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23 pages, 2384 KB

Open AccessArticle

Investigation of the Gelation Process of a Polymer Composition Based on an Acrylic Polymer

by Inzir Raupov, Tatiana Nosenko, Victoria Grigoreva, Vasiliy Zazulya, Gennadiy Sukhoroslov and Vyacheslav Shkodkin

Gels 2026, 12(3), 204; https://doi.org/10.3390/gels12030204 - 28 Feb 2026

Viewed by 388

Abstract

The aim of this work is to describe the gelation process of a crosslinked polymer composition depending on its flow rate in free space and in pore space. The object of the study is a polymer solution based on partially hydrolyzed polyacrylonitrile and chromium acetate. A team of researchers has proposed a new approach to describing the kinetic viscosity curve of a crosslinked polymer system in a free volume. This approach takes into account oscillatory variations in the structural and mechanical characteristics relative to a smoothly increasing gelation curve. The nonlinear effects are linked to the processes of structural formation and, simultaneously, destruction due to mechanical, thermobaric, and chemical destruction under varying flow conditions. The proposed solution is based on the Verhulst differential equation and tested on five values of shear rates with the addition of correction factors. The article explains the processes of gel formation and the destruction of polymer compounds, and compares the equation of limited growth with the Kenneth Sorbie method, which is employed in the PC-GEL simulator. The limitations of the modern gel invasion model used in the UTCHEM and BPOPE simulator within the porous media (within a narrow gap) are revealed. Full article

(This article belongs to the Special Issue Polymer Gels for Oil Recovery and Industry Applications)

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20 pages, 742 KB

Open AccessArticle

Parameters Determination via Fuzzy Inference Systems for the Logistic Populations Growth Model

by Yuney Gorrin-Ortega, Selene Lilette Cardenas-Maciel, Jorge Antonio Lopez-Renteria and Nohe Ramon Cazarez-Castro

Axioms 2025, 14(1), 36; https://doi.org/10.3390/axioms14010036 - 3 Jan 2025

Cited by 2 | Viewed by 1941

Abstract

This study addresses the fuzzy parameters (coefficient) determination for the logistic population growth model, proposing a novel methodology based on fuzzy logic concepts. Population dynamics are often modeled using differential equations whose parameters represent critical ecological information, where the parameters determination is a problem itself. Unlike those approaches, the proposed methodology leverages ecosystem variables as inputs to a fuzzy inference system, which then generates fuzzy coefficients that better capture the inherent uncertainties in population dynamics. The approach was tested on a case study involving marine fish populations, where the fuzzy coefficients for growth rate and carrying capacity were calculated and integrated into the logistic model. The results illustrate that the fuzzy model with the proposed coefficients provide a robust framework for modeling population growth, preserving the increasing trajectory of the population under different scenarios. This method allows for the incorporation of expert knowledge and linguistic variables into the model, offering a more flexible and accurate representation of real-world ecosystems. The study concludes that this methodology significantly enhances the model’s applicability and predictive power, particularly in situations where precise data are not available. Full article

(This article belongs to the Special Issue Advances in Dynamical Systems and Control)

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15 pages, 744 KB

Open AccessArticle

Differential Equations and Applications to COVID-19

by Tierry Mitonsou Hounkonnou and Laure Gouba

Mathematics 2024, 12(17), 2738; https://doi.org/10.3390/math12172738 - 2 Sep 2024

Viewed by 2485

Abstract

This paper focuses on the application of the Verhulst logistic equation to model in retrospect the total COVID-19 cases in Senegal during the period from April 2022 to April 2023. Our predictions for April 2023 are compared with the real COVID-19 data for April 2023 to assess the accuracy of the model. The data analysis is conducted using Python programming language, which allows for efficient data processing and prediction generation. Full article

(This article belongs to the Special Issue Functional Differential Equations and Epidemiological Modelling, 2nd Edition)

