Article
Mathematics
Rongrong Jin, Guangcun Lu
Summary: In this paper, analogues of the Ekeland-Hofer and Hofer-Zehnder symplectic capacities are constructed based on a class of Hamiltonian boundary value problems inspired by Clarke's and Ekeland's work. Generalizations of important results about the original two capacities (such as the famous Weinstein conjecture, representation formula for cEH and cHZ, and a theorem by Evgeni Neduv) are also studied.
JOURNAL OF GEOMETRIC ANALYSIS
(2023)
Article
Mathematics, Applied
Rongrong Jin, Guangcun Lu
Summary: In this paper, we prove representation formulas for the coisotropic Hofer-Zehnder capacities of bounded convex domains with special coisotropic submanifolds and the leaf relation. We also study their estimates and relations with the Hofer-Zehnder capacity, give some interesting corollaries, and obtain corresponding versions of a Brunn-Minkowski type inequality by Artstein-Avidan and Ostrover, as well as a theorem by Evgeni Neduv.
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Michael Khanevsky, Fabian Ziltener
Summary: The article investigates the natural inclusion of the Hamiltonian group on a symplectic manifold, deriving an upper bound based on Hofer norms. This leads to upper bounds on the asymptotic Hofer-Lipschitz constant and the relative Hofer diameter of a subset, typically with the first bound being sharp and the second one being sharp up to a factor of 2.
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
(2022)
Article
Mathematics, Applied
Kun Shi, Guangcun Lu
Summary: Inspired by Pazit Haim-Kislev's work on Ekeland-Hofer-Zehnder capacities, we have derived corresponding formulas for psi-Ekeland-Hofer-Zehnder and coisotropic Ekeland-Hofer-Zehnder capacities of convex polytopes. Additionally, we have shown that the coisotropic Hofer-Zehnder capacities exhibit superadditivity for specific hyperplane cuts in two-dimensional convex domains, contrary to previous results.
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
(2021)
Article
Mathematics
Simon Allais
Summary: We extend Shelukhin's proof of the homology version of the Hofer-Zehnder conjecture to weighted projective spaces, which are symplectic orbifolds. In particular, we show that if the number of fixed points, counted with their isotropy order as multiplicity, of a non-degenerate Hamiltonian diffeomorphism in such a space is larger than the minimum possible value, then there are infinitely many periodic points.
COMPOSITIO MATHEMATICA
(2023)
Article
Mathematics
Simon Allais
Summary: In this study, we use generating function techniques to deduce a proof in CPd of the homological generalization of Franks theorem due to Shelukhin. This result proves the Hofer-Zehnder conjecture in the nondegenerate case.
INTERNATIONAL JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics
Xianzhe Dai, Yihan Li
Summary: In this paper, we investigate the behavior of the spectral flow of a one-parameter family {Ds} of Dirac operators acting on a twisted spinor bundle S with a vector bundle E. The study focuses on the asymptotic behavior of the spectral flow when the parameter s belongs to the interval [0,r] and r is sufficiently large. Our method involves the variation of eta invariant and local index theory technique, with a key step being the establishment of a uniform estimate of the eta invariant (eta) over bar (D-r) using local index theory technique and heat kernel estimate.
MATHEMATISCHE ZEITSCHRIFT
(2023)
Article
Environmental Sciences
Yi Lin, Siyuan Liu, Lei Yan, Kai Yan, Yelu Zeng, Bin Yang
Summary: Directional area scattering factor (DASF) is a critical parameter for vegetation monitoring. The current method to estimate DASF has biases due to neglecting variations in biochemical constituents. This study proposes a new approach that accounts for variations in concentrations and improves DASF estimation.
