Analytical model of reactive transport processes with spatially variable coefficients

Analytical solutions of partial differential equation (PDE) models describing reactive transport phenomena in saturated porous media are often used as screening tools to provide insight into contaminant fate and transport processes. While many practical modelling scenarios involve spatially variable coefficients, such as spatially variable flow velocity, v(x), or spatially variable decay rate, k(x), most analytical models deal with constant coefficients. Here we present a framework for constructing exact solutions of PDE models of reactive transport. Our approach is relevant for advection-dominant problems, and is based on a regular perturbation technique. We present a description of the solution technique for a range of one-dimensional scenarios involving constant and variable coefficients, and we show that the solutions compare well with numerical approximations. Our general approach applies to a range of initial conditions and various forms of v(x) and k(x). Instead of simply documenting specific solutions for particular cases, we present a symbolic worksheet, as supplementary material, which enables the solution to be evaluated for different choices of the initial condition, v(x) and k(x). We also discuss how the technique generalizes to apply to models of coupled multispecies reactive transport as well as higher dimensional problems.

A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area

Motivated by a problem from fluid mechanics, we consider a generalization of the standard curve shortening flow problem for a closed embedded plane curve such that the area enclosed by the curve is forced to decrease at a prescribed rate. Using formal asymptotic and numerical techniques, we derive possible extinction shapes as the curve contracts to a point, dependent on the rate of decreasing area; we find there is a wider class of extinction shapes than for standard curve shortening, for which initially simple closed curves are always asymptotically circular. We also provide numerical evidence that self-intersection is possible for non-convex initial conditions, distinguishing between pinch-off and coalescence of the curve interior.

Effects of oxygen provision on the physiology of baker's yeast Saccharomyces cerevisiae

The availability of oxygen has a major effect on all organisms. The yeast Saccharomyces cerevisiae is able to adapt its metabolism for growth in different conditions of oxygen provision, and to grow even under complete lack of oxygen. Although the physiology of S. cerevisiae has mainly been studied under fully aerobic and anaerobic conditions, less is known of metabolism under oxygen-limited conditions and of the adaptation to changing conditions of oxygen provision. This study compared the physiology of S. cerevisiae in conditions of five levels of oxygen provision (0, 0.5, 1.0, 2.8 and 20.9% O2 in feed gas) by using measurements on metabolite, transcriptome and proteome levels. On the transcriptional level, the main differences were observed between the three level groups, 0, 0.5 2.8 and 20.9% O2 which led to fully fermentative, respiro-fermentative and fully respiratory modes of metabolism, respectively. However, proteome analysis suggested post-transcriptional regulation at the level of 0.5 O2. The analysis of metabolite and transcript levels of central carbon metabolism also suggested post-transcriptional regulation especially in glycolysis. Further, a global upregulation of genes related to respiratory pathways was observed in the oxygen-limited conditions and the same trend was seen in the proteome analysis and in the activities of enzymes of the TCA cycle. The responses of intracellular metabolites related to central carbon metabolism and transcriptional responses to change in oxygen availability were studied. As a response to sudden oxygen depletion, concentrations of the metabolites of central carbon metabolism responded faster than the corresponding levels of gene expression. In general, the genome-wide transcriptional responses to oxygen depletion were highly similar when two different initial conditions of oxygen provision (20.9 and 1.0% O2) were compared. The genes related to growth and cell proliferation were transiently downregulated whereas the genes related to protein degradation and phosphate uptake were transiently upregulated. In the cultures initially receiving 1.0% O2, a transient upregulation of genes related to fatty acid oxidation, peroxisomal biogenesis, response to oxidative stress and pentose phosphate pathway was observed. Additionally, this work analysed the effect of oxygen on transcription of genes belonging to the hexose transporter gene family. Although the specific glucose uptake rate was highest in fully anaerobic conditions, none of the hxt genes showed highest expression in anaerobic conditions. However, the expression of genes encoding the moderately low affinity transporters decreased with the decreasing oxygen level. Thus it was concluded that there is a relative increase in high affinity transport in anaerobic conditions supporting the high uptake rate.

