Parameter estimation in water-distribution systems by least squares

The weighted-least-squares method using sensitivity-analysis technique is proposed for the estimation of parameters in water-distribution systems. The parameters considered are the Hazen-Williams coefficients for the pipes. The objective function used is the sum of the weighted squares of the differences between the computed and the observed values of the variables. The weighted-least-squares method can elegantly handle multiple loading conditions with mixed types of measurements such as heads and consumptions, different sets and number of measurements for each loading condition, and modifications in the network configuration due to inclusion or exclusion of some pipes affected by valve operations in each loading condition. Uncertainty in parameter estimates can also be obtained. The method is applied for the estimation of parameters in a metropolitan urban water-distribution system in India.

Solvation dynamics, energy distribution and trapping of a light solute ion

In the theoretical treatments of the dynamics of solvation of a newly created ion in a dipolar solvent, the self-motion of the solute is usually ignored. Recently, it has been shown that for a light ion the translational motion of the ion can significantly enhance its own rate of solvation. Therefore, solvation itself may not be the rate determining step in the equilibration. Instead, the rate determining step is the search of the low energy configuration which serves to localize the light ion. In this article a microscopic calculation of the probability distribution of the interaction energy of the nascent charge with the dipolar solvent molecules is presented in order to address this problem of solute trapping. It is found that to a good approximation, this distribution is Gaussian and the second moment of this distribution is exactly equal to the half of its own solvation energy. It is shown that this is in excellent agreement with the simulation results that are available for the model Brownian dipolar lattice and for liquid acetonitrile. If the distortion of the solvent by the ion is negligible then the same relation gives the energy distribution for the solvated ion, with the average centered at the final equilibrium solvation energy. These results are expected to be useful in understanding various chemical processes in dipolar liquids. Another interesting outcome of the present study is a simple dynamic argument that supports Onsager's ''inverse snow-ball'' conjecture of solvation of a light ion. A simple derivation of the semi-phenomenological relation between the solvation time correlation function and the single particle orientation, reported recently by Maroncelli et al. (J. Phys. Chem. 97 (1993) 13), is also presented.

Single-molecule thermodynamics: the heat distribution function of a charged particle in a static magnetic field

Interest in the applicability of fluctuation theorems to the thermodynamics of single molecules in external potentials has recently led to calculations of the work and total entropy distributions of Brownian oscillators in static and time-dependent electromagnetic fields. These calculations, which are based on solutions to a Smoluchowski equation, are not easily extended to a consideration of the other thermodynamic quantity of interest in such systems-the heat exchanges of the particle alone-because of the nonlinear dependence of the heat on a particle's stochastic trajectory. In this paper, we show that a path integral approach provides an exact expression for the distribution of the heat fluctuations of a charged Brownian oscillator in a static magnetic field. This approach is an extension of a similar path integral approach applied earlier by our group to the calculation of the heat distribution function of a trapped Brownian particle, which was found, in the limit of long times, to be consistent with experimental data on the thermal interactions of single micron-sized colloids in a viscous solvent.

Low-frequency variability and the galactic distribution of electron-density fluctuation

A sample of 96 compact flat-spectrum extragalactic sources, spread evenly over all galactic latitudes, has been studied at 327 MHz for variability over a time interval of about 15 yr. The variability shows a dependence on galactic latitude being less both at low and high latitudes and peaking around absolute value of b approximately 15-degrees. The latitude dependence is surprisingly similar in both the galactic centre and anticentre directions. Assuming various single and multi-component distributions for the ionized, irregular interstellar plasma, we have tried to generate the observed dependence using a semi-qualitative treatment of refractive interstellar scintillations. We find that it is difficult to fit our data with any single or double component cylindrical distribution. Our data suggests that the observed variability could be influenced by the spiral structure of our Galaxy.

Patterns of distribution of macrolichens in western parts of Nanda Devi Biosphere Reserve

A total of 76 species of macrolichens were recorded from 16 transects of 50 m x 10 m between altitudes of 2100 m and 4500 m in western parts of Nanda Devi Biosphere Reserve of Garhwal Himalayas. Forty-one of these are lignicolous species occurring on woody, 14 are terricolous growing on soil and 10 are saxicolous inhabiting rocks only, The other 11 species occur on more than one major types of substrate, Lichen species diversity is at its highest in middle altitudes between 2700 m and 3700 m where all three major substrates are simultaneously available, Lichen species diversity of Nanda Devi Biosphere Reserve appears to be under threat from deforestation and fires, as well as from loss of soil microhabitats due to overgrowth of weeds seemingly caused by cessation of summer grazing in alpine pastures.

