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The aim of this paper is to present the numerical simulation of the population dynamics model with density‐dependent migrations and the Allee effects using the homotopy perturbation method (HPM).

The paper applied HPM and the results obtained by this method are compared to the exact solution. The results show applicability, accuracy and efficiency of HPM in solving the transient non‐linear advection‐diffusion‐reaction equation.

In this study, HPM is applied to solve the model of population dynamics with density‐ dependent migrations and the Allee effects. Numerical approximations show a high degree of accuracy. The numerical results we obtained justify the advantage of this methodology, even in the few terms approximation is accurate. Errors can be made smaller by taking new terms of the iteration formulas.

It is confirmed that the work has not been published in any other journal.

The susceptible-infectious-susceptible (SIS) infectious disease models without spatial heterogeneity have limited applications, and the numerical simulation without considering models’ global existence and uniqueness of classical solutions might converge to an impractical solution. This paper aims to develop a robust and reliable numerical approach to the SIS epidemic model with spatial heterogeneity, which characterizes the horizontal and vertical transmission of the disease.

This study used stability analysis methods from nonlinear dynamics to evaluate the stability of SIS epidemic models. Additionally, the authors applied numerical solution methods from diffusion equations and heat conduction equations in fluid mechanics to infectious disease transmission models with spatial heterogeneity, which can guarantee a robustly stable and highly reliable numerical process. The findings revealed that this interdisciplinary approach not only provides a more comprehensive understanding of the propagation patterns of infectious diseases across various spatial environments but also offers new application directions in the fields of fluid mechanics and heat flow. The results of this study are highly significant for developing effective control strategies against infectious diseases while offering new ideas and methods for related fields of research.

Through theoretical analysis and numerical simulation, the distribution of infected persons in heterogeneous environments is closely related to the location parameters. The finding is suitable for clinical use.

The theoretical analysis of the stability theorem and the threshold dynamics guarantee robust stability and fast convergence of the numerical solution. It opens up a new window for a robust and reliable numerical study.

In this article, the author discusses dynamical behaviors of a prey-predator population model with nonlinear harvesting rate and offers a mathematical analysis of the model.

The design is by using modelization of populations interaction, qualitative theory of ordinary différential equations, bifurcations analysis, invariant center manifolds theory and Dulac's criterion.

The author studies the stability of solutions and the existence of periodic solutions in the model, and proves the existence of some invariant sets and the production of a transcritical together with a saddle-node bifurcation.

The author studies the effects of harvesting on the persistence and extinction properties and its influence in the perspectives of economic views.

The authors considers a predator–prey model with a new nonlinear form of harvesting rate. The author’s intention is to make conceptual adjustments to a well-known predator–prey model in order to incorporate the effects of harvesting.

The original v2-based sectional method assumes that the selected property quantity of particles is uniformly distributed in each section, which makes particle size distribution (PSD) fluctuate dramatically in the entire size range. The number concentration in each section as well as the zeroth moment of PSD also cannot be correctly predicted in case there are not enough sections used in calculation. In order to provide a more appropriate representation of PSD, different approximate models are used to close the conservation equations. The paper aims to discuss these issues.

The uniform distribution of the selected property quantity of particles in each section is not necessarily satisfied. Instead, the distribution is approximated using an expression with an approximation factor. Different models are investigated on recovering the initial size distribution and predicting the time evolution of size distribution as well as the first three moments so that the advantages and disadvantages of each model can be compared.

The approximate model with an approximation factor of 0.8 is capable of predicting the time evolution of the zeroth moment accurately no matter how many sections are used in simulations. The original v2-based model is recommended to calculate the first and second moments as long as the section number is larger than 50, otherwise, the model with an approximation factor of 0.15 would be a preferred choice.

Different approximate models can be used to improve the accuracy of the results supposing we know which moment is of great importance in calculation.

The purpose of this paper is to obtain analytic solutions of the (1+1) and (2+1)‐dimensional dispersive long wave equations by the homotopy analysis and the homotopy Padé methods.

The obtained approximation by using homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series.

The approximation solutions by [m,m] homotopy Padé technique is often independent of auxiliary parameter ℏ and this technique accelerates the convergence of the related series.

In this paper, analytic solutions of the (1+1) and (2+1)‐dimensional dispersive long wave equations are obtained by the homotopy analysis and the homotopy Padé methods. The obtained approximation by using homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by [m,m] homotopy Padé technique are often independent of auxiliary parameter ℏ and this technique accelerates the convergence of the related series.

Estuaries and shallow coastal areas are among the most productive ecosystems in the world, being recognized as important nursery areas for marine fish. The aim of this paper is to provide a comprehensive overview of the causes and consequences of recruitment variability in marine fish, contributing to ecosystem‐based management strategies of estuarine and coastal areas.

