Conical Sonic-Supersonic Solutions for the 3-D Steady Full Euler Equations

This paper concerns the sonic-supersonic structures of the transonic crossflow generated by the steady supersonic flow past an infinite cone of arbitrary cross section.Under the conical assumption,the three-dimensional(3-D)steady Euler equations can be projected onto the unit sphere and the state of fluid can be characterized by the polar and azimuthal angles.Given a segment smooth curve as a conical-sonic line in the polar-azimuthal angle plane,we construct a classical conical-supersonic solution near the curve under some reasonable assumptions.To overcome the difficulty caused by the parabolic degeneracy,we apply the characteristic decomposition technique to transform the Euler equations into a new degenerate hyperbolic system in a partial hodograph plane.The singular terms are isolated from the highly nonlinear complicated system and then can be handled successfully.We establish a smooth local solution to the new system in a suitable weighted metric space and then express the solution in terms of the original variables.

The Use of Edge Enhancement Methods and Euler Deconvolution to Estimate an Ore Deposit Depth from Gravity Data

The Hercynian massif of the central Jebilet (Morocco) is characterized by the outcrop of many gossans with great economic importance. This work focuses on interpreting gravity data of Benslimane gossan, located about thirty kilometres to the North-West of Marrakech. The residual gravity map of the study area highlights several anomalies which coincide with the mining and geological contexts. Applying edge detection methods, for example, tilt angle derivative (TDR), the total horizontal derivative of the tilt angle derivative (HDR_TDR) and the 3D Euler deconvolution, allowed us to estimate the depth of the Benslimane deposit. As a result, the average depth of the ore deposit was estimated to exceed 200 m. The results are promising, and the processing methods must be applied to the other gossan in the Jebilet massif for further exploration studies.

Viscous Approximations and Decay Rate of Maximal Vorticity Function for 3-D Axisymmetric Euler Equations

In this paper, we are first concerned with viscous approximations for the three-dimensional axisymmetric incompressible Euler equations. It is proved that the viscous approximations, which are the solutions of the corresponding Navier-Stokes equations, converge strongly in provided that they have strong convergence in the region away from the symmetry axis. This result has been proved by the authors for the approximate solutions generated by smoothing the initial data, with no restriction of the sign of the initial data. Then we discuss the decay rate for maximal vorticity function, which is established for both approximate solutions generated by smoothing the initial data and viscous approximations respectively. One sufficient condition to guarantee the strong convergence in the region away from the symmetry axis is given, and a decay rate for maximal vorticity function in the region away from the symmetry axis is obtained for non-negative initial vorticity.

东营凹陷典型剖面重磁电震综合解释方法研究

潜山内幕、砂砾岩和深层地质体是东营凹陷地震勘探相对困难的目标。为此,选择总长度约100 km的SL616测线进行了重磁电震综合解释方法的研究,该测线依次经过广饶凸起、东营凹陷和陈家庄凸起3个二级构造单元。阐述了航磁资料的三维欧拉反褶积、电法资料的快速松弛反演(RRI)和重力资料的约束正反演等处理方法。地震勘探中存在屏蔽效应的潜山、砂砾岩体等隐蔽地质目标在重磁电资料上有明显的异常特征。通过重磁电震资料的综合对比分析,重新认识了潜山内幕、砂砾岩体、边界断裂和深部地层,发现了新的地质体。认为陈家庄凸起并非是单一的太古界地层,其内部存在断裂和低阻、低密度体;根据地震资料解释的东营凹陷古生界顶面最深点应向北偏移。

Combined Electromagnetic and Drift Diffusion Models for Microwave Semiconductor Device

In this work, we present a numerical model to solve the drift diffusion equations coupled with electromagnetic model, where all simulations codes are implemented using MATLAB code software. As first, we present a one-dimensional (1-D) PIN diode structure simulation achieved by solving the drift diffusion model (DDM). Backward Euler algorithm is used for the discretization of the proposed model. The aim is to accomplish time-domain integration. Also, finite different method (FDM) is considered to achieve space-Domain mesh. We introduced an iterative scheme to solve the obtained matrix systems, which combines the Gummel’s iteration with an efficient direct numerical UMFPACK method. The obtained solutions of the proposed algorithm provide the time and space distribution of the unknown functions like electrostatic potential and carrier’s concentration for the PIN diode. As second case, the finite-difference time-domain (FDTD) technique is adopted to analyze the entire 3-D structure of the stripline circuit including the lumped element PIN diode. The microwave circuit is located in an unbounded medium, requiring absorbing boundaries to avoid nonphysical reflections. Active device results were presented and show a good agreement with other reference. Electromagnetic results are qualitatively in agreement with other results obtained using SILVACO-TCAD.