Spectral properties of a limit-periodic Schr\"odinger operator in dimension two

We study Schr\"{o}dinger operator $H=-\Delta+V(x)$ in dimension two, $V(x)$ being a limit-periodic potential. We prove that the spectrum of $H$ contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves $e^{i\langle \vec k,\vec x\rangle }$ at the high energy region. Second, the isoenergetic curves in the space of momenta $\vec k$ corresponding to these eigenfunctions have a form of slightly distorted circles with holes (Cantor type structure). Third, the spectrum corresponding to the eigenfunctions (the semiaxis) is absolutely continuous.Comment: 89 pages, 6 figure

Transition behavior of k-surface from hyperbola to ellipse

The transition behavior of the k-surface of a lossy anisotropic indefinite slab is investigated. It is found that, if the material loss is taken into account, the k-surface does not show a sudden change from hyperbola to the ellipse when one principle element of the permittivity tensor changes from negative to positive. In fact, after introducing a small material loss, the shape of the k-surface can be a combination of a hyperbola and an ellipse, and a selective high directional transmission can be obtained in such a slab

Erosion-induced massive organic carbon burial and carbon emission in the Yellow River basin, China

Soil erosion and terrestrial deposition of soil organic carbon (SOC) can potentially play a significant role in global carbon cycling. Assessing the redistribution of SOC during erosion and subsequent transport and burial is of critical importance. Using hydrological records of soil erosion and sediment load, and compiled organic carbon (OC) data, estimates of the eroded soils and OC induced by water in the Yellow River basin during the period 1950–2010 were assembled. The Yellow River basin has experienced intense soil erosion due to combined impact of natural process and human activity. Over the period, 134.2 ± 24.7 Gt of soils and 1.07 ± 0.15 Gt of OC have been eroded from hillslopes based on a soil erosion rate of 1.7–2.5 Gt yr⁻¹. Approximately 63% of the eroded soils were deposited in the river system, while only 37% were discharged into the ocean. For the OC budget, approximately 0.53 ± 0.21 Gt (49.5%) was buried in the river system, 0.25 ± 0.14 Gt (23.5%) was delivered into the ocean, and the remaining 0.289 ± 0.294 Gt (27%) was decomposed during the erosion and transport processes. This validates the commonly held assumption that 20–40% of the eroded OC would be oxidized after erosion. Erosion-induced OC redistribution on the landscape likely represented a carbon source, although a large proportion of OC was buried. In addition, about half of the terrestrially redeposited OC (49.4%) was buried behind dams, revealing the importance of dam trapping in sequestering the eroded OC. Although several uncertainties need to be better constrained, the obtained budgetary results provide a means of assessing the redistribution of the eroded OC within the Yellow River basin. Human activities have significantly altered its redistribution pattern over the past decades

Design and finite element mode analysis of noncircular gear

The noncircular gear transmission is an important branch of the gear transmission, it is characterized by its compact structure, good dynamic equilibration and other advantages, and can be used in the automobile, engineering machine, ship, machine tool, aviation and spaceflight field etc. Studying on the dynamics feature of noncircular gear transmission can improve the ability to carry loads of, reduce the vibration and noise of, increase the life of the noncircular gear transmission machine, provides guidance for the design of the noncircular gear, and has significant theories and practical meanings. In this paper, the gear transmission technique is used to studied the design method of the noncircular gear, which contains distribution of teeth on the pitch curve, designs of the tooth tip curve and the tooth root curve, design of the tooth profile curve, the gear system dynamics principle is introduced to establish dynamics model for the noncircular gear; basic theory of finite element and mode analysis method are applied, finite element model for the noncircular gear is established, natural vibration characteristic of the noncircular gear is studied. And the oval gear is taken as an example, the mathematics software MathCAD, the 3D modeling software UG and the finite element software ABAQUS are used to realize precise 3D model of the oval gear. The finite element method is used, the natural vibration characteristic of the oval gear is studied, the main vibration types and natural frequencies of the oval gear and that of the equivalent cylindrical gears are analyzed and compared, the conclusions received reflect the dynamics performance of the oval gear, and solid foundation is laid for dynamics research and engineering application of the oval gear transmission

Spontaneous spin ordering of Dirac spin liquid in a magnetic field

The Dirac spin liquid was proposed to be the ground state of the spin-1/2 Kagome antiferromagnets. In a magnetic field $B$, we show that the state with Fermi pocket is unstable to the Landau level (LL) state. The LL state breaks the spin rotation around the axis of the magnetic field. We find that the LL state has an in-plane 120$^{\circ}$ $q=0$ magnetization $M$ which scales with the external field $M\sim B^{\alpha}$, where $\alpha$ is an intrinsic calculable universal number of the Dirac spin liquid. We discuss the related experimental implications which can be used to detect the possible Dirac spin liquid phase in Herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$.Comment: rewritten for clarit

Geomorphometric assessment of the impacts of dam construction on river disconnectivity and flow regulation in the Yangtze basin

open4Rivers are under increasing pressure from anthropogenic impacts with incremental dam construction, experiencing global and regional alteration due to river disconnectivity, flow regulation, and sediment reduction. Assessing the cumulative impacts of dams on river disconnectivity in large river basins can help us better understand how humans disintegrate river systems and change the natural flow regimes. Using the Yangtze basin as the study area, this study employed three modified metrics (river connectivity index, RCI; basin disconnectivity index, BDI; and the degree of regulation for each river section, DOR) to evaluate the cumulative impacts on river disconnectivity over the past 50 years. The results indicated that the Yangtze had experienced strong alterations, despite varying degrees and spatial patterns. Among the major tributaries, the greatest impact (lowest RCI value) happened in the Wu tributary basin due to the construction of cascade dams on the main stem of the tributary, while the lowest impact (highest RCI value) happened in the Fu tributary basin, which still has no dams on its main stem. Collectively, rivers in the upper Yangtze reaches experienced more serious disturbances than their counterparts in the middle and lower reaches. The BDI results displayed that a substantial part of the Yangtze River, especially the Wu, Min, Jialing, and Yuan tributaries, only maintain connectivity among one to three representative river systems. No part of the Yangtze connects all the 12 representative river systems. This study also revealed that small dams can also exert significant impacts in flow regulation on regional river systems through their sheer number and density. The study results can help promote more environmentally sustainable river management policies in the Yangtze basin.openYang X.; Lu X.; Ran L.; Tarolli P.Yang, X.; Lu, X.; Ran, L.; Tarolli, P