Depth above a Drop of the Channel Bottom after Free-Surface Discontinuity Decay

This paper reports experimental data on the depth above a bottom drop in a rectangular channel after removal of a shield that produces the initial difference in the free-surface level. It is shown that at a sufficiently large height of the drop, this depth is approximately 40 % smaller than that obtained in the first shallow-water approximation.     

Stochastic stability and robust control for sampled-data systems with Markovian jump parameters

In this paper, the problems of stochastic stability and robust control for a class of uncertain sampled-data systems are studied. The systems consist of random jumping parameters described by finite-state semi-Markov process. Sufficient conditions for stochastic stability or exponential mean square stability of the systems are presented. The conditions for the existence of a sampled-data feedback control and a multirate sampled-data optimal control for the continuous-time uncertain Markovian jump systems are also obtained. The design procedure for robust multirate sampled-data control is formulated as linear matrix inequalities (LMIs), which can be solved efficiently by available software toolboxes. Finally, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed techniques.     

Water retention of nonwoven polyester geotextiles

Planar polymeric geotextile materials are increasingly used in geotechnical and geoenvironmental engineering applications to perform various functions such as filtration, drainage and reinforcement. In most cases, they are placed above the groundwater table where soil and geotextiles pores are filled with water and air (i.e. under unsaturated conditions). In this respect, the development of the geotextile water-retention curves is of great importance to model the transient water flow in earthen systems containing geotextiles where unsaturated conditions may prevail. This paper, presents the results of a study on the cross-plane and in-plane water-retention characteristics of two nonwoven, polyester geotextiles. The geotextiles’ cross plane water-retention data demonstrated their hydrophobic nature with both specimens being essentially non-conductive to water beyond suction heads of 0.2–0.3 kPa. Pore size and porosity seemed to have a controlling effect on both the desaturation and resaturation processes. The geotextile with the larger apparent opening size and porosity de-saturated at very low suction pressure (0.4 kPa), whereas a slightly higher suction (0.9 kPa) was needed to de-saturate the geotextile with smaller apparent opening size and porosity. Both specimens exhibited significant hysteresis in their water-retention function, such that at a given suction a geotextile contained more water when drying than when wetting. The in-plane water retention of drying geotextiles indicates that both geotextile specimens absorbed no water at suctions greater than zero; thus the water retention of a dry specimen in the in-plane direction is effectively equal to zero. This implies that the geotextiles used in the present study were more hydrophobic in the in-plane than the cross-plane direction during wetting.     

多元弱酸的准确滴定

用二元弱酸滴定的林邦滴定曲线方程推导第一和第二滴定突跃绝对值,用第一和第二滴定突跃绝对值推导二元弱酸第一和第二级解离的H+准确滴定的条件,并将其应用于多元弱酸的准确滴定.     

低煤级煤热解H2生成动力学及其与第一次煤化作用跃变的关系

用开放体系的热重-质谱联用仪(TG/MS)研究了7种低煤级煤的热解特征、H2的生成动力学特征以及它们与第一次煤化作用跃变的关系. 结果显示, 煤热解失重率在碳含量(Cdaf)为80%(质量分数)和镜质组最大反射率(R0max)为0.60%附近发生转折; 氢气生成的特征温度参数以及动力学参数均在Cdaf为80%(R0max为0.60%)左右表现为最低; 氢气的总产率在此处最大. 这些特征参数的极值点刚好与第一次煤化作用跃变点一致, 说明这些参数可以反映第一次煤化作用跃变的发生. 结合傅立叶变换红外(FTIR)光谱法获得的煤结构特征, 对影响机制进行了分析解释, 认为是由以下3个方面的原因导致的: (1)煤中脂肪类含氧官能团的演化特征; (2)可溶有机质的低温热缩聚作用; (3)有机质的“两极分化”作用.     

