Pub Date : 2023-09-16DOI: 10.1007/s11587-023-00815-8
Andrea Giacobbe, Carla Perrone
Abstract When a fluid fills an infinite layer between two rigid plates in relative motion, and it is simultaneously subject to a gradient of pressure not parallel to the motion, the base flow is a combination of Couette–Poiseuille in the direction along the boundaries’ relative motion, but it also possess a Poiseuille component in the transverse direction. For this reason the linearised equations include all variables x , y , z , and not only explicitly two variables x , z as it typically happens in the literature. For convenience, we indicate as streamwise the direction of the relative motions of the plates, and spanwise the orthogonal direction. We use Chebyshev collocation method to investigate the monotonic behaviour of the energy along perturbations of general streamwise Couette–Poiseuille plus spanwise Poiseuille base flow, thus obtaining energy-critical Reynolds numbers depending on two parameters. We finally compute the spectrum of the linearisation at such base flows, and hence determine spectrum-critical Reynolds numbers depending on the two parameters. The choice of convex combinations of Couette and Poiseuille flows along the streamwise direction, and spanwise Poiseuille flow, affects the value of the energy-critical Reynolds and wave numbers in interesting ways. Also the spectrum-critical Reynolds and wave numbers depend on the type of base flow in peculiar ways. These dependencies are not described in the literature.
当流体在相对运动的两个刚性板之间的无限层内填充时，同时受到不平行于运动的压力梯度，基流在边界相对运动方向上是库埃-泊泽维尔分量的组合，但在横向上也具有泊泽维尔分量。由于这个原因，线性化方程包括所有变量x, y, z，而不仅仅是像文献中通常发生的那样明确地包含两个变量x, z。为方便起见，我们将两板块相对运动的方向表示为流方向，而将正交方向表示为展向。利用切比雪夫配点法研究了一般沿流库埃-泊泽维尔和沿展向泊泽维尔基流沿扰动的能量单调行为，从而得到了依赖于两个参数的能量临界雷诺数。我们最后计算了这种基流的线性化谱，从而根据这两个参数确定了谱临界雷诺数。库埃特流和泊泽维尔流沿流方向和展向泊泽维尔流的凸组合的选择以有趣的方式影响能量临界雷诺数和波数的值。此外，谱临界雷诺数和波数以特殊的方式依赖于基流的类型。这些依赖关系在文献中没有描述。
{"title":"Spectral and Energy–Lyapunov stability of streamwise Couette–Poiseuille and spanwise Poiseuille base flows","authors":"Andrea Giacobbe, Carla Perrone","doi":"10.1007/s11587-023-00815-8","DOIUrl":"https://doi.org/10.1007/s11587-023-00815-8","url":null,"abstract":"Abstract When a fluid fills an infinite layer between two rigid plates in relative motion, and it is simultaneously subject to a gradient of pressure not parallel to the motion, the base flow is a combination of Couette–Poiseuille in the direction along the boundaries’ relative motion, but it also possess a Poiseuille component in the transverse direction. For this reason the linearised equations include all variables x , y , z , and not only explicitly two variables x , z as it typically happens in the literature. For convenience, we indicate as streamwise the direction of the relative motions of the plates, and spanwise the orthogonal direction. We use Chebyshev collocation method to investigate the monotonic behaviour of the energy along perturbations of general streamwise Couette–Poiseuille plus spanwise Poiseuille base flow, thus obtaining energy-critical Reynolds numbers depending on two parameters. We finally compute the spectrum of the linearisation at such base flows, and hence determine spectrum-critical Reynolds numbers depending on the two parameters. The choice of convex combinations of Couette and Poiseuille flows along the streamwise direction, and spanwise Poiseuille flow, affects the value of the energy-critical Reynolds and wave numbers in interesting ways. Also the spectrum-critical Reynolds and wave numbers depend on the type of base flow in peculiar ways. These dependencies are not described in the literature.","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135304632","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}
Pub Date : 2023-09-12DOI: 10.1007/s11587-023-00814-9
G. Gambino, M. C. Lombardo, R. Rizzo, M. Sammartino
Abstract In this paper, we shall study a spatially extended version of the FitzHugh-Nagumo model, where one describes the motion of the species through cross-diffusion. The motivation comes from modeling biological species where reciprocal interaction influences spatial movement. We shall focus our analysis on the excitable regime of the system. In this case, we shall see how cross-diffusion terms can destabilize uniform equilibrium, allowing for the formation of close-to-equilibrium patterns; the species are out-of-phase spatially distributed, namely high concentration areas of one species correspond to a low density of the other (cross-Turing patterns). Moreover, depending on the magnitude of the inhibitor’s cross-diffusion, the pattern’s development can proceed in either case of the inhibitor/activator diffusivity ratio being higher or smaller than unity. This allows for spatial segregation of the species in both cases of short-range activation/long-range inhibition or long-range activation/short-range inhibition.