Entire Solutions of Hydrodynamical Equations with Exponential Dissipation

We consider a modification of the three-dimensional Navier-Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as e(vertical bar k vertical bar/kd) at high wavenumbers vertical bar k vertical bar. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than e-(C(k/kd) ln(vertical bar k vertical bar/kd)) for any C < 1/(2 ln 2). The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with C = C-* = 1/ ln 2. The same behavior with a universal constant C-* is conjectured for the Navier-Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier-Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.

Towards the Use of Radar Winds in Numerical Weather Prediction

Numerical weather prediction (NWP) models provide the basis for weather forecasting by simulating the evolution of the atmospheric state. A good forecast requires that the initial state of the atmosphere is known accurately, and that the NWP model is a realistic representation of the atmosphere. Data assimilation methods are used to produce initial conditions for NWP models. The NWP model background field, typically a short-range forecast, is updated with observations in a statistically optimal way. The objective in this thesis has been to develope methods in order to allow data assimilation of Doppler radar radial wind observations. The work has been carried out in the High Resolution Limited Area Model (HIRLAM) 3-dimensional variational data assimilation framework. Observation modelling is a key element in exploiting indirect observations of the model variables. In the radar radial wind observation modelling, the vertical model wind profile is interpolated to the observation location, and the projection of the model wind vector on the radar pulse path is calculated. The vertical broadening of the radar pulse volume, and the bending of the radar pulse path due to atmospheric conditions are taken into account. Radar radial wind observations are modelled within observation errors which consist of instrumental, modelling, and representativeness errors. Systematic and random modelling errors can be minimized by accurate observation modelling. The impact of the random part of the instrumental and representativeness errors can be decreased by calculating spatial averages from the raw observations. Model experiments indicate that the spatial averaging clearly improves the fit of the radial wind observations to the model in terms of observation minus model background (OmB) standard deviation. Monitoring the quality of the observations is an important aspect, especially when a new observation type is introduced into a data assimilation system. Calculating the bias for radial wind observations in a conventional way can result in zero even in case there are systematic differences in the wind speed and/or direction. A bias estimation method designed for this observation type is introduced in the thesis. Doppler radar radial wind observation modelling, together with the bias estimation method, enables the exploitation of the radial wind observations also for NWP model validation. The one-month model experiments performed with the HIRLAM model versions differing only in a surface stress parameterization detail indicate that the use of radar wind observations in NWP model validation is very beneficial.

Phase-Field Simulation of Fusion Interface Events during Solidification of Dissimilar Welds: Effect of Composition Inhomogeneity

We investigate the events near the fusion interfaces of dissimilar welds using a phase-field model developed for single-phase solidification of binary alloys. The parameters used here correspond to the dissimilar welding of a Ni/Cu couple. The events at the Ni and the Cu interface are very different, which illustrate the importance of the phase diagram through the slope of the liquidus curves. In the Ni side, where the liquidus temperature decreases with increasing alloying, solutal melting of the base metal takes place; the resolidification, with continuously increasing solid composition, is very sluggish until the interface encounters a homogeneous melt composition. The growth difficulty of the base metal increases with increasing initial melt composition, which is equivalent to a steeper slope of the liquidus curve. In the Cu side, the initial conditions result in a deeply undercooled melt and contributions from both constrained and unconstrained modes of growth are observed. The simulations bring out the possibility of nucleation of a concentrated solid phase from the melt, and a secondary melting of the substrate due to the associated recalescence event. The results for the Ni and Cu interfaces can be used to understand more complex dissimilar weld interfaces involving multiphase solidification.

