A Nonlinear Approach for Re-entry Guidance of Reusable Launch Vehicles Using Model Predictive Static Programming

A nonlinear suboptimal guidance scheme is developed for the reentry phase of the reusable launch vehicles. A recently developed methodology, named as model predictive static programming (MPSP), is implemented which combines the philosophies of nonlinear model predictive control theory and approximate dynamic programming. This technique provides a finite time nonlinear suboptimal guidance law which leads to a rapid solution of the guidance history update. It does not have to suffer from computational difficulties and can be implemented online. The system dynamics is propagated through the flight corridor to the end of the reentry phase considering energy as independent variable and angle of attack as the active control variable. All the terminal constraints are satisfied. Among the path constraints, the normal load is found to be very constrictive. Hence, an extra effort has been made to keep the normal load within a specified limit and monitoring its sensitivity to the perturbation.

Structural Insights into the acyl-intermediates of plasmodium falciparum fatty acid synthesis pathway; the mechanism of expansion of acyl carrier protein core

Acyl carrier protein (ACP) plays a central role in fatty acid biosynthesis. However, the molecular machinery that mediates its function is not yet fully understood. Therefore, structural studies were carried out on the acyl-ACP intermediates of Plasmodium falciparum using NMR as a spectroscopic probe. Chemical shift perturbation studies put forth a new picture of the interaction of ACP molecule with the acyl chain, namely, the hydrophobic core can protect up to 12 carbon units, and additional carbons protrude out from the top of the hydrophobic cavity. The latter hypothesis stems from chemical shift changes observed in C-alpha and C-beta of Ser-37 in tetradecanoyl-ACP. C-13, N-15-Double-filtered nuclear Overhauser effect (NOE) spectroscopy experiments further substantiate the concept; in octanoyl (C-8)- and dodecanoyl (C-12)-ACP, a long range NOE is observed within the phosphopantetheine arm, suggesting an arch-like conformation. This NOE is nearly invisible in tetradecanoyl (C-14)-ACP, indicating a change in conformation of the prosthetic group. Furthermore, the present study provides insights into the molecular mechanism of ACP expansion, as revealed from a unique side chain-to-backbone hydrogen bond between two fairly conserved residues, Ile-55 HN and Glu-48 O. The backbone amide of Ile-55 HN reports a pK(a) value for the carboxylate, similar to 1.9 pH units higher than model compound value, suggesting strong electrostatic repulsion between helix II and helix III. Charge-charge repulsion between the helices in combination with thrust from inside due to acyl chain would energetically favor the separation of the two helices. Helix III has fewer structural restraints and, hence, undergoes major conformational change without altering the overall-fold of P. falciparum ACP.

Sensitivity of Eigen Value to Damage and Its Identification

The reduction in natural frequencies,however small, of a civil engineering structure, is the first and the easiest method of estimating its impending damage. As a first level screening for health-monitoring, information on the frequency reduction of a few fundamentalmodes can be used to estimate the positions and the magnitude of damage in a smeared fashion. The paper presents the Eigen value sensitivity equations, derived from first-order perturbation technique, for typical infra-structural systems like a simply supported bridge girder, modelled as a beam, an endbearing pile, modelled as an axial rod and a simply supported plate as a continuum dynamic system. A discrete structure, like a building frame is solved for damage using Eigen-sensitivity derived by a computationalmodel. Lastly, neural network based damage identification is also demonstrated for a simply supported bridge beam, where the known-pairs of damage-frequency vector is used to train a neural network. The performance of these methods under the influence of measurement error is outlined. It is hoped that the developed method could be integrated in a typical infra-structural management program, such that magnitudes of damage and their positions can be obtained using acquired natural frequencies, synthesized from the excited/ambient vibration signatures.

