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This paper aims to introduce a new numerical approach based on the local weak form and the Petrov–Galerkin idea to numerically simulation of a predator–prey system with two-species, two chemicals and an additional chemotactic influence.

In the first proceeding, the space derivatives are discretized by using the direct meshless local Petrov–Galerkin method. This generates a nonlinear algebraic system of equations. The mentioned system is solved by using the Broyden’s method which this technique is not related to compute the Jacobian matrix.

This current work tries to bring forward a trustworthy and flexible numerical algorithm to simulate the system of predator–prey on the nonrectangular geometries.

The proposed numerical results confirm that the numerical procedure has acceptable results for the system of partial differential equations.

This work compares the performance of the three boundary element techniques for solving Helmholtz problems: dual reciprocity, multiple reciprocity and direct interpolation. All techniques transform domain integrals into boundary integrals, despite using different principles to reach this purpose.

Comparisons here performed include the solution of eigenvalue and response by frequency scanning, analyzing many features that are not comprehensively discussed in the literature, as follows: the type of boundary conditions, suitable number of degrees of freedom, modal content, number of primitives in the multiple reciprocity method (MRM) and the requirement of internal interpolation points in techniques that use radial basis functions as dual reciprocity and direct interpolation.

Among the other aspects, this work can conclude that the solution of the eigenvalue and response problems confirmed the reasonable accuracy of the dual reciprocity boundary element method (DRBEM) only for the calculation of the first natural frequencies. Concerning the direct interpolation boundary element method (DIBEM), its interpolation characteristic allows more accessibility for solving more elaborate problems. Despite requiring a greater number of interpolating internal points, the DIBEM has presented higher-quality results for the eigenvalue and response problems. The MRM results were satisfactory in terms of accuracy just for the low range of frequencies; however, the neglected higher-order primitives impact the accuracy of the dynamic response as a whole.

There are safe alternatives for solving engineering stationary dynamic problems using the boundary element method (BEM), but there are no suitable comparisons between these different techniques. This paper presents the particularities and detailed comparisons approaching the accuracy of the three important BEM techniques, aiming at response and frequency evaluation, which are not found in the specialized literature.

Two-dimensional (2D) problems are governed by unsteady anisotropic modified-Helmholtz equation of time–space dependent coefficients are considered. The problems are transformed into a boundary-only integral equation which can be solved numerically using a standard boundary element method (BEM). Some examples are solved to show the validity of the analysis and examine the accuracy of the numerical method.

The 2D problems which are governed by unsteady anisotropic modified-Helmholtz equation of time–space dependent coefficients are solved using a combined BEM and Laplace transform. The time–space dependent coefficient equation is reduced to a time-dependent coefficient equation using an analytical transformation. Then, the time-dependent coefficient equation is Laplace transformed to get a constant coefficient equation, which can be written as a boundary-only integral equation. By utilizing a BEM, this integral equation is solved to find numerical solutions to the problems in the frame of the Laplace transform. These solutions are then inversely transformed numerically to obtain solutions in the original time–space frame.

The main finding of this research is the derivation of a boundary-only integral equation for the solutions of initial-boundary value problems governed by a modified-Helmholtz equation of time–space dependent coefficients for anisotropic functionally graded materials with time-dependent properties.

The originality of the research lies on the time dependency of properties of the functionally graded material under consideration.

The main objective of this paper is to investigate the response of human skin to an intense temperature drop at the surface. In addition, this paper aims to evaluate the efficiency of finite difference and finite volume methods in solving the highly nonlinear form of Pennes’ bioheat equation.

One-dimensional linear and nonlinear forms of Pennes’ bioheat equation with uniform grids were used to study the behavior of human skin. The specific heat capacity, thermal conductivity and blood perfusion rate were assumed to be linear functions of temperature. The nonlinear form of the bioheat equation was solved using the Newton linearization method for the finite difference method and the Picard linearization method for the finite volume method. The algorithms were validated by comparing the results from both methods.

The study demonstrated the capacity of both finite difference and finite volume methods to solve the one-dimensional and highly nonlinear form of the bioheat equation. The investigation of human skin’s thermal behavior indicated that thermal conductivity and blood perfusion rate are the most effective properties in mitigating a surface temperature drop, while specific heat capacity has a lesser impact and can be considered constant.

This paper modeled the transient heat distribution within human skin in a one-dimensional manner, using temperate-dependent physical properties. The nonlinear equation was solved with two numerical methods to ensure the validity of the results, despite the complexity of the formulation. The findings of this study can help in understanding the behavior of human skin under extreme temperature conditions, which can be beneficial in various fields, including medical and engineering.

The aim of this paper is to provide a simple yet accurate and efficient geometric method for thermal homogenization of impregnated and non-impregnated coil winding technologies based on the concept of thermal resistance.

For regular windings, the periodic microscopic cell in the winding space is identified. Also, for irregular windings, the average microscopic cell of the winding is determined. An approximation is used to calculate the thermal resistance of the winding cell. Based on this approximation, the winding insulation is considered as a circular ring around the wire. Mathematical equations are obtained to calculate the equivalent thermal resistance of the cell. The equivalent thermal conductivity of the winding is calculated using equivalent thermal resistance of the cell. Winding thermal homogenization is completed by determining the equivalent thermal properties of the cell.