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9 pages, 320 KB

Open AccessArticle

Using Physics-Informed Neural Networks (PINNs) for Tumor Cell Growth Modeling

by José Alberto Rodrigues

Mathematics 2024, 12(8), 1195; https://doi.org/10.3390/math12081195 - 16 Apr 2024

Cited by 18 | Viewed by 6018

Abstract

This paper presents a comprehensive investigation into the applicability and performance of two prominent growth models, namely, the Verhulst model and the Montroll model, in the context of modeling tumor cell growth dynamics. Leveraging the power of Physics-Informed Neural Networks (PINNs), we aim to assess and compare the predictive capabilities of these models against experimental data obtained from the growth patterns of tumor cells. We employed a dataset comprising detailed measurements of tumor cell growth to train and evaluate the Verhulst and Montroll models. By integrating PINNs, we not only account for experimental noise but also embed physical insights into the learning process, enabling the models to capture the underlying mechanisms governing tumor cell growth. Our findings reveal the strengths and limitations of each growth model in accurately representing tumor cell proliferation dynamics. Furthermore, the study sheds light on the impact of incorporating physics-informed constraints on the model predictions. The insights gained from this comparative analysis contribute to advancing our understanding of growth models and their applications in predicting complex biological phenomena, particularly in the realm of tumor cell proliferation. Full article

(This article belongs to the Special Issue Network Biology and Machine Learning in Bioinformatics)

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14 pages, 292 KB

Open AccessArticle

A Unified Grey Riccati Model

by Ming-Feng Yeh, Ming-Hung Chang and Ching-Chuan Luo

Axioms 2022, 11(8), 364; https://doi.org/10.3390/axioms11080364 - 26 Jul 2022

Viewed by 1862

Abstract

The grey Riccati model (GRM) is a generalization of the grey Verhulst model (GVM). Both the GRM and GVM generally perform well in simulating and forecasting the raw sequences with a bell-shaped or single peak feature. Although there are several methods to solve the Riccati differential equation, the existing time response functions of the GRM are generally complicated. In order to reduce the computational complexity of the time response function, this study attempts to transform the Riccati equation into a Bernoulli equation with the help of a known particular solution. Then, a unified time response function of the GRM is obtained by the proposed methodology. The simulation results demonstrate that the proposed unified grey Riccati model performs the same as the grey generalized Verhulst model (a kind of grey Riccati model) and is better than the traditional grey Verhulst model. The fact also reveals that the newly developed grey Riccati model is reasonable and effective. Full article

15 pages, 4053 KB

Open AccessArticle

The Verhulst-Like Equations: Integrable OΔE and ODE with Chaotic Behavior

by Igor Andrianov, Galina Starushenko, Sergey Kvitka and Lelya Khajiyeva

Symmetry 2019, 11(12), 1446; https://doi.org/10.3390/sym11121446 - 25 Nov 2019

Cited by 7 | Viewed by 4218

Abstract

In this paper, we study various variants of Verhulst-like ordinary differential equations (ODE) and ordinary difference equations (O

Δ

E). Usually Verhulst ODE serves as an example of a deterministic system and discrete logistic equation is a classic example of a simple system [...] Read more.

In this paper, we study various variants of Verhulst-like ordinary differential equations (ODE) and ordinary difference equations (O

Δ

E). Usually Verhulst ODE serves as an example of a deterministic system and discrete logistic equation is a classic example of a simple system with very complicated (chaotic) behavior. In our paper we present examples of deterministic discretization and chaotic continualization. Continualization procedure is based on Padé approximants. To correctly characterize the dynamics of obtained ODE we measured such characteristic parameters of chaotic dynamical systems as the Lyapunov exponents and the Lyapunov dimensions. Discretization and continualization lead to a change in the symmetry of the mathematical model (i.e., group properties of the original ODE and O

Δ

E). This aspect of the problem is the aim of further research. Full article

(This article belongs to the Special Issue Asymptotic Methods in the Mechanics and Nonlinear Dynamics)

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