On the source of quasi-periodic oscillations of the black hole candidate GRS 1915+105: some new observations and their interpretation

A few classes of the light curve of the black hole candidate GRS 1915+105 have been analysed in detail. We discover that unlike the previous findings, quasi-periodic oscillations (QPOs) occasionally occur even in the so-called 'On' or softer states. Such findings may require a revision of the accretion/wind scenario of the black hole candidates. We conjecture that considerable winds that are produced in 'Off' states cool down as a result of Comptonization and fall back to the disc, creating an excess accretion rate and producing the so-called 'On' state. After the drainage of the excess matter, the disc goes back to the 'Off' state. Our findings strengthen the shock oscillation model for QPOs.     

Sonochemical Degradation of Pharmaceutical Wastewater

This study presents the influence of the addition of additives such as activated carbon, carbon tetra chloride, hydrogen peroxide, and potassium dichromate on ultrasonic reduction of pharmaceutical wastewater chemical oxygen demand (COD) under laboratory conditions. The addition of activated carbon increased the % COD reduction whereas the combined addition of activated carbon and H₂O₂/CCl₄/K₂Cr₂O₇ was found to show higher reduction. Among the various combinations investigated, the combined addition of activated carbon and CCl₄ was found to be the best combination. However, the environmental and health problems associated with these chemicals limit the applicability of the process in an industrial level. Further investigation with this system showed that the initial pH and initial COD have significant influence on the removal rate. The data obtained were fitted with first order and Langmuir–Hinshelwood kinetic models. The values of the rate constants obtained indicated that the pharmaceutical wastewater can be treated efficiently by the proposed methods.     

Is a chaotic multi‐fractal approach for rainfall possible?

An Erratum has been published for this article in Hydrological Processes 15 (12) 2001, 2381–2382. Applications of the ideas gained from fractal theory to characterize rainfall have been one of the most exciting areas of research in recent times. The studies conducted thus far have nearly unanimously yielded positive evidence regarding the existence of fractal behaviour in rainfall. The studies also revealed the insufficiency of the mono‐fractal approaches to characterizing the rainfall process in time and space and, hence, the necessity for multi‐fractal approaches. The assumption behind multi‐fractal approaches for rainfall is that the variability of the rainfall process could be directly modelled as a stochastic (or random) turbulent cascade process, since such stochastic cascade processes were found to generically yield multi‐fractals. However, it has been observed recently that multi‐fractal approaches might provide positive evidence of a multi‐fractal nature not only in stochastic processes but also in, for example, chaotic processes. The purpose of the present study is to investigate the presence of both chaotic and fractal behaviours in the rainfall process to consider the possibility of using a chaotic multi‐fractal approach for rainfall characterization. For this purpose, daily rainfall data observed at the Leaf River basin in Mississippi are studied, and only temporal analysis is carried out. The autocorrelation function, the power spectrum, the empirical probability distribution function, and the statistical moment scaling function are used as indicators to investigate the presence of fractal, whereas the presence of chaos is investigated by employing the correlation dimension method. The results from the fractal identification methods indicate that the rainfall data exhibit multi‐fractal behaviour. The correlation dimension method yields a low dimension, suggesting the presence of chaotic behaviour. The existence of both multi‐fractal and chaotic behaviours in the rainfall data suggests the possibility of a chaotic multi‐fractal approach for rainfall characterization. Copyright © 2001 John Wiley & Sons, Ltd.     

