Abel Integral Equation Research Articles

Modelling transport time to trauma centres and 30-day mortality in road accidents in Switzerland: an exploratory study.

Rapid access to a trauma centre for severely injured road accident victims, conceptualised as the Golden Hour, links access time to definitive treatment within 1 hour of trauma with reduced risks of morbidity and mortality. Access times have not been studied in Switzerland. The aim of this work was to model the transport time by ambulance of seriously injured road traffic accident victims to one of the 12 trauma centres in Switzerland and to investigate whether this time influenced mortality. Isochronous travel curves in 10-minute increments were modelled around each of the 12 Swiss trauma centres to assess travel times at the Swiss national level, based on the shortest travel time from the location of a serious road accident to the nearest trauma centre. We used the national database of the Federal Roads Office, which provided the geolocation of these accidents occurring between 2011 and 2017. The association between mortality and transport time to the nearest trauma centre was then analysed. The current distribution of trauma centres allowed access time within the Golden Hour for accidents occurring on the Swiss plateau, but the time was more prolonged in the Alps or the Jura. An association existed between mortality and prehospital transport time from the site of an accident to the nearest trauma centre. For each additional 10-minute isochrone, an average increase of 0.4% in mortality was observed. This work showed an adequate distribution of trauma centres in Switzerland and suggests a positive relationship between transport time to the nearest trauma centre and mortality. The numerous confounding factors not systematically collected in publicly available databases limit the robustness of our results. This study confirms the importance of having a national trauma registry to allow quality analyses to guide public health decisions.

Uniqueness of Solutions of the Generalized Abel Integral Equations in Banach Spaces

This paper studies the uniqueness of solutions for several generalized Abel’s integral equations and a related coupled system in Banach spaces. The results derived are new and based on Babenko’s approach, Banach’s contraction principle and the multivariate Mittag–Leffler function. We also present some examples for the illustration of our main theorems.

Development and mechanical properties of HDPE/PA6 blends: Polymer-blend geocells

Geocells are three-dimensional expandable panels composed of polymers such as polyolefin polymers. Currently, geocells are being extensively used in various geotechnical engineering applications; however, its applications are limited because of the sizeable long-term deformation under constant loading and poor tensile strength. Owing to the rapid growth rate of geocells, it has become necessary to develop a polymer material with excellent creep resistance and tensile strength. To this end, a polymer-blend geocell (PBG) is developed in this study using a twin-screw extruder with high-density polyethylene (HDPE), polyamide 6, and compatibilizer. The polymer formula is determined by the tear fracture surface and scanning electron microscopy. The tensile properties of the blends with different formulas are studied in terms of yield strength, tensile strength, and elongation at break. Finally, three types of PBG and HDPE geocells are selected to study the long-term creep behavior using accelerated creep tests. The analysis results of raw creep data, master creep curve, and isochronous creep curves indicated that the PBG had a better creep resistance than the HDPE geocells.

Approximate solution of Abel integral equation in Daubechies wavelet basis

This paper presents a new computational method for solving Abel integral equation (both first kind and second kind). The numerical scheme is based on approximations in Daubechies wavelet basis. The properties of Daubechies scale functions are employed to reduce an integral equation to the solution of a system of algebraic equations. The error analysis associated with the method is given. The method is illustrated with some examples and the present method works nicely for low resolution.

Steady azimuthal flow field induced by a rotating sphere near a rigid disk or inside a gap between two coaxially positioned rigid disks

Geometric confinements play an important role in many physical and biological processes and significantly affect the rheology and behavior of colloidal suspensions at low Reynolds numbers. On the basis of the linear Stokes equations, we investigate theoretically and computationally the viscous azimuthal flow induced by the slow rotation of a small spherical particle located in the vicinity of a rigid no-slip disk or inside a gap between two coaxially positioned rigid no-slip disks of the same radius. We formulate the solution of the hydrodynamic problem as a mixed-boundary-value problem in the whole fluid domain, which we subsequently transform into a system of dual integral equations. Near a stationary disk, we show that the resulting integral equation can be reduced into an elementary Abel integral equation that admits a unique analytical solution. Between two coaxially positioned stationary disks, we demonstrate that the flow problem can be transformed into a system of two Fredholm integral equations of the first kind. The latter are solved by means of numerical approaches. Using our solution, we further investigate the effect of the disks on the slow rotational motion of a colloidal particle and provide expressions of the hydrodynamic mobility as a function of the system geometry. We compare our results with corresponding finite-element simulations and observe very good agreement.