Molecular line and continuum studies of the early stages of star formation

New stars form in dense interstellar clouds of gas and dust called molecular clouds. The actual sites where the process of star formation takes place are the dense clumps and cores deeply embedded in molecular clouds. The details of the star formation process are complex and not completely understood. Thus, determining the physical and chemical properties of molecular cloud cores is necessary for a better understanding of how stars are formed. Some of the main features of the origin of low-mass stars, like the Sun, are already relatively well-known, though many details of the process are still under debate. The mechanism through which high-mass stars form, on the other hand, is poorly understood. Although it is likely that the formation of high-mass stars shares many properties similar to those of low-mass stars, the very first steps of the evolutionary sequence are unclear. Observational studies of star formation are carried out particularly at infrared, submillimetre, millimetre, and radio wavelengths. Much of our knowledge about the early stages of star formation in our Milky Way galaxy is obtained through molecular spectral line and dust continuum observations. The continuum emission of cold dust is one of the best tracers of the column density of molecular hydrogen, the main constituent of molecular clouds. Consequently, dust continuum observations provide a powerful tool to map large portions across molecular clouds, and to identify the dense star-forming sites within them. Molecular line observations, on the other hand, provide information on the gas kinematics and temperature. Together, these two observational tools provide an efficient way to study the dense interstellar gas and the associated dust that form new stars. The properties of highly obscured young stars can be further examined through radio continuum observations at centimetre wavelengths. For example, radio continuum emission carries useful information on conditions in the protostar+disk interaction region where protostellar jets are launched. In this PhD thesis, we study the physical and chemical properties of dense clumps and cores in both low- and high-mass star-forming regions. The sources are mainly studied in a statistical sense, but also in more detail. In this way, we are able to examine the general characteristics of the early stages of star formation, cloud properties on large scales (such as fragmentation), and some of the initial conditions of the collapse process that leads to the formation of a star. The studies presented in this thesis are mainly based on molecular line and dust continuum observations. These are combined with archival observations at infrared wavelengths in order to study the protostellar content of the cloud cores. In addition, centimetre radio continuum emission from young stellar objects (YSOs; i.e., protostars and pre-main sequence stars) is studied in this thesis to determine their evolutionary stages. The main results of this thesis are as follows: i) filamentary and sheet-like molecular cloud structures, such as infrared dark clouds (IRDCs), are likely to be caused by supersonic turbulence but their fragmentation at the scale of cores could be due to gravo-thermal instability; ii) the core evolution in the Orion B9 star-forming region appears to be dynamic and the role played by slow ambipolar diffusion in the formation and collapse of the cores may not be significant; iii) the study of the R CrA star-forming region suggests that the centimetre radio emission properties of a YSO are likely to change with its evolutionary stage; iv) the IRDC G304.74+01.32 contains candidate high-mass starless cores which may represent the very first steps of high-mass star and star cluster formation; v) SiO outflow signatures are seen in several high-mass star-forming regions which suggest that high-mass stars form in a similar way as their low-mass counterparts, i.e., via disk accretion. The results presented in this thesis provide constraints on the initial conditions and early stages of both low- and high-mass star formation. In particular, this thesis presents several observational results on the early stages of clustered star formation, which is the dominant mode of star formation in our Galaxy.

