This paper concerns the higher-dimensional food chain model with a general logistic source ut = Δu + u(1 − uα−1 − v − w), vt = Δv − ∇·(ξv∇u) + v(1 − vβ−1 + u − w), wt = Δw − ∇·(χw∇v) + w(1 − wγ−1 + v + u) in a smooth bounded domain Ω ⊂ Rn(n ≥ 2) with homogeneous Neumann boundary conditions. It is shown that for some conditions on the logistic degradation rates, this problem possesses a globally defined bounded classical solution.
{"title":"Global boundedness for a food chain model with general logistic source","authors":"Lu Xu, Li Yang, Qiao Xin","doi":"10.1063/5.0151144","DOIUrl":"https://doi.org/10.1063/5.0151144","url":null,"abstract":"This paper concerns the higher-dimensional food chain model with a general logistic source ut = Δu + u(1 − uα−1 − v − w), vt = Δv − ∇·(ξv∇u) + v(1 − vβ−1 + u − w), wt = Δw − ∇·(χw∇v) + w(1 − wγ−1 + v + u) in a smooth bounded domain Ω ⊂ Rn(n ≥ 2) with homogeneous Neumann boundary conditions. It is shown that for some conditions on the logistic degradation rates, this problem possesses a globally defined bounded classical solution.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"42 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80176500","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 paper, we find two different solutions for the self-dual Maxwell–Higgs model coupled with gravitational fields by employing variational methods. One is a local minimizer and the other is the mountain pass solution.
{"title":"Mountain pass solution for the self-dual Einstein–Maxwell–Higgs model on compact surfaces","authors":"Juhee Sohn","doi":"10.1063/5.0151106","DOIUrl":"https://doi.org/10.1063/5.0151106","url":null,"abstract":"In this paper, we find two different solutions for the self-dual Maxwell–Higgs model coupled with gravitational fields by employing variational methods. One is a local minimizer and the other is the mountain pass solution.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"34 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81475878","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}
We generalize Prodan’s construction of radially localized generalized Wannier bases [E. Prodan, J. Math. Phys. 56(11), 113511 (2015)] to gapped quantum systems without time-reversal symmetry, including, in particular, magnetic Schrödinger operators, and we prove some basic properties of such bases. We investigate whether this notion might be relevant to topological transport by considering the explicitly solvable case of the Landau operator.
{"title":"Ultra-generalized Wannier bases: Are they relevant to topological transport?","authors":"Massimo Moscolari, G. Panati","doi":"10.1063/5.0137320","DOIUrl":"https://doi.org/10.1063/5.0137320","url":null,"abstract":"We generalize Prodan’s construction of radially localized generalized Wannier bases [E. Prodan, J. Math. Phys. 56(11), 113511 (2015)] to gapped quantum systems without time-reversal symmetry, including, in particular, magnetic Schrödinger operators, and we prove some basic properties of such bases. We investigate whether this notion might be relevant to topological transport by considering the explicitly solvable case of the Landau operator.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73076019","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}
Neural network-based machine learning is capable of approximating functions in very high dimension with unprecedented efficiency and accuracy. This has opened up many exciting new possibilities, one of which is to use machine learning algorithms to assist multi-scale modeling. In this review, we use three examples to illustrate the process involved in using machine learning in multi-scale modeling: ab initio molecular dynamics, ab initio meso-scale models, such as Landau models and generalized Langevin equation, and hydrodynamic models for non-Newtonian flows.
{"title":"Machine learning-assisted multi-scale modeling","authors":"W. E, H. Lei, Pinchen Xie, Linfeng Zhang","doi":"10.1063/5.0149861","DOIUrl":"https://doi.org/10.1063/5.0149861","url":null,"abstract":"Neural network-based machine learning is capable of approximating functions in very high dimension with unprecedented efficiency and accuracy. This has opened up many exciting new possibilities, one of which is to use machine learning algorithms to assist multi-scale modeling. In this review, we use three examples to illustrate the process involved in using machine learning in multi-scale modeling: ab initio molecular dynamics, ab initio meso-scale models, such as Landau models and generalized Langevin equation, and hydrodynamic models for non-Newtonian flows.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"73 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72944371","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 paper concerns two-dimensional incompressible magnetohydrodynamic (MHD) equations with damping only in the vertical component of velocity equations and horizontal diffusion in magnetic equations. If the magnetic field is not taken into consideration the system is reduced to Euler-like equations with an extra Riesz transform-type term. The global well-posedness of Euler-like equations remains an open problem in the whole plane R2. When coupled with the magnetic field, the global well-posedness and the stability for the MHD system in R2 have yet to be settled too. This paper here focuses on the space domain T×R, with T being a 1D periodic box. We establish the global well-posedness of the 2D anisotropic MHD system. In addition, the algebraic decay rate in the H2-setting has also been obtained. We solve this by decomposing the physical quantity into the horizontal average and its corresponding oscillation portion, establishing strong Poincaré-type inequalities and some anisotropic inequalities and combining the symmetry conditions imposed on the initial data.
