Transport Phenomena Equations: Modelling and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 11432

Special Issue Editors

Istituto per le Applicazioni del Calcolo “M. Picone” - Consiglio Nazionale delle Ricerche, Napoli, Italy
Interests: mathematical modeling; nonlinear diffusion problems; qualitative analysis and stability
Special Issues, Collections and Topics in MDPI journals
Istituto per le Applicazioni del Calcolo “M. Picone” - Consiglio Nazionale delle Ricerche, 00015 Napoli, Italy
Interests: numerical and statistical methods; stochastic processes

Special Issue Information

Dear Colleagues,

Transport theory has always been an area of wide interest. The term "transport" is often applied to the study of phenomena governing the rates of flow of mass, energy and momentum (or fluid flow). These phenomena are found in a number of combined processes in various fields  as chemical, food, biomedical and environmental sciences.

This Special Issue focuses on Transport Equations research with an emphasis on its recent advancements and its use in various applications.

It will provide state-of-the-art expositions of major advances by theoretical, numerical and experimental studies from a molecular, microscopic, mesoscopic or macroscopic point of view across the spectrum of transport phenomena, from scientific enquiries to practical applications.

This special issue will collect high-quality contributions from leading experts and researchers actively working in the field, reflecting both theoretical/analytical aspects and important recent advances in computational methods and applications. Topics of interest include, but are not limited to:

Models described by partial differential equations and originating from various subjects in population biology, such as physiologically structured equations and bacterial movement;

Inverse problems for such models: parameter estimation and model identification;

Stochastic differential equations and their applications;

Stochastic perturbation of differential models;

Transport in porous media using mass diffusion and different convective flow models such as Darcy and the Brinkman models;

Transport equations with applications to traffic problems;

Dr. Torcicollo Isabella
Dr. Carfora Maria Francesca
Guest Editors

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Keywords

  • Transport Phenomena

  • Heat Transfer
  • Mass Transfer
  • Molecular – microscopic - macroscopic models
  • Model identification

Published Papers (7 papers)

