New explicit multi-symplectic scheme for nonlinear wave equation

Based on splitting multi-symplectic structures, a new multi-symplectic scheme is proposed and applied to a nonlinear wave equation. The explicit multi-symplectic scheme of the nonlinear wave equation is obtained, and the corresponding multi-symplectic conservation property is proved. The backward error analysis shows that the explicit multi-symplectic scheme has good accuracy. The sine-Gordon equation and the Klein-Gordon equation are simulated by an explicit multi-symplectic scheme. The numerical results show that the new explicit multi-symplectic scheme can well simulate the solitary wave behaviors of the nonlinear wave equation and approximately preserve the relative energy error of the equation.

Seasonal Variation of Tritium and Major Elements in Snow and Precipitation in Niigata, Japan

In order to evaluate seasonal and regional variations in precipitation in Niigata City, 65 hourly precipitation samples were collected from October 2009 to June 2011 including two snow events. In this work, major ions （Na＋, K＋, Ca2＋, Mg2＋, NH4＋, SO4^2-, NO3- and Cl-） were combined with tritium （^3H or T） concentration （T specific activity） in both precipitation and snow, and transformation patterns of polluted air mass in Niigata region were revealed. The low level tritium in precipitation was measured by a distillation process and an electrolytic enrichment process. Each tritium concentration in the precipitation sample thus obtained was measured by liquid scintillation counter. On the basis of the above measurement and analysis, it was found that the tritium and nss （non-sea-salt） calcium concentrations showed a seasonal variation with a highest value in spring over one year.

Oxygen Stable Isotopic Ratio in Precipitations in Niigata Prefecture, Japan

Time-course of oxygen stable isotopic ratios （i.e., δ^18O） as well as seasonal variation of δ^18O has been examined to investigate the characteristics, sources and the passing route of precipitations in Niigata Prefecture. The precipitation samples have been mainly collected with a filtrating bulk sampler at the rooftop of Niigata University. Furthermore, backward trajectories analyses have been also conducted for these samples taken sequentially for a short period. Consequently, the following features have been mainly clarified for the precipitations in Niigata Prefecture： （1） the δ^18O values varied between -14.57%o and -3.86%0 in the precipitations of Niigata University; （2） as for the comparison among sampling points, the mean value of δ^18O at seaside spots （i.e., Niigata City： -6.93%0） is larger than that of inland spots （Sanjyo City： -8.68%0）; （3） δ^18O value was generally small in the rainy or typhoon season, and relatively large in summer; （4） decreasing δ^18O content with time is a predominant feature of sequentially sampled rainfalls as predicted by Rayleigh models of atmospheric vapor condensation.

Chemical characteristics of trace metals in PM10 and their concentrated weighted trajectory analysis at Central Delhi,India

Trace metals associated with PM10 aerosols and their variation during day and nighttime as well as during different seasons have been studied for the year 2012. PCA analysis suggested5 PCs,which accounted for 86.8% cumulative variance. PC1 accounted for 30% with a significant loading of metals of anthropogenic origin,while PC2 showed 28% variance with the loading of metals of crustal origin. These trace metals showed seasonal distinct day and night time characteristics. The concentrations of Cu,Pb,and Cd were found to be higher during nighttime in all the seasons. Only Fe was observed with significantly higher mean concentrations during daytime of all seasons except monsoon. The highest mean values of Cu,Cd,Zn,and Pb during post-monsoon might be attributed to winds advection over the regions of waste/biomass burning and industrial activities in Punjab and Haryana regions.Furthermore,concentration weighted trajectory analysis suggested that metals of crustal origin were contributed by long-range transport while metals of anthropogenic and industrial activities were contributed by regional/local source regions.

BACKWARD ERROR ANALYSIS OF SYMPLECTIC INTEGRATORS FOR LINEAR SEPARABLE HAMILTONIAN SYSTEMS

Presents a study that analyzed the symplecticness, stability and asymptotic of Runge-Kutta, partitioned Runge-Kutta, and Runge-Kutta-Nystr ? m methods applied to linear Hamiltonian systems. Numerical representation of the problem; Results in connection to P-stability; Details of the application of backward error analysis in the study.

Multi-SymplecticMethod for the Zakharov-Kuznetsov Equation

A newscheme for the Zakharov-Kuznetsov(ZK)equationwith the accuracy order of O(△t^(2)+△x+△y^(2))is proposed.The multi-symplectic conservation property of the new scheme is proved.The backward error analysis of the newmulti-symplectic scheme is also implemented.The solitary wave evolution behaviors of the Zakharov-Kunetsov equation is investigated by the new multi-symplectic scheme.The accuracy of the scheme is analyzed.

Structure-Preserving Algorithms for a Class of Dynamical Systems

In this paper, we study structure-preserving algorithms for dynamical systems defined by ordinary differential equations in R^n The equations are assumed to be of the form y^· = A（y） ＋ D（y） ＋ R（y）, where A（y） is the conservative part subject to （A（y）, y） = 0; D（y） is the damping part or the part describing the coexistence of damping and expanding; R（y） reflects strange phenomenon of the system. It is shown that the numerical solutions generated by the symplectic Runge-Kutta（SRK） methods with bi 〉 0 （ i = 1,..., s） have long-time approximations to the exact ones, and these methods can describe the structural properties of the quadratic energy for these systems. Some numerical experiments and backward error analysis also show that these methods are better than other methods including the general algebraically stable Runge-Kutta（RK）methods.

Dry deposition of PM_(10) over the Yellow Sea during Asian dust events from 2001 to 2007

Dry deposition velocities and fluxes of PM10 during Asian dust events over the Yellow Sea from 2001 to 2007 were investigated using observation data in Qingdao, China and Jeju, Korea. The dry deposition velocities of PM 10 during dust events over the Yellow Sea ranged from 0.19 to 8.17 cm/sec, with an average of 3.38 cm/sec. Dry deposition fluxes of PM10 during dust events over the Yellow Sea were in the range of 68.5-2647.1 mg/（m2.day）, with an average of 545.4 mg/（m2.day）, which is 2-10 times higher than those reported by other studies for both dust and non-dust periods. It was estimated that 2.6× 10^11-48.7 × 10^11 g dust particles deposit to the Yellow Sea during dust events through dry deposition every year. Compared with the results in previous studies, it was found that the dry deposition of PM10 over the Yellow Sea during dust events in the years with high frequency of dust could account for a large or overwhelming fraction of the annual total dry deposition. Backward air mass trajectory analysis showed that dust events influenced Jeju mainly originated from the desert regions located in Mongolia and Inner Mongolia, China. There were 119 backward trajectories influenced both Qingdao and Jeju during 15 dust events from 2001 to 2007, accounting for 61.3% of the total trajectories of 194, indicating that Qingdao and Jeju were usually on the same pathway of dust transport downwind from source areas.