A prey-predator model with prey dependent Holling type-II functional response and a generalist predator exhibits complex dynamics in response to parameter variation. Generalist predators implicitly exploiting multiple food resources reduce predation pressure on their focal prey species that causes it to become more stable compared to a prey-predator system with specialist predator. In the temporal system, bistability and tristability are observed along with various global and local bifurcations. Existence of homogeneous and heterogeneous positive steady state solutions are shown to exist for suitable ranges of parameter values in the spatiotemporal diffusive system. Weakly nonlinear analysis using multi-scale perturbation technique is employed to derive amplitude equation for the stationary patterns near the Turing bifurcation threshold. The analytical results of the amplitude equations are validated using numerical simulations. We also identify bifurcation of multiple stable stationary patch solutions as well as dynamic pattern solution for parameter values in the Turing and Turing-Hopf regions.
{"title":"Analytical detection of stationary Turing pattern in a predator-prey system with generalist predator","authors":"Subrata Dey, M. Banerjee, S. Ghorai","doi":"10.1051/mmnp/2022032","DOIUrl":"https://doi.org/10.1051/mmnp/2022032","url":null,"abstract":"A prey-predator model with prey dependent Holling type-II functional response and a generalist predator exhibits complex dynamics in response to parameter variation. Generalist predators implicitly exploiting multiple food resources reduce predation pressure on their focal prey species that causes it to become more stable compared to a prey-predator system with specialist predator. In the temporal system, bistability and tristability are observed along with various global and local bifurcations. Existence of homogeneous and heterogeneous positive steady state solutions are shown to exist for suitable ranges of parameter values in the spatiotemporal diffusive system. Weakly nonlinear analysis using multi-scale perturbation technique is employed to derive amplitude equation for the stationary patterns near the Turing bifurcation threshold. The analytical results of the amplitude equations are validated using numerical simulations. We also identify bifurcation of multiple stable stationary patch solutions as well as dynamic pattern solution for parameter values in the Turing and Turing-Hopf regions.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48805153","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. Maslovskaya, C. Kuttler, A. Chebotarev, A. Kovtanyuk
The use of external enzymes provides an alternative way of reducing communication in pathogenic bacteria that may lead to the degradation of their signal and the loss of their pathogeneity. The present study considers an optimal control problem for the semilinear reaction-diffusion model of bacterial quorum sensing under the impact of external enzymes. Estimates of the solution of the controlled system are obtained, on the basis of which the solvability of the extremal problem is proved and the necessary optimality conditions of the first-order are derived. A numerical algorithm to find a solution of the optimal control problem is constructed and implemented. The conducted numerical experiments demonstrate an opportunity to build an effective strategy of the enzymes impact for treatment.
{"title":"Optimal multiplicative control of bacterial quorum sensing under external enzyme impact","authors":"A. Maslovskaya, C. Kuttler, A. Chebotarev, A. Kovtanyuk","doi":"10.1051/mmnp/2022031","DOIUrl":"https://doi.org/10.1051/mmnp/2022031","url":null,"abstract":"The use of external enzymes provides an alternative way of reducing communication in pathogenic bacteria that may lead to the degradation of their signal and the loss of their pathogeneity. The present study considers an optimal control problem for the semilinear reaction-diffusion model of bacterial quorum sensing under the impact of external enzymes. Estimates of the solution of the controlled system are obtained, on the basis of which the solvability of the extremal problem is proved and the necessary optimality conditions of the first-order are derived. A numerical algorithm to find a solution of the optimal control problem is constructed and implemented. The conducted numerical experiments demonstrate an opportunity to build an effective strategy of the enzymes impact for treatment.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47182272","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}
The goal of this research is to conduct a theoretical investigation about the effect of the electroosmotic forces on the swimming of sperms throughout the cervical canal. To imitate male semen with self-propulsive spermatozoa, a hyperbolic tangent fluid is used as the base liquid. Swimming sperms move inside a ciliated cervical canal and peristalsis occurs due to the ciliated walls. The perturbation method is used to solve the controlling partial differential set of equations analytically. Due to self-propulsion of swimmers and long wavelength assumption, a creeping flow protocol is used throughout the stream. The stream pattern, velocity distribution, and pressure gradient (above and below the swimming sheet) solutions are produced and displayed with the relevant parameters. The outcomes of this manuscript show that the rheological parameters of hyperbolic tangent fluid are more appropriate to simulate and discuss the motility of cervical fluid. Moreover, the motility of mucus velocity is more applicable for small values of power law index n at the upper swimming sheet of propulsive spermatozoa. In addition, the mucus velocity increases in both region (upper and lower region of swimming sheet) with an increase of the electroosmotic parameter and Helmholtz-Smoluchowski velocity .
