A Mathematical Model for Hysteretic Two-Phase Flow in Porous Media

We develop a mathematical model for hysteretic two-phase flow (of oil and water) in waterwet porous media. To account for relative permeability hysteresis, an irreversible trapping-coalescence process is described. According to this process, oil ganglia are created (during imbibition) and released (during drainage) at different rates, leading to history-dependent saturations of trapped and connected oil. As a result, the relative permeability to oil, modelled as a unique function of the connected oil saturation, is subject to saturation history. A saturation history is reflected by history parameters, that is by both the saturation state (of connected and trapped oil) at the most recent flow reversal and the most recent water saturation at which the flow was a primary drainage. Disregarding capillary diffusion, the flow is described by a hyperbolic equation with the connected oil saturation as unknown. This equation contains functional relationships which depend on the flow mode (drainage or imbibition) and the history parameters. The solution consists of continuous waves (expansion waves and constant states), shock waves (possibly connecting different modes) and stationary discontinuities (connecting different saturation histories). The entropy condition for travelling waves is generalized to include admissible shock waves which coincide with flow reversals. It turns out that saturation history generally has a strong influence on both the type and the speed of the waves from which the solution is constructed.     

THEORETICAL RELATIONS OF BOUNDARY DISPLACEMENT DERIVATIVES AND TRACTIONS AT SINGULAR BOUNDARY POINT FOR 2D ISOTROPIC ELASTIC PROBLEMS

Although boundary displacement and traction are independent field variables in boundary conditions of an elasticity problem at a non-singular boundary point, there exist definite relations of singularity intensities between boundary displacement derivatives and tractions at a singular boundary point. The analytical forms of the relations at a singular smooth point for 2D isotropic elastic problems have been established in this work. By using the relations, positions of the singular boundary points and the corresponding singularity intensities of the unknown boundary field variables can be determined a priori. Therefore, more appropriate shape functions of the unknown boundary field variables in singular elements can be constructed. A numerical example shows that the accuracy of the BEM analysis using the developed theory is greatly increased.     

An Improved Tiered Head Pose Estimation Network with Self-Adjust Loss Function

As an important task in computer vision, head pose estimation has been widely applied in both academia and industry. However, there remains two challenges in the field of head pose estimation: (1) even given the same task (e.g., tiredness detection), the existing algorithms usually consider the estimation of the three angles (i.e., roll, yaw, and pitch) as separate facets, which disregard their interplay as well as differences and thus share the same parameters for all layers; and (2) the discontinuity in angle estimation definitely reduces the accuracy. To solve these two problems, a THESL-Net (tiered head pose estimation with self-adjust loss network) model is proposed in this study. Specifically, first, an idea of stepped estimation using distinct network layers is proposed, gaining a greater freedom during angle estimation. Furthermore, the reasons for the discontinuity in angle estimation are revealed, including not only labeling the dataset with quaternions or Euler angles, but also the loss function that simply adds the classification and regression losses. Subsequently, a self-adjustment constraint on the loss function is applied, making the angle estimation more consistent. Finally, to examine the influence of different angle ranges on the proposed model, experiments are conducted on three popular public benchmark datasets, BIWI, AFLW2000, and UPNA, demonstrating that the proposed model outperforms the state-of-the-art approaches.     

Analysis of the structural properties of the solutions to speed gradient traffic flow model

In this paper, we carry out an analysis of the structural properties of the solutions to the speed gradient (SG) traffic flow model. Under the condition that the relaxation effect can be neglected, it is shown that a 1-shock or a 1-rarefaction is associated with the first characteristic, but on the other hand, a contact discontinuity rather than a 2-shock or a 2-rarefaction is associated with the second characteristic. Since the existence of a 2-shock or 2-rarefaction violates the physical mechanism of the traffic flow, the SG model is more reasonable. If the relaxation effect cannot be neglected, it is somewhat difficult to carry out the analytical analysis and the numerical simulation results should be obtained. The project supported by the National Natural Science Foundation of China (10272101)     

Time and Classical and Quantum Mechanics: Indeterminacy Versus Discontinuity

It is postulated there is not a precise static instant in time underlying a dynamical physical process at which the relative position of a body in relative motion or a specific physical magnitude would theoretically be precisely determined. It is concluded it is exactly because of this that time (relative interval as indicated by a clock) and the continuity of a physical process is possible, with there being a necessary trade off of all precisely determined physical values at a time, for their continuity through time. This explanation is also shown to be the correct solution to the motion and infinity paradoxes, excluding the Stadium, originally conceived by the ancient Greek mathematician Zeno of Elea. Quantum Cosmology, Imaginary Time and Chronons are also then discussed, with the latter two appearing to be superseded on a theoretical basis.     

