Differential Equations in Engineering

Goyal, Nupur; Kulczycki, Piotr; Ram, Mangey

doi:10.1201/9781003105145

Cited by 2 publications

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“…Recent studies have used diferential equations to describe a variety of applications, such as [1][2][3][4][5][6][7][8]. Population models, a central topic in many sciences due to their signifcance, study population change over time.…”

Section: Introductionmentioning

confidence: 99%

Predator Interference in a Predator–Prey Model with Mixed Functional and Numerical Responses

Alebraheem

2023

Journal of Mathematics

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Predator interference refers to the competition effect on individuals of the same species through preventing or limiting access to a resource. In this paper, a novel predator–prey model that includes predator interference is considered. In the novel model, a high prey density is taken into consideration by investigating Crowley–Martin as a numerical response, while the growth rate of prey is logistically described and Holling type II is used as a functional response. In contrast to literature, this model has distinct and notable features: predator and prey species have an intraspecific competition, and this model has a numerical response that generalizes several of the commonly utilized depictions of predator interference. The boundedness of the model is proved. Predator interference effects are theoretically and numerically studied in terms of stability, coexistence, and extinction. Theoretical results show that the system has no effect on coexistence or extinction in these types of models. Numerical simulations present two different dynamics with identical results on the theoretical side of model stabilization for both dynamics. Moreover, the numerical simulations show that there is a change from periodic to steady state dynamics as the value of predator interference increases. This means that the coexistence probability of the model increases. The attained results are explained from both a mathematical and an ecological points of view.

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Section: Introductionmentioning

confidence: 99%

Predator Interference in a Predator–Prey Model with Mixed Functional and Numerical Responses

Alebraheem

2023

Journal of Mathematics

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Swirling Capillary Instability of Rivlin–Ericksen Liquid with Heat Transfer and Axial Electric Field

Yadav,

Awasthi,

Kumar

et al. 2024

Physics

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The mutual influences of the electric field, rotation, and heat transmission find applications in controlled drug delivery systems, precise microfluidic manipulation, and advanced materials’ processing techniques due to their ability to tailor fluid behavior and surface morphology with enhanced precision and efficiency. Capillary instability has widespread relevance in various natural and industrial processes, ranging from the breakup of liquid jets and the formation of droplets in inkjet printing to the dynamics of thin liquid films and the behavior of liquid bridges in microgravity environments. This study examines the swirling impact on the instability arising from the capillary effects at the boundary of Rivlin–Ericksen and viscous liquids, influenced by an axial electric field, heat, and mass transmission. Capillary instability arises when the cohesive forces at the interface between two fluids are disrupted by perturbations, leading to the formation of characteristic patterns such as waves or droplets. The influence of gravity and fluid flow velocity is disregarded in the context of capillary instability analyses. The annular region is formed by two cylinders: one containing a viscous fluid and the other a Rivlin–Ericksen viscoelastic fluid. The Rivlin–Ericksen model is pivotal for comprehending the characteristics of viscoelastic fluids, widely utilized in industrial and biological contexts. It precisely characterizes their rheological complexities, encompassing elasticity and viscosity, critical for forecasting flow dynamics in polymer processing, food production, and drug delivery. Moreover, its applications extend to biomedical engineering, offering insights crucial for medical device design and understanding biological phenomena like blood flow. The inside cylinder remains stationary, and the outside cylinder rotates at a steady pace. A numerically analyzed quadratic growth rate is obtained from perturbed equations using potential flow theory and the Rivlin–Ericksen fluid model. The findings demonstrate enhanced stability due to the heat and mass transfer and increased stability from swirling. Notably, the heat transfer stabilizes the interface, while the density ratio and centrifuge number also impact stability. An axial electric field exhibits a dual effect, with certain permittivity and conductivity ratios causing perturbation growth decay or expansion.

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Differential Equations in Engineering

Cited by 2 publications

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Predator Interference in a Predator–Prey Model with Mixed Functional and Numerical Responses

Predator Interference in a Predator–Prey Model with Mixed Functional and Numerical Responses

Swirling Capillary Instability of Rivlin–Ericksen Liquid with Heat Transfer and Axial Electric Field

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