The generalized Onsager model for a binary gas mixture

The Onsager model for the secondary flow field in a high-speed rotating cylinder is extended to incorporate the difference in mass of the two species in a binary gas mixture. The base flow is an isothermal solid-body rotation in which there is a balance between the radial pressure gradient and the centrifugal force density for each species. Explicit expressions for the radial variation of the pressure, mass/mole fractions, and from these the radial variation of the viscosity, thermal conductivity and diffusion coefficient, are derived, and these are used in the computation of the secondary flow. For the secondary flow, the mass, momentum and energy equations in axisymmetric coordinates are expanded in an asymptotic series in a parameter epsilon = (Delta m/m(av)), where Delta m is the difference in the molecular masses of the two species, and the average molecular mass m(av) is defined as m(av) = (rho(w1)m(1) + rho(w2)m(2))/rho(w), where rho(w1) and rho(w2) are the mass densities of the two species at the wall, and rho(w) = rho(w1) + rho(w2). The equation for the master potential and the boundary conditions are derived correct to O(epsilon(2)). The leading-order equation for the master potential contains a self-adjoint sixth-order operator in the radial direction, which is different from the generalized Onsager model (Pradhan & Kumaran, J. Fluid Mech., vol. 686, 2011, pp. 109-159), since the species mass difference is included in the computation of the density, viscosity and thermal conductivity in the base state. This is solved, subject to boundary conditions, to obtain the leading approximation for the secondary flow, followed by a solution of the diffusion equation for the leading correction to the species mole fractions. The O(epsilon) and O(epsilon(2)) equations contain inhomogeneous terms that depend on the lower-order solutions, and these are solved in a hierarchical manner to obtain the O(epsilon) and O(epsilon(2)) corrections to the master potential. A similar hierarchical procedure is used for the Carrier-Maslen model for the end-cap secondary flow. The results of the Onsager hierarchy, up to O(epsilon(2)), are compared with the results of direct simulation Monte Carlo simulations for a binary hard-sphere gas mixture for secondary flow due to a wall temperature gradient, inflow/outflow of gas along the axis, as well as mass and momentum sources in the flow. There is excellent agreement between the solutions for the secondary flow correct to O(epsilon(2)) and the simulations, to within 15 %, even at a Reynolds number as low as 100, and length/diameter ratio as low as 2, for a low stratification parameter A of 0.707, and when the secondary flow velocity is as high as 0.2 times the maximum base flow velocity, and the ratio 2 Delta m/(m(1) + m(2)) is as high as 0.5. Here, the Reynolds number Re = rho(w)Omega R-2/mu, the stratification parameter A = root m Omega R-2(2)/(2k(B)T), R and Omega are the cylinder radius and angular velocity, m is the molecular mass, rho(w) is the wall density, mu is the viscosity and T is the temperature. The leading-order solutions do capture the qualitative trends, but are not in quantitative agreement.

Spectrum sensing using distributed sequential detection via noisy reporting MAC

This paper considers cooperative spectrum sensing algorithms for Cognitive Radios which focus on reducing the number of samples to make a reliable detection. We propose algorithms based on decentralized sequential hypothesis testing in which the Cognitive Radios sequentially collect the observations, make local decisions and send them to the fusion center for further processing to make a final decision on spectrum usage. The reporting channel between the Cognitive Radios and the fusion center is assumed more realistically as a Multiple Access Channel (MAC) with receiver noise. Furthermore the communication for reporting is limited, thereby reducing the communication cost. We start with an algorithm where the fusion center uses an SPRT-like (Sequential Probability Ratio Test) procedure and theoretically analyze its performance. Asymptotically, its performance is close to the optimal centralized test without fusion center noise. We further modify this algorithm to improve its performance at practical operating points. Later we generalize these algorithms to handle uncertainties in SNR and fading. (C) 2014 Elsevier B.V. All rights reserved.