The Principle Underlying Quantum Mechanics

The present article reports on the finding of the principle behind quantum mechanics. The principle, referred to as genuine fortuitousness, implies that the basic event, a click in a counter, comes without any cause and thus as a discontinuity in spacetime. From this principle, the formalism of quantum mechanics emerges with a radically new content, no longer dealing with things (atoms, particles, or fields) to be measured. Instead, quantum mechanics is recognized as the theory of distributions of uncaused clicks that form patterns laid down by spacetime symmetry and is thereby revealed as a subject of unexpected simplicity and beauty. The departure from usual quantum mechanics is strikingly borne out by the absence of Planck's constant from the theory. The elimination of indeterminate particles as cause for the clicks, which the principle of genuine fortuitousness implies, is analogous to the elimination of the ether implied by the principle of relativity.     

Multiple crack fatigue growth modeling by displacement discontinuity method with crack-tip elements

This paper presents a numerical approach for modeling multiple crack fatigue growth in a plane elastic infinite plate. It involves a generation of Bueckner’s principle, a displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author and an extension of Paris’ law to a multiple crack problem under mixed-mode loading. Because of an intrinsic feature of the boundary element method, a general multiple crack growth problem can be solved in a single-region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Crack extension is conveniently modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. Fatigue growth modeling of an inclined crack in an infinite plate under biaxial cyclic loads is taken into account to illustrate the effectiveness of the present numerical approach. As an example, the present numerical approach is used to study the fatigue growth of three parallel cracks with same length under uniaxial cyclic load. Many numerical results are given.     

一种控制界面参数插值的新方法

通过对有限容积法界面插值的分析,提出了一种较调和平均法更为直接、更为有效的用于计算控制容积法控制界面参数的插值方法,并给出了调和平均法失效的算例。数值算例表明,本文方法与Kirchhoff变换法相比具有相当的精度,但又不像Kirchhoff变换法那样需要完成大量的积分运算,计算工作量小,简单可靠。     

Numerical treatment of a discontinuous top surface in 2D shallow water mixed flow modeling

This paper presents a numerical strategy based on shallow water equations (SWE) coupled with the 2D Preissmann slot model to handle a ceiling step discontinuity in finite volume schemes for mixed flow modeling. In practice, a typical situation would be a closed structure, such as a bridge or culvert, which induces a sudden vertical flow constriction and may even run partly or totally full in high flow conditions. In such case, both the inlet and outlet of the structure involve a discontinuity in the top elevation. This special singularity is topologically represented by inserting a fictitious cell between 2 adjacent computational cells characterized by sharply different ceiling elevation. The 2D SWE are solved by means of a well‐balanced quasi‐conservative Godunov‐type numerical scheme based on the Slope Limiter Centered (SLIC) scheme. The flow variables at each boundary of the fictitious cell are reconstructed by adopting the cross‐sectional shape of the adjoining cell. Accordingly, the dynamic effect of the structure deck on the flow is suitably modeled, and the C‐property for a stationary solution is rigorously satisfied, even when the closed structure is partially full. The capability of the numerical scheme is verified by comparison with both novel analytical solutions of 1D Riemann problems with a ceiling step discontinuity and experimental data of steady and unsteady mixed flows available in literature. Finally, a real‐scale application to a multiple arch bridge is presented. The results show that the method is robust and effective in predicting the 2D features induced by a crossing structure on the flow dynamics.     

A high‐resolution scheme for compressible multicomponent flows with shock waves

A simple methodology for a high‐resolution scheme to be applied to compressible multicomponent flows with shock waves is investigated. The method is intended for use with direct numerical simulation or large eddy simulation of compressible multicomponent flows. The method dynamically adds non‐linear artificial diffusivity locally in space to capture different types of discontinuities such as a shock wave, contact surface or material interface while a high‐order compact differencing scheme resolves a broad range of scales in flows. The method is successfully applied to several one‐dimensional and two‐dimensional compressible multicomponent flow problems with shock waves. The results are in good agreement with experiments and earlier computations qualitatively and quantitatively. The method captures unsteady shock and material discontinuities without significant spurious oscillations if initial start‐up errors are properly avoided. Comparisons between the present numerical scheme and high‐order weighted essentially non‐oscillatory (WENO) schemes illustrate the advantage of the present method for resolving a broad range of scales of turbulence while capturing shock waves and material interfaces. Also the present method is expected to require less computational cost than popular high‐order upwind‐biased schemes such as WENO schemes. The mass conservation for each species is satisfied due to the strong conservation form of governing equations employed in the method. Copyright © 2010 John Wiley & Sons, Ltd.