sharp estimates like sharp coefficient bounds, Fekete-Szegö estimate, and sharp second order Hankel determinant for the functions having logarithmic coefficient and for the inverse coefficient, respectively, for the defined functions class.

Analysis of Inverse Coefficient Problem for Euler-Bernoulli Equation with Periodic and Integral Conditions

The research, we investigate the solution of the inverse problem of a linear Euler-Bernoulli equation. For this purpose, the existence of this problem, its uniqueness and its constant dependence on the data are demonstrated using the Picard and Fourier methods.

Inverse coefficient problem for a time‐fractional wave equation with initial‐boundary and integral type overdetermination conditions

This paper considers the inverse problem of determining the time‐dependent coefficient in the time‐fractional diffusion‐wave equation. In this case, an initial boundary value problem was set for the fractional diffusion‐wave equation, and an additional condition was given for the inverse problem of determining the coefficient from this equation. First of all, it was considered the initial boundary value problem. By the Fourier method, this problem is reduced to equivalent integral equations. Then, using the Mittag‐Leffler function and the generalized singular Gronwall inequality, we get a priori estimate for solution via unknown coefficient which we will need to study of the inverse problem. The inverse problem is reduced to the equivalent integral of equation of Volterra type. The principle of contracted mapping is used to solve this equation. Local existence and global uniqueness results are proved. The stability estimate is also obtained.

Neumann series of Bessel functions for inverse coefficient problems

Consider the Sturm–Liouville equation with a real‐valued potential . Let be its solution satisfying certain initial conditions for a number of , where , and are some complex numbers. Denote , where . We propose a method for solving the inverse problem of the approximate recovery of the potential and number from the following data . In general, the problem is ill‐posed; however, it finds numerous practical applications. Such inverse problems as the recovery of the potential from a Weyl function or the inverse two‐spectra Sturm–Liouville problem are its special cases. Moreover, the inverse problem of determining the shape of a human vocal tract also reduces to the considered inverse problem. The proposed method is based on special Neumann series of Bessel functions representations for solutions of Sturm–Liouville equations. With their aid the problem is reduced to the classical inverse Sturm–Liouville problem of recovering from two spectra, which is solved again with the help of the same representations. The overall approach leads to an efficient numerical algorithm for solving the inverse problem. Its numerical efficiency is illustrated by several examples.

The impact of safety climate on human-technology interaction and sustainable development: Evidence from Indonesian oil and gas industry

This study investigates the intricate dynamics of human-technology interaction in the context of safety within the Indonesian oil and gas industry, specifically focusing on the integration of the internet of things and cyber-physical systems. The aim is to uncover the interplay between safety climate, human-technology interaction, and sustainable development, ultimately providing insights for enhancing safety and sustainability in this critical sector. Through a comprehensive analysis, this research employs a quantitative methods approach, combining survey and interview data with a data analysis using structural equation modeling. It assesses safety climate perceptions among employees, evaluates the impact of human-technology interaction on safety, and explores the moderating effect of safety climate on the relationship between human-technology interaction and sustainable development in Indonesia's upstream oil and gas sector. The study's findings illuminate the utmost importance of cultivating a robust safety culture within Indonesian upstream oil and gas companies. It reveals that negative safety climate can disrupt the positive influence of human-technology interaction on sustainable development, leading to an inverse path coefficient. This research emphasizes continuous safety performance evaluation, comprehensive employee training for effective human-technology interaction, and the seamless integration of sustainable development principles into all operational aspects. This holistic approach underscores the industry's commitment to the well-being of its workforce, the integrity of technological advancements, and its dedication to sustainable practices in an era dominated by human-technology interaction and cyber-physical systems.

Inverse coefficient problem by fractional Taylor series method

This study focus on determining the unknown function of time or space in space-time fractional differential equation by fractional Taylor series method. A significant advantage of this method is that over-measured data is not used unlike most inverse problems. This advantage allows us to determine the unknown function with less error. The presented examples illustrate that the obtained solutions are in a high agreement with the exact solutions of the corresponding inverse problems.