Measuring nonlinear dependence in hydrologic time series

It has been a common practice to employ the correlation dimension method to investigate the presence of nonlinearity and chaos in hydrologic processes. Although the method is generally reliable, potential limitations that exist in its applications to hydrologic data cannot be dismissed altogether. As for these limitations, two issues have dominated the discussions thus far: small data size and presence of noise. Another issue that is equally important, but less discussed in the literature, is the selection of delay time (τ _d ) for reconstruction of the phase-space, which is an essential first step in the correlation dimension method, or any other chaos identification and prediction method for that matter. It has also been increasingly recognized that fixing the delay time window (τ _w ) rather than just the delay time itself could be more appropriate, since the delay time window is the one that is of actual interest at the end to represent the dynamics. To this effect, Kim et al. (1998a) [Phys Rev E 58(5):5676–5682] developed a procedure for fixing the delay time window and demonstrated its effectiveness on three artificial chaotic series, and followed it up with the development of the C–C method to estimate both the delay time and the delay time window. The purpose of the present study is to test this procedure on real hydrologic time series and, hence, to assess their nonlinear deterministic characteristics. Three hydrologic time series are studied: (1) daily streamflow series from St. Johns near Cocoa, FL, USA; (2) biweekly volume time series from the Great Salt Lake, UT, USA; and (3) daily rainfall series from Seoul, South Korea. The results are also compared with those obtained using the conventional autocorrelation function (ACF) method.     

The Effect of Spatial Correlation of Cone Tip Resistance on the Bearing Capacity of Shallow Foundations

The effect of directional behaviour of correlation structure of cone tip resistance on the bearing capacity of shallow strip footing resting on cohesionless soil deposit in 2-D random field is analysed using probabilistic approach. The results obtained from the analysis show that the assumption of perfect (or infinite) correlation of cone tip resistance data leads to lower values of probability of failure. In contrast, the isotropic assumption of correlation behaviour based on vertical scale of fluctuation leads to higher values of probability of failure. The results also show that the transformation model would play a major role in the evaluation of variability of design property. In conclusion, the need for a proper evaluation methodology for calculation of correlation lengths of soil properties and their influence in foundation design is highlighted.     

Three-dimensional analysis of vertical square anchor plate in cohesionless soil

ABSTRACT

Vertical anchor plates are often provided to increase the performance of various geotechnical engineering structures such as sheet pile walls, bulkheads, bridge abutments and offshore structures. Hence, the safe design of such structures needs a better understanding of the 3D behaviour of the anchor plate. This paper presents and discusses the results obtained from a series of 3D finite-difference analyses of vertical square anchor plate embedded in cohesionless soil. The 3D model is found to closely predict experimental pullout load–displacement relationship. The failure mechanism observed in the numerical model is found to be very similar to the failure reported in experimental studies. For a given embedment depth, the stiffness of the breakout factor–displacement response substantially reduces with increase in anchor plate size. However, the ultimate reduction in anchor capacity is found to approximately 8% with an increase in anchor size from 0.1 to 1 m. Numerical analysis reveals that at deeper embedment depth, the friction angle of sand is the critical parameter in enhancing the performance of anchor plate. The obtained 3D model results are then compared with the published results and are found to be reasonably in good agreement with each other.     

Influence of operating parameters on treatment of egg processing effluent by electrocoagulation process

The treatment of egg processing effluent was investigated in a batch electrocoagulation reactor using aluminum as sacrificial electrodes. The influence of operating parameters such as electrode distance, stirring speed, electrolyte concentration, pH, current density and electrolysis time on percentage turbidity, chemical oxygen demand and biochemical oxygen demand removal were analyzed. From the experimental results, 3-cm electrode distance, 150 rpm, 1.5 g/l sodium chloride, pH of 6, 20 mA/cm² current density, and 30-min electrolysis time were found to be optimum for maximum removal of turbidity, chemical oxygen demand and biochemical oxygen demand. The removal of turbidity, chemical oxygen demand and biochemical oxygen demand under the optimum condition was found to be 96, 89 and 84 %, respectively. The energy consumption was varied from 7.91 to 27.16 kWh/m³, and operating cost was varied from 1.36 to 4.25 US $/m³ depending on the operating conditions. Response surface methodology has been employed to evaluate the individual and interactive effects of four independent parameters such as electrolyte concentration (0.5–2.5 g/l), initial pH (4–8), current density (10–30 mA/cm²) and electrolysis time (10–50 min) on turbidity, chemical oxygen demand and biochemical oxygen demand removal. The results have been analyzed using Pareto analysis of variance to predict the responses. Based on the analysis, second-order polynomial mathematical models were developed and found to be good fit with the experimental data.