Minimization Problems Based on Relative alpha-Entropy I: Forward Projection

Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative alpha-entropies (denoted I-alpha), arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual relative entropy (Kullback-Leibler divergence). Just like relative entropy, these relative alpha-entropies behave like squared Euclidean distance and satisfy the Pythagorean property. Minimizers of these relative alpha-entropies on closed and convex sets are shown to exist. Such minimizations generalize the maximum Renyi or Tsallis entropy principle. The minimizing probability distribution (termed forward I-alpha-projection) for a linear family is shown to obey a power-law. Other results in connection with statistical inference, namely subspace transitivity and iterated projections, are also established. In a companion paper, a related minimization problem of interest in robust statistics that leads to a reverse I-alpha-projection is studied.

Minimization Problems Based on Relative alpha-Entropy II: Reverse Projection

In part I of this two-part work, certain minimization problems based on a parametric family of relative entropies (denoted I-alpha) were studied. Such minimizers were called forward I-alpha-projections. Here, a complementary class of minimization problems leading to the so-called reverse I-alpha-projections are studied. Reverse I-alpha-projections, particularly on log-convex or power-law families, are of interest in robust estimation problems (alpha > 1) and in constrained compression settings (alpha < 1). Orthogonality of the power-law family with an associated linear family is first established and is then exploited to turn a reverse I-alpha-projection into a forward I-alpha-projection. The transformed problem is a simpler quasi-convex minimization subject to linear constraints.

Growth of ZnO Nanotetrapods with Hexagonal Crown

ZnO nanotetrapods with hexagonal crown were synthesized on a silicon wafer by vapor transport process at a low temperature of 630 °C and normal pressure without the presence of catalysts. The results demonstrated that the as-synthesized products with slender legs and regular hexagonal crown are single crystal with wurtzite structure and preferentially grow up along 001 direction. Photoluminescence spectra revealed that the green emission originated from oxygen vacancies overwhelmed that of the near-band-edge ultraviolet peak, which suggests the peculiar-shaped nanotetrapods may have potential applications in multichannel nano-optoelectronic devices.

Application of Electrical Resistance Tomography System to Monitor Gas/Liquid Two-Phase Flow in a Horizontal Pipe

The Electrical Resistance Tomography (ERT) technique possesses great potential in monitoring widely exiting industrial two/multi-phase flow. For vertical pipe flow and inclined pipe flow, some application studies with exciting results have been reported, but there is rarely a paper regarding the application of ERT to horizontal gas/liquid pipe flow. This paper addresses this issue and proposes a smart method, Liquid Level Detection method, to conventional ERT system. The enhanced ERT system using the new method can monitor horizontal pipe flow effectively and its application is no longer restricted by the flow conditions. Some experimental results from monitoring an air/water slug pipe flow are presented.

Experimental Study of Pore Pressure and Deformation of Suction Bucket Foundations Under Horizontal Dynamic Loading

Centrifuge experiments are carried out to investigate the responses of suction bucket foundations under horizontal dynamic loading. The effects of loading amplitude, the size of the bucket and the structural weight on the dynamic responses are investigated. It is shown that, when the loading amplitude is over a critical value, the sand at the upper part around the bucket softens or even liquefies. The liquefactio...

The Response of Bucket Foundation under Horizontal Dynamic Loading

The experimental investigation of the response of suction bucket foundation in fine sand layer under horizontal dynamic loading has been carried out. The developments of settlement and excess pore pressure of sand foundation have been mainly studied. It is shown that the sand surrounding the bucket softens or even liquefies at the first stage if the loading amplitude is over a critical value, at later stage, the bucket settles and the sand layer consolidates gradually. With the solidification of the liquefied sand layer and the settlement of the bucket, the movement of the sand layer and the bucket reach a stable state.

On the mechanism of the formation of horizontal cracks in a vertical column of saturated sand

Extended horizontal cracks have! been observed experimentally in a vertical column of saturated sand when a flow of water is forced to percolate upward through it. This paper provides a theory for this phenomenon. It will be shown that the presence of inhomogeneity in permeability along the length of the column is essential for such cracks to develop. It will also be shown that small initial inhomogeneity may be magnified through the transport of the finer component of the sand by percolation. Under certain conditions liquefaction takes place at a section of the sand column causing a crack to initiate and grow there. This theory is found to be in good qualitative agreement with the experimental findings.

Influence of Coriolis force on bulk flows during horizontal Bridgman growth on a centrifuge: a numerical study

Three-dimensional and time-dependent numerical simulations are performed For melt convection in horizontal Bridgman crystal growth tinder high gravity conditions by means of a centrifuge. The numerical results show that Coriolis Force can cause a stabilizing effect on the fluctuations of the melt flow under a specific relation direction and relation rates of the centrifuge as reported in previous experiments (Ma et al., Materials Processing in High Gravity, Plenum Press, New York, 1994, p. 61). The present simulation provides details of the now features associated with the effect of the Coriolis force. There are also some differences between the present three-dimensional and former two-dimensional numerical solutions particularly in the prediction of the critical conditions and flow patterns.

Gamma-Ray Attenuation Technique For Measuring Void Fraction In Horizontal Gas-Liquid Two-Phase Flow

The measurement of void fraction is of importance to the oil industry and chemical industry. In this article, the principle and mathematical method of determining the void fraction of horizontal gas-liquid flow by using a single-energy gamma-ray system is described. The gamma-ray source is the radioactive isotope of Am-241 with gamma-ray energy of 59.5 keV. The time-averaged value of the void fraction in a 50.0-mm i.d. transparent horizontal pipeline is measured under various combinations of the liquid flow and gas flow. It is found that increasing the gas flow rate at a fixed liquid flow rate would increase the void fraction. Test data are compared with the predictions of the correlations and a good agreement is found. The result shows that the designed gamma-ray system can be used for measuring the void fraction in a horizontal gas-liquid two-phase flow with high accuracy.

Numerical Simulation Of Horizontal Migration Of Proppant

The horizontal migration of proppant was numerically investigated with a two-fluid model, in which the interaction between fracturing fluid and proppant, along with that among proppants was taken into account through interphase forces. The migration process and the volumetric concentration of the proppant were examined under various conditions, and the. averaged volumetric concentration of the proppant was obtained. The present research might be useful in the process design of the hydraulic fracturing in the oilfields.

Experimental Investigation On The Slip Between Oil And Water In Horizontal Pipes

This work is devoted to study of the slip phenomenon between phases in water-oil two-phase flow in horizontal pipes. The emphasis is placed on the effects of input fluids flow rates, pipe diameter and viscosities of oil phase on the slip. Experiments were conducted to measure the holdup in two horizontal pipes with 0.05 m diameter and 0.025 m diameter, respectively, using two different viscosities of white oil and tap water as liquid phases. Results showed that the ratios of in situ oil to water velocity at the pipe of small diameter are higher than those at the pipe of big diameter when having same input flow rates. At low input water flow rate, there is a large deviation on the holdup between two flow systems with different oil viscosities and the deviation becomes gradually smaller with further increased input water flow rate. (C) 2008 Elsevier Inc. All rights reserved.