IMPROVEMENT OF THE NON-DESTRUCTIVE METHOD FOR DETERMINING THE MECHANICAL CHARACTERISTICS OF ELEMENTS OF MULTILAYER STRUCTURES ON THE EXAMPLE OF PAVEMENTS

The article is devoted to solving the urgent problem of improving the method of nondestructive testing of the condition of non-rigid road clothes. In addition to the previously developed approach to determining the mechanical parameters of materials of structural layers of nonrigid road coverings based on solving the inverse coefficient problem of restoring operational elastic modules providing specified displacement fields, an approach was developed that allows determining the parameters of energy dissipation in the structure of multilayer road pavement based on the correction of dynamic hysteresis loops recorded in the field and calculated using mathematical model of dynamic VAT. The article presents the results of numerical simulation of dynamic hysteresis loops for two different variants of multilayer structures. The possibilities of correcting the shape of hysteresis loops and their area by varying the tangents of the energy loss angles in layers of a multilayer medium and the elastic modulus of a homogeneous half-space are shown. The complex correction of the elastic modulus values of the structural layers of road clothes and the calculated loops of dynamic hysteresis made it possible to fully take into account the processes of energy attenuation at a distance from the point of application of the load. During the correction, it was found that the values of the elastic modulus of the road layers and the tangents of the loss angles in them have a complex effect on the areas of dynamic hysteresis loops and the nature of energy attenuation at a distance from the point of application of the load. At the same time, the elastic modulus of the underlying half-space is not limited in thickness to the greatest extent on the area of dynamic hysteresis loops (which led to an increase in the elastic modulus of the underlying half-space from 120 and 150 MPa for road construction variants with a reinforced and non-reinforced base to 170 and 160 MPa, respectively), and a decrease in the dissipated energy at a distance from the point of application This is primarily due to the tangent of the angle of energy loss in the half-space. The obtained values of the tangents of the loss angles are obviously related to the patterns of energy dissipation at the boundaries of the contacting layers of the pavement, and also take into account all possible anomalies and delaminations in the calculated structures. Within the framework of this article, calculated hysteresis loops on the surface of the pavement were obtained for the first time, the deformation energy was calculated based on their areas, and the possibility of their comparison with those registered experimentally was proved.

ON THE RECONSTRUCTION OF PRESTRESS FIELDS IN A HOLLOW CYLINDER

The present research is devoted to the development of the theoretical foundations of nondestructive acoustic method for identifying inhomogeneous prestress fields in a hollow cylinder, depending on the probing loading type. A linearized model of steady oscillations of an elastic body in the presence of an inhomogeneous prestress field of arbitrary nature is considered in the standard and weak formulations. On the basis of this model, we formulate a problem for a cantilever-clamped prestressed hollow cylinder that performs steady axisymmetric vibrations under three types of probing loading. A corresponding weak formulation of the problem in the cylindrical coordinate system is presented, in which six independent components of the prestress tensor are taken into account. At that, a case of prestress fields obtained by applying some initial mechanical external static load is considered. In the presence and absence of prestresses of various types, amplitude-frequency dependences are analyzed, and resonant and natural frequencies are found in a wide frequency range. Numerical calculations were carried out using the FEM on a non-uniform grid; mesh refinement is carried out in the vicinity of the boundary points, where the type of boundary conditions changes. Based on the numerical solution of an auxiliary set of direct problems, seven types of prestress fields are constructed, differing in the types of initial loading, most often encountered in practice. To assess the possibility of implementing the procedure for reconstructing prestresses of each of the considered types, a sensitivity analysis was additionally performed, which showed that for some prestress types there are frequencies and types of probing loading for which the presence of prestress is practically not manifested. The sensitivity analysis performed made it possible to implement the optimal method of probing loading when solving the inverse coefficient problem. The statement of the new inverse problem on the restoration of arbitrary inhomogeneous prestress fields in the considered finite hollow cylinder is formulated. When restoring the prestress of a given structure, the inverse problem is reduced to finding a set of parameters from an ill-conditioned algebraic system, which was studied with the help of the A.N. Tikhonov regularization method. Additional data for solving the inverse problem was obtained on the basis of probing both via a single load and via combined probing modes. It has been found that it is most effective to use a combined loading mode and use a sufficiently wide frequency range when selecting sounding frequencies. The results of computational experiments on the reconstruction of six components of the prestress tensor are presented and analyzed, and recommendations are proposed for choosing the optimal modes of acoustic sounding.