Spatial distribution of oil in groundnut and sunflower seeds by nuclear magnetic resonance imaging

The nuclear magnetic resonance imaging technique has been used to obtain images of different transverse and vertical sections in groundnut and sunflower seeds. Separate images have been obtained for oil and water components in the seeds. The spatial distribution of oil and water inside the seed has been obtained from the detailed analysis of the images. In the immature groundnut seeds obtained commercially, complementary oil and water distributions have been observed. Attempts have been made to explain these results.

Stable carbon isotope ratios in Asian elephant collagen: implications for dietary studies

Stable carbon isotope ratios in bone collagen have been used in a variety of dietary studies in modern and fossil animals, including humans. Inherent in the stable isotope technique is the assumption that the isotopic signature is a reflection of the diet and is persistent in collagen because this is a relatively inert protein. Carbon isotope analyses of bones from a southern Indian population of Asian elephant (Elephas maximus), a long-lived mammal that alternates seasonally between a predominantly C3 (browse) and C4 (grass) plant diet, showed two patterns that have important implications for dietary interpretation based on isotopic studies. Relative to the quantity of the two plant types consumed on average, the ?13C signal in collagen indicated that more carbon was incorporated from C3 plants, possibly due to their higher protein contribution. There was a much greater variance in ?13C values of collagen in sub-adult (range -10.5� to-22.7�, variance=14.51) compared to adult animals (range -16.0� to -20.3�, variance=1.85) pointing to high collagen turnover rates and non-persistent isotopic signatures in younger, growing animals. It thus seems important to correct for any significant relative differences in nutritive value of food types and also consider the age of an animal before drawing definite conclusions about its diet from isotope ratios.

WLS method for parameter estimation in water distribution networks

The weighted-least-squares method based on the Gauss-Newton minimization technique is used for parameter estimation in water distribution networks. The parameters considered are: element resistances (single and/or group resistances, Hazen-Williams coefficients, pump specifications) and consumptions (for single or multiple loading conditions). The measurements considered are: nodal pressure heads, pipe flows, head loss in pipes, and consumptions/inflows. An important feature of the study is a detailed consideration of the influence of different choice of weights on parameter estimation, for error-free data, noisy data, and noisy data which include bad data. The method is applied to three different networks including a real-life problem.

On the isotope effect in some cuprate superconductors

The combined mechanism involving phonon and lochon (local charged boson) induced pairing of fermions developed earlier for cuprate superconductors is used to study the variation of the oxygen isotope effect (alpha(0)) in these systems. The recently observed results for some cuprates are in agreement with the calculated trend in which (alpha(0)) tends to larger value when the critical temperature (T-c) is reduced by appropriate doping. These results support the combined phononic and electronic (lochonic) mechanism for cuprates with the latter dominating in the higher T-c regions.

Multi-installment load distribution in tree networks with delays

This paper presents a new strategy for load distribution in a single-level tree network equipped with or without front-ends. The load is distributed in more than one installment in an optimal manner to minimize the processing time. This is a deviation and an improvement over earlier studies in which the load distribution is done in only one installment. Recursive equations for the general case, and their closed form solutions for a special case in which the network has identical processors and identical links, are derived. An asymptotic analysis of the network performance with respect to the number of processors and the number of installments is carried out. Discussions of the results in terms of some practical issues like the tradeoff relationship between the number of processors and the number of installments are also presented.

Ultrafast solvation dynamics in water: Isotope effects and comparison with experimental results

A detailed theoretical study of solvation dynamics in water is presented. The motivation of the present study comes from the recent experimental observation that the dynamics of solvation of an ion in water is ultrafast and the solvation time correlation function decays with a time constant of about 55 fs. The slower decay in the long time can be described by a sum of two exponentials with time constants equal to 126 and 880 fs. The molecular theory (developed earlier) predicts a time constant equal to 52 fs for the initial Gaussian decay and time constants equal to 134 and 886 fs for the two exponential components at the long time. This nearly perfect agreement is obtained by using the most detailed dynamical information available in the literature. The present study emphasizes the importance of the intermolecular vibrational band originating from the O...O stretching mode of the O�H...O units in the initial dynamics and raises several interesting questions regarding the nature of the decay of this mode. We have also studied the effects of isotope substitution on solvation dynamics. It is predicted that a significant isotope effect may be observed in the long time. The experimental results have also been compared with the prediction of the dynamic mean spherical approximation (DMSA); the agreement is not satisfactory at the long time. It is further found that the molecular theory and the DMSA lead to virtually identical results if the translational modes of the solvent molecules are neglected in the former. DMSA has also been used to investigate the dynamics of solvation of a dipolar solute in water. It is found that the dynamics of dipolar solvation exhibit features rather different from those of ion solvation. © 1995 American Institute of Physics.

