An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems

A finite element method for solving multidimensional population balance systems is proposed where the balance of fluid velocity, temperature and solute partial density is considered as a two-dimensional system and the balance of particle size distribution as a three-dimensional one. The method is based on a dimensional splitting into physical space and internal property variables. In addition, the operator splitting allows to decouple the equations for temperature, solute partial density and particle size distribution. Further, a nodal point based parallel finite element algorithm for multi-dimensional population balance systems is presented. The method is applied to study a crystallization process assuming, for simplicity, a size independent growth rate and neglecting agglomeration and breakage of particles. Simulations for different wall temperatures are performed to show the effect of cooling on the crystal growth. Although the method is described in detail only for the case of d=2 space and s=1 internal property variables it has the potential to be extendable to d+s variables, d=2, 3 and s >= 1. (C) 2011 Elsevier Ltd. All rights reserved.

Reinforcement learning applications in dynamic pricing of retail markets

In this paper, we investigate the use of reinforcement learning (RL) techniques to the problem of determining dynamic prices in an electronic retail market. As representative models, we consider a single seller market and a two seller market, and formulate the dynamic pricing problem in a setting that easily generalizes to markets with more than two sellers. We first formulate the single seller dynamic pricing problem in the RL framework and solve the problem using the Q-learning algorithm through simulation. Next we model the two seller dynamic pricing problem as a Markovian game and formulate the problem in the RL framework. We solve this problem using actor-critic algorithms through simulation. We believe our approach to solving these problems is a promising way of setting dynamic prices in multi-agent environments. We illustrate the methodology with two illustrative examples of typical retail markets.

Population, globalization and urbanization: Trends and underlying prosesses

Third World hinterlands provide most of the settings in which the quality of human life has improved the least over the decade since Our Common Future was published. This low quality of life promotes a desire for large number of offspring, fuelling population growth and an exodus to the urban centres of the Third World, Enhancing the quality of life of these people in ways compatible with the health of their environments is therefore the most significant of the challenges from the perspective of sustainable development. Human quality of life may be viewed in terms of access to goods, services and a satisfying social role. The ongoing processes of globalization are enhancing flows of goods worldwide, but these hardly reach the poor of Third World countrysides. But processes of globalization have also vastly improved everybody's access to Information, and there are excellent opportunities of putting this to good use to enhance the quality of life of the people of Third World countrysides through better access to education and health. More importantly, better access to information could promote a more satisfying social role through strengthening grass-roots involvement in development planning and management of natural resources. I illustrate these possibilities with the help of a series of concrete experiences form the south Indian state of Kerala. Such an effort does not call for large-scare material inputs, rather it calls for a culture of inform-and-share in place place of the prevalent culture of control-and-command. It calls for openness and transparency in transactions involving government agencies, NGOs, and national and transnational business enterprises. It calls for acceptance of accountability by such agencies.

Tensile force distribution along the reinforcement for reinforced soil foundations

In a reinforced soil bed system reinforcement layer is usually placed with or without end anchorage. Since soil is weak in tension reinforcement develop tension under the applied load or the displacement of the footing. This tensile force is distributed along the length of the reinforcement subjected to the end condition. The reinforccement tension helps in distributing the load over a wider area, and becomes more effective at large induced settlements. As a result, vertical componenent of tensile force generated becomes effective in reducing applied load. However, very few studies to quantify the tensile force along the reinforcement have been reported in the literature. In this paper an attempt has been made to obtain the true nature of tensile force distribution along the reinforcement. For a reinforced soil bed below a strip footing this paper brings out induced tensile force distribution along the reinforcement at different load levels and for different types of reinforcements.

A neural network based automatic generation control design through reinforcement learning

This paper presents the design and implementation of a learning controller for the Automatic Generation Control (AGC) in power systems based on a reinforcement learning (RL) framework. In contrast to the recent RL scheme for AGC proposed by us, the present method permits handling of power system variables such as Area Control Error (ACE) and deviations from scheduled frequency and tie-line flows as continuous variables. (In the earlier scheme, these variables have to be quantized into finitely many levels). The optimal control law is arrived at in the RL framework by making use of Q-learning strategy. Since the state variables are continuous, we propose the use of Radial Basis Function (RBF) neural networks to compute the Q-values for a given input state. Since, in this application we cannot provide training data appropriate for the standard supervised learning framework, a reinforcement learning algorithm is employed to train the RBF network. We also employ a novel exploration strategy, based on a Learning Automata algorithm,for generating training samples during Q-learning. The proposed scheme, in addition to being simple to implement, inherits all the attractive features of an RL scheme such as model independent design, flexibility in control objective specification, robustness etc. Two implementations of the proposed approach are presented. Through simulation studies the attractiveness of this approach is demonstrated.

Reinforcement learning controllers for automatic generation control in power systems having re-heat units with GRC and dead-band

A new automatic generation controller (AGC) design approach, adopting reinforcement learning (RL) techniques, was recently pro- posed [1]. In this paper we demonstrate the design and performance of controllers based on this RL approach for automatic generation control of systems consisting of units having complex dynamics—the reheat type of thermal units. For such systems, we also assess the capabilities of RL approach in handling realistic system features such as network changes, parameter variations, generation rate constraint (GRC), and governor deadband.