Ultrasound tomography based on the coefficient inverse problem as a way to combat structural noise

The paper proposes to use the ultrasound tomography method based on the solution of the inverse coefficient problem to reduce the level of structural noise. Mathematical models used in ultrasonic tomogra-phy well describe such physical effects as refraction, diffraction and redispersion effects. It is logical to ex-pect that reconstruction of the internal structure of metallic samples using ultrasound tomography will be more efficient compared to digital antenna focusing (DAF) techniques. Due to the nonlinearity of the inverse problem of ultrasound tomography, an iterative MultiStage method is used to ensure convergence to the glob-al minima of the non-convexity functional. The paper presents the results of numerical experiments to restore the image of the internal structure of the welded joint, which may contain lateral cylindrical holes and crack models. The region of the welded metal is represented in the form of sections constructed according to the principle of Voronoi diagrams. In each section the velocity is constant and its value is randomly distributed. In the model adopted in the paper, the structural noise is formed due to multiple scattering at the boundaries of sections with different sound velocity. It was assumed that the antenna array is located on the outer surface of the control object of known thickness. The results obtained show that the tomographic method allows us to determine the shape and speed of sound in low-contrast reflectors, for which the CFA method is ineffective.

Inverse Coefficient Problem for Fractional Wave Equation with the Generalized Riemann–Liouville Time Derivative

Inverse Coefficient Problem for Fractional Wave Equation with the Generalized Riemann–Liouville Time Derivative

Lattice distortion induced by rare‐earth ions doping in (Bi0.5Na0.5)TiO3‐based thin films with high piezoelectric properties

AbstractHigh‐performance lead‐free piezoelectric thin films are urgently required for microelectromechanical systems. In this study, thin films based on the 0.8Bi0.5Na0.5TiO3–0.2(Sr0.7Bi0.2□0.1)TiO3 system were prepared on Pt(111)/TiOx/SiO2/Si substrates by a sol–gel method. The large lattice distortions were induced by introducing five rare‐earth ions with different ionic radii (Er/Pr/Sm/Nd/La) to achieve the purpose of regulating the piezoelectric response of the thin films with the maximum inverse piezoelectric coefficient up to 425.9 pm/V. X‐ray diffraction, Raman spectroscopy, Piezoresponse force microscope, and additional testing methods were used to observe the phase composition and microstructure of the thin films to investigate the effect of doping rare‐earth elements with different ionic radii at the A‐site on lattice distortion, and to summarize the transformation law. This study is significant for improving the piezoelectric properties of thin films and has crucial applications in microelectronic sensing.

Inverse Problem Numerical Analysis of Forager Bee Losses in Spatial Environment without Contamination

We consider an inverse problem of recovering the mortality rate in the honey bee difference equation model, that tracks a forage honeybee leaving and entering the hive each day. We concentrate our analysis to the model without pesticide contamination in the symmetric spatial environment. Thus, the mathematical problem is formulated as a symmetric inverse problem for reaction coefficient at final time constraint. We use the overspecified information to transform the inverse coefficient problem to the forward problem with non-local terms in the differential operator and the initial condition. First, we apply semidiscretization in space to the new nonsymmetric differential operator. Then, the resulting non-local nonsymmetric system of ordinary differential equations (ODEs) is discretized by three iterative numerical schemes using different time stepping. Results of numerical experiments which compare the efficiency of the numerical schemes are discussed. Results from numerical tests with synthetic and real data are presented and discussed, as well.

On Determination of the Electrical Conductivity of a Local Inclusion of Piecewise-Constant Isotropic Medium

Abstract—This work is a continuation of the authors' research on solving inverse problems of mathematical geophysics in a linear formulation. Unlike previous works, where the solution was built on the basis of volumetric integral equations, boundary integral representations and emerging boundary integral equations are used here to solve the inverse coefficient problem of geoelectrics to find the constant electrical conductivity of a local isotropic inclusion, located in a piecewise-constant electrical conductivity isotropic enclosing medium.