{"title":"Excitable FitzHugh-Nagumo model with cross-diffusion: long-range activation instabilities","authors":"G. Gambino, M. C. Lombardo, R. Rizzo, M. Sammartino","doi":"10.1007/s11587-023-00814-9","DOIUrl":"https://doi.org/10.1007/s11587-023-00814-9","url":null,"abstract":"Abstract In this paper, we shall study a spatially extended version of the FitzHugh-Nagumo model, where one describes the motion of the species through cross-diffusion. The motivation comes from modeling biological species where reciprocal interaction influences spatial movement. We shall focus our analysis on the excitable regime of the system. In this case, we shall see how cross-diffusion terms can destabilize uniform equilibrium, allowing for the formation of close-to-equilibrium patterns; the species are out-of-phase spatially distributed, namely high concentration areas of one species correspond to a low density of the other (cross-Turing patterns). Moreover, depending on the magnitude of the inhibitor’s cross-diffusion, the pattern’s development can proceed in either case of the inhibitor/activator diffusivity ratio being higher or smaller than unity. This allows for spatial segregation of the species in both cases of short-range activation/long-range inhibition or long-range activation/short-range inhibition.","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135830770","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}
Pub Date : 2023-09-11DOI: 10.1007/s11587-023-00816-7
G. Gambino, M. C. Lombardo, R. Rizzo, M. Sammartino
Abstract In this paper, we shall study the formation of stationary patterns for a reaction-diffusion system in which the FitzHugh-Nagumo (FHN) kinetics, in its excitable regime, is coupled to linear cross-diffusion terms. In (Gambino et al. in Excitable Fitzhugh-Nagumo model with cross-diffusion: long-range activation instabilities, 2023), we proved that the model supports the emergence of cross-Turing patterns, i.e., close-to-equilibrium structures occurring as an effect of cross-diffusion. Here, we shall construct the cross-Turing patterns close to equilibrium on 1-D and 2-D rectangular domains. Through this analysis, we shall show that the species are out-of-phase spatially distributed and derive the amplitude equations that govern the pattern dynamics close to criticality. Moreover, we shall classify the bifurcation in the parameter space, distinguishing between super-and sub-critical transitions. In the final part of the paper, we shall numerically investigate the impact of the cross-diffusion terms on large-amplitude pulse-like solutions existing outside the cross-Turing regime, showing their emergence also in the case of lateral activation and short-range inhibition .
