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In eddy current nondestructive testing, ferrite-cored probes are usually used to detect and locate defects such as cracks and corrosion in conductive materials. However, the generic analytical model for evaluating corrosion in layered conductor using ferrite-cored probe has not yet been developed. The purpose of this paper is to propose and verify the analytical model of an E-cored probe for evaluating corrosion in layered conductive materials.

A cylindrical coordinate system is adopted and the solution domain is truncated in the radial direction. The magnetic vector potential of each region excited by a filamentary coil is derived first, and then the expansion coefficients of the solution are obtained by matching the boundary and interface conditions between the regions and the subregions. Finally the closed-form expression of the impedance of the multi-turn coil is derived by using the truncated region eigenfunction expansion (TREE) method, and the impedance calculation is carried out in Mathematica. In the frequency range of 100 Hz to 10 kHz, the impedance changes of the E-cored coil and air-cored coil due to the layered conductor containing corrosion are calculated, respectively, and the influences of corrosion on the coil impedance change are investigated.

An analytical model for the detection and evaluating of corrosion in layered conductive materials using E-cored probe is proposed. The model can quickly and accurately calculate the impedance change of E-cored coil due to corrosion in layered conductor. The correctness of the analytical model is verified by finite element method and experiments.

An accurate theoretical model of E-cored probe for evaluating corrosion of multilayer conductor is presented. The analytical model can be used to detect the inhomogeneity of layered conductor, design ferrite-cored probe or directly evaluate the corrosion defects of layered conductors.

The purpose of this paper is to investigate a variety of Painlevé integrable equations derived from a Hamiltonian equation.

The newly developed Painlevé integrable equations have been handled by using Hirota’s direct method. The authors obtain multiple soliton solutions and other kinds of solutions for these six models.

The developed Hamiltonian models exhibit complete integrability in analogy with the original equation.

The present study is to address these two main motivations: the study of the integrability features and solitons and other useful solutions for the developed equations.

The work introduces six Painlevé-integrable equations developed from a Hamiltonian model.

The work presents useful algorithms for constructing new integrable equations and for handling these equations.

The paper presents an original work with newly developed integrable equations and shows useful findings.

With the pressing need for environmental conservation, regulatory authorities are actively looking for measures to prevent global warming. In the proposed inventory model for deteriorating items, demand is dependent on the selling price and green technology investment (or carbon reduction investment) for the green product (GP), as well as an investment in price-based preservation technology to slow down the pace of deterioration. Furthermore, emission reduction measures are put in place to reduce carbon emissions (CEs).

The current study executed a thorough literature review to determine how to improve supply chain management performance. Furthermore, assumptions are made to fill research gaps, and a mathematical model is created to address the problem mentioned above. To collect the data, the available inventory literature was reviewed. Additionally, numerical illustrations and sensitivity analyses are presented to emphasize the model's robustness.

The research indicates that it is more prudent to invest in preservation technology based on its selling price in order to control the rate of deterioration. In addition, the proposed model facilitates the management of deteriorated waste through salvage trading and emission reduction investment. The findings validate sustainable practices with a 20.86% increase in profit and a 21.4% decrease in CEs, thereby signifying environmental and economic benefits.

The proposed model enhances understanding of the impact of investments in price-based preservation technology and carbon reduction efforts on consumer perceptions of their intention to purchase GPs. Moreover, the study provides valuable insights by identifying important recommendations for policymakers regarding areas that require further investigation. This guideline can help identify both current and unexplored gaps, enabling researchers to direct future research efforts toward producing new products.

The purpose of this study is to analyze the thermo-diffusion process in a semi-infinite nonlocal fiber-reinforced double porous thermoelastic diffusive material with voids (FRDPTDMWV) in light of the fractional-order Lord–Shulman thermo-elasto-diffusion (LSTED) model. By virtue of Eringen’s nonlocal elasticity theory, the governing equations for the considered material are developed. The free surface of the substrate is governed by the inclined mechanical load and thermal and chemical shocks.

With the aid of the normal mode technique, the solutions of the nondimensional coupled governing equations have been obtained.

The expressions of field variables are obtained analytically. By using MATHEMATICA software, various graphical implementations are presented to describe the impacts of angle of inclination, fractional-order and nonlocality parameters. The present model is also validated on the basis of some comparative studies with some preestablished cases.

As observed from the literature survey, many different studies have been carried out by taking into account the deformation analysis in nonlocal double porous thermoelastic material structures and thermo-mechanical interaction in fiber-reinforced medium under fractional-order thermoelasticity theories. However, to the best of the authors’ knowledge, no research emphasizing the thermo-elasto-diffusive interactions in a nonlocal FRDPTDMWV has been carried out. Moreover, the effect of fractional-order LSTED theory on fiber-reinforced thermoelastic diffusive half-space with double porosity has not been illuminated till now, which significantly defines the novelty of the conducted research.

The purpose of this paper is to investigate the behavior of a non-Newtonian nanofluid caused by peristaltic waves along an asymmetric channel. Additionally considered is the production of thermal radiation and activation energy.

The equations of momentum, mass and temperature of Sutterby nanofluids are obtained for long wavelength. By taking into account the velocity, temperature and concentration, the formulation is further finished.

Analyses of the physical variables influencing flow features are represented graphically. The present investigation shows that an enhancement in the temperature ratio parameter results in an increase in both the temperature and concentration. The investigation also shows that the dimensionless reaction rate significantly raises the kinetic energy of the reactant, which permits more particle collisions and as a result, raises the temperature field.

