In this article, we examine the mechanism of cobalt and tantalum nanoparticles through a hybrid fluid model. The nanofluid is propagating through an anisotropically tapered artery with three different configurations: converging, diverging and non-tapered. To examine the rheology of the blood we have incorporated a Williamson fluid model which reveals both Newtonian and non-Newtonian effects. Mathematical and physical formulations are derived using the lubrication approach for continuity, momentum and energy equations. The impact of magnetic field, porosity and viscous dissipation are also taken into the proposed formulation. A perturbation approach is used to determine the solutions of the formulated nonlinear coupled equations. The physical behavior of all the leading parameters is discussed for velocity, temperature, impedance and streamlines profile. The current analysis has the intention to be used in therapeutic treatments of anemia because cobalt promotes the production of red blood cells since it is a component of vitamin B12, this is in addition to having tantalum that is used in the bone implants and in the iodinated agents for blood imaging due to its long circulation time.
{"title":"Scientific breakdown of a ferromagnetic nanofluid in hemodynamics: Enhanced therapeutic approach","authors":"M. M. Bhatti, S. Abdelsalam","doi":"10.1051/mmnp/2022045","DOIUrl":"https://doi.org/10.1051/mmnp/2022045","url":null,"abstract":"In this article, we examine the mechanism of cobalt and tantalum nanoparticles through a hybrid fluid model. The nanofluid is propagating through an anisotropically tapered artery with three different configurations: converging, diverging and non-tapered. To examine the rheology of the blood we have incorporated a Williamson fluid model which reveals both Newtonian and non-Newtonian effects. Mathematical and physical formulations are derived using the lubrication approach for continuity, momentum and energy equations. The impact of magnetic field, porosity and viscous dissipation are also taken into the proposed formulation. A perturbation approach is used to determine the solutions of the formulated nonlinear coupled equations. The physical behavior of all the leading parameters is discussed for velocity, temperature, impedance and streamlines profile. The current analysis has the intention to be used in therapeutic treatments of anemia because cobalt promotes the production of red blood cells since it is a component of vitamin B12, this is in addition to having tantalum that is used in the bone implants and in the iodinated agents for blood imaging due to its long circulation time.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48634895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In Southern Italy, since 2013, there has been an ongoing Olive Quick Decline Syndrome (OQDS) outbreak, due to the bacterium {it Xylella fastidiosa}, which has caused a dramatic impact from both socio-economic and environmental points of view. Current agronomic practices are mainly based on uprooting the sick olive trees and their surrounding ones, with later installment of olive cultivars more resistant to the bacterium infection. Unfortunately, both of these practices are having an undesirable impact on the environment and on the economy. Here, a spatially structured mathematical model has been proposed to include a predator {it Zelus renardii } as a possible biocontrol agent of the {it Xylella} epidemic. The fact that {it Z. renardii} has been reported to be a generalist predator implies that its introduction is not an efficient control strategy to eradicate a {it Xylella} epidemic. Instead, a specialist predator, whenever identified, would lead to the eventual eradication of a {it Xylella} epidemic. In either cases it has been confirmed that a significant reduction of the weed biomass can lead to the eradication of the vector population, hence of a {it Xylella} epidemic, independently of the presence of predators.
{"title":"Predators as a possible strategy for controlling a {it Xylella} epidemic?","authors":"V. Capasso, S. Anita, Simone Scacchi, M. Montagna","doi":"10.1051/mmnp/2022043","DOIUrl":"https://doi.org/10.1051/mmnp/2022043","url":null,"abstract":"In Southern Italy, since 2013, there has been an ongoing Olive\u0000\u0000Quick Decline Syndrome (OQDS) outbreak, due to the bacterium {it\u0000\u0000Xylella fastidiosa},\u0000\u0000 which has caused a dramatic impact from both socio-economic and environmental points of view.\u0000\u0000\u0000\u0000 Current agronomic practices are mainly based on uprooting the sick olive trees and their surrounding ones,\u0000\u0000 with later installment of olive cultivars more resistant to the bacterium infection.\u0000\u0000 Unfortunately, both of these practices are having an undesirable impact on the environment and on the economy.\u0000Here, a spatially structured\u0000\u0000mathematical model has been proposed to include a predator {it Zelus renardii } as a possible biocontrol agent of the {it\u0000\u0000Xylella} epidemic. The fact that {it Z. renardii} has been\u0000\u0000reported to be a generalist predator implies that\u0000\u0000its introduction is not an efficient control strategy to eradicate a\u0000\u0000{it Xylella} epidemic. Instead, a specialist predator, whenever\u0000\u0000identified, would lead to the eventual eradication of a {it\u0000\u0000Xylella} epidemic. In either cases it has been confirmed that a significant\u0000\u0000reduction of the weed biomass can lead to the eradication of\u0000\u0000the vector population, hence of a {it Xylella} epidemic,\u0000\u0000independently of the presence of predators.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48521765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A nonlocal theory for thermoelastic materials with voids based on Mindlin’s strain gradient theory was derived in this paper with some qualitative properties. We have also established the size effect of nonlocal heat conduction with the aids of extended irreversible thermodynamics and generalized free energy. The obtained system of equations is a coupling of three equations with higher gradients terms due to the length scale parameters ϖ and l . This poses some new mathematical difficulties due to the lack of regularity. Based on nonlinear semigroups and the theory of monotone operators, we establish existence and uniqueness of weak and strong solutions to the one dimensional problem. By an approach based on the Gearhart-HerbstPrüss-Huang theorem, we prove that the associated semigroup is exponentially stable; but not analytic.
