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Bounds on the growth of energy for particles on the torus with unbounded time dependent perturbations 环面上粒子能量增长的约束与无限制的时间相关扰动
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-07 DOI: 10.1063/5.0196229
Dario Bambusi
{"title":"Bounds on the growth of energy for particles on the torus with unbounded time dependent perturbations","authors":"Dario Bambusi","doi":"10.1063/5.0196229","DOIUrl":"https://doi.org/10.1063/5.0196229","url":null,"abstract":"We prove a C∞ version of Nekhoroshev theorem for time dependent Hamiltonians in Rd×Td. Precisely, we prove a result showing that for all times the energy of the system is bounded by a constant times ⟨t⟩ɛ. We apply the result to the dynamics of a charged particle in Td subject to a time dependent electromagnetic field.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"85 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Classical solvability to the free boundary problem for a foam drainage equation. II. From the interface to the bottom 泡沫排水方程自由边界问题的经典可解性。II.从界面到底部
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-06 DOI: 10.1063/5.0155457
Atusi Tani, Marie Tani
{"title":"Classical solvability to the free boundary problem for a foam drainage equation. II. From the interface to the bottom","authors":"Atusi Tani, Marie Tani","doi":"10.1063/5.0155457","DOIUrl":"https://doi.org/10.1063/5.0155457","url":null,"abstract":"We study a nonlinear partial differential equation describing the evolution of a foam drainage in one dimensional case which was proposed by Goldfarb et al. in 1988 in order to investigate the flow of liquid through channels (Plateau borders) and nodes (intersections of four channels) between the bubbles, driven by gravity and capillarity. Its mathematical studies so far are mainly restricted within numerical and particular solutions; as for mathematical analysis of it there are only a few. We prove that the free boundary problem for the foam drainage equation in the region below an interface to the bottom in a foam column admits a unique global-in-time classical solution by the standard classical mathematical method, the maximum principle. Moreover, the existence of its steady solution and its stability are shown.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"64 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Classical solvability to the free boundary problem for a foam drainage equation. I. From the top to the interface 泡沫排水方程自由边界问题的经典可解性。I. 从顶部到界面
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-06 DOI: 10.1063/5.0155449
Atusi Tani, Marie Tani
{"title":"Classical solvability to the free boundary problem for a foam drainage equation. I. From the top to the interface","authors":"Atusi Tani, Marie Tani","doi":"10.1063/5.0155449","DOIUrl":"https://doi.org/10.1063/5.0155449","url":null,"abstract":"We study a nonlinear partial differential equation describing the evolution of a foam drainage in one dimensional case which was proposed by Goldfarb et al. [Izv. Akad. Nauk SSSR Mekh. Ghidk. Gaza 2, 103–108 (1988)] in order to investigate the flow of liquid through channels (Plateau borders) and nodes (intersections of four channels) between the bubbles, driven by gravity and capillarity. Its mathematical studies so far are mainly restricted within numerical and particular solutions; as for mathematical analysis of it there are only a few. We prove that the free boundary problem for the foam drainage equation in the region from the top to the interface in a foam column admits a unique global-in-time classical solution by the standard classical mathematical method, the maximum principle and the comparison theorem. Moreover, the existence of its steady solution and its stability are discussed.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"23 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Next-order correction to the Dirac exchange energy of the free electron gas in the thermodynamic limit and generalized gradient approximations 热力学极限和广义梯度近似中自由电子气体的狄拉克交换能的下阶修正
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-06 DOI: 10.1063/5.0152359
Thiago Carvalho Corso, Gero Friesecke
