On the solution of bivariate population balance equations for aggregation: X-discretization of space for expansion and contraction of computational domain

A new structured discretization of 2D space, named X-discretization, is proposed to solve bivariate population balance equations using the framework of minimal internal consistency of discretization of Chakraborty and Kumar [2007, A new framework for solution of multidimensional population balance equations. Chem. Eng. Sci. 62, 4112-4125] for breakup and aggregation of particles. The 2D space of particle constituents (internal attributes) is discretized into bins by using arbitrarily spaced constant composition radial lines and constant mass lines of slope -1. The quadrilaterals are triangulated by using straight lines pointing towards the mean composition line. The monotonicity of the new discretization makes is quite easy to implement, like a rectangular grid but with significantly reduced numerical dispersion. We use the new discretization of space to automate the expansion and contraction of the computational domain for the aggregation process, corresponding to the formation of larger particles and the disappearance of smaller particles by adding and removing the constant mass lines at the boundaries. The results show that the predictions of particle size distribution on fixed X-grid are in better agreement with the analytical solution than those obtained with the earlier techniques. The simulations carried out with expansion and/or contraction of the computational domain as population evolves show that the proposed strategy of evolving the computational domain with the aggregation process brings down the computational effort quite substantially; larger the extent of evolution, greater is the reduction in computational effort. (C) 2011 Elsevier Ltd. All rights reserved.

On the solution of bivariate population balance equations for aggregation: Pivotwise expansion of solution domain

The solution of a bivariate population balance equation (PBE) for aggregation of particles necessitates a large 2-d domain to be covered. A correspondingly large number of discretized equations for particle populations on pivots (representative sizes for bins) are solved, although at the end only a relatively small number of pivots are found to participate in the evolution process. In the present work, we initiate solution of the governing PBE on a small set of pivots that can represent the initial size distribution. New pivots are added to expand the computational domain in directions in which the evolving size distribution advances. A self-sufficient set of rules is developed to automate the addition of pivots, taken from an underlying X-grid formed by intersection of the lines of constant composition and constant particle mass. In order to test the robustness of the rule-set, simulations carried out with pivotwise expansion of X-grid are compared with those obtained using sufficiently large fixed X-grids for a number of composition independent and composition dependent aggregation kernels and initial conditions. The two techniques lead to identical predictions, with the former requiring only a fraction of the computational effort. The rule-set automatically reduces aggregation of particles of same composition to a 1-d problem. A midway change in the direction of expansion of domain, effected by the addition of particles of different mean composition, is captured correctly by the rule-set. The evolving shape of a computational domain carries with it the signature of the aggregation process, which can be insightful in complex and time dependent aggregation conditions. (c) 2012 Elsevier Ltd. All rights reserved.

Molecular analysis of Friedreich's ataxia locus in the Indian population

Friedreich's ataxia (FRDA) is an autosomal recessive neurodegenerative disorder caused by expansion of GAA repeats in the frataxin gene. We have carried out the first molecular analysis at the Friedreich's ataxia locus in the Indian population. Materials and methods - Three families clinically diagnosed for Friedreich's ataxia were analyzed for GAA expansion at the FRDA locus. The distribution of GAA repeats was also estimated in normal individuals of Indian origin. Results - All patients clinically diagnosed for Friedreich's ataxia were found to be homozygous for GAA repeat expansion. The GAA repeat in the normal population show a bimodal distribution with 94% of alleles ranging from 7-16 repeats. Conclusion - Indian patients with expansion at the FRDA locus showed typical clinical features of Friedreich's ataxia. The low frequency of large normal alleles (6%) could indicate that the prevalence of this disease in the Indian population is likely to be low.