REMOTE SENSING OF ENVIRONMENT
(2023)
Article
Chemistry, Physical
Hang Zhang, Zhiyu Wang, Huagen Li, Manohar Salla, Yuxi Song, Songpeng Huang, Shiqiang Huang, Xun Wang, Kaipeng Liu, Guoqiang Xu, Jigang Huang, Cheng-Wei Qu, Qing Wang
Summary: This research demonstrates a low-cost continuous electricity generator that converts diurnal temperature variation into electricity using a charging-free thermally regenerative electrochemical cycle (TREC) and graphene as a bifunctional solar absorber and radiative cooler. The TREC system achieves a thermoelectric efficiency of 19.91% relative to Carnot efficiency, almost five times higher than the highest reported efficiency of charging-free TRECs, and a maximum power density exceeding ten times the best reported charging-free TRECs. The rooftop demonstration shows its practical capability for self-power supply at both daytime and night with significantly enhanced power density compared to other thermoelectric generators at night.
Article
Engineering, Geological
Xiaoyu Chen, Dongsheng Wang
Summary: A new automatic baseline correction method based on the Hilbert spectral analysis is proposed to recover accurate baseline offset, permanent displacement, and stable peak ground motion displacement from raw ground motion records. The method eliminates the need for selecting the start time of strong motion and can extract complex frequency changes in the baseline offset time histories.
SOIL DYNAMICS AND EARTHQUAKE ENGINEERING
(2022)
Article
Physics, Multidisciplinary
Ying Liu, Ranming Niu, Andrzej Majchrowski, Krystian Roleder, Kumara Cordero-Edwards, Julie M. Cairney, Jordi Arbiol, Gustau Catalan
Summary: Using aberration-corrected scanning transmission electron microscopy, we observed the coexistence of the antiferroelectric and ferrielectric phases in PbZrO3. The ferrielectric phase, with a dipole arrangement of 4,14, appears as translational boundaries at room temperature. The dual nature of the ferrielectric phase poses symmetry constraints on its growth, which are overcome by the sideways motion of boundaries forming stripe domains within the antiferroelectric matrix.
PHYSICAL REVIEW LETTERS
(2023)
Article
Mathematics
Jacopo De Simoi, Vadim Kaloshin, Martin Leguil
Summary: This passage discusses billiards obtained by removing finitely many strictly convex analytic obstacles from the plane, satisfying the non-eclipse condition. The dynamics restricted to the set of non-escaping orbits is conjugated to a subshift, which naturally labels periodic orbits. We demonstrate that under suitable symmetry and genericity assumptions, the Marked Length Spectrum determines the geometry of the billiard table.
INVENTIONES MATHEMATICAE
(2023)
Article
Construction & Building Technology
Bingji Lan, Haoxiang He, Shan Wu, Yifei Chen, Shitao Cheng
Summary: This paper introduces the local toggle-brace-damper system (LTBDS) and its extended form, the local toggle energy dissipation device (LTEDD). These systems can improve the energy dissipation efficiency by amplifying the deformation of the damper, and a geometric optimization method is proposed to improve their amplification capacity. The LTBDS and LTEDD overcome the issues of parameter dependence, limited characterization, and large space requirements in existing systems.
JOURNAL OF BUILDING ENGINEERING
(2022)
Article
Physics, Multidisciplinary
Yang Wang, Pingyu Zhu, Shichuan Xue, Yingwen Liu, Junjie Wu, Xuejun Yang, Ping Xu
Summary: In this experiment, a high-spectral-purity single-photon source is engineered using a single-interferometer-coupled silicon microring. By adjusting the interferometer, different coupling conditions are achieved, leading to different quality factors for the pump and signal/idler. The spectral correlation of the signal and idler is intuitively demonstrated, and it is shown that higher quality factors result in increased spectral purity. The measurement of time-integrated second-order correlation of the signal photons yields a high value, indicating the potential for enhancing quantum interference and on-chip quantum information processing.
Article
Multidisciplinary Sciences
Woo Young Kim, Bo Wook Seo, Sang Hoon Lee, Tae Gyung Lee, Sin Kwon, Won Seok Chang, Sang-Hoon Nam, Nicholas X. Fang, Seok Kim, Young Tae Cho
Summary: A challenge in making a flexible mold stamp using roll-to-roll nanoimprint lithography is to increase area while minimizing perceptible seams. A method that enables the fabrication of scalable, quasi-seamless functional surfaces without the use of alignment marks is proposed. This method is capable of fabricating scalable functional surfaces and imprint molds with quasi-seamless and alignment mark-free patterning.
NATURE COMMUNICATIONS
(2023)
