The Expansion of a Wedge of Gas into Vacuum with Small Angle in Two-Dimensional Isothermal Flow

In this paper, the authors consider the expansion problem of a wedge of gas into vacuum for the two-dimensional Euler equations in isothermal flow. By the bootstrapping argument, they prove the global existence of the smooth solution through the direct method in the case 0 〈 θ 〈 -θ=arctan 1/（√2＋√5）, where θ is the half angle of the wedge. Furthermore, they get the uniform C^1,1 estimates of the solution to the expansion problem.

Local well-posedness of a multidimensional shock wave for the steady supersonic isothermal flow

In this paper, we prove the local existence, uniqueness and stability of a supersonic shock for the supersonic isothermal incoming flow past a curved cone. Major difficulties include constructing an appropriate solution and treatincg the Neumann boundary conditions and local stability condition.

Simulation of Polymer Melt Flow Fields in Intermeshing Co-Rotating Three-Screw Extruders

Three-dimension isothermal flows of polymer melt in the kneading blocks of triangularly-arranged and parallelly-arranged intermeshing co-rotating three-screw extruders are simulated using the finite element package POLYFLOW. Based on the velocity fields calculated, the particle trajectories in both machines are visualized using particle tracking technique. The numerical results indicate that the flow patterns in three-screw extruders are similar to those in twin-screw extruders. The triangularly-arranged three-screw extruder has the largest pumping capacity and also the highest extrusion stability in terms of flowrate fluctuation with screw rotation. The instantaneous mixing and cumulative residence time distribution （RTD） characteristics are also analyzed and compared with traditional intermeshing co-rotating twin-screw extruders. It is shown that the start section of the cumulative RTD curve for the triangularly-arranged machine has a small shoulder, which is attributed to the faster flow in the central region of this type of extruder.

Depth to the bottom of magnetic layer in South America and its relationship to Curie isotherm,Moho depth and seismicity behavior

We have estimated the DBML（depth to the bottom of the magnetic layer） in South America from the inversion of magnetic anomaly data extracted from the EMAG2 grid. The results show that the DBML values, interpreted as the Curie isotherm, vary between -10 and -60 km. The deepest values（〉-45） are mainly observed forming two anomalous zones in the central part of the Andes Cordillera. To the east of the Andes, in most of the stable cratonic area of South America, intermediate values（between -25 and-45 km） are predominant. The shallowest values（〈-25 km） are present in northwestern corner of South America, southern Patagonia, and in a few sectors to the east of the Andes Cordillera. Based on these results, we estimated the heat flow variations along the study area and found a very good correlation with the DBML. Also striking is the observation that the thermal anomalies of low heat flow are closely related to segments of flat subduction, where the presence of a cold and thick subducting oceanic slab beneath the continent, with a virtual absence of hot mantle wedge, leads to a decrease in the heat transfer from the deeper parts of the system.After comparing our results with the Moho depths reported by other authors, we have found that the Curie isotherm is deeper than Moho in most of the South American Platform（northward to -20°S）, which is located in the stable cratonic area at the east of the Andes. This is evidence that the lithospheric mantle here is magnetic and contributes to the long wavelength magnetic signal. Also, our results support the hypothesis that the Curie isotherm may be acting as a boundary above which most of the crustal seismicity is concentrated. Below this boundary the occurrence of seismic events decreases dramatically.

OPERATOR SPLITTING SCHEMES FOR THE NON-STATIONARY THERMAL CONVECTION PROBLEMS

In this work, a new numerical scheme is proposed for thermal/isothermal incompressible viscous flows based on operator splitting. Unique solvability and stability analysis are presented. Some numerical result are given, which show that the proposed scheme is highly efficient for the thermal/isothermal incompressible viscous flows.