{"title":"Next-order correction to the Dirac exchange energy of the free electron gas in the thermodynamic limit and generalized gradient approximations","authors":"Thiago Carvalho Corso, Gero Friesecke","doi":"10.1063/5.0152359","DOIUrl":"https://doi.org/10.1063/5.0152359","url":null,"abstract":"We derive the next order correction to the Dirac exchange energy for the free electron gas in a box with zero boundary conditions in the thermodynamic limit. The correction is of the order of the surface area of the box, and comes from three different contributions: (i) a real-space boundary layer, (ii) a boundary-condition-induced small shift of Fermi momentum and bulk density, and (iii) a long-range electrostatic finite-size correction. Moreover we show that the local density approximation, in addition to capturing the bulk term exactly, also produces a correction of the correct order but not the correct size. Generalized gradient approximation (GGA) corrections are found to be capable of capturing the surface term exactly, provided the gradient enhancement factor satisfies a simple explicit integral constraint. For current GGAs such as B88 and Perdew, Burke and Ernzerhof we find that the new constraint is not satisfied and the size of the surface correction is overestimated by about ten percent. The new constraint might thus be of interest for the design of future exchange functionals.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"539 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniqueness of blowup at singular points for superconductivity problem 超导问题奇点炸裂的唯一性
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-05 DOI: 10.1063/5.0213622
Lili Du, Xu Tang, Cong Wang
{"title":"Uniqueness of blowup at singular points for superconductivity problem","authors":"Lili Du, Xu Tang, Cong Wang","doi":"10.1063/5.0213622","DOIUrl":"https://doi.org/10.1063/5.0213622","url":null,"abstract":"In this paper, we investigate the uniqueness of blowup at singular points of the free boundary in the superconductivity problem. We provide a sufficient condition and demonstrate that this condition can be verified in certain special cases. The proof of the main results in this paper is primarily based on Weiss-type and Monneau-type monotonicity formulas, and is inspired by the recent paper [Chen et al. arXiv: 2204.11426v2 (2022)].","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solutions to a generalized Chern–Simons Higgs model on finite graphs by topological degree 有限图上广义切尔恩-西蒙斯希格斯模型的拓扑度解决方案
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-05 DOI: 10.1063/5.0210421
Songbo Hou, Wenjie Qiao
{"title":"Solutions to a generalized Chern–Simons Higgs model on finite graphs by topological degree","authors":"Songbo Hou, Wenjie Qiao","doi":"10.1063/5.0210421","DOIUrl":"https://doi.org/10.1063/5.0210421","url":null,"abstract":"Consider a finite connected graph denoted as G = (V, E). This study explores a generalized Chern-Simons Higgs model, characterized by the equation Δu=λeu(eu−1)2p+1+f, where Δ denotes the graph Laplacian, λ is a real number, p is a non-negative integer, and f is a function on V. Through the computation of the topological degree, this paper demonstrates the existence of a single solution for the model. Further analysis of the interplay between the topological degree and the critical group of an associated functional reveals the presence of multiple solutions. These findings extend the work of Li et al. [Calc. Var. 63, 81 (2024)] and Chao and Hou [J. Math. Anal. Appl. 519, 126787 (2023)].","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"35 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rigidity on quantum symmetry for a certain class of graph C*-algebras 某类图 C* 结构的量子对称刚性
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-05 DOI: 10.1063/5.0177215
Ujjal Karmakar, Arnab Mandal
{"title":"Rigidity on quantum symmetry for a certain class of graph C*-algebras","authors":"Ujjal Karmakar, Arnab Mandal","doi":"10.1063/5.0177215","DOIUrl":"https://doi.org/10.1063/5.0177215","url":null,"abstract":"Quantum symmetry of graph C*-algebras has been studied, under the consideration of different formulations, in the past few years. It is already known that the compact quantum group (C(S1)∗C(S1)∗⋯∗C(S1)︸|E(Γ)|−times,Δ) [in short, *|E(Γ)|C(S1),Δ] always acts on a graph C*-algebra for a finite, connected, directed graph Γ in the category introduced by Joardar and Mandal, where |E(Γ)| ≔ number of edges in Γ. In this article, we show that for a certain class of graphs including Toeplitz algebra, quantum odd sphere, matrix algebra etc. the quantum symmetry of their associated graph C*-algebras remains *|E(Γ)|C(S1),Δ in the category as mentioned before. More precisely, if a finite, connected, directed graph Γ satisfies the following graph theoretic properties: (i) there does not exist any cycle of length ≥2 (ii) there exists a path of length (|V(Γ)| − 1) which consists all the vertices, where |V(Γ)| ≔ number of vertices in Γ (iii) given any two vertices (may not be distinct) there exists at most one edge joining them, then the universal object coincides with *|E(Γ)|C(S1),Δ. Furthermore, we have pointed out a few counter examples whenever the above assumptions are violated.