Pure and Applied Mathematics Quarterly最新文献

Semi-global controllability of a geometric wave equation 几何波方程的半全局可控性

IF 0.7 4区数学

Pure and Applied Mathematics Quarterly Pub Date : 2024-07-18 DOI: 10.4310/pamq.2024.v20.n4.a9

Joachim Krieger, Shengquan Xiang

引用次数: 0

On tidal energy in Newtonian two-body motion with infinite initial separation 关于牛顿二体运动中无限初始分离的潮汐能

IF 0.7 4区数学

Pure and Applied Mathematics Quarterly Pub Date : 2024-07-18 DOI: 10.4310/pamq.2024.v20.n4.a14

Shuang Miao, Lan Zhang

{"title":"On tidal energy in Newtonian two-body motion with infinite initial separation","authors":"Shuang Miao, Lan Zhang","doi":"10.4310/pamq.2024.v20.n4.a14","DOIUrl":"https://doi.org/10.4310/pamq.2024.v20.n4.a14","url":null,"abstract":"In $href{https://doi.org/10.48550/arXiv.1708.04307}{[8]}$ we have studied the dynamics of tidal energy in Newtonian two-body motion and how it affects the center-of-mass orbit of two identical gravitating fluid bodies. It is shown in $href{https://doi.org/10.48550/arXiv.1708.04307}{[8]}$ that for a class of initial configuration, the tidal energy caused by the deformation of boundaries of two fluid bodies can be made arbitrarily large relative to the positive conserved total energy of the entire system. This reveals the possibility that the center-of-mass orbit, which is unbounded initially, may become bounded during the evolution. This result in $href{https://doi.org/10.48550/arXiv.1708.04307}{[8]}$ is based on a quantitative relation between the tidal energy and the distance of two bodies. However, this relation only holds when the two-body distance are within multiples of the first closest approach, due to the fact that initially the tidal energy vanishes but the two-body distance is finite. In this work, based on the a priori estimates established in $href{https://doi.org/10.48550/arXiv.1708.04307}{[8]}$, we construct a solution to the same two-body problem as in $href{https://doi.org/10.48550/arXiv.1708.04307}{[8]}$ but with infinite initial separation. Therefore the above mentioned quantitative relation holds during the entire evolution up to the first closest approach.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743349","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}

引用次数: 0

Supertranslation invariance of angular momentum at null infinity in double null gauge 双空规中无穷远处角动量的超平移不变性

IF 0.7 4区数学

Pure and Applied Mathematics Quarterly Pub Date : 2024-07-18 DOI: 10.4310/pamq.2024.v20.n4.a5

Po-Ning Chen, Mu-Tao Wang, Ye-Kai Wang, Shing-Tung Yau

引用次数: 0

Null Penrose inequality in a perturbed Schwarzschild spacetime 扰动施瓦兹柴尔德时空中的彭罗斯零不等式

IF 0.7 4区数学

Pure and Applied Mathematics Quarterly Pub Date : 2024-07-18 DOI: 10.4310/pamq.2024.v20.n4.a6

Pengyu Le

{"title":"Null Penrose inequality in a perturbed Schwarzschild spacetime","authors":"Pengyu Le","doi":"10.4310/pamq.2024.v20.n4.a6","DOIUrl":"https://doi.org/10.4310/pamq.2024.v20.n4.a6","url":null,"abstract":"In this paper, we review the proof of the null Penrose inequality in a perturbed Schwarzschild spacetime. The null Penrose inequality conjectures that, on an incoming null hypersurface, the Hawking mass of the outmost marginally trapped surface is not greater than the Bondi mass at past null infinity. An approach to prove the null Penrose inequality is to construct a foliation on the null hypersurface starting from the marginally trapped surface to past null infinity, on which the Hawking mass is monotonically nondecreasing. However to achieve a proof, there arises an obstacle on the asymptotic geometry of the foliation at past null infinity. In order to overcome this obstacle, Christodoulou and Sauter proposed a strategy by varying the hypersurface to search for another null hypersurface where asymptotic geometry of the foliation becomes round. This strategy leads us to study the perturbation of null hypersurfaces systematically. Applying the perturbation theory of null hypersurfaces in a perturbed Schwarzschild spacetime, we carry out the strategy of Christodoulou and Sauter successfully. We find a one-parameter family of null hypersurfaces on which the null Penrose inequality holds. This paper gives a overview of our proof.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"36 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743340","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}

