Mathematical modelling of neurons and neural networks

The basic concepts and techniques involved in the development and analysis of mathematical models for individual neurons and networks of neurons are reviewed. Some of the interesting results obtained from recent work in this field are described. The current status of research in this field in India is discussed

Mathematical modelling of divided blast cupola

A pseudo 2-D mathematical model has been developed to simulate a cupola with one row and two rows of tuyere. The simulation results predicted higher spout temperature and combustion ratio for cupola with two rows of tuyere compared to that with one row. Further, the model has been used to study the effect of the distance of separation between the two rows of tuyere on cupola performance. The computed results shows that the spout temperature increases with tuyere level separation and attains the maximum at an optimum distance of separation between two rows of tuyere. Above the optimum, the spout temperature starts decreasing. The exit gas temperature and combustion ratio increases monotonously with the increase in tuyere level separation. These results agree well with the reported experimental observations. The mechanism behind the improved cupola performance with two rows of tuyere has been deduced from the computed temperature and composition profiles inside the cupola.

Advances in the Mathematical Modelling of Hepatitis C Virus Dynamics

Mathematical models have provided key insights into the pathogenesis of hepatitis C virus (HCV) in vivo, suggested predominant mechanism(s) of drug action, explained confounding patterns of viral load changes in HCV infected patients undergoing therapy, and presented a framework for therapy optimization. In this article, I present an overview of the major advances in the mathematical modeling of HCV dynamics.

Simulation and modelling of orbital debris environment by equivalent breakups

It is well known that the increasing space activities pose a serious threat to future missions. This is mainly due to the presence of spent stages, rockets spacecraft and fragments which can lead to collisions. The calculation of the collision probability of future space vehicles with the orbital debris is necessary for estimating the risk. There is lack of adequately catalogued and openly available detailed information on the explosion characteristics of trackable and untrackable debris data. Such a situation compels one to develop suitable mathematical modelling of the explosion and the resultant debris environment. Based on a study of the available information regarding the fragmentation, subsequent evolution and observation, it turns out to be possible to develop such a mathematical model connecting the dynamical features of the fragmentation with the geometrical/orbital characteristics of the debris and representing the environment through the idea of equivalent breakup. (C) 1997 COSPAR.

Impact of compost, vermicompost and biochar on soil fertility, maize yield and soil erosion in Northern Vietnam: A three year mesocosm experiment

Compost, vermicompost and biochar amendments are thought to improve soil quality and plant yield. However, little is known about their long-term impact on crop yield and the environment in tropical agro-ecosystems. In this study we investigated the effect of organic amendments (buffalo manure, compost and verrnicompost) and biochar (applied alone or with vermicompost) on plant yield, soil fertility, soil erosion and water dynamics in a degraded Acrisol in Vietnam. Maize growth and yield, as well as weed growth, were examined for three years in terrestrial mesocosms under natural rainfall. Maize yield and growth showed high inter-annual variability depending on the organic amendment. Vermicompost improved maize growth and yield but its effect was rather small and was only significant when water availability was limited (year 2). This suggests that vermicompost could be a promising substrate for improving the resistance of agrosystems to water stress. When the vermicompost biochar mixture was applied, further growth and yield improvements were recorded in some cases. When applied alone, biochar had a positive influence on maize yield and growth, thus confirming its interest for improving long-term soil productivity. All organic amendments reduced water runoff, soil detachment and NH4+ and NO3- transfer to water. These effects were more significant with vermicompost than with buffalo manure and compost, highlighting that the beneficial influence of vermicompost is not limited to its influence on plant yield. In addition, this study showed for the first time that the combination of vermicompost and biochar may not only improve plant productivity but also reduce the negative impact of agriculture on water quality. (C) 2015 Elsevier B.V. All rights reserved.

Influence of time step in the simulation modelling of evapotranspiration

Three simulations of evapotranspiration were done with two values of time step,viz 10 min and one day. Inputs to the model were weather data, including directly measured upward and downward radiation, and soil characteristics. Three soils were used for each simulation. Analysis of the results shows that the time step has a direct influence on the prediction of potential evapotranspiration, but a complex interaction of this effect with the soil moisture characteristic, rate of increase of ground cover and bare soil evaporation determines the actual transpiration predicted. The results indicate that as small a time step as possible should be used in the simulation.

Modelling of void initiation and breaking phenomena in a packed bed

Void breaking and formation in a packed bed are important phenomena in stabilising and optimising the performance of reactors such as the blast furnace, spouted bed and catalytic regenerator. These phenomena have been studied using a mathematical model. The model is based on a previously published force balance approach to predict the cavity size. Limited numbers of experiments, at room temperature, have been carried out in order to compare the experimental results with theory. A good agreement has been found between the experimental and theoretical results. In addition, the predictions have been compared with published data, which give reasonable agreement. The role of various forces (friction, pressure and bed weight) on void initiation and breaking has been investigated. The effect of bed height, particle diameter and density, void fraction, as well as gas flow rate on void formation and breaking has also been studied.