{"title":"Global well-posedness and decay of the 2D incompressible MHD equations with horizontal magnetic diffusion","authors":"Hongxia Lin, Heng Zhang, Sen Liu, Qing Sun","doi":"10.1063/5.0155296","DOIUrl":"https://doi.org/10.1063/5.0155296","url":null,"abstract":"This paper concerns two-dimensional incompressible magnetohydrodynamic (MHD) equations with damping only in the vertical component of velocity equations and horizontal diffusion in magnetic equations. If the magnetic field is not taken into consideration the system is reduced to Euler-like equations with an extra Riesz transform-type term. The global well-posedness of Euler-like equations remains an open problem in the whole plane R2. When coupled with the magnetic field, the global well-posedness and the stability for the MHD system in R2 have yet to be settled too. This paper here focuses on the space domain T×R, with T being a 1D periodic box. We establish the global well-posedness of the 2D anisotropic MHD system. In addition, the algebraic decay rate in the H2-setting has also been obtained. We solve this by decomposing the physical quantity into the horizontal average and its corresponding oscillation portion, establishing strong Poincaré-type inequalities and some anisotropic inequalities and combining the symmetry conditions imposed on the initial data.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"86 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88111871","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 work is concerned with a stochastic magnetohydrodynamic (MHD) system in a 3D thin domain. Although the individual solution may be chaotic in fluid dynamics, the stationary measure is essential to capture complex dynamical behaviors in the view of statistics. We first borrow the α-approximation model to derive the stationary measure of the 3D stochastic MHD system. Then, we further prove that the stationary measure of the system converges weakly to the counterpart of the corresponding 2D stochastic MHD system as the thickness of the thin domain tends to zero.
{"title":"Limit stationary measures of the stochastic magnetohydrodynamic system in a 3D thin domain","authors":"Wenhu Zhong, Guanggan Chen, Yuanyuan Zhang","doi":"10.1063/5.0131817","DOIUrl":"https://doi.org/10.1063/5.0131817","url":null,"abstract":"This work is concerned with a stochastic magnetohydrodynamic (MHD) system in a 3D thin domain. Although the individual solution may be chaotic in fluid dynamics, the stationary measure is essential to capture complex dynamical behaviors in the view of statistics. We first borrow the α-approximation model to derive the stationary measure of the 3D stochastic MHD system. Then, we further prove that the stationary measure of the system converges weakly to the counterpart of the corresponding 2D stochastic MHD system as the thickness of the thin domain tends to zero.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"16 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78332135","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}
Pradeep Boggarapu, H. Mejjaoli, Shyam Swarup Mondal, P. Senapati
The (k, a)-generalized wavelet transform is a novel addition to the class of wavelet transforms, which has gained a respectable status in the realm of time-frequency signal analysis within a short period of time. Since the study of time-frequency analysis is both theoretically interesting and practically useful, in this article, we investigated several subjects of time-frequency analysis for the (k, a)-generalized wavelet transform. First, we analyze the concentration of this transform on sets of finite measure. In particular, we prove Donoho–Stark and Benedicks-type uncertainty principles. We prove several versions of Heisenberg-type uncertainty principles for this transformation. Furthermore, involving the reproducing kernel and spectral theories, we investigate the time frequency and study the scalogram for the same wavelet transform. Finally, we provide Shapiro’s mean dispersion type theorems at the end.
