The origin of anomalous Hall effect (AHE) in ferromagnetic metallic glasses (MGs) is not yet understood completely. Here, the AHE is explored in Fe78Si9B13 MGs. We find the behavior of resistivity at low temperature seems to be more likely due to structure effect rather than Kondo-type effect. More importantly, we firstly find the primitive experiment anomalous Hall conductivity ({sigma}AH) without separation of extrinsic contribution has a linear magnetization (Mz) dependence when temperature is changing, which is another feature of intrinsic mechanism and indicates intrinsic contribution is dominated. Furthermore, the {sigma}AH normalized by Mz is independent of longitudinal conductivity ({sigma}xx), which shows the characteristic of dissipationless intrinsic mechanism. We suggest the intrinsic contribution can be understood from the density of Berry curvature integrated over occupied energies proposed for aperiodic materials recently, and the linear magnetization dependence can be understood qualitatively from the fluctuations of spin orientation and the proportional relationship between Berry curvature and magnetization. Moreover, based on the recent theory report of topological amorphous metals, we make a prediction that the large intrinsic {sigma}AH (616 S/cm) in Fe78Si9B13 MGs implies some topological properties of MGs waiting for further discovery.
For $(mathbb{C} P^2 # 5{overline {mathbb{C} P^2}},omega)$, let $N_{omega}$ be the number of $(-2)$-symplectic spherical homology classes.We completely determine the Torelli symplectic mapping class group (Torelli SMCG): the Torelli SMCG is trivial if $N_{omega}>8$; it is $pi_0(Diff^+(S^2,5))$ if $N_{omega}=0$ (by Paul Seidel and Jonathan Evans); it is $pi_0(Diff^+(S^2,4))$ in the remaining case. Further, we completely determine the rank of $pi_1(Symp(mathbb{C} P^2 # 5{overline {mathbb{C} P^2}}, omega)$ for any given symplectic form. Our results can be uniformly presented regarding Dynkin diagrams of type $mathbb{A}$ and type $mathbb{D}$ Lie algebras. We also provide a solution to the smooth isotopy problem of rational $4$-manifolds.
Topological insulator is a recently discovered class of material with topologically protected surface state. YbB6 is predicted to be moderately correlated Z2 topological insulator similar to SmB6. Here, I experimentally test the resistance property of bulk YbB6 to verify its topological property. By changing the thickness of YbB6, I found out that although the data curves did not completely conform to the theory of topology, the experimental observation to the overall trend showed a similar topological phenomenon.
In this survey article, we summarize some recent progress and problems on the symplectomorphism groups, with an emphasis on the connection to the space of ball-packings.
In the past decade, unmanned aerial vehicles (UAVs) have been widely used in various civilian applications, most of which only require a single UAV. In the near future, it is expected that more and more applications will be enabled by the cooperation of multiple UAVs. To facilitate such applications, it is desirable to utilize a general control platform for cooperative UAVs. However, existing open-source control platforms cannot fulfill such a demand because (1) they only support the leader-follower mode, which limits the design options for fleet control, (2) existing platforms can support only certain UAVs and thus lack of compatibility, and (3) these platforms cannot accurately simulate a flight mission, which may cause a big gap between simulation and real flight. To address these issues, we propose a general control and monitoring platform for cooperative UAV fleet, namely, CoUAV, which provides a set of core cooperation services of UAVs, including synchronization, connectivity management, path planning, energy simulation, etc. To verify the applicability of CoUAV, we design and develop a prototype and we use the new system to perform an emergency search application that aims to complete a task with the minimum flying time. To achieve this goal, we design and implement a path planning service that takes both the UAV network connectivity and coverage into consideration so as to maximize the efficiency of a fleet. Experimental results by both simulation and field test demonstrate that the proposed system is viable.
We study Dehn twists along Lagrangian submanifolds that are finite quotients of spheres. We decribe the induced auto-equivalences to the derived Fukaya category and explain its relation to twists along spherical functors.
We give characterizations of a finite group $G$ acting symplectically on a rational surface ($mathbb{C}P^2$ blown up at two or more points). In particular, we obtain a symplectic version of the dichotomy of $G$-conic bundles versus $G$-del Pezzo surfaces for the corresponding $G$-rational surfaces, analogous to a classical result in algebraic geometry. Besides the characterizations of the group $G$ (which is completely determined for the case of $mathbb{C}P^2# Noverline{mathbb{C}P^2}$, $N=2,3,4$), we also investigate the equivariant symplectic minimality and equivariant symplectic cone of a given $G$-rational surface.
We generalize Bangerts non-hyperbolicity result for uniformly tamed almost complex structures on standard symplectic $R^{2n}$ to asymtotically standard symplectic manifolds.
In this paper we introduce the following new ingredients: (1) rework on part of the Lagrangian surgery theory; (2) constructions of Lagrangian cobordisms on product symplectic manifolds; (3) extending Biran-Cornea Lagrangian cobordism theory to the immersed category. As a result, we manifest Seidels exact sequences (both the Lagrangian version and the symplectomorphism version), as well as Wehrheim-Woodwards family Dehn twist sequence (including the codimension-1 case missing in the literature) as consequences of our surgery/cobordism constructions. Moreover, we obtain an expression of the autoequivalence of Fukaya category induced by Dehn twists along Lagrangian $mathbb{RP}^n$, $mathbb{CP}^n$ and $mathbb{HP}^n$, which matches Huybrechts-Thomass mirror prediction of the $mathbb{CP}^n$ case modulo connecting maps. We also prove the split generation of any symplectomorphism by Dehn twists in $ADE$-type Milnor fibers.
We define a version of spectral invariant in the vortex Floer theory for a $G$-Hamiltonian manifold $M$. This defines potentially new (partial) symplectic quasi-morphism and quasi-states when $M//G$ is not semi-positive. We also establish a relation between vortex Hamiltonian Floer homology and Woodwards quasimap Floer homology by constructing a closed-open string map between them. This yields applications to study non-displaceability problems of subsets in $M//G$
