SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 362-386, April 2024. Abstract. A lubrication model can be used to describe the dynamics of a weakly volatile viscous fluid layer on a hydrophobic substrate. Thin layers of the fluid are unstable to perturbations and break up into slowly evolving interacting droplets. A reduced-order dynamical system is derived from the lubrication model based on the nearest-neighbor droplet interactions in the weak condensation limit. Dynamics for periodic arrays of identical drops and pairwise droplet interactions are investigated, providing insights into the coarsening dynamics of a large droplet system. Weak condensation is shown to be a singular perturbation, fundamentally changing the long-time coarsening dynamics for the droplets and the overall mass of the fluid in two additional regimes of long-time dynamics.
{"title":"Coarsening of Thin Films with Weak Condensation","authors":"Hangjie Ji, Thomas P. Witelski","doi":"10.1137/23m1559336","DOIUrl":"https://doi.org/10.1137/23m1559336","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 362-386, April 2024. <br/> Abstract. A lubrication model can be used to describe the dynamics of a weakly volatile viscous fluid layer on a hydrophobic substrate. Thin layers of the fluid are unstable to perturbations and break up into slowly evolving interacting droplets. A reduced-order dynamical system is derived from the lubrication model based on the nearest-neighbor droplet interactions in the weak condensation limit. Dynamics for periodic arrays of identical drops and pairwise droplet interactions are investigated, providing insights into the coarsening dynamics of a large droplet system. Weak condensation is shown to be a singular perturbation, fundamentally changing the long-time coarsening dynamics for the droplets and the overall mass of the fluid in two additional regimes of long-time dynamics.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140043897","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 338-361, April 2024. Abstract. In this paper, a study is carried out on the spatiotemporal dynamics of a Lengyel–Epstein model describing the chlorite-iodine-malonic-acid (CIMA) reaction with time delay and the Neumann boundary condition in a two-dimensional region. The existences for Turing, Hopf, Turing–Turing, Turing–Hopf, and Bogdanov–Takens bifurcations are derived by analyzing the dispersion relation between eigenvalues and wave numbers. In particular, to study the dynamics around a Turing–Hopf bifurcation singularity, the amplitude equations near a codimension-two bifurcation point are derived by employing the weakly nonlinear analysis method. Different spatiotemporal patterns for the system in parameter space are classified and various patterns identified, including spatially homogeneous periodic solutions, mixed mode, coexistence mode, bistable phenomenon, square, hexagon, black eye, two-phase oscillating staggered hexagon lattice, and other complex spatiotemporal patterns. The theoretical predictions are verified by numerical simulations showing an excellent agreement with many reported experiment results not only in chemistry but also in physics and biology. Results presented in this article reveal the mechanism of generating the spatiotemporal patterns of the CIMA reaction.
{"title":"Spatiotemporal Patterns in a Lengyel–Epstein Model Near a Turing–Hopf Singular Point","authors":"Shuangrui Zhao, Pei Yu, Hongbin Wang","doi":"10.1137/23m1552668","DOIUrl":"https://doi.org/10.1137/23m1552668","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 338-361, April 2024. <br/> Abstract. In this paper, a study is carried out on the spatiotemporal dynamics of a Lengyel–Epstein model describing the chlorite-iodine-malonic-acid (CIMA) reaction with time delay and the Neumann boundary condition in a two-dimensional region. The existences for Turing, Hopf, Turing–Turing, Turing–Hopf, and Bogdanov–Takens bifurcations are derived by analyzing the dispersion relation between eigenvalues and wave numbers. In particular, to study the dynamics around a Turing–Hopf bifurcation singularity, the amplitude equations near a codimension-two bifurcation point are derived by employing the weakly nonlinear analysis method. Different spatiotemporal patterns for the system in parameter space are classified and various patterns identified, including spatially homogeneous periodic solutions, mixed mode, coexistence mode, bistable phenomenon, square, hexagon, black eye, two-phase oscillating staggered hexagon lattice, and other complex spatiotemporal patterns. The theoretical predictions are verified by numerical simulations showing an excellent agreement with many reported experiment results not only in chemistry but also in physics and biology. Results presented in this article reveal the mechanism of generating the spatiotemporal patterns of the CIMA reaction.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140017601","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 317-337, April 2024. Abstract. A method for computing the Riesz [math]-capacity, [math], of a general set [math] is given. The method is based on simulations of isotropic [math]-stable motion paths in [math]-dimensions. The familiar walk-on-spheres method, often utilized for simulating Brownian motion, is modified to a novel walk-in-and-out-of-balls method adapted for modeling the stable path process on the exterior of regions “probed” by this type of generalized random walk. It accounts for the propensity of this class of random walk to jump through boundaries because of the path discontinuity. This method allows for the computationally efficient simulation of hitting locations of stable paths launched from the exterior of probed sets. Reliable methods of computing capacity from these locations are given, along with non-standard confidence intervals. Illustrative calculations are performed for representative types of sets [math], where both [math] and [math] are varied.