Limiting ionic conductance of symmetrical, rigid ions in aqueous solutions: Temperature dependence and solvent isotope effects

Limiting ionic conductance (Lambda(0)) of rigid symmetrical unipositive ions in aqueous solution shows a strong temperature dependence. For example, Lambda(0) more than doubles when the temperature is increased from 283 to 318 K. A marked variation also occurs when the solvent is changed from ordinary water (H2O) to heavy water (D2O). In addition, Lambda(0) shows a nonmonotonic size dependence with a skewed maximum near Cs+. Although these important results have been known for a long time, no satisfactory theoretical explanation exists for these results. In this article we present a simple molecular theory which provides a nearly quantitative explanation in terms of microscopic structure and dynamics of the solvent. A notable feature of this theory is that it does not invoke any nonquantifiable models involving solvent-berg or clatherates. We find the strong temperature dependence of Lambda(0) to arise from a rather large number of microscopic factors, each providing a small but nontrivial contribution, but all acting surprisingly in the same direction. This work, we believe, provides, for the first time, a satisfactory explanation of both the anomalous size and temperature dependencies of Lambda(0) of unipositive ions in molecular terms. The marked change in Lambda(0) as the solvent is changed from H2O to D2O is found to arise partly from a change in the dielectric relaxation and partly from a change in the effective interaction of the ion with the solvent.

Autocalibration of dynamic bacterial growth model for water distribution system using GA

The presence of residual chlorine and organic matter govern the bacterial regrowth within a water distribution system. The bacterial growth model is essential to predict the spatial and temporal variation of all these substances throughout the system. The parameters governing the bacterial growth and biodegradable dissolved organic carbon (BDOC) utilization are difficult to determine by experimentation. In the present study, the estimation of these parameters is addressed by using simulation-optimization procedure. The optimal solution by genetic algorithm (GA) has indicated that the proper combination of parameter values are significant rather than correct individual values. The applicability of the model is illustrated using synthetic data generated by introducing noise in to the error-free measurements. The GA was found to be a potential tool in estimating the parameters controlling the bacterial growth and BDOC utilization. Further, the GA was also used for evaluating the sensitivity issues relating parameter values and objective function. It was observed that mu and k(cl) are more significant and dominating compared to the other parameters. But the magnitude of the parameters is also an important issue in deciding the dominance of a particular parameter. GA is found to be a useful tool in autocalibration of bacterial growth model and a sensitivity study of parameters.

Velocity distribution function for a dilute granular material in shear flow

The velocity distribution function for the steady shear flow of disks (in two dimensions) and spheres (in three dimensions) in a channel is determined in the limit where the frequency of particle-wall collisions is large compared to particle-particle collisions. An asymptotic analysis is used in the small parameter epsilon, which is naL in two dimensions and na(2)L in three dimensions, where; n is the number density of particles (per unit area in two dimensions and per unit volume in three dimensions), L is the separation of the walls of the channel and a is the particle diameter. The particle-wall collisions are inelastic, and are described by simple relations which involve coefficients of restitution e(t) and e(n) in the tangential and normal directions, and both elastic and inelastic binary collisions between particles are considered. In the absence of binary collisions between particles, it is found that the particle velocities converge to two constant values (u(x), u(y)) = (+/-V, O) after repeated collisions with the wall, where u(x) and u(y) are the velocities tangential and normal to the wall, V = (1 - e(t))V-w/(1 + e(t)), and V-w and -V-w, are the tangential velocities of the walls of the channel. The effect of binary collisions is included using a self-consistent calculation, and the distribution function is determined using the condition that the net collisional flux of particles at any point in velocity space is zero at steady state. Certain approximations are made regarding the velocities of particles undergoing binary collisions :in order to obtain analytical results for the distribution function, and these approximations are justified analytically by showing that the error incurred decreases proportional to epsilon(1/2) in the limit epsilon --> 0. A numerical calculation of the mean square of the difference between the exact flux and the approximate flux confirms that the error decreases proportional to epsilon(1/2) in the limit epsilon --> 0. The moments of the velocity distribution function are evaluated, and it is found that [u(x)(2)] --> V-2, [u(y)(2)] similar to V-2 epsilon and -[u(x)u(y)] similar to V-2 epsilon log(epsilon(-1)) in the limit epsilon --> 0. It is found that the distribution function and the scaling laws for the velocity moments are similar for both two- and three-dimensional systems.

Residence time distribution for a class of Gaussian Markov processes

We study the distribution of residence time or equivalently that of "mean magnetization" for a family of Gaussian Markov processes indexed by a positive parameter alpha. The persistence exponent for these processes is simply given by theta=alpha but the residence time distribution is nontrivial. The shape of this distribution undergoes a qualitative change as theta increases, indicating a sharp change in the ergodic properties of the process. We develop two alternate methods to calculate exactly but recursively the moments of the distribution for arbitrary alpha. For some special values of alpha, we obtain closed form expressions of the distribution function. [S1063-651X(99)03306-1].