Analytical solution of Abel integral equation

Analytical solution of Abel integral equation

Numerical solutions of Abel integral equations via Touchard and Laguerre polynomials

In this article, two numerical methods based on Touchard and Laguerre polynomials were presented to solve Abel integral (AI) equations. Touchard and Laguerre matrices were utilized to transform Abel integral equations into an algebraic system of linear equations. Solve this system of these equations to obtain Touchard and Laguerre parameters. Four examples are given to demonstrate the presented methods. The solutions were compared with the solutions in the literature.

Investigation of the Thermal Strength of Steam Turbine Diaphragms with Reduction of Axial Dimensions

The problem of reducing the axial dimensions of steam turbine diaphragms is associated with the problem of steam turbine modernization performed by increasing the number of reactive blading stages and using existing foundations. Evaluation of the suitability of diaphragm design versions with established steam flow characteristics was carried out with constraints on short- and long-term strength conditions, as well as the accumulation of axial deflections due to creep. For computational research, there was introduced a methodology using the finite element method and Yu. M. Rabotnov’s theory of strain aging. The calculation of creep was reduced to solving an elastic-plastic problem with a deformation curve, which was represented by an isochronous creep curve for the time chosen. A software was used providing for the automated construction of the original computer diaphragm model with the help of guide-vane profile drawings and axial cross-sections of the diaphragm rim and body, as well as several geometric parameters. The calculated model of a welded diaphragm reproduces the main essential features of the structure, the material properties of its elements, as well as steam load. The exploratory studies of diaphragms with reduced axial dimensions were performed on the example of the second- and third-stage diaphragms of the high-pressure cylinder of the K-325-23.5 steam turbine. The original second- and third-stage diaphragm designs were considered to be basic, in relation to which, according to strength and rigidity parameters, the alternative ones were compared. Calculated data for the basic diaphragm design versions for 100 thousand operating hours were obtained. According to the calculations, maximum deflections are achieved at diaphragm edges, and the stresses, that are maximum at the points where the guide vanes are attached to the diaphragm rim and body, undergo a significant redistribution due to creep. Two approaches to the reduction of the axial dimensions of the second-stage diaphragm design of the steam turbine high pressure cylinder were involved. In the first approach, the reduction of the dimensions was achieved by proportionally reducing the guide-vane profile with a corresponding increase in the number of the guide vanes. In the second approach, the profile remained unchanged, but the axial dimensions of the diaphragm rim and body were reduced. The parameters of strength both in the elastic state at the beginning of operation and in the conditions of creep, as well as the accumulation of axial deflections were investigated. Based on the comparisons with the basic design, it was established that the second approach is more effective. Additional recommendations for the use of more heat-resistant steels for outlet guide vanes and the conditions of diaphragm attachment in the turbine casing are given.

AN EFFICIENT NUMERICAL APPROACH FOR SOLVING ABEL’S INTEGRAL EQUATIONS BY USING MODIFIED TAYLOR WAVELETS

In this paper, a modified Taylor wavelet method (MTWM) is developed for numerical solutions of various types of Abel's integral equations. This method is based on the modified Taylor wavelet (MTW) approximation. The purpose behind using the MTW approximation is to transform the introduction problems into an equivalent set of algebraic equations. To check the accuracy and applicability of the proposed method, some examples have been solved and compared with other existing methods.

SOLUTION OF INTEGRAL EQUATIONS BY BESSEL WAVELET TRANSFORM

The integral equations of the first kind arise in many areas of science and engineering fields such as image processing and electromagnetic theory. The wavelet transform technique to solve integral equation allows the creation of very fast algorithms when compared with known algorithms. Various wavelet methods are used to solve certain type of integral equations. To find the most accurate and stable solution of the integral equation Bessel wavelet is the appropriate method. To study the properties of solution of integral equations on distribution spaces Bessel wavelet transform is also used. In this paper, we accomplished the concept of Hankel convolution and continuous Bessel wavelet transform to solve certain types of integral equations (Volterra integral equation of first kind, Volterra integral equation of second kind and Abel integral equation). Also distributional wavelet transform and generalized convolution will be applied to find the solution of certain Integral equations.