Nonlinear ensemble prediction of chaotic daily rainfall

The significance of treating rainfall as a chaotic system instead of a stochastic system for a better understanding of the underlying dynamics has been taken up by various studies recently. However, an important limitation of all these approaches is the dependence on a single method for identifying the chaotic nature and the parameters involved. Many of these approaches aim at only analyzing the chaotic nature and not its prediction. In the present study, an attempt is made to identify chaos using various techniques and prediction is also done by generating ensembles in order to quantify the uncertainty involved. Daily rainfall data of three regions with contrasting characteristics (mainly in the spatial area covered), Malaprabha, Mahanadi and All-India for the period 1955-2000 are used for the study. Auto-correlation and mutual information methods are used to determine the delay time for the phase space reconstruction. Optimum embedding dimension is determined using correlation dimension, false nearest neighbour algorithm and also nonlinear prediction methods. The low embedding dimensions obtained from these methods indicate the existence of low dimensional chaos in the three rainfall series. Correlation dimension method is done on th phase randomized and first derivative of the data series to check whether the saturation of the dimension is due to the inherent linear correlation structure or due to low dimensional dynamics. Positive Lyapunov exponents obtained prove the exponential divergence of the trajectories and hence the unpredictability. Surrogate data test is also done to further confirm the nonlinear structure of the rainfall series. A range of plausible parameters is used for generating an ensemble of predictions of rainfall for each year separately for the period 1996-2000 using the data till the preceding year. For analyzing the sensitiveness to initial conditions, predictions are done from two different months in a year viz., from the beginning of January and June. The reasonably good predictions obtained indicate the efficiency of the nonlinear prediction method for predicting the rainfall series. Also, the rank probability skill score and the rank histograms show that the ensembles generated are reliable with a good spread and skill. A comparison of results of the three regions indicates that although they are chaotic in nature, the spatial averaging over a large area can increase the dimension and improve the predictability, thus destroying the chaotic nature. (C) 2010 Elsevier Ltd. All rights reserved.

Primordial Perturbations from a Self-interacting Curvaton

Inflation is a period of accelerated expansion in the very early universe, which has the appealing aspect that it can create primordial perturbations via quantum fluctuations. These primordial perturbations have been observed in the cosmic microwave background, and these perturbations also function as the seeds of all large-scale structure in the universe. Curvaton models are simple modifications of the standard inflationary paradigm, where inflation is driven by the energy density of the inflaton, but another field, the curvaton, is responsible for producing the primordial perturbations. The curvaton decays after inflation as ended, where the isocurvature perturbations of the curvaton are converted into adiabatic perturbations. Since the curvaton must decay, it must have some interactions. Additionally realistic curvaton models typically have some self-interactions. In this work we consider self-interacting curvaton models, where the self-interaction is a monomial in the potential, suppressed by the Planck scale, and thus the self-interaction is very weak. Nevertheless, since the self-interaction makes the equations of motion non-linear, it can modify the behaviour of the model very drastically. The most intriguing aspect of this behaviour is that the final properties of the perturbations become highly dependent on the initial values. Departures of Gaussian distribution are important observables of the primordial perturbations. Due to the non-linearity of the self-interacting curvaton model and its sensitivity to initial conditions, it can produce significant non-Gaussianity of the primordial perturbations. In this work we investigate the non-Gaussianity produced by the self-interacting curvaton, and demonstrate that the non-Gaussianity parameters do not obey the analytically derived approximate relations often cited in the literature. Furthermore we also consider a self-interacting curvaton with a mass in the TeV-scale. Motivated by realistic particle physics models such as the Minimally Supersymmetric Standard Model, we demonstrate that a curvaton model within the mass range can be responsible for the observed perturbations if it can decay late enough.

Numerical procedure for second order non-linear ordinary differential equations and application to heat transfer problem

In this paper, we have first given a numerical procedure for the solution of second order non-linear ordinary differential equations of the type y″ = f (x;y, y′) with given initial conditions. The method is based on geometrical interpretation of the equation, which suggests a simple geometrical construction of the integral curve. We then translate this geometrical method to the numerical procedure adaptable to desk calculators and digital computers. We have studied the efficacy of this method with the help of an illustrative example with known exact solution. We have also compared it with Runge-Kutta method. We have then applied this method to a physical problem, namely, the study of the temperature distribution in a semi-infinite solid homogeneous medium for temperature-dependent conductivity coefficient.