{"title":"Computation of Riesz [math]-Capacity [math] of General Sets in [math] Using Stable Random Walks","authors":"John P. Nolan, Debra J. Audus, Jack F. Douglas","doi":"10.1137/23m1568077","DOIUrl":"https://doi.org/10.1137/23m1568077","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 317-337, April 2024. <br/> Abstract. A method for computing the Riesz [math]-capacity, [math], of a general set [math] is given. The method is based on simulations of isotropic [math]-stable motion paths in [math]-dimensions. The familiar walk-on-spheres method, often utilized for simulating Brownian motion, is modified to a novel walk-in-and-out-of-balls method adapted for modeling the stable path process on the exterior of regions “probed” by this type of generalized random walk. It accounts for the propensity of this class of random walk to jump through boundaries because of the path discontinuity. This method allows for the computationally efficient simulation of hitting locations of stable paths launched from the exterior of probed sets. Reliable methods of computing capacity from these locations are given, along with non-standard confidence intervals. Illustrative calculations are performed for representative types of sets [math], where both [math] and [math] are varied.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140007537","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 285-315, February 2024. Abstract. We analyze and quantify the amount of heat generated by a nanoparticle, injected in a background medium, while excited by incident electromagnetic waves. These nanoparticles are dispersive with electric permittivity following the Lorentz model. The purpose is to determine the quantity of heat generated extremely close to the nanoparticle (at a distance proportional to the radius of the nanoparticle). This study extends our previous results, derived in the 2D TM and TE regimes, to the full Maxwell system. We show that by exciting the medium with incident frequencies close to the plasmonic or Dielectric resonant frequencies, we can generate any desired amount of heat close to the injected nanoparticle while the amount of heat decreases away from it. These results offer a wide range of potential applications in the areas of photo-thermal therapy, drug delivery, and material science, to cite a few. To do so, we employ time-domain integral equations and asymptotic analysis techniques to study the corresponding mathematical model for heat generation. This model is given by the heat equation where the body source term comes from the modulus of the electric field generated by the used incident electromagnetic field. Therefore, we first analyze the dominant term of this electric field by studying the full Maxwell scattering problem in the presence of plasmonic or all-dielectric nanoparticles. As a second step, we analyze the propagation of this dominant electric field in the estimation of the heat potential. For both the electromagnetic and parabolic models, the presence of the nanoparticles is translated into the appearance of large scales in the contrasts for the heat-conductivity (for the parabolic model) and the permittivity (for the full Maxwell system) between the nanoparticle and its surroundings.