Effect of concrete particles confinement on the creep behaviour of scrap tire strips and geogrid

In order to study the effect of concrete particle confinement on the creep properties of geomaterials, a series of laboratory creep tests with concrete particles confinement were performed at different load levels. The creep characteristics of geomaterials curve and the strain-load isochronous curve were systematically analysed. The test results show that, compared with geogrid, the average creep strain of scrap tire strips increases by 3.73 times, 3.13 times and 2.38 times, at ultimate tensile strength (UTS) of 26%, 42% and 58% respectively. Under different normal stress, the maximum strain rate of tire was 224% and 220%, while that of geogrid was only 193% and 215%. Through regression analysis of different creep model parameters, three typical empirical creep models were obtained, and the creep develop regulations under different UTS and load levels were analysed.

A novel method for determining the time-temperature superposition relationship of SBS modified bitumen: Effects of bitumen source, modifier type and aging

The time-temperature superposition principle (TTSP) is frequently applied in rheological characterization of styrene-butadiene−styrene triblock copolymer (SBS) modified bitumen (SBSMB). The time-temperature superposition relationship is traditionally determined through optimizing the horizontal displacement of isothermal curves to minimize the errors between measured and predicted rheological data. Different from traditional method, the newly proposed method can determine the time-temperature superposition relationship of SBSMB according to its special points of phase angle plateau regions in isochronal curves. Nevertheless, the validity of this new method is only demonstrated for limited sources of SBSMB in previous study. In present paper, the effects of bitumen source, modifier type and aging on validity of the newly proposed method for determining the time-temperature superposition relationship of SBSMB were investigated. The results indicated that the shape of phase angle plateau region can be totally sorted into “convex” and “S” two types for all kinds of SBSMB samples. Although the rheological properties of SBSMB are affected by different bitumen sources and modifier types, the proposed method is demonstrated to be applicable to SBSMB samples prepared by different bitumen sources and modifier types. The proposed method cannot be applied to short-term or long-term aged SBSMB samples due to disappearance of phase angle plateau region. And the shift factors of original SBSMB obtained from the newly proposed method are no longer suitable for its aged SBSMB samples.

Development of a structural integrity evaluation program for elevated temperature service according to ASME code

A structural integrity evaluation program (STEP) was developed for the high temperature reactor design evaluation according to the ASME Boiler and Pressure Vessel Code (ASME B&PV), Section III, Rules for Construction of Nuclear Facility Components, Division 5, High Temperature Reactors, Subsection HB. The program computerized HBB-3200 (the design by analysis procedures for primary stress intensities in high temperature services) and Appendix T (HBB-T) (the evaluation procedures for strain, creep and fatigue in high temperature services). For evaluation, the material properties and isochronous curves presented in Section II, Part D and HBB-T were computerized for the candidate materials for high temperature reactors. The program computerized the evaluation procedures and the constants for the weldment. The program can generate stress/temperature time histories of various loads and superimpose them for creep damage evaluation. The program increases the efficiency of high temperature reactor design and eliminates human errors due to hand calculations. Comparisons that verified the evaluation results that used the STEP and the direct calculations that used the Excel confirmed that the STEP can perform complex evaluations in an efficient and reliable way. In particular, fatigue and creep damage assessment results are provided to validate the operating conditions with multiple types of cycles.

Solutions to viscous Burgers equations with time dependent source term

We study the existence and uniqueness of weak solutions for a Cauchy problem of a viscous Burgers equation with a time dependent reaction term involving Dirac measure. After applying a Hopf like transformation, we investigate the associated two initial boundary value problems by assuming a common boundary. The existence of the boundary data is shown with the help of Abel's integral equation. We then derive explicit representation of the boundary function. Also, we prove that the solutions of associated initial boundary value problems converge uniformly to a nonzero constant on compact sets as t approaches infinity.
 For more information see https://ejde.math.txstate.edu/Volumes/2021/02/abstr.html

Creep Fracture Characteristics of Fractured Rock Mass Strengthened with Toughened Epoxy Resin

For improving the toughness and long‐term strength of the fractured rock mass reinforced with epoxy resin and reducing the opening displacement of the crack tip, three types of converging cracks are established according to the deformation and failure characteristics of the rock mass, structural planes, and epoxy resin composite structure. The stress intensity factor of the type II compound crack and the analytical formula of the crack surface tip opening displacement are obtained. An improved Kelvin nonlinear creep model is proposed. Through the creep isochronous curve, the time and long‐term strength of accelerated creep failure are obtained, as well as creep rupture coupling characteristics. The ductile plastic deformation is used to characterize the toughness, and the toughness of epoxy resin is enhanced by adding mud powder, and the relationship between toughness and long‐term strength is established. Combined with experimental verification, when the drying mud powder content is 20%, the toughness of the epoxy resin has a good correlation with the long‐term strength; when the mud powder content exceeds 30%, its ductility and long‐term strength decrease, and at the same time the toughness effect is significantly weakened. The research results can provide a useful reference for toughened epoxy resin to strengthen fractured rock mass engineering.

