Self polarization in GaAs–(Ga, Al)As quantum well wires: electric field and geometrical effects

The response of an electron to an external electric field in different shapes of infinite quantum well wires has been investigated. The self-polarization effect which can be defined as the influence of the barrier potential on the impurity electron is studied for the quantum well wire of square, rectangular and cylindrical cross-sections. An external electric field vanishes due to the self-polarization effect has been calculated. It is shown that the self-polarization effect outside of the center depends on both the geometrical form of the wire and the impurity position in the same structure.     

Classification of non‐well‐founded sets and an application

A complete list of Finsler, Scott and Boffa sets whose transitive closures contain 1, 2 and 3 elements is given. An algorithm for deciding the identity of hereditarily finite Scott sets is presented. Anti‐well‐founded (awf) sets, i. e., non‐well‐founded sets whose all maximal ∈‐paths are circular, are studied. For example they form transitive inner models of ZFC minus foundation and empty set, and they include uncountably many hereditarily finite awf sets. A complete list of Finsler and Boffa awf sets with 2 and 3 elements in their transitive closure is given. Next the existence of infinite descending ∈‐sequences in Aczel universes is shown. Finally a theorem of Ballard and Hrbá?ek concerning nonstandard Boffa universes of sets is considerably extended.     

深基坑工程渗流场特性分析

深基坑工程的施工特点决定了其渗流场水力条件的复杂性。大量的工程实践显示，渗流问题是许多基坑工程事故的主要或重要原因。本文采用有限单元法分析了基坑渗流场分布特性。比较了不同水力条件下渗流作用对基坑土体渗透稳定性的影响，探讨了工程中可能出现的不利因素，特别是防渗体破坏情况对基坑安全造成的危害性。本文的工作也表明，利用数值方法分析基坑渗流场分布特性，对于深基坑工程的安全性评价和工程施工都具有重要的指导意义。     

Numerically induced oscillations in finite element approximations to the shallow water equations

Numerical noise has been a problem with finite element solutions to the shallow water equations. Two methods used to reduce the noise level are evaluated, and these results are compared with published results for equal-order interpolations. The two methods are mixed-interpolation (quadratic interpolation for velocity and linear interpolation for sea level) and a spectral form of the wave equation. Whereas mixed interpolation removes the troublesome sea level mode, it can still have considerable noise in velocity. The spectral wave equation is efficient and does not contain the spurious eigenmodes which contribute to high noise levels.     

A second-order radiation boundary condition for the shallow water wave equations on two-dimensional unstructured finite element grids

A second-order radiation boundary condition (RBC) is derived for 2D shallow water problems posed in ‘wave equation’ form and is implemented within the Galerkin finite element framework. The RBC is derived by matching the dispersion relation for the interior wave equation with an approximate solution to the exterior problem for outgoing waves. The matching is correct to second order, accounting for curvature of the wave front and the geometry. Implementation is achieved by using the RBC as an evolution equation for the normal gradient on the boundary, coupled through the natural boundary integral of the Galerkin interior problem. The formulation is easily implemented on non-straight, unstructured meshes of simple elements. Test cases show fidelity to solutions obtained on extended meshes and improvement relative to simpler first-order RBCs.     

Numerical integration of the shallow water equations over a sloping shelf

A finite-difference method is described for the numerical integration of the one-dimensional shallow water equations over a sloping shelf that allows for a continuously moving shoreline. An application of the technique is made to the propagation of non-breaking waves towards the shoreline. The results of the computation are compared with an evaluation based upon an exact analytical treatment of the non-linear equations. Excellent agreement is found for both tsunami and tidal scale oscillations.     

Wave equation hydrodynamics on deforming elements

The shallow water wave equation is derived in a general deforming co-ordinate system. A weak form is developed which displays the natural boundary condition prominently and which may be implemented on C⁰ elements. A time-stepping algorithm is implemented with clastic mapping of interior node motion. Lossless test cases show agreement with analytic solutions. A simple hypothetical test case shows intuitively good behaviour at length scales approaching those required of estuarine simulations.     

Numerical simulation of liquefied fuel spills: II. Instantaneous and continuous LNG spills on an unconfined water surface

A simple numerical model based on the shallow water equations in radial symmetry is used to simulate both instantaneous and continuous spills of liquefied natural gas (LNG) onto a water surface. Using the computed results, a study is made of the similarities and differences in the pool structure resulting from the two types of spills. For instantaneous spills a relation linear on a logarithmic plot is suggested between the maximum pool size and the spill volume. The effects of shear forces and surface cohesivity on the evolution of the spill are also examined.     

Stability of a shallow arch with one end moving at constant speed

In this paper we consider a shallow arch with rise parameter h, free of lateral loading, but subject to prescribed end motion e with constant speed c. Attention is focused on finding out whether dynamic snap-through will occur. Quasi-static analysis is first performed to identify all equilibrium configurations and their stability properties when e and h are specified. If the arch is stretched quasi-statically, it will be straightened up and no snap-through will occur. However, when the speed c is not negligible it is possible for the arch to snap to the other side dynamically. Careful analysis shows that the only possible situation when dynamic snap-through may occur is and . In this case, to prevent dynamic snap-through to occur the end speed c must not exceed a critical speed, which is a function of e and h. The minimum critical stretching speed is found to be 25.9 for all possible combinations of e and h.     

Upwind-biased FORCE schemes with applications to free-surface shallow flows

In this paper we develop numerical fluxes of the centred type for one-step schemes in conservative form for solving general systems of conservation laws in multiple-space dimensions on structured meshes. The proposed method is an extension of the multidimensional FORCE flux developed by Toro et al. (2009) [14]. Here we introduce upwind bias by modifying the shape of the staggered mesh of the original FORCE method. The upwind bias is evaluated using an estimate of the largest eigenvalue, which in any case is needed for selecting a time step. The resulting basic flux is first-order accurate and monotone. For the linear advection equation, the proposed UFORCE method reproduces exactly the upwind Godunov method. Extension to non-linear systems has been done empirically via the two-dimensional inviscid shallow water equations. Second order of accuracy in space and time on structured meshes is obtained in the framework of finite volume methods. The proposed method improves the accuracy of the solution for small Courant numbers and intermediate waves associated with linearly degenerate fields (contact discontinuities, shear waves and material interfaces). It achieves comparable accuracy to that of upwind methods with approximate Riemann solvers, though retaining the simplicity and efficiency of centred methods. The performance of the schemes is assessed on a suite of test problems for the two-dimensional shallow water equations.