The Fifth Coefficient Approximation of The Inverse Strongly Convex Function

This paper discusses the fifth coefficient approximation of the inverse strongly convex function. Strongly convex function is a subclass of convex function. Those functions are included as univalent functions. Using corresponding lemmas, we give sharp limits for the fifth coefficient of the inverse strongly convex function. The limit is sharp if the value of the approximation has the same value as the limit. We verify that the limit of the fifth coefficient of the inverse strongly convex function differs from that of the strongly convex function in some interval but still have the same value in a point. Besides, we also explain that the sharp limit of the fifth inverse coefficient is less than or equal to one.

Inverse coefficient problems for a time-fractional wave equation with the generalized Riemann-Liouville time derivative

This paper considers the inverse problem of determining the time-dependent coeffiicient in the fractional wave equation with Hilfer derivative. In this case, the direct problem is initial-boundary value problem for this equation with Cauchy type initial and nonlocal boundary conditions. As overdetermination condition nonlocal integral condition with respect to direct problem solution is given. By the Fourier method, this problem is reduced to equivalent integral equations. Then, using the Mittag-Leffler function and the generalized singular Gronwall inequality, we get apriori estimate for solution via unknown coefficient which we will need to study of the inverse problem. The inverse problem is reduced to the equivalent integral of equation of Volterra type. The principle of contracted mapping is used to solve this equation. Local existence and global uniqueness results are proved.

Research on Innovative Reform of Vocal Music Teaching Mode in Colleges and Universities Based on Network Vocal Music Teaching Model

Abstract Improving timbre recognition and Internet technology have created new avenues for developing vocal teaching models in colleges and universities. In this paper, several people propose a timbre-based Internet vocal teaching model based on the cross-classification vocal teaching model. The timbre is extracted and divided into training and test data, dimensionality reduction and classification processes to form the general process of timbre recognition. A GMM-HMM timbre recognition model is proposed by describing the observed timbre probabilities using GMM so that the observed timbre states of HMM are continuous. The SVM classification algorithm is employed to categorize the identified timbres and determine the specific distribution of incorrect timbres. In the vocal teaching test, the Mayer inversion coefficient achieved a higher RPA when the number of candidate pitches was less than 4. If the number of candidate pitches exceeds 5, the amplitude-free weighting method will increase slowly.

Active and passive microrheology with large tracers in hard colloids.

The dynamics of a tracer particle in a bath of quasi-hard colloidal spheres is studied by Langevin dynamics simulations and mode coupling theory (MCT); the tracer radius is varied from equal to up to seven times larger than the bath particles radius. In the simulations, two cases are considered: freely diffusing tracer (passive microrheology) and tracer pulled with a constant force (active microrheology). Both cases are connected by linear response theory for all tracer sizes. It links both the stationary and transient regimes of the pulled tracer (for low forces) with the equilibrium correlation functions; the velocity of the pulled tracer and its displacement are obtained from the velocity auto-correlation function and the mean squared displacement, respectively. The MCT calculations give insight into the physical mechanisms: At short times, the tracer rattles in its cage of neighbours, with the frequency increasing linearly with the tracer radius asymptotically. The long-time tracer diffusion coefficient from passive microrheology, which agrees with the inverse friction coefficient from the active case, arises from the transport of transverse momentum around the tracer. It can be described with the Brinkman equation for the transverse flow field obtained in extension of MCT, but cannot be recovered from the MCT kernel coupling to densities only. The dynamics of the bath particles is also studied; for the unforced tracer the dynamics is unaffected. When the tracer is pulled, the velocity field in the bath follows the prediction of the Brinkman model, but different from the case of a Newtonian fluid.

Inverse coefficient problem for a fractional-diffusion equation with a Bessel operator

The second initial-boundary value problem in a bounded domain for a fractional-diffusion equation with the Bessel operator and the Gerasimov-Caputo derivative is investigated. Theorems of existence and uniqueness of the solution of the inverse problem of determining the lowest coefficient in a one-dimensional fractional diffusion equation under the condition of integral observation are obtained. The Schauder principle was used to prove the existence of the solution.

Inverse Coefficient Problems for a Time-Fractional Wave Equation with the Generalized Riemann–Liouville Time Derivative

Inverse Coefficient Problems for a Time-Fractional Wave Equation with the Generalized Riemann–Liouville Time Derivative