{"title":"Heat Generation Using Lorentzian Nanoparticles. The Full Maxwell System","authors":"Arpan Mukherjee, Mourad Sini","doi":"10.1137/23m1547597","DOIUrl":"https://doi.org/10.1137/23m1547597","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 285-315, February 2024. <br/> Abstract. We analyze and quantify the amount of heat generated by a nanoparticle, injected in a background medium, while excited by incident electromagnetic waves. These nanoparticles are dispersive with electric permittivity following the Lorentz model. The purpose is to determine the quantity of heat generated extremely close to the nanoparticle (at a distance proportional to the radius of the nanoparticle). This study extends our previous results, derived in the 2D TM and TE regimes, to the full Maxwell system. We show that by exciting the medium with incident frequencies close to the plasmonic or Dielectric resonant frequencies, we can generate any desired amount of heat close to the injected nanoparticle while the amount of heat decreases away from it. These results offer a wide range of potential applications in the areas of photo-thermal therapy, drug delivery, and material science, to cite a few. To do so, we employ time-domain integral equations and asymptotic analysis techniques to study the corresponding mathematical model for heat generation. This model is given by the heat equation where the body source term comes from the modulus of the electric field generated by the used incident electromagnetic field. Therefore, we first analyze the dominant term of this electric field by studying the full Maxwell scattering problem in the presence of plasmonic or all-dielectric nanoparticles. As a second step, we analyze the propagation of this dominant electric field in the estimation of the heat potential. For both the electromagnetic and parabolic models, the presence of the nanoparticles is translated into the appearance of large scales in the contrasts for the heat-conductivity (for the parabolic model) and the permittivity (for the full Maxwell system) between the nanoparticle and its surroundings.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139909629","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 262-284, February 2024. Abstract. In this paper, we develop a general mathematical framework for perfect and approximate hydrodynamic cloaking and shielding of electro-osmotic flow, which is governed by a coupled PDE system via the field-effect electro-osmosis. We first establish the representation formula of the solution of the coupled system using the layer potential techniques. Based on the Fourier series, the perfect hydrodynamic cloaking and shielding conditions are derived for the control region with the cross-sectional shape being an annulus or a confocal ellipses. Then we further propose an optimization scheme for the design of approximate cloaks and shields within general geometries. The well-posedness of the optimization problem is proved. In particular, the conditions that can ensure the occurrence of approximate cloaks and shields for general geometries are also established. Our theoretical findings are validated and supplemented by a variety of numerical results. The results in this paper also provide a mathematical foundation for more complex hydrodynamic cloaking and shielding.
{"title":"A Mathematical Theory of Microscale Hydrodynamic Cloaking and Shielding by Electro-Osmosis","authors":"Hongyu Liu, Zhi-Qiang Miao, Guang-Hui Zheng","doi":"10.1137/23m1554837","DOIUrl":"https://doi.org/10.1137/23m1554837","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 262-284, February 2024. <br/> Abstract. In this paper, we develop a general mathematical framework for perfect and approximate hydrodynamic cloaking and shielding of electro-osmotic flow, which is governed by a coupled PDE system via the field-effect electro-osmosis. We first establish the representation formula of the solution of the coupled system using the layer potential techniques. Based on the Fourier series, the perfect hydrodynamic cloaking and shielding conditions are derived for the control region with the cross-sectional shape being an annulus or a confocal ellipses. Then we further propose an optimization scheme for the design of approximate cloaks and shields within general geometries. The well-posedness of the optimization problem is proved. In particular, the conditions that can ensure the occurrence of approximate cloaks and shields for general geometries are also established. Our theoretical findings are validated and supplemented by a variety of numerical results. The results in this paper also provide a mathematical foundation for more complex hydrodynamic cloaking and shielding.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139771008","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}
Jeffrey Galkowski, Pierre Marchand, Jian Wang, Maciej Zworski
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 246-261, February 2024. Abstract. The scattering phase, defined as [math] where [math] is the (unitary) scattering matrix, is the analogue of the counting function for eigenvalues when dealing with exterior domains and is closely related to Kreĭn’s spectral shift function. We revisit classical results on asymptotics of the scattering phase and point out that it is never monotone in the case of strong trapping of waves. Perhaps more importantly, we provide the first numerical calculations of scattering phases for nonradial scatterers. They show that the asymptotic Weyl law is accurate even at low frequencies and reveal effects of trapping such as lack of monotonicity. This is achieved by using the recent high level multiphysics finite element software FreeFEM.
{"title":"The Scattering Phase: Seen at Last","authors":"Jeffrey Galkowski, Pierre Marchand, Jian Wang, Maciej Zworski","doi":"10.1137/23m1547147","DOIUrl":"https://doi.org/10.1137/23m1547147","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 246-261, February 2024. <br/> Abstract. The scattering phase, defined as [math] where [math] is the (unitary) scattering matrix, is the analogue of the counting function for eigenvalues when dealing with exterior domains and is closely related to Kreĭn’s spectral shift function. We revisit classical results on asymptotics of the scattering phase and point out that it is never monotone in the case of strong trapping of waves. Perhaps more importantly, we provide the first numerical calculations of scattering phases for nonradial scatterers. They show that the asymptotic Weyl law is accurate even at low frequencies and reveal effects of trapping such as lack of monotonicity. This is achieved by using the recent high level multiphysics finite element software FreeFEM.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139771047","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 215-245, February 2024. Abstract. We develop the steady-state regularized 13-moment equations in the linear regime for rarefied gas dynamics with general collision models. For small Knudsen numbers, the model is accurate up to the super-Burnett order, and the resulting system of moment equations is shown to have a symmetric structure. We also propose Onsager boundary conditions for the moment equations that guarantee the stability of the equations. The validity of our model is verified by benchmark examples for the one-dimensional channel flows.