{"title":"On Behavioral Response of Ciliated Cervical Canal on the Development of Electroosmotic Forces in Spermatic Fluid","authors":"S. Abdelsalam, A. Z. Zaher","doi":"10.1051/mmnp/2022030","DOIUrl":"https://doi.org/10.1051/mmnp/2022030","url":null,"abstract":"The goal of this research is to conduct a theoretical investigation about the effect of the electroosmotic forces on the swimming of sperms throughout the cervical canal. To imitate male semen with self-propulsive spermatozoa, a hyperbolic tangent fluid is used as the base liquid. Swimming sperms move inside a ciliated cervical canal and peristalsis occurs due to the ciliated walls. The perturbation method is used to solve the controlling partial differential set of equations analytically. Due to self-propulsion of swimmers and long wavelength assumption, a creeping flow protocol is used throughout the stream. The stream pattern, velocity distribution, and pressure gradient (above and below the swimming sheet) solutions are produced and displayed with the relevant parameters. The outcomes of this manuscript show that the rheological parameters of hyperbolic tangent fluid are more appropriate to simulate and discuss the motility of cervical fluid. Moreover, the motility of mucus velocity is more applicable for small values of power law index n at the upper swimming sheet of propulsive spermatozoa. In addition, the mucus velocity increases in both region (upper and lower region of swimming sheet) with an increase of the electroosmotic parameter and Helmholtz-Smoluchowski velocity .","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44625749","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}
Analysis of longitudinal vibration in a nanorod is an important subject in science and engineering due to its vast application in nanotechnology. This paper introduces a port-Hamiltonian formulation for the longitudinal vibrations in a nanorod, which shows that this model is essentially hyperbolic. Furthermore, it investigates the spectral properties of the associated system operator. Standard distributed control and feedback are shown not to be controllable nor stabilizing.
{"title":"Nonlocal longitudinal vibration in a nanorod, a system theoretic analysis","authors":"Hanif Heidari, H. Zwart","doi":"10.1051/mmnp/2022028","DOIUrl":"https://doi.org/10.1051/mmnp/2022028","url":null,"abstract":"Analysis of longitudinal vibration in a nanorod is an important subject in science and engineering due to its vast application in nanotechnology. This paper introduces a port-Hamiltonian formulation for the longitudinal vibrations in a nanorod, which shows that this model is essentially hyperbolic. Furthermore, it investigates the spectral properties of the associated system operator. Standard distributed control and feedback are shown not to be controllable nor stabilizing.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43551718","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}
Ana P. Lemos-Paião, H. Maurer, Cristiana J. Silva, Delfim F. M. Torres
We improve a recent mathematical model for cholera by adding a time delay that represents the time between the instant at which an individual becomes infected and the instant at which he begins to have symptoms of cholera disease. We prove that the delayed cholera model is biologically meaningful and analyze the local asymptotic stability of the equilibrium points for positive time delays. An optimal control problem is proposed and analyzed, where the goal is to obtain optimal treatment strategies, through quarantine, that minimize the number of infective individuals and the bacterial concentration, as well as treatment costs. Necessary optimality conditions are applied to the delayed optimal control problem, with a $L^1$ type cost functional. We show that the delayed cholera model fits better the cholera outbreak that occurred in the Department of Artibonite -- Haiti, from 1 November 2010 to 1 May 2011, than the non delayed model. Considering the data of the cholera outbreak in Haiti, we solve numerically the delayed optimal control problem and propose solutions for the outbreak control and eradication.