{"title":"Time-frequency analysis of (k, a)-generalized wavelet transform and applications","authors":"Pradeep Boggarapu, H. Mejjaoli, Shyam Swarup Mondal, P. Senapati","doi":"10.1063/5.0152806","DOIUrl":"https://doi.org/10.1063/5.0152806","url":null,"abstract":"The (k, a)-generalized wavelet transform is a novel addition to the class of wavelet transforms, which has gained a respectable status in the realm of time-frequency signal analysis within a short period of time. Since the study of time-frequency analysis is both theoretically interesting and practically useful, in this article, we investigated several subjects of time-frequency analysis for the (k, a)-generalized wavelet transform. First, we analyze the concentration of this transform on sets of finite measure. In particular, we prove Donoho–Stark and Benedicks-type uncertainty principles. We prove several versions of Heisenberg-type uncertainty principles for this transformation. Furthermore, involving the reproducing kernel and spectral theories, we investigate the time frequency and study the scalogram for the same wavelet transform. Finally, we provide Shapiro’s mean dispersion type theorems at the end.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"64 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86900455","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 Heisenberg supermagnet model is a supersymmetric system and has a close relationship with the strong electron-correlated Hubbard model. In this paper, the supersymmetric prolongation structure is used to analyze the high order supersymmetric nonlinear equation. The Lax representation is constructed for the prolongation algebra of this equation. The Bäcklund transformation of the supersymmetric nonlinear Schrödinger equation is obtained by simplified calculation.
{"title":"Prolongation structure of supersymmetric nonlinear equation and its Bäcklund transformation","authors":"Yangjie Jia, Sheng-Nan Wang, Ban Maduojie","doi":"10.1063/5.0151842","DOIUrl":"https://doi.org/10.1063/5.0151842","url":null,"abstract":"The Heisenberg supermagnet model is a supersymmetric system and has a close relationship with the strong electron-correlated Hubbard model. In this paper, the supersymmetric prolongation structure is used to analyze the high order supersymmetric nonlinear equation. The Lax representation is constructed for the prolongation algebra of this equation. The Bäcklund transformation of the supersymmetric nonlinear Schrödinger equation is obtained by simplified calculation.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"8 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73818322","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 paper, we are concerned with the integrable decomposition for the (2+1)-dimensional Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy. By utilizing recursive relations and symmetric reductions, we propose that the (n2 − n1 + 1)-flow of the (2+1)-dimensional AKNS hierarchy can be decomposed into the corresponding n1-flow and n2-flow of the (1+1)-dimensional AKNS hierarchy, both in the coupled and reduced cases. As an appropriate generalization, the integrable decompositions for the standard (2+1)-dimensional Heisenberg ferromagnet equation, the standard (2+1)-dimensional modified Heisenberg ferromagnet equation, and their two coupled generalizations are investigated. With no loss of generality, one-soliton solutions and their dynamic projections for the relevant gauge equivalent structures are discussed and illustrated through some figures.
本文研究了(2+1)维ablowitz - kap - newwell - segur (AKNS)层次的可积分解问题。利用递归关系和对称约简，我们提出(2+1)维AKNS层次结构中的(n2−n1 +1)-流可以分解为(1+1)维AKNS层次结构中相应的n1-流和n2-流，无论在耦合情况下还是在约简情况下。作为一种适当的推广，研究了标准(2+1)维Heisenberg铁磁体方程、标准(2+1)维修正Heisenberg铁磁体方程的可积分解及其耦合推广。在不丧失一般性的情况下，讨论了相关规范等效结构的单孤子解及其动态投影，并通过一些图加以说明。
{"title":"Integrable decomposition for the (2+1)-dimensional AKNS hierarchy and its applications","authors":"Xiaoming Zhu","doi":"10.1063/5.0133017","DOIUrl":"https://doi.org/10.1063/5.0133017","url":null,"abstract":"In this paper, we are concerned with the integrable decomposition for the (2+1)-dimensional Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy. By utilizing recursive relations and symmetric reductions, we propose that the (n2 − n1 + 1)-flow of the (2+1)-dimensional AKNS hierarchy can be decomposed into the corresponding n1-flow and n2-flow of the (1+1)-dimensional AKNS hierarchy, both in the coupled and reduced cases. As an appropriate generalization, the integrable decompositions for the standard (2+1)-dimensional Heisenberg ferromagnet equation, the standard (2+1)-dimensional modified Heisenberg ferromagnet equation, and their two coupled generalizations are investigated. With no loss of generality, one-soliton solutions and their dynamic projections for the relevant gauge equivalent structures are discussed and illustrated through some figures.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"111 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80582839","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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