Optimal Linear Glauber Model

Contrary to the actual nonlinear Glauber model, the linear Glauber model (LGM) is exactly solvable, although the detailed balance condition is not generally satisfied. This motivates us to address the issue of writing the transition rate () in a best possible linear form such that the mean squared error in satisfying the detailed balance condition is least. The advantage of this work is that, by studying the LGM analytically, we will be able to anticipate how the kinetic properties of an arbitrary Ising system depend on the temperature and the coupling constants. The analytical expressions for the optimal values of the parameters involved in the linear are obtained using a simple Moore-Penrose pseudoinverse matrix. This approach is quite general, in principle applicable to any system and can reproduce the exact results for one dimensional Ising system. In the continuum limit, we get a linear time-dependent Ginzburg-Landau equation from the Glauber's microscopic model of non-conservative dynamics. We analyze the critical and dynamic properties of the model, and show that most of the important results obtained in different studies can be reproduced by our new mathematical approach. We will also show in this paper that the effect of magnetic field can easily be studied within our approach; in particular, we show that the inverse of relaxation time changes quadratically with (weak) magnetic field and that the fluctuation-dissipation theorem is valid for our model.

Use of permeable reactive barrier to mitigate groundwater nitrate contamination from on-site sanitation

Nearly 50% of India's population depends on variants of pit-toilet systems for human waste disposal. Nitrate contamination of groundwater by pit-toilet leachate is a major environmental concern in the country as it sources a major proportion (50-80%) of potable water from aquifers. Therefore, minimizing nitrate contamination of groundwater due to leachate infiltration from pit-toilet systems is essential. Batch and column experiments demonstrated the capability of bentonite-enhanced sand (BES) specimens to reduce nitrate concentrations in synthetic solutions (initial NO3-N concentration = 22.7 mg/L, C/N = 3) by about 85-90% in 10 to 24 hour by a heterotrophic denitrification process. Based on the laboratory results, it is recommended that use of a BES-permeable reactive barrier layer at the base of pit-toilets will facilitate heterotrophic denitrification and mitigate nitrate contamination of the underlying aquifer.

Numerical study of solidification of A356 aluminum alloy flowing on an oblique plate with experimental validation

Molten A356 aluminum alloy flowing on an oblique plate is water cooled from underneath. The melt partially solidifies on plate wall with continuous formation of columnar dendrites. These dendrites are continuously sheared off into equiaxed/fragmented grains and carried away with the melt by producing semisolid slurry collected at plate exit. Melt pouring temperature provides required solidification whereas plate inclination enables necessary shear for producing slurry of desired solid fraction. A numerical model concerning transport equations of mass, momentum, energy and species is developed for predicting velocity, temperature, macrosegregation and solid fraction. The model uses FVM with phase change algorithm, VOF and variable viscosity. The model introduces solid phase movement with gravity effect as well. Effects of melt pouring temperature and plate inclination on hydrodynamic and thermo-solutal behaviors are studied subsequently. Slurry solid fractions at plate exit are 27%, 22%, 16%, and 10% for pouring temperatures of 620 degrees C, 625 degrees C, 630 degrees C, and 635 degrees C, respectively. And, are 27%, 25%, 22%, and 18% for plate inclinations of 30, 45, 60, and 75, respectively. Melt pouring temperature of 625 degrees C with plate inclination of 60 generates appropriate quality of slurry and is the optimum. Both numerical and experimental results are in good agreement with each other. (C) 2015 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Lesion Detection in Breast Ultrasound Images Using Tissue Transition Analysis

Breast cancer is one of the leading cause of cancer related deaths in women and early detection is crucial for reducing mortality rates. In this paper, we present a novel and fully automated approach based on tissue transition analysis for lesion detection in breast ultrasound images. Every candidate pixel is classified as belonging to the lesion boundary, lesion interior or normal tissue based on its descriptor value. The tissue transitions are modeled using a Markov chain to estimate the likelihood of a candidate lesion region. Experimental evaluation on a clinical dataset of 135 images show that the proposed approach can achieve high sensitivity (95 %) with modest (3) false positives per image. The approach achieves very similar results (94 % for 3 false positives) on a completely different clinical dataset of 159 images without retraining, highlighting the robustness of the approach.