{"title":"A SIQRB delayed model for cholera and optimal control treatment","authors":"Ana P. Lemos-Paião, H. Maurer, Cristiana J. Silva, Delfim F. M. Torres","doi":"10.1051/mmnp/2022027","DOIUrl":"https://doi.org/10.1051/mmnp/2022027","url":null,"abstract":"We improve a recent mathematical model for cholera by adding a time delay that represents the time between the instant at which an individual becomes infected and the instant at which he begins to have symptoms of cholera disease. We prove that the delayed cholera model is biologically meaningful and analyze the local asymptotic stability of the equilibrium points for positive time delays. An optimal control problem is proposed and analyzed, where the goal is to obtain optimal treatment strategies, through quarantine, that minimize the number of infective individuals and the bacterial concentration, as well as treatment costs. Necessary optimality conditions are applied to the delayed optimal control problem, with a $L^1$ type cost functional. We show that the delayed cholera model fits better the cholera outbreak that occurred in the Department of Artibonite -- Haiti, from 1 November 2010 to 1 May 2011, than the non delayed model. Considering the data of the cholera outbreak in Haiti, we solve numerically the delayed optimal control problem and propose solutions for the outbreak control and eradication.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44850207","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}
The Sterile Insect Technique (SIT) is a classic vector control method that has been successfully applied to fight against diverse insect plagues since the 1950s . In recent years, this strategy has been used to control mosquito populations, in order to limit the spread of the diseases they transmit. In this paper, we consider a system of reaction-diffusion equations to model the mosquito population and study the effect of the release of sterile mosquito males. Then we propose to analyze the release in a limited area inside a wider area containing natural mosquito population. We are interested in protecting a mosquito free region from invasion by mosquitoes from an exterior domain by controlling the population in a release band at the border between the two regions: we construct a barrier blocking the invasion of mosquitoes from the exterior. We adapt the geometric method of Lewis and Keener in this framework and extend their main result to find relations on the size of the release region and the density of the released sterile males that allow us to block the invasion. Numerical simulations are also performed to illustrate our results.
{"title":"Wave blocking in a bistable system by local introduction of a population~: application to sterile insect techniques on mosquito populations\u0000p, li { white-space: pre-wrap; }","authors":"L. Almeida, J. Estrada, N. Vauchelet","doi":"10.1051/mmnp/2022026","DOIUrl":"https://doi.org/10.1051/mmnp/2022026","url":null,"abstract":"The Sterile Insect Technique (SIT) is a classic vector control method that has been successfully applied to fight against diverse insect plagues since the 1950s . In recent years, this strategy has been used to control mosquito populations, in order to limit the spread of the diseases they transmit. In this paper, we consider a system of reaction-diffusion equations to model the mosquito population and study the effect of the release of sterile mosquito males. Then we propose to analyze the release in a limited area inside a wider area containing natural mosquito population. We are interested in protecting a mosquito free region from invasion by mosquitoes from an exterior domain by controlling the population in a release band at the border between the two regions: we construct a barrier blocking the invasion of mosquitoes from the exterior. We adapt the geometric method of Lewis and Keener in this framework and extend their main result to find relations on the size of the release region and the density of the released sterile males that allow us to block the invasion. Numerical simulations are also performed to illustrate our results.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47675404","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}
The present study signifies the effect of distinct solids on the phase speed and attenuation of Rayleigh surface wave propagating on the boundary of composite porous matrix saturated with fluids. Secular equation depicting propagation of Rayleigh wave is obtained and solved numerically for obtaining phase speed and attenuation coefficient. Two different types of composite materials are considered for numerical study to analyze the effect of solids present in the structure. The study depicts that increase in rigidity of the composite increases the phase speed of the Rayleigh surface wave. Significant effect of the density and bulk modulus of fluid mixture present in the pores is also observed on the phase speed of the wave. The effect of porosity on the phase speed of the Rayleigh wave and the particle motion during the propagation of the wave is also analyzed.