REPERTOIRE OF PROTEIN KINASES ENCODED IN THE GENOME OF ZEBRAFISH SHOWS REMARKABLY LARGE POPULATION OF PIM KINASES

In recent times, zebrafish has garnered lot of popularity as model organism to study human cancers. Despite high evolutionary divergence from humans, zebrafish develops almost all types of human tumors when induced. However, mechanistic details of tumor formation have remained largely unknown. Present study is aimed at analysis of repertoire of kinases in zebrafish proteome to provide insights into various cellular components. Annotation using highly sensitive remote homology detection methods revealed ``substantial expansion'' of Ser/Thr/Tyr kinase family in zebrafish compared to humans, constituting over 3% of proteome. Subsequent classification of kinases into subfamilies revealed presence of large number of CAMK group of kinases, with massive representation of PIM kinases, important for cell cycle regulation and growth. Extensive sequence comparison between human and zebrafish PIM kinases revealed high conservation of functionally important residues with a few organism specific variations. There are about 300 PIM kinases in zebrafish kinome, while human genome codes for only about 500 kinases altogether. PIM kinases have been implicated in various human cancers and are currently being targeted to explore their therapeutic potentials. Hence, in depth analysis of PIM kinases in zebrafish has opened up new avenues of research to verify the model organism status of zebrafish.

Precipitation In Small Systems--II. Mean Field Equations More Effective Than Population Balance

Part I (Manjunath et al., 1994, Chem. Engng Sci. 49, 1451-1463) of this paper showed that the random particle numbers and size distributions in precipitation processes in very small drops obtained by stochastic simulation techniques deviate substantially from the predictions of conventional population balance. The foregoing problem is considered in this paper in terms of a mean field approximation obtained by applying a first-order closure to an unclosed set of mean field equations presented in Part I. The mean field approximation consists of two mutually coupled partial differential equations featuring (i) the probability distribution for residual supersaturation and (ii) the mean number density of particles for each size and supersaturation from which all average properties and fluctuations can be calculated. The mean field equations have been solved by finite difference methods for (i) crystallization and (ii) precipitation of a metal hydroxide both occurring in a single drop of specified initial supersaturation. The results for the average number of particles, average residual supersaturation, the average size distribution, and fluctuations about the average values have been compared with those obtained by stochastic simulation techniques and by population balance. This comparison shows that the mean field predictions are substantially superior to those of population balance as judged by the close proximity of results from the former to those from stochastic simulations. The agreement is excellent for broad initial supersaturations at short times but deteriorates progressively at larger times. For steep initial supersaturation distributions, predictions of the mean field theory are not satisfactory thus calling for higher-order approximations. The merit of the mean field approximation over stochastic simulation lies in its potential to reduce expensive computation times involved in simulation. More effective computational techniques could not only enhance this advantage of the mean field approximation but also make it possible to use higher-order approximations eliminating the constraints under which the stochastic dynamics of the process can be predicted accurately.

Homogeneous isotropic turbulence: large momentum expansion

High temperature expansion is an effective tool for studying second order phase transitions. With this in mind, we have looked at a high momentum expansion for homogeneous isotropic turbulence. Combining our results with those of the inertial range, we give another view of extended self-similarity (ESS).

On the moulding of population viscosity by natural selection

In this paper, we explore the conjoint evolution of dispersal and social behaviour. The model investigated is of a population distributed over a number of sites each with a carrying capacity of two adults and an episode of dispersal in the juvenile stage. The fertilities are governed by whether an individual and its neighbour are selfish or co-operative. It is shown that the best dispersal strategy for the co-operative genotype always involves lower levels of dispersal; and further that ecological conditions favouring low levels of dispersal increase the selective advantage of a co-operative genotype. Given this positive feedback, we suggest that in any taxon viscosity and co-operativity will tend to be correlated and bimodally distributed. Hence we predict the existence of two kinds of animal societies; viscous and co-operative (e.g. quasi-social wasps such as Mischocyttarus), and non-viscous and selfish (e.g. communal sphecid wasps such as Cerceris), and relatively few social groups with intermediate levels of co-operativity and viscosity. We also suggest that when one of the two sexes disperses, it will be the sex with lower potential for co-operative behaviour.

