Homoclinic solutions for a class of asymptotically autonomous Hamiltonian systems with indefinite sign nonlinearities

In this paper, we obtain the multiplicity of homoclinic solutions for a class of asymptotically autonomous Hamiltonian systems with indefinite sign potentials. The concentration-compactness principle is applied to show the compactness. As a byproduct, we obtain the uniqueness of the positive ground state solution for a class of autonomous Hamiltonian systems and the best constant for Sobolev inequality which are of independent interests

Constructing multi-level urban clusters based on population distributions and interactions

A city (or an urban cluster) is not an isolated spatial unit, but a combination of areas with closely linked socio-economic activities. However, so far, we lack a consistent and quantitative approach to define multi-level urban clusters through these socio-economic connections. Here, using granular population distribution and flow data from China, we propose a bottom-up aggregation approach to quantify urban clusters at multiple spatial scales. We reveal six 'phases' (i.e., levels) in the population density-flow diagram, each of which corresponds to a spatial configuration of urban clusters from large to small. Besides, our results show that Zipf's law appears only after the fifth level, confirming the spatially dependent nature of urban laws. Our approach does not need pre-defined administrative boundaries and can be applied effectively on a global scale

Homoclinic orbits for a class of second-order Hamiltonian systems with concave–convex nonlinearities

In this paper, we study the existence of multiple homoclinic solutions for the following second order Hamiltonian systems \begin{equation*} \ddot{u}(t)-L(t)u(t)+\nabla W(t,u(t))=0, \end{equation*} where $L(t)$ satisfies a boundedness assumption which is different from the coercive condition and $W$ is a combination of subquadratic and superquadratic terms

Rapid intensification of Typhoon Hato (2017) over shallow water

© The Author(s), 2019. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Pun, I., Chan, J. C. L., Lin, I., Chan, K. T. E., Price, J. F., Ko, D. S., Lien, C., Wu, Y., & Huang, H. Rapid intensification of Typhoon Hato (2017) over shallow water. Sustainability, 11(13), (2019): 3709, doi:10.3390/su11133709.On 23 August, 2017, Typhoon Hato rapidly intensified by 10 kt within 3 h just prior to landfall in the city of Macau along the South China coast. Hato’s surface winds in excess of 50 m s−1 devastated the city, causing unprecedented damage and social impact. This study reveals that anomalously warm ocean conditions in the nearshore shallow water (depth < 30 m) likely played a key role in Hato’s fast intensification. In particular, cooling of the sea surface temperature (SST) generated by Hato at the critical landfall point was estimated to be only 0.1–0.5 °C. The results from both a simple ocean mixing scheme and full dynamical ocean model indicate that SST cooling was minimized in the shallow coastal waters due to a lack of cool water at depth. Given the nearly invariant SST in the coastal waters, we estimate a large amount of heat flux, i.e., 1.9k W m−2, during the landfall period. Experiments indicate that in the absence of shallow bathymetry, and thus, if nominal cool water had been available for vertical mixing, the SST cooling would have been enhanced from 0.1 °C to 1.4 °C, and sea to air heat flux reduced by about a quarter. Numerical simulations with an atmospheric model suggest that the intensity of Hato was very sensitive to air-sea heat flux in the coastal region, indicating the critical importance of coastal ocean hydrography.The work of I.-F.P. is supported by Taiwan’s Ministry of Science and Technology Grant MOST 107-2111-M-008-001-MY3. The work of J.C.L.C. is supported by the Research Grants Council of Hong Kong Grant E-CityU101/16. The work of I.-I.L. is supported by Taiwan’s Ministry of Science and Technology (MOST 106-2111-M-002-011-MY3, MOST 108-2111-M-002-014-MY2). The work of K.T.F.C. is jointly supported by the National Natural Science Foundation of China (41775097), and the National Natural Science Foundation of China and Macau Science and Technology Development Joint Fund (NSFC-FDCT), China and Macau (41861164027)