On Coupled KdV Equations with Self-consistent Sources

The coupled Korteweg-de Vries （CKdV） equation with self-consistent sources （CKdVESCS） and its Lax representation are derived. We present a generalized binary Darboux transformation （GBDT） with an arbitrary time- dependent function for the CKdVESCS as well as the formula for the N-times repeated GBDT. This GBDT provides non-auto-Biicklund transformation between two CKdVESCSs with different degrees of sources and enables us to construct more generM solutions with N arbitrary t-dependent functions. We obtain positon, negaton, complexiton, and negaton- positon solutions of the CKdVESCS.

Coupling model for waves propagating over a porous seabed

The wave-seabed interaction issue is of great importance for the design of foundation around marine infrastructures. Most previous investigations for such a problem have been limited to uncoupled or one- way coupled methods connecting two separated wave and seabed sub models with the continuity of pressures at the seabed surface. In this study, a strongly coupled model was proposed to realize both wave and seabed processes in a same program and to calculate the wave fields and seabed response simultaneously. The information between wave fields and seabed fields were strongly shared and thus results in a more profound investigation of the mechanism of the wave-seabed interaction. In this letter, the wave and seabed models were validated with previous experimental tests. Then, a set of application of present model were discussed in prediction of the wave-induced seabed response. Numerical results show the wave-induced liquefaction area of coupled model is smaller than that of uncoupled model.

Plasma density enhancement in radio-frequency hollow electrode discharge

The plasma density enhancement outside hollow electrodes in capacitively coupled radio-frequency(RF) discharges is investigated by a two-dimensional(2D) particle-in-cell/Monte-Carlo collision(PIC/MCC) model. Results show that plasma exists inside the cavity when the sheath inside the hollow electrode hole is fully collapsed, which is an essential condition for the plasma density enhancement outside hollow electrodes. In addition, the existence of the electron density peak at the orifice is generated via the hollow cathode effect(HCE), which plays an important role in the density enhancement. It is also found that the radial width of bulk plasma at the orifice affects the magnitude of the density enhancement, and narrow radial plasma bulk width at the orifice is not beneficial to obtain high-density plasma outside hollow electrodes.Higher electron density at the orifice, combined with larger radial plasma bulk width at the orifice,causes higher electron density outside hollow electrodes. The results also imply that the HCE strength inside the cavity cannot be determined by the magnitude of the electron density outside hollow electrodes.

A Study of the Rhenium-Osmium Geochronometry of Molybdenites

This study deals with the first application of the isotope dilution - inductively coupled plasma mass spectrometry in the rhenium-osmium geochronometry in China. The chemical separation procedure included decomposition of samples by means of alkali fusion, extraction of rhenium by acetone and extraction of osmium by distillation. The recovery of both elements in the entire process was more than 90% . The blanks of analyses were 0.07 ng for rhenium and 0.01 ng for 187Os. The mineralization ages of molybdenites from four molybdenum deposits in China were determined by using this method, with a precision (2σ)of about ±3% . These results agree satisfactorily with their geological backgrounds. The Re-Os method can directly determine ages of metal deposits and reflect the true ages more reliably than other dating methods that only determine the ages of country rocks from which mineralization ages are inferred. As many hydrothermal sulphide deposits usually contain molybdenites, this method has bright prospects of wide application.

Blow-up Sets to a Coupled Heat System

This paper deals with a heat system coupled via local and localized sources subject to null Dirichlet boundary conditions. In a previous paper of the authors, a complete result on the multiple blow-up rates was obtained. In the present paper, we continue to consider the blow-up sets to the system via a complete classification for the nonlinear parameters. That is the discussion on single point versus total blow-up of the solutions. It is mentioned that due to the influence of the localized sources, there is some substantial difficulty to be overcomed there to deal with the single point blow-up of the solutions.