{"title":"Mathematical modelling in nonlocal Mindlin’s strain gradient thermoelasticity with voids","authors":"M. Aouadi","doi":"10.1051/mmnp/2022042","DOIUrl":"https://doi.org/10.1051/mmnp/2022042","url":null,"abstract":"A nonlocal theory for thermoelastic materials with voids based on Mindlin’s strain gradient theory was derived in this paper with some qualitative properties. We have also established the size effect of nonlocal heat conduction with the aids of extended irreversible thermodynamics and generalized free energy. The obtained system of equations is a coupling of three equations with higher gradients terms due to the length scale parameters ϖ and l . This poses some new mathematical difficulties due to the lack of regularity. Based on nonlinear semigroups and the theory of monotone operators, we establish existence and uniqueness of weak and strong solutions to the one dimensional problem. By an approach based on the Gearhart-HerbstPrüss-Huang theorem, we prove that the associated semigroup is exponentially stable; but not analytic.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44488418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Evgeniy Dats, Sergey Minaev, Vladimir Gubernov, Junnosuke Okajima
The propagation of one and two-dimensional waves of populations are numerically investigated in the framework of the ``predator-prey'' model with the Arditi - Ginzburg trophic function. The propagation of prey and predator population waves and the propagation of co-existing populations' waves are considered. The simulations demonstrate that even in the case of an unstable quasi-equilibrium state of the system, which is established behind the front of a traveling wave, the propagation velocity of the joint population wave is a well-defined function. The calculated average propagation velocity of a cellular non-stationary wave front is determined uniquely for a given set of problem parameters. The estimations of the wave propagation velocity are obtained for both the case of a plane and cellular wave fronts of populations. The structure and velocity of outward propagating circular cellular wave are investigated to clarify the local curvature and scaling effects on the wave dynamics.
{"title":"The normal velocity of the population front in the \"predator-prey\" model","authors":"Evgeniy Dats, Sergey Minaev, Vladimir Gubernov, Junnosuke Okajima","doi":"10.1051/mmnp/2022039","DOIUrl":"https://doi.org/10.1051/mmnp/2022039","url":null,"abstract":"The propagation of one and two-dimensional waves of populations are numerically investigated in the framework of the ``predator-prey'' model with the Arditi - Ginzburg trophic function. The propagation of prey and predator population waves and the propagation of co-existing populations' waves are considered. The simulations demonstrate that even in the case of an unstable quasi-equilibrium state of the system, which is established behind the front of a traveling wave, the propagation velocity of the joint population wave is a well-defined function. The calculated average propagation velocity of a cellular non-stationary wave front is determined uniquely for a given set of problem parameters. The estimations of the wave propagation velocity are obtained for both the case of a plane and cellular wave fronts of populations. The structure and velocity of outward propagating circular cellular wave are investigated to clarify the local curvature and scaling effects on the wave dynamics.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48741916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This research is devoted to Fornasnisi-Marchesini model (FM). More precisely, the investigation of the control problem for the second model discrete-time FM. Random packet dropouts, time delays and quantization are taken into consideration in the feedback control problem simultaneously. Measured signals are quantized before being communicated. A logarithmic quantizer is utilized and quantized signal measurements are handled by a sector bound method. The random packet dropouts are modeled as a Bernoulli process. A control law model which depends on packet dropouts and quantization is formulated. Notably, we lighten the assumptions by using the Schur complement. Besides, both a state feedback controller and an observer-based output feedback controller are designed to ensure corresponding closed-loop systems asymptotically stability. Sufficient conditions on mean square asymptotic stability in terms of LMIs have been obtained. Finally, two numerical example show the feasibility of our theoretical results.