Effects of dip coating parameters on the morphology and transport properties of cellulose acetate–ceramic composite membranes

This work presents the fabrication of cellulose acetate (CA)–ceramic composite membranes using dip coating technique. Ceramic supports used in this work were prepared from kaolin with an average pore size of 560 nm and total porosity of 33%. The dip coating parameters studied experimentally were the concentration of CA solution (varying from 2 wt% to 8 wt%) in acetone and dipping time (varying from 30 s to 150 s). The fabricated composite membranes were characterized using scanning electron microscope, gas permeation, pure water flux and ultrafiltration (UF) experiments using bovine serum albumin (BSA). It was observed that the membrane prepared with 2 wt% and 4 wt% CA were suitable for microfiltration applications and those with 6 wt% and 8 wt% were for ultrafiltration applications. Theoretical investigation was conducted to know the macroporous and mesoporous structure of the prepared membranes using Knudsen and viscous permeability analysis of air. A resistance in series model was applied to identify different resistances responsible for the flux decline. Phenomenological models were proposed to illustrate the dependency of hydraulic resistance of membrane on the structural parameters such as average pore size, effective porosity as well as dip coating parameters like dipping time and concentration of CA. It was found that, the growth rate of CA film on the ceramic support followed exponential growth law with respect to dipping time. The total hydraulic resistance of the membrane was evaluated to be inversely proportional to the ratio of pore sizes of top layer and ceramic support. The resistance due to the CA film was found to be depended to the order of 1.73 with respect to concentration of CA. An increase in the concentration of CA was found to be more effective than dipping time to reduce the membrane pore size.     

Stochastic stability of positive Markov jump linear systems with fixed dwell time

This paper studies the stochastic stability of positive Markov jump linear systems with a fixed dwell time. By constructing an auxiliary system that originated from the initial system with state jumps, sufficient and necessary conditions of stochastic stability for positive Markov jump linear systems are obtained with both exactly known and partially known transition rates. The main idea in the latter case is applying a convex combination to convert bilinear programming into linear programming problems. On this basis, multiple piecewise linear co-positive Lyapunov functions are provided to achieve less conservative results. Then state feedback controller is designed to stabilize the positive Markov jump linear systems by solving linear programming problems. Numerical examples are presented to illustrate the viability of our conclusions.     

A Markov Risk Model with Two Classes of Insurance Business

A Markov risk model with two classes of insurance business is studied. In this model, the two classes of insurance business are independent. Each of the two independent claim number processes is the number of jumps of a Markov jump process from time 0 to t, whichever has not independent increments in general. An integral equation satisfied by the ruin probability is obtained and the bounds for the convergence rate of the ruin probability are given by using a generalized renewal technique.     

Sufficient Stochastic Maximum Principle for the Optimal Control of Semi-Markov Modulated Jump-Diffusion with Application to Financial Optimization

The finite state semi-Markov process is a generalization over the Markov chain in which the sojourn time distribution is any general distribution. In this article, we provide a sufficient stochastic maximum principle for the optimal control of a semi-Markov modulated jump-diffusion process in which the drift, diffusion, and the jump kernel of the jump-diffusion process is modulated by a semi-Markov process. We also connect the sufficient stochastic maximum principle with the dynamic programming equation. We apply our results to finite horizon risk-sensitive control portfolio optimization problem and to a quadratic loss minimization problem.     

Group invariant solution for a pre-existing fracture driven by a power-law fluid in impermeable rock

The effect of power-law rheology on hydraulic fracturing is investigated. The evolution of a two-dimensional fracture with non-zero initial length and driven by a power-law fluid is analyzed. Only fluid injection into the fracture is considered. The surrounding rock mass is impermeable. With the aid of lubrication theory and the PKN approximation a partial differential equation for the fracture half-width is derived. Using a linear combination of the Lie-point symmetry generators of the partial differential equation, the group invariant solution is obtained and the problem is reduced to a boundary value problem for an ordinary differential equation. Exact analytical solutions are derived for hydraulic fractures with constant volume and with constant propagation speed. The asymptotic solution near the fracture tip is found. The numerical solution for general working conditions is obtained by transforming the boundary value problem to a pair of initial value problems. Throughout the paper, hydraulic fracturing with shear thinning, Newtonian and shear thickening fluids are compared.