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Research

14 pages, 1569 KiB  
Article
Propagation of Elastic Waves in Homogeneous Media: 2D Numerical Simulation for a Concrete Specimen
by Giuseppe Alì, Francesco Demarco and Carmelo Scuro
Mathematics 2022, 10(15), 2673; https://0-doi-org.brum.beds.ac.uk/10.3390/math10152673 - 29 Jul 2022
Cited by 6 | Viewed by 1204
Abstract
This paper addresses the theoretical foundation of a localization method for crack detection in a concrete sample based on the time of arrival of the elastic wave generated by the crack formation to a group of sensors positioned on the boundary of the [...] Read more.
This paper addresses the theoretical foundation of a localization method for crack detection in a concrete sample based on the time of arrival of the elastic wave generated by the crack formation to a group of sensors positioned on the boundary of the sample. The equations of motion for the elastic waves are carefully presented, including a body force term which accounts for the sudden formation of a crack. Then, a localization method based on the detection of acoustic emissions, and specifically on their arrival times, is described. Finally, a discretization scheme for the 2D equations of elasticity is developed, and some numerical experiments are performed to assess the validity of the method. Full article
(This article belongs to the Special Issue Transport Phenomena Equations: Modelling and Applications)
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11 pages, 720 KiB  
Article
Traveling Band Solutions in a System Modeling Hunting Cooperation
by Maria Francesca Carfora and Isabella Torcicollo
Mathematics 2022, 10(13), 2303; https://0-doi-org.brum.beds.ac.uk/10.3390/math10132303 - 01 Jul 2022
Cited by 1 | Viewed by 1053
Abstract
A classical Lotka–Volterra model with the logistical growth of prey-and-hunting cooperation in the functional response of predators to prey was extended by introducing advection terms, which included the velocities of animals. The effect of velocity on the kinetics of the problem was analyzed. [...] Read more.
A classical Lotka–Volterra model with the logistical growth of prey-and-hunting cooperation in the functional response of predators to prey was extended by introducing advection terms, which included the velocities of animals. The effect of velocity on the kinetics of the problem was analyzed. In order to examine the band behavior of species over time, traveling wave solutions were introduced, and conditions for the coexistence of both populations and/or extinction were found. Numerical simulations illustrating the obtained results were performed. Full article
(This article belongs to the Special Issue Transport Phenomena Equations: Modelling and Applications)
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13 pages, 1070 KiB  
Article
Mathematical Modeling of Recursive Drug Delivery with Diffusion, Equilibrium, and Convection Coupling
by Rosaura Hernandez-Montelongo, Javiera Salazar-Araya, Jacobo Hernandez-Montelongo and Juan Paulo Garcia-Sandoval
Mathematics 2022, 10(13), 2171; https://0-doi-org.brum.beds.ac.uk/10.3390/math10132171 - 22 Jun 2022
Cited by 3 | Viewed by 1630
Abstract
In this work, a mathematical model to describe drug delivery from polymer coatings on implants is proposed. Release predictability is useful for development and understanding of drug release mechanisms from controlled delivery systems. The proposed model considers a unidirectional recursive diffusion process which [...] Read more.
In this work, a mathematical model to describe drug delivery from polymer coatings on implants is proposed. Release predictability is useful for development and understanding of drug release mechanisms from controlled delivery systems. The proposed model considers a unidirectional recursive diffusion process which follows Fick’s second law while considering the convective phenomena from the polymer matrix to the liquid where the drug is delivered and the polymer–liquid drug distribution equilibrium. The resulting model is solved using Laplace transformation for two scenarios: (1) a constant initial condition for a single drug delivery experiment; and (2) a recursive delivery process where the liquid medium is replaced with fresh liquid after a fixed period of time, causing a stepped delivery rate. Finally, the proposed model is validated with experimental data. Full article
(This article belongs to the Special Issue Transport Phenomena Equations: Modelling and Applications)
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11 pages, 270 KiB  
Article
Transport Phenomena in Excitable Systems: Existence of Bounded Solutions and Absorbing Sets
by Monica De Angelis
Mathematics 2022, 10(12), 2041; https://0-doi-org.brum.beds.ac.uk/10.3390/math10122041 - 12 Jun 2022
Cited by 3 | Viewed by 1022
Abstract
In this paper, the transport phenomena of synaptic electric impulses are considered. The FitzHugh–Nagumo and FitzHugh–Rinzel models appear mathematically appropriate for evaluating these scientific issues. Moreover, applications of such models arise in several biophysical phenomena in different fields such as, for instance, biology, [...] Read more.
In this paper, the transport phenomena of synaptic electric impulses are considered. The FitzHugh–Nagumo and FitzHugh–Rinzel models appear mathematically appropriate for evaluating these scientific issues. Moreover, applications of such models arise in several biophysical phenomena in different fields such as, for instance, biology, medicine and electronics, where, by means of nanoscale memristor networks, scientists seek to reproduce the behavior of biological synapses. The present article deals with the properties of the solutions of the FitzHugh–Rinzel system in an attempt to achieve, by means of a suitable “energy function”, conditions ensuring the boundedness and existence of absorbing sets in the phase space. The results obtained depend on several parameters characterizing the system, and, as an example, a concrete case is considered. Full article
(This article belongs to the Special Issue Transport Phenomena Equations: Modelling and Applications)
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15 pages, 318 KiB  
Article
An Evaluation of Propagation of the HIV-Infected Cells via Optimization Problem