{"title":"Linear Regularized 13-Moment Equations with Onsager Boundary Conditions for General Gas Molecules","authors":"Zhenning Cai, Manuel Torrilhon, Siyao Yang","doi":"10.1137/23m1556472","DOIUrl":"https://doi.org/10.1137/23m1556472","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 215-245, February 2024. <br/> Abstract. We develop the steady-state regularized 13-moment equations in the linear regime for rarefied gas dynamics with general collision models. For small Knudsen numbers, the model is accurate up to the super-Burnett order, and the resulting system of moment equations is shown to have a symmetric structure. We also propose Onsager boundary conditions for the moment equations that guarantee the stability of the equations. The validity of our model is verified by benchmark examples for the one-dimensional channel flows.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139668694","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 189-214, February 2024. Abstract. To overcome some limits of classical neuronal models, we propose a Markovian generalization of the classical model based on Jacobi processes by introducing downwards jumps to describe the activity of a single neuron. The statistical analysis of interspike intervals is performed by studying the first passage times of the proposed Markovian Jacobi process with jumps through a constant boundary. In particular, we characterize its Laplace transform, which is expressed in terms of some generalization of hypergeometric functions that we introduce, and deduce a closed-form expression for its expectation. Our approach, which is original in the context of first-passage-time problems, relies on intertwining relations between the semigroups of the classical Jacobi process and its generalization, which have been recently established in [P. Cheridito et al., J. Ec. Polytech. - Math., 8 (2021), pp. 331–378]. A numerical investigation of the firing rate of the considered neuron is performed for some choices of the involved parameters and of the jump distributions.
{"title":"Jacobi Processes with Jumps as Neuronal Models: A First Passage Time Analysis","authors":"Giuseppe D’Onofrio, Pierre Patie, Laura Sacerdote","doi":"10.1137/22m1516877","DOIUrl":"https://doi.org/10.1137/22m1516877","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 189-214, February 2024. <br/> Abstract. To overcome some limits of classical neuronal models, we propose a Markovian generalization of the classical model based on Jacobi processes by introducing downwards jumps to describe the activity of a single neuron. The statistical analysis of interspike intervals is performed by studying the first passage times of the proposed Markovian Jacobi process with jumps through a constant boundary. In particular, we characterize its Laplace transform, which is expressed in terms of some generalization of hypergeometric functions that we introduce, and deduce a closed-form expression for its expectation. Our approach, which is original in the context of first-passage-time problems, relies on intertwining relations between the semigroups of the classical Jacobi process and its generalization, which have been recently established in [P. Cheridito et al., J. Ec. Polytech. - Math., 8 (2021), pp. 331–378]. A numerical investigation of the firing rate of the considered neuron is performed for some choices of the involved parameters and of the jump distributions.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139668699","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 165-188, February 2024. Abstract. We consider the problem of elastic diffraction tomography, which consists in reconstructing elastic properties (i.e., mass density and elastic Lamé parameters) of a weakly scattering medium from full-field data of scattered waves outside the medium. Elastic diffraction tomography refers to the elastic inverse scattering problem after linearization using a first-order Born approximation. In this paper, we prove the Fourier diffraction theorem, which relates the two-dimensional Fourier transform of scattered waves with the Fourier transform of the scatterer in the three-dimensional spatial Fourier domain. Elastic wave mode separation is performed, which decomposes a wave into five modes. A new two-step inversion process is developed, providing information on the modes first and second on the elastic parameters. Finally, we discuss reconstructions with plane wave excitation experiments for different tomographic setups and with different plane wave excitation frequencies, respectively.