Strong shock with radiation near the surface of a star

The propagation of a shock wave, originating in a stellar interior, is considered when it approaches the surface of the star and assumes a self-similar character, "forgetting" its initial conditions. The flow behind the shock is assumed to be spatially isothermal rather than adiabatic to simulate the conditions of large radiative transfer near the stellar surface. The adiabatic and isothermal flows behind such a shock are compared. The exact shock-propagation laws, obtained by solving the equations in similarity variables, for different values of the parameter δ in the undisturbed density law, ρ0 ∝ xδ, and γ, the ratio of specific heats, are compared with the approximate values calculated by Whitham's characteristic rule and the two show a generally good agreement.

Optimal Blood Glucose Regulation using Single Network Adaptive Critics

Diabetes is a serious disease during which the body's production and use of insulin is impaired, causing glucose concentration level toincrease in the bloodstream. Regulating blood glucose levels as close to normal as possible, leads to a substantial decrease in long term complications of diabetes. In this paper, an intelligent neural network on-line optimal feedback treatment strategy based on nonlinear optimal control theory is presented for the disease using subcutaneous treatment strategy. A simple mathematical model of the nonlinear dynamics of glucose and insulin interaction in the blood system is considered based on the Bergman's minimal model. A glucose infusion term representing the effect of glucose intake resulting from a meal is introduced into the model equations. The efficiency of the proposed controllers is shown taking random parameters and random initial conditions in presence of physical disturbances like food intake. A comparison study with linear quadratic regulator theory brings Out the advantages of the nonlinear control synthesis approach. Simulation results show that unlike linear optimal control, the proposed on-line continuous infusion strategy never leads to severe hypoglycemia problems.

Sliding Modes for the Simulation of Mechanical and Electrical Systems Defined by Differential-Algebraic Equations

We offer a technique, motivated by feedback control and specifically sliding mode control, for the simulation of differential-algebraic equations (DAEs) that describe common engineering systems such as constrained multibody mechanical structures and electric networks. Our algorithm exploits the basic results from sliding mode control theory to establish a simulation environment that then requires only the most primitive of numerical solvers. We circumvent the most important requisite for the conventionalsimulation of DAEs: the calculation of a set of consistent initial conditions. Our algorithm, which relies on the enforcement and occurrence of sliding mode, will ensure that the algebraic equation is satisfied by the dynamic system even for inconsistent initial conditions and for all time thereafter. [DOI:10.1115/1.4001904]

Suboptimal reentry guidance of a reusable launch vehicle using pitch plane maneuver

Using the recently developed model predictive static programming (MPSP) technique, a nonlinear suboptimal reentry guidance scheme is presented in this paper for a reusable launch vehicle (RLV). Unlike traditional RLV guidance, the problem considered over here is restricted only to pitch plane maneuver of the vehicle, which allows simpler mission planning and vehicle load management. The computationally efficient MPSP technique brings in the philosophy of trajectory optimization into the framework of guidance design, which in turn results in very effective guidance schemes in general. In the problem addressed in this paper, it successfully guides the RLV through the critical reentry phase both by constraining it to the allowable narrow flight corridor as well as by meeting the terminal constraints at the end of the reentry segment. The guidance design is validated by considering possible aerodynamic uncertainties as well as dispersions in the initial conditions. (C) 2010 Elsevier Masson SAS. All rights reserved.

The Alfvén Wave Equation for Magnetospheric Plasmas

It is shown that besides the continuous spectrum which damps away as inverse power of time, the coupled Alfvén wave equation, which gives coupling between a shear Alfvén wave and a surface wave, can also admit a well behaved harmonic solution in the closed form for a set of initial conditions. This solution, though valid for finite time intervals, points out that the Alfvén surface waves can have a band of frequency (instead of a monochromatic frequency for a nonsheared magnetic field) within which the local field line resonance frequency can lie, and thus can excite magnetic pulsations with latitude-dependent frequency. By considering magnetic fields not only varying in magnitude but also in direction, it is shown that the time interval for the validity of the harmonic solution depend upon the angle between the magnetic field directions on either side of the magnetopause. For small values of the angle the time interval can become appreciably large.