引用次数: 0

On the non-existence of trapped surfaces under low-regularity bounds 论低规则性约束下陷阱曲面的不存在性

IF 0.7 4区数学

Pure and Applied Mathematics Quarterly Pub Date : 2024-07-18 DOI: 10.4310/pamq.2024.v20.n4.a1

Jonathan Luk, Georgios Moschidis

引用次数: 0

Masses at null infinity for Einstein's equations in harmonic coordinates 谐波坐标下爱因斯坦方程空无穷远处的质量

IF 0.7 4区数学

Pure and Applied Mathematics Quarterly Pub Date : 2024-07-18 DOI: 10.4310/pamq.2024.v20.n4.a3

Lili He, Hans Lindblad

引用次数: 0

Gravitational solitons and complete Ricci flat Riemannian manifolds of infinite topological type 引力孤子与无限拓扑类型的完整里奇平坦黎曼流形

IF 0.7 4区数学

Pure and Applied Mathematics Quarterly Pub Date : 2024-07-18 DOI: 10.4310/pamq.2024.v20.n4.a12

Marcus Khuri, Martin Reiris, Gilbert Weinstein, Sumio Yamada

引用次数: 0

Remark on the nonlinear stability of Minkowski spacetime: a rigidity theorem 关于闵科夫斯基时空非线性稳定性的备注：刚性定理

IF 0.7 4区数学

Pure and Applied Mathematics Quarterly Pub Date : 2024-07-18 DOI: 10.4310/pamq.2024.v20.n4.a7

Jin Jia, Pin Yu

引用次数: 0

Derivation of the half-wave maps equation from Calogero–Moser spin systems 从卡洛吉罗-莫泽自旋系统推导半波图方程

IF 0.7 4区数学

Pure and Applied Mathematics Quarterly Pub Date : 2024-07-18 DOI: 10.4310/pamq.2024.v20.n4.a10

Enno Lenzmann, Jérémy Sok

引用次数: 0

Covariant guiding laws for fields 场的协变指导定律

IF 0.7 4区数学

Pure and Applied Mathematics Quarterly Pub Date : 2024-07-18 DOI: 10.4310/pamq.2024.v20.n4.a13

Maaneli Derakhshani, Michael K.-H. Kiessling, A. Shadi Tahvildar-Zadeh

{"title":"Covariant guiding laws for fields","authors":"Maaneli Derakhshani, Michael K.-H. Kiessling, A. Shadi Tahvildar-Zadeh","doi":"10.4310/pamq.2024.v20.n4.a13","DOIUrl":"https://doi.org/10.4310/pamq.2024.v20.n4.a13","url":null,"abstract":"After reviewing the passage from classical Hamilton–Jacobi formulation of non-relativistic point-particle dynamics to the non-relativistic quantum dynamics of point particles whose motion is guided by a wave function that satisfies Schrödinger’s or Pauli’s equation, we study the analogous question for the Lorentz-covariant dynamics of fields on spacelike slices of spacetime. We establish a relationship, between the DeDonder–Weyl–Christodoulou formulation of covariant Hamilton–Jacobi equations for the classical field evolution, and the Lorentz-covariant Dirac-type wave equation proposed by Kanatchikov amended by our proposed guiding equation for such fields. We show that Kanatchikov’s equation is well-posed and generally solvable, and we establish the correspondence between plane-wave solutions of Kanatchikov’s equation and solutions of the covariant Hamilton–Jacobi equations ofDeDonder–Weyl–Christodoulou. We propose a covariant guiding law for the temporal evolution of fields defined on constant time slices of spacetime, and show that it yields, at each spacetime point, the existence of a finite measure on the space of field values at that point that is equivariant with respect to the flow induced by the solution of Kanatchikov’s equation that is guiding the actual field, so long as it is a plane-wave solution. We show that our guiding law is local in the sense of Einstein’s special relativity, and therefore it cannot be used to analyze Bell-type experiments. We conclude by suggesting directions to be explored in future research.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"65 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743348","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}

引用次数: 0