{"title":"Controllability of Delayed Discret Fornasini-Marchesini Model via Quantization and Random Packet Dropouts","authors":"Adnen Adnen","doi":"10.1051/mmnp/2022040","DOIUrl":"https://doi.org/10.1051/mmnp/2022040","url":null,"abstract":"This research is devoted to Fornasnisi-Marchesini model (FM). More precisely, the investigation of the control problem for the second model discrete-time FM. Random packet dropouts, time delays and quantization are taken into consideration in the feedback control problem simultaneously. Measured signals are quantized before being communicated. A logarithmic quantizer is utilized and quantized signal measurements are handled by a sector bound method. The random packet dropouts are modeled as a Bernoulli process. A control law model which depends on packet dropouts and quantization is formulated. Notably, we lighten the assumptions by using the Schur complement. Besides, both a state feedback controller and an observer-based output feedback controller are designed to ensure corresponding closed-loop systems asymptotically stability. Sufficient conditions on mean square asymptotic stability in terms of LMIs have been obtained. Finally, two numerical example show the feasibility of our theoretical results.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48083437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we mainly characterize stochastic bifurcations and tipping phenomena of insect outbreak dynamical systems driven by $alpha$-stable L'evy processes. In one-dimensional insect outbreak model, we find the fixed points representing refuge and outbreak from the bifurcation curves, and carry out a sensitivity analysis with respect to small changes in the model parameters, the stability index and the noise intensity. We perform the numerical simulations of dynamical trajectories using Monte Carlo methods, which contribute to looking at stochastic hysteresis phenomenon. As for two-dimensional insect outbreak system, we identify the global stability properties of fixed points and express the probability density function by the stationary solution of the nonlocal Fokker-Planck equation. Through numerical modelling, the phase portrait makes it possible to detect critical transitions among the stable states. It is then worth describing stochastic bifurcation associated with tipping points induced by noise through a careful examination of the dynamical paths of the insect outbreak system with external forcing. The results give new insight into the sensitivity of ecosystems to realistic environmental changes represented by stochastic perturbations.
{"title":"Stochastic bifurcations and tipping phenomena of insect outbreak systems driven by α-stable Lévy processes","authors":"S. Yuan, Yang Li, Zhigang Zeng","doi":"10.1051/mmnp/2022037","DOIUrl":"https://doi.org/10.1051/mmnp/2022037","url":null,"abstract":"In this work, we mainly characterize stochastic bifurcations and tipping phenomena of insect outbreak dynamical systems driven by $alpha$-stable L'evy processes. In one-dimensional insect outbreak model, we find the fixed points representing refuge and outbreak from the bifurcation curves, and carry out a sensitivity analysis with respect to small changes in the model parameters, the stability index and the noise intensity. We perform the numerical simulations of dynamical trajectories using Monte Carlo methods, which contribute to looking at stochastic hysteresis phenomenon. As for two-dimensional insect outbreak system, we identify the global stability properties of fixed points and express the probability density function by the stationary solution of the nonlocal Fokker-Planck equation. Through numerical modelling, the phase portrait makes it possible to detect critical transitions among the stable states. It is then worth describing stochastic bifurcation associated with tipping points induced by noise through a careful examination of the dynamical paths of the insect outbreak system with external forcing. The results give new insight into the sensitivity of ecosystems to realistic environmental changes represented by stochastic perturbations.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41259543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Radiation is known to cause genetic damage to highly proliferative cells such as cancer cells. However, the radiotherapy effects to bone cells is not completely known. In this work we present a mathematical modeling framework to test hypotheses related to the radiation-induced effects on bone metastasis. Thus, we pose an optimal control problem based on a Komarova model describing the interactions between cancer cells and bone cells at a single site of bone remodeling. The radiotherapy treatment is included in the form of a functional which minimizes the use of radiation using a penalty function. Moreover, we are interested to model the 'on' and the 'off' time states of the radiation schedules; so we propose an optimal control problem with a L1-type objective functional. Bang-bang or singular arc solutions are the obtained optimal control solutions. We characterize both solutions types and explicitly give necessary optimality conditions for them. We present numerical simulations to analyze the different possible radiation effects on the bone and cancer cells. We also evaluate the more significant parameters to shift from a bang-bang solution to a singular arc solution and vice versa. Additionally, we study a fractionated radiotherapy model.