The authors conducted a literature review, exploring the role of estuaries as nursery areas for marine fish, and analyzed the connectivity between estuaries and coastal areas, the main processes driving recruitment variability in marine fish during their pelagic (larval) and estuarine residency (juveniles) phases, and how it can be translated into variable coastal stocks.

Recruitment variability in marine fish is still one of the most important issues in marine fisheries ecology. In this paper, the authors demonstrate the potential of several processes for inducing variability in recruitment, including density‐independent mechanisms such as temperature, hydrodynamics, river flow and large‐scale factors, as well as density‐dependent processes, related with food abundance, competition and predation. Lastly, the authors evaluated the connectivity between estuaries and the ocean, and how this relationship can influence coastal stocks in the future. The main findings were analyzed in the context of climate change, which has been demonstrated to influence marine life at the individual, population and ecosystem levels.

This paper is a valuable tool for marine researchers and stakeholders, since it summarizes some of the most important processes that drive recruitment variability in marine fish, and how this information can be used for establishing sustainable ecosystem management programmes.

As in real applications several alternating current (AC) currents may be injected to the electronic devices, this study aims to analyze their effects on the lifetime of the solder joints and, consequently, shed the light on these effects at the design phase for other researchers to consider.

In this paper, the authors investigated on current waveform shapes on the performance and reliability of the solder joints in electronic package. Three common and extensively used current shapes in several simulations and experiments were selected to study their effects on the solder joint performance.

The results demonstrate a sever thermal swing and stress fluctuation in the solder joint induced in the case of triangle current type because the critical states lack any relaxation time. In fact, the stress intensification in the solder under application of the triangle current type has been shown to contribute to increasing brittle intermetallic compounds. An accelerated increase of on-state voltage of power semiconductor was also observed in under application of the triangle current type.

The originality of this paper is confirmed.

The purpose of this paper is to find out the applicability of the many-body dissipative particle dynamics (MDPD) method for various real fluids by specifically focusing on the effects of the MDPD parameters on the MDPD fluid properties.

In this study, the MDPD method based on van der Waals (vdw) equation of state is employed. The simulations are conducted by using LAMMPS with some modifications of the original package to include the many-body features in the simulation. The simulations are investigated in a three-dimensional Cartesian box solution domain in which MDPD particles are distributed. In order to evaluate the MDPD liquid characteristics for a stationary liquid film, self-diffusivity, viscosity, Schmidt number (Sc) and surface tension, are estimated for different MDPD parameters. The parameters are carefully selected based on previous studies. A set of single-droplet simulations is also performed to analyze the droplet characteristics and its behavior on a solid-wall. Besides, the relationship between the characteristic length in the DPD simulations and scaling parameters for the stationary liquid-film case is discussed by employing the Ohnesorge number.

The results show that the liquid properties in the MDPD simulations can be widely ranged by varying the MDPD parameters. The values are highly influenced by the many-body feature in the conservative force which is not included in the original DPD method. It is also found that the wetting ability of the MDPD fluid on solid walls can be easily controlled by changing a many-body parameter. The characteristic length between the MDPD reduced unit and real unit is related for the stationary liquid-film case by employing the Ohnesorge number.

The present parametric study shows that the liquid properties in the MDPD method can vary by carefully controlling the MDPD parameters, which demonstrates the high-potential applicability of the method for various real fluids. This will contribute to research areas in multi-phase transport phenomena at nano and sub-micron scales in, for example, fuel cells, batteries and other engineering devices involving porous media.

This paper aims to provide a comprehensive literature review on modelling electro-osmotic flow in porous media.

Modelling electro-osmosis in fluid systems without solid particles has been first introduced. Then, after a brief description of the existing approaches for porous media modelling, electro-osmotic flow in porous media has been considered by analysing the main contributions to the development of this topic.

The analysis of literature has highlighted the absence of a universal model to analyse electro-osmosis in porous media, whereas many different methods and assumptions are used.

For the first time, the existing approaches for modelling electro-osmotic flow in porous have been collected and analysed to provide detailed indications for future works concerning this topic.

We investigate the competitive consequence of vertical integration on organizational performance using a comprehensive dataset of U.S. motion picture production companies, which includes information on their vertical scope and competitive overlaps. Vertical integration appears to change the dynamics of competition in two ways: (i) it buffers the vertically integrated firms from environmental dependence and (ii) it intensifies competition among non-integrated organizations. In contrast to the existing literature, our results suggest that vertical integration has implications well beyond both the level of the individual transaction and even the internal efficiency of the integrated firm.