在本文中，我们将研究一个反应扩散系统中FitzHugh-Nagumo (FHN)动力学在其可激区与线性交叉扩散项耦合的平稳模式的形成。在(Gambino et al. In Excitable fitzhuh - nagumo model with cross-diffusion:远程激活不稳定性，2023)中，我们证明了该模型支持交叉图灵模式的出现，即作为交叉扩散的影响而出现的接近平衡结构。在这里，我们将在1-D和2-D矩形域上构造接近平衡的交叉图灵模式。通过这种分析，我们将证明物种是非相空间分布的，并推导出接近临界的控制模式动力学的振幅方程。此外，我们将对参数空间中的分岔进行分类，区分超临界和次临界跃迁。在本文的最后一部分，我们将在数值上研究交叉扩散项对存在于交叉图灵区之外的大振幅脉冲解的影响，表明它们也出现在横向激活和短程抑制的情况下。
{"title":"Excitable FitzHugh-Nagumo model with cross-diffusion: close and far-from-equilibrium coherent structures","authors":"G. Gambino, M. C. Lombardo, R. Rizzo, M. Sammartino","doi":"10.1007/s11587-023-00816-7","DOIUrl":"https://doi.org/10.1007/s11587-023-00816-7","url":null,"abstract":"Abstract In this paper, we shall study the formation of stationary patterns for a reaction-diffusion system in which the FitzHugh-Nagumo (FHN) kinetics, in its excitable regime, is coupled to linear cross-diffusion terms. In (Gambino et al. in Excitable Fitzhugh-Nagumo model with cross-diffusion: long-range activation instabilities, 2023), we proved that the model supports the emergence of cross-Turing patterns, i.e., close-to-equilibrium structures occurring as an effect of cross-diffusion. Here, we shall construct the cross-Turing patterns close to equilibrium on 1-D and 2-D rectangular domains. Through this analysis, we shall show that the species are out-of-phase spatially distributed and derive the amplitude equations that govern the pattern dynamics close to criticality. Moreover, we shall classify the bifurcation in the parameter space, distinguishing between super-and sub-critical transitions. In the final part of the paper, we shall numerically investigate the impact of the cross-diffusion terms on large-amplitude pulse-like solutions existing outside the cross-Turing regime, showing their emergence also in the case of lateral activation and short-range inhibition .","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135935276","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}
Pub Date : 2023-09-11DOI: 10.1007/s11587-023-00812-x
Oleg Zubelevich
{"title":"A note on the Caristi fixed point theorem","authors":"Oleg Zubelevich","doi":"10.1007/s11587-023-00812-x","DOIUrl":"https://doi.org/10.1007/s11587-023-00812-x","url":null,"abstract":"","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135939160","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}
Pub Date : 2023-08-28DOI: 10.1007/s11587-023-00808-7
Coşkun Kuş, K. Karakaya, Caner Tanış, Y. Akdoğan, Sümeyra Sert, Fahreddin Kalkan
{"title":"Compound transmuted family of distributions: properties and applications","authors":"Coşkun Kuş, K. Karakaya, Caner Tanış, Y. Akdoğan, Sümeyra Sert, Fahreddin Kalkan","doi":"10.1007/s11587-023-00808-7","DOIUrl":"https://doi.org/10.1007/s11587-023-00808-7","url":null,"abstract":"","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47464398","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}
Pub Date : 2023-08-28DOI: 10.1007/s11587-023-00811-y
F. Capone, R. De Luca, G. Massa
{"title":"Throughflow effect on bi-disperse convection","authors":"F. Capone, R. De Luca, G. Massa","doi":"10.1007/s11587-023-00811-y","DOIUrl":"https://doi.org/10.1007/s11587-023-00811-y","url":null,"abstract":"","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43927608","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}
Pub Date : 2023-08-22DOI: 10.1007/s11587-023-00807-8
B. Buonomo, A. d’Onofrio
{"title":"The Rionero’s special type of Lyapunov function and its application to a diffusive epidemic model with information","authors":"B. Buonomo, A. d’Onofrio","doi":"10.1007/s11587-023-00807-8","DOIUrl":"https://doi.org/10.1007/s11587-023-00807-8","url":null,"abstract":"","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49007313","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}
Pub Date : 2023-08-11DOI: 10.1007/s11587-023-00799-5
G. Consolo, O. Gomonay, Pierandrea Vergallo
{"title":"Modelling domain-wall orientation in antiferromagnets driven by magnetoelastic interactions and volume variations","authors":"G. Consolo, O. Gomonay, Pierandrea Vergallo","doi":"10.1007/s11587-023-00799-5","DOIUrl":"https://doi.org/10.1007/s11587-023-00799-5","url":null,"abstract":"","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42231801","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}
Pub Date : 2023-08-05DOI: 10.1007/s11587-023-00803-y
Ş. B. Bozkurt Altindağ, I. Milovanovic, E. Milovanovic
{"title":"New upper bounds for graph energy","authors":"Ş. B. Bozkurt Altindağ, I. Milovanovic, E. Milovanovic","doi":"10.1007/s11587-023-00803-y","DOIUrl":"https://doi.org/10.1007/s11587-023-00803-y","url":null,"abstract":"","PeriodicalId":21373,"journal":{"name":"Ricerche di Matematica","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45899096","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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