{"title":"The effect of composite material on Rayleigh wave at free surface of composite matrix saturated by fluids.","authors":"A. Arora, N. Bala","doi":"10.1051/mmnp/2022025","DOIUrl":"https://doi.org/10.1051/mmnp/2022025","url":null,"abstract":"The present study signifies the effect of distinct solids on the phase speed and attenuation of Rayleigh surface wave propagating on the boundary of composite porous matrix saturated with fluids. Secular equation depicting propagation of Rayleigh wave is obtained and solved numerically for obtaining phase speed and attenuation coefficient. Two different types of composite materials are considered for numerical study to analyze the effect of solids present in the structure. The study depicts that increase in rigidity of the composite increases the phase speed of the Rayleigh surface wave. Significant effect of the density and bulk modulus of fluid mixture present in the pores is also observed on the phase speed of the wave. The effect of porosity on the phase speed of the Rayleigh wave and the particle motion during the propagation of the wave is also analyzed.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43113476","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}
Blood vessels exhibit highly nonlinear, anisotropic behaviour with numerous mechanical interactions. Since exact modelling of all involved effects would yield a computationally prohibitive procedure, a practical clinical simulation tool needs to account for a minimum threshold of relevant factors. In this study, we analyse needed modelling assumptions for a reliable simulation of the end-to-side anastomosis. The artery wall is modelled in a geometrically exact setting as a pre-stressed fibre-reinforced composite. The study focuses on the sensitivity analysis of post-anastomosis stress fields concerning the modelling assumptions. Toward that end, a set of full-scale finite element simulations is carried out for three sensitivity cases: (i) The post-operational stresses are estimated with and without taking the residual stresses into account. (ii) Different geometries of the cut in the recipient vessel are examined. (iii) The influence of errors in material stiffness identification on the post-operational stress field is estimated. The studied cases (i)---(iii) have shown a substantial impact of the considered modelling assumptions on the predictive capabilities of the simulation. Approaches to more accurate predictions of post-operational stress distribution are outlined, and a quest for more accurate experimental procedures is made. As a by-product, the occurrence of the pseudo-aneurysm is explained.
{"title":"Rational choice of modelling assumptions for simulation of blood vessel end-to-side anastomosis","authors":"I. I. Tagiltsev, D. Parshin, A. Shutov","doi":"10.1051/mmnp/2022022","DOIUrl":"https://doi.org/10.1051/mmnp/2022022","url":null,"abstract":"Blood vessels exhibit highly nonlinear, anisotropic behaviour with numerous mechanical interactions. Since exact modelling of all involved effects would yield a computationally prohibitive procedure, a practical clinical simulation tool needs to account for a minimum threshold of relevant factors. In this study, we analyse needed modelling assumptions for a reliable simulation of the end-to-side anastomosis. The artery wall is modelled in a geometrically exact setting as a pre-stressed fibre-reinforced composite. The study focuses on the sensitivity analysis of post-anastomosis stress fields concerning the modelling assumptions. Toward that end, a set of full-scale finite element simulations is carried out for three sensitivity cases: (i) The post-operational stresses are estimated with and without taking the residual stresses into account. (ii) Different geometries of the cut in the recipient vessel are examined. (iii) The influence of errors in material stiffness identification on the post-operational stress field is estimated. The studied cases (i)---(iii) have shown a substantial impact of the considered modelling assumptions on the predictive capabilities of the simulation. Approaches to more accurate predictions of post-operational stress distribution are outlined, and a quest for more accurate experimental procedures is made. As a by-product, the occurrence of the pseudo-aneurysm is explained.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49185666","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}
Abstract. We consider a class of biological models represented by a system composed of reaction-diffusion PDE coupled with difference equations (renewal equations) in $n$-dimensional space, with nonlocal dispersal terms and implicit time delays. The difference equation generally arises, by means of the method of characteristics, from an age-structured partial differential system. Using upper and lower solutions, we study the existence of monotonic planar traveling wave fronts connecting the extinction state to the uniform positive state. The corresponding minimum wave speed is also obtained. In addition, we investigate the effect of the parameters on this minimum wave speed and we give a detailed analysis of its asymptotic behavior.