Transmission loss analysis of rectangular expansion chamber with arbitrary location of inlet/outlet by means of Green's functions

Transmission loss of a rectangular expansion chamber, the inlet and outlet of which are situated at arbitrary locations of the chamber, i.e., the side wall or the face of the chamber, are analyzed here based on the Green's function of a rectangular cavity with homogeneous boundary conditions. The rectangular chamber Green's function is expressed in terms of a finite number of rigid rectangular cavity mode shapes. The inlet and outlet ports are modeled as uniform velocity pistons. If the size of the piston is small compared to wavelength, then the plane wave excitation is a valid assumption. The velocity potential inside the chamber is expressed by superimposing the velocity potentials of two different configurations. The first configuration is a piston source at the inlet port and a rigid termination at the outlet, and the second one is a piston at the outlet with a rigid termination at the inlet. Pressure inside the chamber is derived from velocity potentials using linear momentum equation. The average pressure acting on the pistons at the inlet and outlet locations is estimated by integrating the acoustic pressure over the piston area in the two constituent configurations. The transfer matrix is derived from the average pressure values and thence the transmission loss is calculated. The results are verified against those in the literature where use has been made of modal expansions and also numerical models (FEM fluid). The transfer matrix formulation for yielding wall rectangular chambers has been derived incorporating the structural–acoustic coupling. Parametric studies are conducted for different inlet and outlet configurations, and the various phenomena occurring in the TL curves that cannot be explained by the classical plane wave theory, are discussed.

Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator–to–superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

Analysis of EXCOBULLE two-phase expansion tests

analysis of a complex physical problem and the close agreement they achieved with observations. However, the following points need to be clarified. First of all the authors assume that during the initial phases of expansion, the Tayior's instability sets in due to the acceleraacceleration of lighter fluid against the more dense cold water.

Ultrasonic velocities and thermal expansion coefficients of amorphous Se80Te20 and Se90Te10 alloys near glass transitions

Precise measurements of the ultrasonic velocities and thermal expansivities of amorphous Se80Te20 and Se90Te10 alloys are reported near the glass transition. The samples are produced by liquid quenching. The longitudinal and transverse velocities are measured at 10 MHz frequency using the McSkimin pulse superposition technique. The thermal expansivities,agr, are measured using a three-terminal capacitance bridge. Theagr-values show a sharp maximum near the glass transition temperature,T g. The ultrasonic velocities also show a large temperature derivative, dV/dT nearT g. The data are discussed in terms of existing theories of the glass transition. The continuous change inagr shows that the glass transition is not a first-order transition, as suggested by some theories. The samples are found to be deformed by small loads nearT g. The ultrasonic velocities and dV/dT have contributions arising from this deformation.

Ultrasonic velocities and thermal expansion coefficients of amorphous Se80Te20 and Se90Te10 alloys near glass transitions

Precise measurements of the ultrasonic velocities and thermal expansivities of amorphous Se80Te20 and Se90Te10 alloys are reported near the glass transition. The samples are produced by liquid quenching. The longitudinal and transverse velocities are measured at 10 MHz frequency using the McSkimin pulse superposition technique. The thermal expansivities,agr, are measured using a three-terminal capacitance bridge. Theagr-values show a sharp maximum near the glass transition temperature,T g. The ultrasonic velocities also show a large temperature derivative, dV/dT nearT g. The data are discussed in terms of existing theories of the glass transition. The continuous change inagr shows that the glass transition is not a first-order transition, as suggested by some theories. The samples are found to be deformed by small loads nearT g. The ultrasonic velocities and dV/dT have contributions arising from this deformation.

Thermal expansion and a new phase transition in pyroelectric LiKSO4

Single crystal macroscopic thermal expansion coefficient measurements have been made on uniaxial lithium potassium sulphate crystal both along and normal to the six fold axis, employing Fizeau’s interferometer method. Measurements were made in the range of −120°C to 500°C. The results show that lithium potassium sulphate exhibits two major anomalies in its expansion coefficients around −95°C and 422°C respectively, the one at −95°C has been observed for the first time. The nature of dimensional changes of the crystal at the upper and lower transition points are opposite in nature. The crystal shows considerable lattice anisotropy. Megaw’s tilt concept has been invoked to explain the relative magnitudes of expansion coefficients alonga andc directions. Structural features responsible for the absence of ferroelectricity in this crystal have been pointed out.