Case History of the Disastrous Debris Flows of Tianmo Watershed in Bomi County, Tibet, China: Some Mitigation Suggestions

Debris flows and landslides, extensively developing and frequently occurring along Parlung Zangbo, seriously damage the Highway from Sichuan to Tiebt(G318) at Bomi County. The disastrous debris flows of the Tianmo Watershed on Sept. 4, 2007, July 25, 2010 and Sept. 4, 2010, blocked Parlung Zangbo River and produced dammed lakes, whose outburst flow made 50 m high terrace collapse at the opposite bank due to intense scouring on the foot of the terrace. As a result, the traffic was interrupted for 16 days in 2010 because that 900 m highway base was destructed and 430 m ruined. These debris flows were initiated by the glacial melting which was induced by continuous higher temperature and the following intensive rainfall, and expanded by moraines along channels and then blocked Parlung Zangbo. At the outlet of watershed,the density, velocity and peak discharge of debris flow was 2.06 t/m3, 12.7 m/s and 3334 m3/s, respectively. When the discharge at the outlet and the deposition volume into river exceeds 2125 m3/s and 126×103 m3, respectively, debris flow will completely blocked Parlung Zangbo. Moreover,if the shear stress of river flow on the foot of terrace and the inclination angel of terrace overruns 0. 377 N/m2 and 26°, respectively, the unconsolidated terrace will be eroded by outburst flow and collapse. It was strongly recommended for mitigation that identify and evade disastrous debris flows, reduce the junction angel of channels between river and watershed, build protecting wall for highway base and keep appropriate distance between highway and the edge of unconsolidated terrace.

Pseudo-differential Operators and Generalized Lax Equations in Symbolic Computation

In this paper, the pseudo-differential operators and the generalized Lax equations in integrable systems are implemented in symbolic software Mathematica. A great deal of differential polynomials which appear in the procedure are dealt with by differential characteristic chain method. Using the program, several classical examples are given.

APPLICATION OF WU ELIMINATION METHOD TO CONSTRAINED DYNAMICS

The polynomial type Lagrange equation and Hamilton equation of finite dimensional constrained dynamics were considered. A new algorithm was presented for solving constraints based on Wu elimination method. The new algorithm does not need to calculate the rank of Hessian matrix and determine the linear dependence of equations, so the steps of calculation decrease greatly. In addition, the expanding of expression occurring in the computing process is smaller. Using the symbolic computation software platform, the new algorithm can be executed in computers.

New algorithms for constrained dynamics based on Faddeev-Jackiw approach

In this paper, the Faddeev Jackiw approach is improved by the Wu elimination method, so a great many complicated computations in solving constraints for the finite-dimensional polynomial-type constrained dynamics can be executed easily by using computers. Moreover, based on the Faddeev Jackiw approach, a new algorithm of solving the constrained dynamics is presented. The new algorithm is simpler and stricter than the Faddeev-Jackiw approach. Using the new algorithm, the second Cawley counterexample is solved.