Estimation of soil hydraulic properties and their uncertainty: comparison between laboratory and field experiment

Often the soil hydraulic parameters are obtained by the inversion of measured data (e.g. soil moisture, pressure head, and cumulative infiltration, etc.). However, the inverse problem in unsaturated zone is ill-posed due to various reasons, and hence the parameters become non-unique. The presence of multiple soil layers brings the additional complexities in the inverse modelling. The generalized likelihood uncertainty estimate (GLUE) is a useful approach to estimate the parameters and their uncertainty when dealing with soil moisture dynamics which is a highly non-linear problem. Because the estimated parameters depend on the modelling scale, inverse modelling carried out on laboratory data and field data may provide independent estimates. The objective of this paper is to compare the parameters and their uncertainty estimated through experiments in the laboratory and in the field and to assess which of the soil hydraulic parameters are independent of the experiment. The first two layers in the field site are characterized by Loamy sand and Loamy. The mean soil moisture and pressure head at three depths are measured with an interval of half hour for a period of 1 week using the evaporation method for the laboratory experiment, whereas soil moisture at three different depths (60, 110, and 200 cm) is measured with an interval of 1 h for 2 years for the field experiment. A one-dimensional soil moisture model on the basis of the finite difference method was used. The calibration and validation are approximately for 1 year each. The model performance was found to be good with root mean square error (RMSE) varying from 2 to 4 cm(3) cm(-3). It is found from the two experiments that mean and uncertainty in the saturated soil moisture (theta(s)) and shape parameter (n) of van Genuchten equations are similar for both the soil types. Copyright (C) 2010 John Wiley & Sons, Ltd.

Stochastic modelling of flexible manufacturing systems

Mathematical modelling plays a vital role in the design, planning and operation of flexible manufacturing systems (FMSs). In this paper, attention is focused on stochastic modelling of FMSs using Markov chains, queueing networks, and stochastic Petri nets. We bring out the role of these modelling tools in FMS performance evaluation through several illustrative examples and provide a critical comparative evaluation. We also include a discussion on the modelling of deadlocks which constitute an important source of performance degradation in fully automated FMSs.

Modelling of metal-slag emulsion

Many industrial processes involve reaction between the two immiscible liquid systems. It is very important to increase the efficiency and productivity of such reactions. One of the important processes that involve such reactions is the metal-slag system. To increase the reaction rate or efficiency, one must increase the contact surface area of one of the phases. This is either done by emulsifying the slag into the metal phase or the metal into the slag phase. The latter is preferred from the stability viewpoint. Recently, we have proposed a simple and elegant mathematical model to describe metal emulsification in the presence of bottom gas bubbling. The same model is being extended here. The effect of slag and metal phase viscosity, density and metal droplet size on the metal droplet velocity in the slag phase is discussed for the above mentioned metal emulsification process. The models results have been compared with experimental data.

Modelling of Effect of Non-Uniform Current Density on the Performance of Soluble Lead Redox Flow Batteries

Soluble lead acid redox flow battery (SLRFB) offers a number of advantages. These advantages can be harnessed after problems associated with buildup of active material on. electrodes (residue) are resolved. A mathematical model is developed to understand residue formation in SLRFB. The model incorporates fluid flow, ion transport, electrode reactions, and non-uniform current distribution on electrode surfaces. A number of limiting cases are studied to conclude that ion transport and electrode reaction on anode simultaneously control battery performance. The model fits the reported cell voltage vs. time profiles very well. During the discharge cycle, the model predicts complete dissolution of deposited material from trailing edge side of the electrodes. With time, the active surface area of electrodes decreases rapidly. The corresponding increase in current density leads to precipitous decrease in cell potential before all the deposited material is dissolved. The successive charge-discharge cycles add to the residue. The model correctly captures the marginal effect of flow rate on cell voltage profiles, and identifies flow rate and flow direction as new variables for controlling residue buildup. Simulations carried out with alternating flow direction and a SLRFB with cylindrical electrodes show improved performance with respect to energy efficiency and residue buildup. (C) 2014 The Electrochemical Society. All rights reserved.

Swelling behaviour of soil-bentonite mixtures

Studies on the swelling behaviour of mixtures of bentonite clay and nonswelling coarser fractions of different sizes and shapes reveal that observed swelling occurs only after the voids of the nonswelling particles are filled up with swollen clay particles. The magnitude of the swell within the voids, called intervoid swelling is large when the size and percentage of the nonswelling coarser fraction is large. The observable swell, after intervoid swelling, is called primary swelling and follows a rectangular hyperbolic relationship with time. The total swell per gram of the clay decreases with an increase in the size of the nonswelling fraction and with a decrease in the percentage of swelling clay. Time-swell relationships show that swelling continues to occur for a long time after the primary swelling, and this is called secondary swelling.

Performance modelling of a fault-tolerant real-time multiprocessor using stochastic Petri nets

The fault-tolerant multiprocessor (ftmp) is a bus-based multiprocessor architecture with real-time and fault- tolerance features and is used in critical aerospace applications. A preliminary performance evaluation is of crucial importance in the design of such systems. In this paper, we review stochastic Petri nets (spn) and developspn-based performance models forftmp. These performance models enable efficient computation of important performance measures such as processing power, bus contention, bus utilization, and waiting times.

Mathematical model of arterial stenosis

A mathematical model for pulsatile flow in a partially occluded tube is presented. The problem has applications in studying the effects of blood flow characteristics on atherosclerotic development. The model brings out the importance of the pulsatility of blood flow on separation and the stress distribution. The results obtained show fairly good agreement with the available experimental results.

Estimation of Cavitation Erosion with Incubation Periods and Material Properties

A detailed study of the normalized correlations between the incubation period tc and the properties of various materials tested in a rotating disk device indicates that, at very high intensities, the strength properties influence the duration of tc. The analysis of extensive data from other laboratories for cavitation and liquid impingement erosion also indicates that, while both energy and strength properties influence the duration of tc, the latter ones predominate for a majority of cases. A fatigue-type failure occurs during tc. For estimating the time required to pierce a metallic specimen in a rotating device a relationship tp = 160 tc0.44 is proposed. A detailed study of normalized correlations between erosion resistance (inverse of erosion rate) and tc values of different materials tested in the rotating disk shows that correlations are good. Analysis of data from eight other investigators clearly points out the validity and the usefulness of this type of prediction.