The thermal pattern of different windings is simulated and compared with the results of different homogenization methods. The results show that the proposed method is applicable for a wide range of windings in terms of winding scheme, packing factor and winding insulation. Also, the results show that the proposed method is more accurate than other winding homogenization methods in calculating the equivalent thermal conductivity of the winding.

In this paper, the change of electrical resistance of the winding with temperature and thermal contact between the sub-components are ignored. Also, liquid insulators, such as oils, and rectangular wires were not investigated. Research in these topics is considered as future work.

Unlike other homogenization methods, the proposed method can be applied to non-impregnated and irregular windings. Also, compared to other homogenization methods, the proposed method has a simpler formulation that makes it easier to program and implement. All of these indicate the efficiency of the proposed method in the thermal analysis of the winding.

Traditional studies in the sociology of science have highlighted the self-organized character of the academic community. This article focuses on recent interrelated changes that alter that distinctive governance structure and its related patterns of competition and cooperation. The changes that we identify here are contractualization and large-scale cooperative research. We use different data sources to exemplify these new patterns and discuss the illustrative role of research clusters in German academia. Research clusters as funded by the German Research Foundation (DFG) are both a highly prestigious scarce good in the competition for reputation and resources and a means of fostering cooperation. Our analysis of this German example reveals that this new institutional configuration of universities as organizations, academic researchers, and the state has a profound effect on organizational practices. We discuss the implications of our empirical findings with regard to collegiality in academia. Ultimately, we anticipate a further weakening of collegial bonds, not only because universities and the state have become more active in shaping the nature of academic competition and cooperation but also because of the increasing strategic and individualistic orientation of academic researchers. In the final section, we summarize our findings and address the need for further research and an international comparative perspective.

This paper aims to overcome the lack of methodologies for optimizing the volume of bulky low-frequency inductors that the authors came across with when working on the design of hybrid active power filters. Sound work was published concerning this well-known technology, but it became evident that the mentioned optimization topic was left unaddressed.

Using the Lagrange multipliers optimization method combined with the electromagnetic laws of inductor design, it was possible to establish a new design method to determine the optimal solutions that fulfil any given scenario of specifications. In other words, it is now possible to obtain the inductor’s geometric and electric parameters that not only satisfy the system’s electromagnetic requirements but also lead to smaller, lighter or economical solutions.

A generalized set of equations was obtained to facilitate the calculations of all the inductor-building parameters. As expected, these equations take as inputs the inductor’s required inductance, its maximum current and the desired resistance, but also a customizable cost function. The later cost function will optimize the inductor’s volumes of copper and iron and can be settled, among other purposes, for minimizing the total weight, volume or cost.

All the mathematical expressions to obtain the general optimal solutions are given as well as practical graphics for the three above-mentioned optimization criteria. Using these charts, the reader will be able to obtain by simple inspection the optimal solutions for a large, generalized universe of intended specifications.

The study aims to show the influence of selected mechanical parameters of the rotor on the maximum speed and parameters of the electric motor.

A simplified mechanical analysis of the rotor of the electric motor was conducted, determining the safety factor of the motor. An analysis of the impact of key rotor parameters (significant from the mechanical strength perspective) on the electromagnetic parameters and the safety factor of the selected high-speed electric motor was carried out. The influence of changes in the rotor’s geometrical dimensions (centrifugal force) on the electromagnetic parameters of the electric motor was shown.

The study shows the impact of changes in selected rotor parameters on electromagnetic parameters and the safety factor of a high-speed electric motor (at its required operating point of 45,000 rpm). The dependence of the safety factor as a function of the maximum motor speed was determined for the proposed rotor modifications.

The proposed modifications can be used in larger drive systems. They have practically no impact on increasing the value of the motor’s moment of inertia (they do not degrade the dynamics of the motor’s operation).

It was proposed to use a new design coefficient which is in relation to the motor’s safety coefficient. It has been shown that a minimal modification of the motor rotor allows to increase its maximum speed by several dozen per cent (while maintaining the safety factor). It has also been shown that when operating at maximum speed within the safe range, the change in the geometrical dimensions of the rotor hardly influences the change in the value of the centrifugal force.

The monetary policy implementation and corporate investment are closely intertwined. The aim of modern monetary policy is to mitigate economic fluctuations and stabilise economic growth. One of the ways of influencing the real economy is influencing the level of investment by enterprises.

This chapter provides evidence on how monetary policy affected corporate investment in Poland between 1Q 2000 and 3Q 2022. We investigate the impact of Polish monetary policy on investment outlays in contexts of high uncertainty.

Using the correlation analysis and the regression model, we show the relation between the monetary policy and the investment outlays of Polish enterprises. We used the least squares method as the most popular in linear model estimation. The evaluation includes model fit, independent variable significance and random component, i.e. constancy of variance, autocorrelation, alignment with normal distribution, along with Fisher–Snedecor test and Breusch–Pagan test.

We find that Polish enterprises are responsive to changes in monetary policy. Hence, the corporate investment level is correlated with the effects of monetary policy (especially with the decision on the central bank's basic interest rate changes). We found evidence that QE policy has a positive impact on Polish investment outlays. The corporate investment in Poland is positively affected by respective monetary policies through Narodowy Bank Polski (NBP) reference rate, inflation, corporate loans, weighted average interest rate on corporate loans.