Due to their importance in the treatment of cancer, activation energy and thermal radiation as a route of heat transfer are crucial and exciting phenomena for researchers. So, the cancer cells are killed, and tumors are reduced in size with heat and making hyperthermia therapy a cutting-edge cancer treatment.

This paper explores how the manufacturer’s strategic choice (acquisition or investment) impacts product quality in a supply chain comprising two complementary suppliers and a common manufacturer.

The manufacturer faces six strategic choices to improve product quality: acquiring or investing in the high-capable supplier, the low-capable supplier, or both. As the Stackelberg leader, the manufacturer determines which strategy is adopted, while suppliers are separately responsible for components’ quality and wholesale prices. The authors use game theory and calculate the model with Mathematica.

The authors develop analytical models to analyze how acquisition costs, investment proportions, component importance and quality improvement coefficients influence decision-makers. The results show that the highest quality may not benefit the manufacturer. Investing in or acquiring a low-capable supplier is better than a high-capable supplier under certain conditions. If the gaps between two suppliers’ quality improvement coefficients and the importance of two components are dramatic, the manufacturer should choose an investment strategy.

This study contributes to the complementary supply chain management by comparing two kinds of strategies-acquisition and investment, with a high-capable supplier and a low-capable supplier.

The purpose of this study, thermal radiation and viscous dissipation impacts on double diffusive convection on peristaltic transport of Williamson nanofluid due to induced magnetic field in a tapered channel is examined. The study of propulsion system is on the rise in aerospace research. In spacecraft technology, the propulsion system uses high-temperature heat transmission governed through thermal radiation process. This study will help in assessment of chyme movement in the gastrointestinal tract and also in regulating the intensity of magnetic field of the blood flow during surgery.

The brief mathematical modelling, along with induced magnetic field, of Williamson nanofluid is given. The governing equations are reduced to dimensionless form by using appropriate transformations. Numerical technique is manipulated to solve the highly nonlinear differential equations. The roll of different variables is graphically analyzed in terms of concentration, temperature, volume fraction of nanoparticles, axial-induced magnetic field, magnetic force function, stream functions, pressure rise and pressure gradient.

The key finding from the analysis above can be summed up as follows: the temperature profile decreases and concentration profile increases due to the rising impact of thermal radiation. Brownian motion parameter has a reducing influence on nanoparticle concentration due to massive transfer of nanoparticles from a hot zone to a cool region, which causes a decrease in concentration profile· The pressure rise enhances due to rising values of thermophoresis and thermal Grashof number in retrograde pumping, free pumping and copumping region.

To the best of the authors’ knowledge, a study that integrates double-diffusion convection with thermal radiation, viscous dissipation and induced magnetic field on peristaltic flow of Williamson nanofluid with a channel that is asymmetric has not been carried out so far.

This study aims to explore novel solitary wave solutions of a new (3 + 1)-dimensional nonlocal Boussinesq equation that illustrates nonlinear water dynamics.

The authors use the Painlevé analysis to study its complete integrability in the Painlevé sense.

The Painlevé analysis demonstrates the compatibility condition for the model integrability with the addition of new extra terms.

The phase shifts, phase variables and Hirota’s bilinear algorithm are used to furnish multiple soliton solutions.

The authors also furnish a variety of numerous periodic solutions, kink solutions and singular solutions.

The work formally furnishes algorithms for investigating several physical systems, including plasma physics, optical communications and oceans and seas, among others.

This paper presents an original work using a newly developed Painlevé integrable model, as well as novel and insightful findings.

The purpose of this paper is to investigate a novel approach toward electromagnetic launch.

The field of linear electromagnetic acceleration aims at accelerating macroscopic masses (up to several kg) to speeds in excess of 2 km/s. This can be achieved using accelerators of the railgun type. The innovation of this work lies in the use of multiphase current instead of the classically used quasi-direct current (DC). The approach taken is to work out in a first step the potential performance of such a configuration, for example, by showing that a constant propulsive force can be realized. Next, the necessary changes for the system setup were carefully analyzed. Both the accelerator and the power supply have to be considerably modified with regard to the classical approach.

Thorough analysis of the electromagnetic behavior of the launcher including nonlinear effects lead to an innovative system design which is considered to be the main finding of the work presented here. Moreover, a prototype was build. The preliminary experimental results obtained are in very good agreement with corresponding simulations validating the underlying modeling approach.

For the purpose of this paper, power levels of only 450 kVA are considered. However, this research can be used to design more powerful devices in the future.

While DC powered railguns are modeled very well in a variety of papers, the use of multiphase alternating current is not very well discussed yet. It could be of value for launch scenarios, for which very high speeds are required such as the launch of micro satellites to space.

The purpose of this case study was to complement existing weeding and retention criteria beyond the most used methods in academic libraries and to consider citation counts in the identification of important scholarly works.

Using a small sample of items chosen for withdrawal from a small liberal arts college library, this case study looks at the use of Google Scholar citation counts as a metric for identification of notable monographs in the social sciences and mathematics.

Google Scholar citation counts are a quick indicator of classic, foundational or discursive monographs in a particular field and should be given more consideration in weeding and retention analysis decisions that impact scholarly collections. Higher citation counts can be an indicator of higher circulation counts.

The authors found little indication in the literature that Google Scholar citation counts are being used as a metric for identification of notable works or for retention of monographs in academic libraries.