{"title":"Mathematical Modelling of Natural Phenomena","authors":"M. Adimy, Abdennasser Chekroun, B. Kazmierczak","doi":"10.1051/mmnp/2022021","DOIUrl":"https://doi.org/10.1051/mmnp/2022021","url":null,"abstract":"Abstract. We consider a class of biological models represented by a system composed of reaction-diffusion PDE coupled with difference equations (renewal equations) in $n$-dimensional space, with nonlocal dispersal terms and implicit time delays. The difference equation generally arises, by means of the method of characteristics, from an age-structured partial differential system. Using upper and lower solutions, we study the existence of monotonic planar traveling wave fronts connecting the extinction state to the uniform positive state. The corresponding minimum wave speed is also obtained. In addition, we investigate the effect of the parameters on this minimum wave speed and we give a detailed analysis of its asymptotic behavior.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45461168","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}
Numerical study is devoted to the spatial transformations of a radially symmetric flow in the liquid, filling a shallow cylindrical cavity covered partially by a solid non-deformable film. The upper part of liquid has a free surface in the center of which a beam of light produces the hot dot. The heating generates a divergent thermocapillary motion along the free surface after that the liquid flows under the immovable solid film. The edge of this film induces the perturbations into the current. At definite values of heat generation these perturbations begin to increase and cause the radial flow symmetry breakdown that visually leads to the origin of the vorticity in azimuthal plane. Three-dimensional calculations have been fulfilled on the base of interfacial hydrodynamics equations using mathematical package “Comsol Multiphysics”. The motion in azimuthal direction becomes more evident with the growth of heating intensity. There is a predominantly radial flow in the region with the free surface. At the same time, the vortices with azimuthal component of velocity are observed under the film. As in experiment, the proportion of free surface area to the covered one determines the number of vortices in azimuthal plane.
{"title":"Structural changes of a radially symmetric thermocapillary flow in the shallow cavity partially covered by a solid film","authors":"V. Demin, M. Petukhov","doi":"10.1051/mmnp/2022019","DOIUrl":"https://doi.org/10.1051/mmnp/2022019","url":null,"abstract":"Numerical study is devoted to the spatial transformations of a radially symmetric flow in the liquid, filling a shallow cylindrical cavity covered partially by a solid non-deformable film. The upper part of liquid has a free surface in the center of which a beam of light produces the hot dot. The heating generates a divergent thermocapillary motion along the free surface after that the liquid flows under the immovable solid film. The edge of this film induces the perturbations into the current. At definite values of heat generation these perturbations begin to increase and cause the radial flow symmetry breakdown that visually leads to the origin of the vorticity in azimuthal plane. Three-dimensional calculations have been fulfilled on the base of interfacial hydrodynamics equations using mathematical package “Comsol Multiphysics”. The motion in azimuthal direction becomes more evident with the growth of heating intensity. There is a predominantly radial flow in the region with the free surface. At the same time, the vortices with azimuthal component of velocity are observed under the film. As in experiment, the proportion of free surface area to the covered one determines the number of vortices in azimuthal plane.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46162963","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：