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"47 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global asymptotic stability in a two-dimensional chemotaxis model arising from tumor invasion 肿瘤侵袭引起的二维趋化模型的全局渐近稳定性
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-05 DOI: 10.1063/5.0145255
Chun Wu
{"title":"Global asymptotic stability in a two-dimensional chemotaxis model arising from tumor invasion","authors":"Chun Wu","doi":"10.1063/5.0145255","DOIUrl":"https://doi.org/10.1063/5.0145255","url":null,"abstract":"This paper considers the chemotaxis model with density-suppressed motility: ut = ∇·(φ(v)∇u) + ∇·(ψ(v)u∇v) + f(u), vt = Δv + wz, wt = −wz, wt = −wz, zt = Δz − z + u, x ∈ Ω, t > 0 under homogeneous Neumann boundary conditions in a smooth bounded domain Ω⊂R2. Given that the positive motility function φ(v) has the lower-upper bound, we can conclude that the system possesses a unique bounded classical solution. Moreover, it is proved that the global bounded solution (u, v, w, z) will converge to r/μ1α−1,v̄0+w̄0,0,r/μ1α−1 as t → ∞.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"64 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Improved regularity criteria for the MHD equations 改进的多流体力学方程正则准则
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-01 DOI: 10.1063/5.0179393
Weihua Wang, Shixia Xu
{"title":"Improved regularity criteria for the MHD equations","authors":"Weihua Wang, Shixia Xu","doi":"10.1063/5.0179393","DOIUrl":"https://doi.org/10.1063/5.0179393","url":null,"abstract":"In this paper, we establish new regularity criteria for the three-dimensional (3D) viscous incompressible magnetohydrodynamic (MHD) equations. It is proved that if the solution of the MHD equations satisfies u3∈Lp(0,T;Lq(R3)),j3∈Lr(0,T;Ls(R3)),2p+3q=1324,7213≤q≤∞;2r+3s=2,32<s≤∞ or u3∈Lp(0,T;Lq(R3)),w3∈Lr(0,T;Ls(R3)),2p+3q=1324,7213≤q≤∞;2r+3s=2,32<s≤∞, then the regularity of the solution on (0, T), where u3, j3 and ω3 are the third component of velocity u, current density ∇ × b and vorticity ∇ × u, respectively. These results give new improvements of regularity theory of weak solutions.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"81 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New lower bounds on the radius of spatial analyticity for the higher order nonlinear dispersive equation on the real line 实线上高阶非线性色散方程空间解析性半径的新下限
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-01 DOI: 10.1063/5.0211479
Zaiyun Zhang, Youjun Deng, Xinping Li
{"title":"New lower bounds on the radius of spatial analyticity for the higher order nonlinear dispersive equation on the real line","authors":"Zaiyun Zhang, Youjun Deng, Xinping Li","doi":"10.1063/5.0211479","DOIUrl":"https://doi.org/10.1063/5.0211479","url":null,"abstract":"In this paper, benefited some ideas of Wang [J. Geom. Anal. 33, 18 (2023)] and Dufera et al. [J. Math. Anal. Appl. 509, 126001 (2022)], we investigate persistence of spatial analyticity for solution of the higher order nonlinear dispersive equation with the initial data in modified Gevrey space. More precisely, using the contraction mapping principle, the bilinear estimate as well as approximate conservation law, we establish the persistence of the radius of spatial analyticity till some time δ. Then, given initial data that is analytic with fixed radius σ0, we obtain asymptotic lower bound σ(t)≥c|t|−12, for large time t ≥ δ. This result improves earlier ones in the literatures, such as Zhang et al. [Discrete Contin. Dyn. Syst. B 29, 937–970 (2024)], Huang–Wang [J. Differ. Equations 266, 5278–5317 (2019)], Liu–Wang [Nonlinear Differ. Equations Appl. 29, 57 (2022)], Wang [J. Geom. Anal. 33, 18 (2023)] and Selberg–Tesfahun [Ann. Henri Poincaré 18, 3553–3564 (2017)].","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"219 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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