CONDITIONS OF TERRITORIAL ACCESSIBILITY OFFERED BY THE NETWORK OF SUSTAINABLE TOURISM ROUTES THAT ARE PART OF THE COFFEE CULTURAL LANDSCAPE - COLOMBIA

Tourist attraction is related to the provision of services in an urban or rural environment; it is possible to find the relat ionship between the tourist potential and performance infrastructure that provides access to the points. Aims: Asses accessibility of the route s that make part of the Coffee Cultural Landscape (CCL). Method: accessibility models based on isochronous curves obtained in the a nalysis of travel time, which allows the determination of population covered by the curves. Results: There is no direct relationship between the sociodemog raphic and socioeconomic variables, due to the low participation of the tourism in the GDP of the CCL.

Study on Triaxial Creep Test and Constitutive Model of Compacted Red Clay

To study the stability of fill roadbeds for railway-private sidings at the Anning refinery in southwest China, a series of triaxial creep tests of compacted red clay was carried out using an SLB-1 stress–strain controlled triaxial shear permeability tester. In this paper, under different confining pressures, stress levels and drainage conditions, the creep characteristics of the red clay compaction were studied. The results showed that the creep characteristics of compacted red clay were significantly affected by confining pressure, stress level and drainage conditions, and the compacted red clay showed the characteristic of creep attenuation. The stress–strain isochronal curves indicated obvious nonlinear characteristics, which formed a cluster of curves with the uniformization procedure, whereas under drainage conditions, the stress–strain isochronal curves presented a certain linear relationship. Moreover, according to the stress–strain curves, the long-term strength of the compacted red clay was 0.54–0.72 times the instantaneous strength. Furthermore, taking the triaxial creep test of the compacted red clay under a confining pressure of 300 kPa as an example, the data were analyzed, and a new empirical creep model was established. Compared with the Burgers model and the Singh–Mitchell model, the calculated curve of the new empirical creep model is in good agreement with the experimental curve. The new model, which has fewer parameters that are easier to get, has the advantage of a higher accuracy. The new empirical model can better reflect and predict the creep characteristics of compacted red clay in the filling roadbeds of the special railway line at the Anning factory refinery in southwest China.

A Generalized Barycentric Rational Interpolation Method for Generalized Abel Integral Equations

The paper is devoted to the numerical solution of generalized Abel integral equation. First, the generalized barycentric rational interpolants have been introduced and their properties investigated thoroughly. Then, a numerical method based on these barycentric rational interpolations and the Legendre–Gauss quadrature rule is developed for solving the generalized Abel integral equation. The main advantages of the presented method is that it provides an infinitely smooth approximate solution with no real poles for the generalized Abel integral equation.

Approximate solution of some nonlinear classes of Abel integral equations using hybrid expansion

Numerical schemes for nonlinear weakly singular Volterra and Fredholm integral equations of the first kind are rarely investigated in the literature. In this paper, we present numerical solutions for these types of equations including Abel equations by hybrid block-pulse functions and Legendre polynomials. Hybrid functions give us the opportunity to attend a highly accurate solution by adjusting the orders of block-pulse functions and Legendre polynomials. The main idea of the scheme is based on using the precise forms of the known functions in the approximation procedure which yields the simplicity, reliability and high accuracy of the method. This simple scheme converts these types of equations into a linear system of equations. The focus of this paper is to investigate the convergence analysis and to show high convergence rate of the scheme. Numerical examples confirm the efficiency and superiority of the present approach in comparison with those already available in the literature.

An efficient solution of system of generalized Abel integral equations using Bernstein polynomials wavelet bases

This work introduces a direct method based on orthonormal Bernstein polynomials wavelet bases, to present a stable algorithm for numerical inversion of a system of generalized Abel integral equations. The application of all the currently existing numerical inversion methods was strictly limited to only one portion of the generalized Abel integral equations. The proposed method is quite accurate, and several numerical illustrations demonstrate the convergence and utilization of the proposed method compared to some of the preexisting numerical solution techniques. The permanence of the numerical result under the effect of small perturbation in input data has been examined, which is depicted with the use of numerical illustrations.