by Donatella Granata and Luca Lorenzi
Mathematics 2022, 10(12), 2021; https://0-doi-org.brum.beds.ac.uk/10.3390/math10122021 - 11 Jun 2022
Cited by 2 | Viewed by 1018
Abstract
Mathematical models have the potential to contribute to design and evaluate the infectivity spreading and growth of human immunodeficiency virus (HIV). Providing a better understanding of the dynamics of HIV infection in vivo and the immune system interactions with the virus can improve [...] Read more.
Mathematical models have the potential to contribute to design and evaluate the infectivity spreading and growth of human immunodeficiency virus (HIV). Providing a better understanding of the dynamics of HIV infection in vivo and the immune system interactions with the virus can improve the classification of the infected cells and drive to an early diagnosis of the disease and drug evaluations. We analyze a two-dimensional environment HIV model from a new perspective, in terms of a multi-objective optimization problem, by introducing a linear modeling approach and providing numerical evidence for its suitability by introducing a general Instantaneous Control Algorithm. Full article
(This article belongs to the Special Issue Transport Phenomena Equations: Modelling and Applications)
17 pages, 1862 KiB  
Article
An Agent-Based Interpretation of Leukocyte Chemotaxis in Cancer-on-Chip Experiments
by Gabriella Bretti and Andrea De Gaetano
Mathematics 2022, 10(8), 1338; https://0-doi-org.brum.beds.ac.uk/10.3390/math10081338 - 18 Apr 2022
Cited by 1 | Viewed by 1518
Abstract
The present paper was inspired by recent developments in laboratory experiments within the framework of cancer-on-chip technology, an immune-oncology microfluidic chip aiming at studying the fundamental mechanisms of immunocompetent behavior. We focus on the laboratory setting where cancer is treated with chemotherapy drugs, [...] Read more.
The present paper was inspired by recent developments in laboratory experiments within the framework of cancer-on-chip technology, an immune-oncology microfluidic chip aiming at studying the fundamental mechanisms of immunocompetent behavior. We focus on the laboratory setting where cancer is treated with chemotherapy drugs, and in this case, the effects of the treatment administration hypothesized by biologists are: the absence of migration and proliferation of tumor cells, which are dying; the stimulation of the production of chemical substances (annexin); the migration of leukocytes in the direction of higher concentrations of chemicals. Here, following the physiological hypotheses made by biologists on the phenomena occurring in these experiments, we introduce an agent-based model reproducing the dynamics of two cell populations (agents), i.e., tumor cells and leukocytes living in the microfluidic chip environment. Our model aims at proof of concept, demonstrating that the observations of the biological phenomena can be obtained by the model on the basis of the explicit assumptions made. In this framework, close adherence of the computational model to the biological results, as shown in the section devoted to the first calibration of the model with respect to available observations, is successfully accomplished. Full article
(This article belongs to the Special Issue Transport Phenomena Equations: Modelling and Applications)
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18 pages, 1265 KiB  
Article
Mathematical Modeling of Lymph Node Drainage Function by Neural Network
by Rufina Tretiakova, Alexey Setukha, Rostislav Savinkov, Dmitry Grebennikov and Gennady Bocharov
Mathematics 2021, 9(23), 3093; https://doi.org/10.3390/math9233093 - 30 Nov 2021
Cited by 7 | Viewed by 2146
Abstract
The lymph node (LN) represents a key structural component of the lymphatic system network responsible for the fluid balance in tissues and the immune system functioning. Playing an important role in providing the immune defense of the host organism, LNs can also contribute [...] Read more.
The lymph node (LN) represents a key structural component of the lymphatic system network responsible for the fluid balance in tissues and the immune system functioning. Playing an important role in providing the immune defense of the host organism, LNs can also contribute to the progression of pathological processes, e.g., the spreading of cancer cells. To gain a deeper understanding of the transport function of LNs, experimental approaches are used. Mathematical modeling of the fluid transport through the LN represents a complementary tool for studying the LN functioning under broadly varying physiological conditions. We developed an artificial neural network (NN) model to describe the lymph node drainage function. The NN model predicts the flow characteristics through the LN, including the exchange with the blood vascular systems in relation to the boundary and lymphodynamic conditions, such as the afferent lymph flow, Darcy’s law constants and Starling’s equation parameters. The model is formulated as a feedforward NN with one hidden layer. The NN complements the computational physics-based model of a stationary fluid flow through the LN and the fluid transport across the blood vessel system of the LN. The physical model is specified as a system of boundary integral equations (IEs) equivalent to the original partial differential equations (PDEs; Darcy’s Law and Starling’s equation) formulations. The IE model has been used to generate the training dataset for identifying the NN model architecture and parameters. The computation of the output LN drainage function characteristics (the fluid flow parameters and the exchange with blood) with the trained NN model required about 1000-fold less central processing unit (CPU) time than computationally tracing the flow characteristics of interest with the physics-based IE model. The use of the presented computational models will allow for a more realistic description and prediction of the immune cell circulation, cytokine distribution and drug pharmacokinetics in humans under various health and disease states as well as assisting in the development of artificial LN-on-a-chip technologies. Full article
(This article belongs to the Special Issue Transport Phenomena Equations: Modelling and Applications)
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