A Spatial Structural Derivative Model for Ultraslow Diffusion

This study investigates the ultraslow diffusion by a spatial structural derivative, in which the exponential function exp(x)is selected as the structural function to construct the local structural derivative diffusion equation model. The analytical solution of the diffusion equation is a form of Biexponential distribution. Its corresponding mean squared displacement is numerically calculated, and increases more slowly than the logarithmic function of time. The local structural derivative diffusion equation with the structural function exp(x)in space is an alternative physical and mathematical modeling model to characterize a kind of ultraslow diffusion.Comment: 13 pages, 3 figure

Characterization of sea surface temperature and air-sea heat flux anomalies associated with mesoscale eddies in the South China Sea

Author Posting. © American Geophysical Union, 2020. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research-Oceans 125(4), (2020): e2019JC015470, doi:10.1029/2019JC015470.This study is to quantify the effects of mesoscale eddies on air‐sea heat fluxes and related air‐sea variables in the South China Sea. Using satellite observations of sea surface temperature (SST) and sea surface height anomaly and a high‐resolution air‐sea heat flux product for the 16‐year period from 2000 to 2015, we conducted the composite patterns of air‐sea fluxes and variables associated with anticyclonic eddies (AEs) and cyclonic eddies (CEs). It is found that the SST‐sea surface height correlations over eddies are not always positive. Only 56% of AEs are corresponded with positive SST anomalies (SSTA), that is, SST+ AEs, and 58% of CEs with negative SSTA, that is, SST− CEs. The percentage of these eddies increases with eddy amplitude and shows slight seasonal variations, higher in winter and lower in summer. Composites of SSTA, air‐sea variables, and fluxes are constructed over all eddies, including both SST+ eddies and SST− eddies. All composites show asymmetric patterns, showing that the centers (where the extrema are located) of the fluxes and variables shift westward and poleward (equatorward) relative to the AEs (CEs) cores. Besides, composites of latent heat flux (LHF), sensible heat flux (SHF), and air temperature show monopole patterns, while composites of wind speed and specific humidity show dipole patterns. For SST+ AEs, the coupling strength is 39.6 ± 6.5 W/m2 (7.2 ± 1.7 W/m2) per degree increase of SSTA for LHF (SHF). For SST− CEs, the coupling strength is 39.0 ± 2.0 W/m2 (9.0 ± 0.96 W/m2) per degree decrease of SSTA for LHF (SHF).This research was conducted while Y. Liu was a visiting graduate student at Woods Hole Oceanographic Institution (WHOI). She sincerely thanks the WHOI Academic Programs Office for hosting her visit and is grateful to the support from China Scholarship Council (CSC). This study was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant XDA19060101), the Key R & D project of Shandong Province (Grant 2019JZZY010102), the Key deployment project of Center for Ocean Mega‐Science, CAS (Grant COMS2019R02), the CAS Program (Grant Y9KY04101L), and the National Natural Science Foundation of China (Grant 41776183 and 41906157). Dr. Xiangze Jin is acknowledged for providing the OAFluxHR analysis and for his programming support and guidance to this study. Heat flux data used in this paper can be downloaded (from https://figshare.com/articles/Eddy‐induced_heat_flux_in_the_South_China_Sea/11949735). AVISO SSH data are downloaded from the website (http://www.aviso.altimetry.fr), OISST from the ftp://eclipse.ncdc.noaa.gov/ site, and OAFluxHR analysis will be available from the project website (http://oaflux.whoi.edu).2020-09-1

Influence of surface tension in the surfactant-driven fracture of closely-packed particulate monolayers

A phase-field model is used to capture the surfactant-driven formation of fracture patterns in particulate monolayers. The model is intended for the regime of closely-packed systems in which the mechanical response of the monolayer can be approximated as a linearly elastic solid. The model approximates the loss in tensile strength of the monolayer as the surfactant concentration increases through the evolution of a damage field. Initial-boundary value problems are constructed and spatially discretized with finite element approximations to the displacement and surfactant damage fields. A comparison between model-based simulations and existing experimental observations indicates a qualitative match in both the fracture patterns and temporal scaling of the fracture process. The importance of surface tension differences is quantified by means of a dimensionless parameter, revealing thresholds that separate different regimes of fracture. These findings are supported by newly performed experiments that validate the model and demonstrate the strong sensitivity of the fracture pattern to differences in surface tension.Comment: 10 pages, 11 figures, and 3 table