水基钻井液中天然气水合物形成实验研究

在钻探过程中,当温压条件合适,钻井液易形成天然气水合物,造成管线堵塞、钻井液性能变化。研究2种水基钻井液对绿峡谷气水合物形成过程中的影响。结果表明实验条件下该2种水基钻井液很易形成水合物,受钻井液组分的影响,两种钻井液中天然气水合物形成速率具有明显差异。在相同的温度下,实验压力越高,天然气水合物越易于形成,反应越剧烈。采用定容压力搜索法,测定了在13~18 MPa时此2种水基钻井液与绿峡谷气形成水合物的相平衡数据,显示一种钻井液能够促进水合物的形成,另外一种钻井液对水合物形成有抑制作用。     

河南栾川县区域群发性泥石流临界雨量分析

栾川县历史上曾多次暴发区域群发性泥石流,以其为研究对象,选择前5日前期降雨量、当日降雨量、24 h最大降雨量、2 h最大降雨量、前72 h直接降雨量和前120 h直接降雨量为特征参数,根据它们的不同组合对栾川县区域群发性泥石流临界雨量进行分析,确定了泥石流预警的临界雨量基准线。分析结果表明2 h最大降雨量为研究区泥石流预报的重要指标,在不考虑前期雨量的情况下,2 h临界雨量为14 mm,研究结论可为当地泥石流防灾减灾提供参考。     

含边界在内的一般极值的必要条件与拉格朗日乘数法

讨论包括定义域边界点在内的极值,称为一般极值.对可导的一元和多元函数给出了一般极值点的必要条件,这些必要条件与经典极值的必要条件是相容的.还利用一般极值的必要条件导出了条件极值的拉格朗日乘数法.     

广义凸函数的特征性质

提出广义凸集、广义凸函数、中间点广义凸函数、端点广义凸函数四个定义,通过定义条件P1,研究条件P1所蕴含的等式关系,进而得到一个基础性定理一稠密性定理和一个相对条件较弱的推论,最后将结果应用于若干不同类型的广义凸函数类,尤其是s-凸函数、几何凸函数、rp-凸函数,得到它们所共有的一个特征性质,即满足稠密性定理．     

Classification with Gaussians and convex loss Ⅱ:improving error bounds by noise conditions

We continue our study on classification learning algorithms generated by Tikhonov regularization schemes associated with Gaussian kernels and general convex loss functions. Our main purpose of this paper is to improve error bounds by presenting a new comparison theorem associated with general convex loss functions and Tsybakov noise conditions. Some concrete examples are provided to illustrate the improved learning rates which demonstrate the effect of various loss functions for learning algorithms. In our ...     

非Lipschitz条件Hilbert空间上扩散过程的短时间大偏差原理

Under the non-Lipschitzian condition, a small time large deviation principle of diffusion processes on Hilbert spaces is established. The operator theory and Gronwall inequality play an important role.     

Improvements on open and traction boundary conditions for Navier–Stokes time-splitting methods

We present in this paper a numerical scheme for incompressible Navier–Stokes equations with open and traction boundary conditions, in the framework of pressure-correction methods. A new way to enforce this type of boundary condition is proposed and provides higher pressure and velocity convergence rates in space and time than found in the present state of the art. We illustrate this result by computing some numerical and physical tests. In particular, we establish reference solutions of a laminar flow in a geometry where a bifurcation takes place and of the unsteady flow around a square cylinder.     

A Poisson–Boltzmann solver on irregular domains with Neumann or Robin boundary conditions on non-graded adaptive grid

We introduce a second-order solver for the Poisson–Boltzmann equation in arbitrary geometry in two and three spatial dimensions. The method differs from existing methods solving the Poisson–Boltzmann equation in the two following ways: first, non-graded Quadtree (in two spatial dimensions) and Octree (in three spatial dimensions) grid structures are used; Second, Neumann or Robin boundary conditions are enforced at the irregular domain’s boundary. The irregular domain is described implicitly and the grid needs not to conform to the domain’s boundary, which makes grid generation straightforward and robust. The linear system is symmetric, positive definite in the case where the grid is uniform, nonsymmetric otherwise. In this case, the resulting matrix is an M-matrix, thus the linear system is invertible. Convergence examples are given in both two and three spatial dimensions and demonstrate that the solution is second-order accurate and that Quadtree/Octree grid structures save a significant amount of computational power at no sacrifice in accuracy.     

CFL Conditions for Runge–Kutta discontinuous Galerkin methods on triangular grids

We study time step restrictions due to linear stability constraints of Runge–Kutta Discontinuous Galerkin methods on triangular grids. The scalar advection equation is discretized in space by the Discontinuous Galerkin method with either the Lax–Friedrichs flux or the upwind flux, and integrated in time with various Runge–Kutta schemes designed for linear wave propagation problems or non-linear applications. Von–Neumann-like analyses are performed on structured periodic grids made up of congruent elements, to investigate the influence of element shape on the stability restrictions. We assess CFL conditions based on different element size measures, among which only the radius of the inscribed circle and the shortest height prove appropriate, although they are not totally independent of the triangle shape. We explain their general behaviour with respect to element quality, and report the corresponding Courant numbers with both types of flux and polynomial order p ranging from 1 to 10, for use as guidelines in practical simulations. We also compare the performance of the Lax–Friedrichs flux and the upwind flux, and we draw general conclusions about the relative computational efficiency of RK schemes. The application of CFL conditions to two examples involving respectively an unstructured and a hybrid grid confirms our results, although it shows that local stability criteria tend to yield too restrictive conditions.