{"title":"Optimal control for a bone metastasis with radiotherapy model using a linear objective functional","authors":"Ariel Camacho, Enrique Diaz-Ocampo, S. Jerez","doi":"10.1051/mmnp/2022038","DOIUrl":"https://doi.org/10.1051/mmnp/2022038","url":null,"abstract":"Radiation is known to cause genetic damage to highly proliferative cells such as cancer cells. However, the radiotherapy effects to bone cells is not completely known. In this work we present a mathematical modeling framework to test hypotheses related to the radiation-induced effects on bone metastasis. Thus, we pose an optimal control problem based on a Komarova model describing the interactions between cancer cells and bone cells at a single site of bone remodeling. The radiotherapy treatment is included in the form of a functional which minimizes the use of radiation using a penalty function. Moreover, we are interested to model the 'on' and the 'off' time states of the radiation schedules; so we propose an optimal control problem with a L1-type objective functional.\u0000\u0000Bang-bang or singular arc solutions are the obtained optimal control solutions. We characterize both solutions types and explicitly give necessary optimality conditions for them. We present numerical simulations to analyze the different possible radiation effects on the bone and cancer cells. We also evaluate the more significant parameters to shift from a bang-bang solution to a singular arc solution and vice versa. Additionally, we study a fractionated radiotherapy model.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47394342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
There are several phenomena in nature governed by simultaneous or intermittent diffusion and advection processes. Many of these systems are networked by their own nature. Here we propose a degree-biased advection processes to undirected networks. For that purpose we define and study the degree-biased advection operator. We then develop a degree-biased advection-diffusion equation on networks and study its general properties. We give computational evidence of the utility of this new model by studying random graphs as well as a real-life patched landscape network in southern Madagascar. In the last case we show that the foraging movement of the species L. catta in this environment occurs mainly in a diffusive way with important contributions of advective motions in agreement with previous empirical observations.
{"title":"DEGREE-BIASED ADVECTION-DIFFUSION ON UNDIRECTED GRAPHS/NETWORKS","authors":"E. Estrada, Manuel Miranda","doi":"10.1051/mmnp/2022034","DOIUrl":"https://doi.org/10.1051/mmnp/2022034","url":null,"abstract":"There are several phenomena in nature governed by simultaneous or intermittent diffusion and advection processes. Many of these systems are networked by their own nature. Here we propose a degree-biased advection processes to undirected networks. For that purpose we define and study the degree-biased advection operator. We then develop a degree-biased advection-diffusion equation on networks and study its general properties. We give computational evidence of the utility of this new model by studying random graphs as well as a real-life patched landscape network in southern Madagascar. In the last case we show that the foraging movement of the species L. catta in this environment occurs mainly in a diffusive way with important contributions of advective motions in agreement with previous empirical observations.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46166069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Paulo Jorge dos Santos Pinto Rebelo, Silvério Simões Rosa, César Augusto Simões Teixeira Marques da Silva
An ecological system comprehended by a pest and its natural enemy, the predator, is considered. Parameters of system are time dependent in order to accompany their variations associated to climate evolutions. Combining the use of pesticides and of extra supply of food to predators, we propose the eradication of pest through optimal control having those two measures as controls. Is established that the resulting problem has a unique solution. Uniqueness is obtained on the whole interval using a recursive argument. The usefulness of model to tackle the pest population is backed by numerical simulation results.
{"title":"Modelling optimal pest control of non-autonomous predator-prey interaction","authors":"Paulo Jorge dos Santos Pinto Rebelo, Silvério Simões Rosa, César Augusto Simões Teixeira Marques da Silva","doi":"10.1051/mmnp/2022033","DOIUrl":"https://doi.org/10.1051/mmnp/2022033","url":null,"abstract":"An ecological system comprehended by a pest and its natural enemy, the predator, is considered. Parameters of system are time dependent in order to accompany their variations associated to climate evolutions. Combining the use of pesticides and of extra supply of food to predators, we propose the eradication of pest through optimal control having those two measures as controls. Is established that the resulting problem has a unique solution. Uniqueness is obtained on the whole interval using a recursive argument. The usefulness of model to tackle the pest population is backed by numerical simulation results.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42777637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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