A new approach to the design of reinforcement schemes for learning automata

On introduit une nouvelle classe de schémas de renforcement des automates d'apprentissage utilisant les estimations des caractéristiques aléatoires de l'environnement. On montre que les algorithmes convergent en probabilité vers le choix optimal des actions. On présente les résultats de simulation et on suggère des applications à un environnement à plusieurs apprentissages

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.

Population crunch in India: is it urban or still rural?

The article attempts to present analysis based on the provisional results of the Census 2011. While there is no doubt that the human social organization of the country is undergoing a transition, the nature of growth however is subject to the lens through which this is viewed. Noting the dichotomy of urban and rural definitions, we question the rationality of the ‘urban’ definition and its relevance.

An operator-splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence

We present a heterogeneous finite element method for the solution of a high-dimensional population balance equation, which depends both the physical and the internal property coordinates. The proposed scheme tackles the two main difficulties in the finite element solution of population balance equation: (i) spatial discretization with the standard finite elements, when the dimension of the equation is more than three, (ii) spurious oscillations in the solution induced by standard Galerkin approximation due to pure advection in the internal property coordinates. The key idea is to split the high-dimensional population balance equation into two low-dimensional equations, and discretize the low-dimensional equations separately. In the proposed splitting scheme, the shape of the physical domain can be arbitrary, and different discretizations can be applied to the low-dimensional equations. In particular, we discretize the physical and internal spaces with the standard Galerkin and Streamline Upwind Petrov Galerkin (SUPG) finite elements, respectively. The stability and error estimates of the Galerkin/SUPG finite element discretization of the population balance equation are derived. It is shown that a slightly more regularity, i.e. the mixed partial derivatives of the solution has to be bounded, is necessary for the optimal order of convergence. Numerical results are presented to support the analysis.

Measurement of effective permeability of reinforcement mats using sensitivity analysis

A methodology using sensitivity analysis is proposed to measure the effective permeability which includes the interaction of the resin and the reinforcement. Initially, mold-filling experiments were performed at isothermal conditions on the test specimen and the positions of the flow front were tracked with time using a flow visualization method. Following this, mold-filling experiments were simulated using a commercial software to obtain the positions of the flow front with time at the process conditions used for experiments. Several iterations were performed using different trial values of the permeability until the experimentally tracked and simulated positions of the flow front with time were matched. Finally, the value of the permeability thus obtained was validated by comparing the positions obtained by performing the experiments at different process conditions with the positions obtained by simulating the experiments. In this study, woven roving and chopped strand mats of E-class glass fiber and unsaturated polyester resin were used for the experiments. From the results, it was found that the measured permeabilities were consistent with varying process conditions. POLYM. COMPOS., 2012. (c) 2012 Society of Plastics Engineers

A finite population model of mlecular evolution: theory and computation

This article is concerned with the evolution of haploid organisms that reproduce asexually. In a seminal piece of work, Eigen and coauthors proposed the quasispecies model in an attempt to understand such an evolutionary process. Their work has impacted antiviral treatment and vaccine design strategies. Yet, predictions of the quasispecies model are at best viewed as a guideline, primarily because it assumes an infinite population size, whereas realistic population sizes can be quite small. In this paper we consider a population genetics-based model aimed at understanding the evolution of such organisms with finite population sizes and present a rigorous study of the convergence and computational issues that arise therein. Our first result is structural and shows that, at any time during the evolution, as the population size tends to infinity, the distribution of genomes predicted by our model converges to that predicted by the quasispecies model. This justifies the continued use of the quasispecies model to derive guidelines for intervention. While the stationary state in the quasispecies model is readily obtained, due to the explosion of the state space in our model, exact computations are prohibitive. Our second set of results are computational in nature and address this issue. We derive conditions on the parameters of evolution under which our stochastic model mixes rapidly. Further, for a class of widely used fitness landscapes we give a fast deterministic algorithm which computes the stationary distribution of our model. These computational tools are expected to serve as a framework for the modeling of strategies for the deployment of mutagenic drugs.

Chromosomal translocations among the healthy human population: implications in oncogenesis

Chromosomal translocations are characteristic features of many cancers, especially lymphoma and leukemia. However, recent reports suggest that many chromosomal translocations can be found in healthy individuals, although the significance of this observation is still not clear. In this review, we summarize recent studies on chromosomal translocations in healthy individuals carried out in different geographical areas of the world and discuss the relevance of the observation with respect to oncogenesis.

On finding a set of healthy individuals from a large population

In this paper, we explore fundamental limits on the number of tests required to identify a given number of ``healthy'' items from a large population containing a small number of ``defective'' items, in a nonadaptive group testing framework. Specifically, we derive mutual information-based upper bounds on the number of tests required to identify the required number of healthy items. Our results show that an impressive reduction in the number of tests is achievable compared to the conventional approach of using classical group testing to first identify the defective items and then pick the required number of healthy items from the complement set. For example, to identify L healthy items out of a population of N items containing K defective items, when the tests are reliable, our results show that O(K(L - 1)/(N - K)) measurements are sufficient. In contrast, the conventional approach requires O(K log(N/K)) measurements. We derive our results in a general sparse signal setup, and hence, they are applicable to other sparse signal-based applications such as compressive sensing also.