{"title":"An Inversion Scheme for Elastic Diffraction Tomography Based on Mode Separation","authors":"Bochra Mejri, Otmar Scherzer","doi":"10.1137/22m1538909","DOIUrl":"https://doi.org/10.1137/22m1538909","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 165-188, February 2024. <br/> Abstract. We consider the problem of elastic diffraction tomography, which consists in reconstructing elastic properties (i.e., mass density and elastic Lamé parameters) of a weakly scattering medium from full-field data of scattered waves outside the medium. Elastic diffraction tomography refers to the elastic inverse scattering problem after linearization using a first-order Born approximation. In this paper, we prove the Fourier diffraction theorem, which relates the two-dimensional Fourier transform of scattered waves with the Fourier transform of the scatterer in the three-dimensional spatial Fourier domain. Elastic wave mode separation is performed, which decomposes a wave into five modes. A new two-step inversion process is developed, providing information on the modes first and second on the elastic parameters. Finally, we discuss reconstructions with plane wave excitation experiments for different tomographic setups and with different plane wave excitation frequencies, respectively.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139668564","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 114-138, February 2024. Abstract. The mechanism of seed dispersal mutualism is fundamental to understanding vegetation diversity and its conservation. In this study, we propose a stochastic model that extends the classical framework of seed dispersal mutualism to explore the effects of environmental stochasticity on mutualistic interactions between seed dispersers and plants. We first provide a comprehensive picture of the long-term dynamics of seed dispersal mutualism in deterministic and stochastic environments. We then analyze the relationship between stochasticity and the probability and time that seed dispersal mutualism tips between stable states. Additionally, we evaluate the extinction risk of seed dispersal mutualism for different population values and accordingly assign extinction warning levels to these values. The analysis reveals that the impact of environmental stochasticity on tipping phenomena is scenario-dependent but follows some interpretable trends. The probability (resp., time) of tipping towards the extinction state typically increases (resp., decreases) monotonically with noise intensity, while the probability of tipping towards the coexistence state typically peaks at intermediate noise intensity. Noise in animal populations contributes to tipping toward the coexistence state, whereas noise in plant populations slows down the tipping toward the coexistence state. Noise-induced changes in warning levels of initial population values are most pronounced near the boundaries of the basin of attraction, but sufficiently loud noise (especially for plant populations) may alter the risk far from these boundaries. These findings provide a theoretical explanation for the effect of environmental stochasticity on multistability transitions in seed dispersal mutualism and can be utilized to study the interplay between other population systems and environmental stochasticity.
{"title":"Tipping Points in Seed Dispersal Mutualism Driven by Environmental Stochasticity","authors":"Tao Feng, Zhipeng Qiu, Hao Wang","doi":"10.1137/22m1531579","DOIUrl":"https://doi.org/10.1137/22m1531579","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 114-138, February 2024. <br/> Abstract. The mechanism of seed dispersal mutualism is fundamental to understanding vegetation diversity and its conservation. In this study, we propose a stochastic model that extends the classical framework of seed dispersal mutualism to explore the effects of environmental stochasticity on mutualistic interactions between seed dispersers and plants. We first provide a comprehensive picture of the long-term dynamics of seed dispersal mutualism in deterministic and stochastic environments. We then analyze the relationship between stochasticity and the probability and time that seed dispersal mutualism tips between stable states. Additionally, we evaluate the extinction risk of seed dispersal mutualism for different population values and accordingly assign extinction warning levels to these values. The analysis reveals that the impact of environmental stochasticity on tipping phenomena is scenario-dependent but follows some interpretable trends. The probability (resp., time) of tipping towards the extinction state typically increases (resp., decreases) monotonically with noise intensity, while the probability of tipping towards the coexistence state typically peaks at intermediate noise intensity. Noise in animal populations contributes to tipping toward the coexistence state, whereas noise in plant populations slows down the tipping toward the coexistence state. Noise-induced changes in warning levels of initial population values are most pronounced near the boundaries of the basin of attraction, but sufficiently loud noise (especially for plant populations) may alter the risk far from these boundaries. These findings provide a theoretical explanation for the effect of environmental stochasticity on multistability transitions in seed dispersal mutualism and can be utilized to study the interplay between other population systems and environmental stochasticity.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139584171","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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