Discrete parameter simulation optimization algorithms with applications to admission control with dependent service times

We propose certain discrete parameter variants of well known simulation optimization algorithms. Two of these algorithms are based on the smoothed functional (SF) technique while two others are based on the simultaneous perturbation stochastic approximation (SPSA) method. They differ from each other in the way perturbations are obtained and also the manner in which projections and parameter updates are performed. All our algorithms use two simulations and two-timescale stochastic approximation. As an application setting, we consider the important problem of admission control of packets in communication networks under dependent service times. We consider a discrete time slotted queueing model of the system and consider two different scenarios - one where the service times have a dependence on the system state and the other where they depend on the number of arrivals in a time slot. Under our settings, the simulated objective function appears ill-behaved with multiple local minima and a unique global minimum characterized by a sharp dip in the objective function in a small region of the parameter space. We compare the performance of our algorithms on these settings and observe that the two SF algorithms show the best results overall. In fact, in many cases studied, SF algorithms converge to the global minimum.

Global lopsided instability in a purely stellar galactic disc

It is shown that pure exponential discs in spiral galaxies are capable of supporting slowly varying discrete global lopsided modes, which can explain the observed features of lopsidedness in the stellar discs. Using linearized fluid dynamical equations with the softened self-gravity and pressure of the perturbation as the collective effect, we derive self-consistently a quadratic eigenvalue equation for the lopsided perturbation in the galactic disc. On solving this, we find that the ground-state mode shows the observed characteristics of the lopsidedness in a galactic disc, namely the fractional Fourier amplitude A(1), increases smoothly with the radius. These lopsided patterns precess in the disc with a very slow pattern speed with no preferred sense of precession. We show that the lopsided modes in the stellar disc are long-lived because of a substantial reduction (approximately a factor of 10 compared to the local free precession rate) in the differential precession. The numerical solution of the equations shows that the groundstate lopsided modes are either very slowly precessing stationary normal mode oscillations of the disc or growing modes with a slow growth rate depending on the relative importance of the collective effect of the self-gravity. N-body simulations are performed to test the spontaneous growth of lopsidedness in a pure stellar disc. Both approaches are then compared and interpreted in terms of long-lived global m = 1 instabilities, with almost zero pattern speed.

Influence of Cooling Rate on the Enthalpy Relaxation and Fragility of a Metallic Glass

Structural relaxation behavior of a rapidly quenched (RQ) and a slowly cooled Pd40Cu30Ni10P20 metallic glass was investigated and compared. Differential scanning calorimetry was employed to monitor the relaxation enthalpies at the glass transition temperature, T-g , and the Kolrausch-Williams-Watts (KWW) stretched exponential function was used to describe its variation with annealing time. It was found that the rate of enthalpy recovery is higher in the ribbon, implying that the bulk is more resistant to relaxation at low temperatures of annealing. This was attributed to the possibility of cooling rate affecting the locations where the glasses get trapped within the potential energy landscape. The RQ process traps a larger amount of free volume, resulting in higher fragility, and in turn relaxes at the slightest thermal excitation (annealing). The slowly cooled bulk metallic glass (BMG), on the other hand, entraps lower free volume and has more short-range ordering, hence requiring a large amount of perturbation to access lower energy basins.

Modelling of solute transport in a mild heterogeneous porous medium using stochastic finite element method: Effects of random source conditions

Randomness in the source condition other than the heterogeneity in the system parameters can also be a major source of uncertainty in the concentration field. Hence, a more general form of the problem formulation is necessary to consider randomness in both source condition and system parameters. When the source varies with time, the unsteady problem, can be solved using the unit response function. In the case of random system parameters, the response function becomes a random function and depends on the randomness in the system parameters. In the present study, the source is modelled as a random discrete process with either a fixed interval or a random interval (the Poisson process). In this study, an attempt is made to assess the relative effects of various types of source uncertainties on the probabilistic behaviour of the concentration in a porous medium while the system parameters are also modelled as random fields. Analytical expressions of mean and covariance of concentration due to random discrete source are derived in terms of mean and covariance of unit response function. The probabilistic behaviour of the random response function is obtained by using a perturbation-based stochastic finite element method (SFEM), which performs well for mild heterogeneity. The proposed method is applied for analysing both the 1-D as well as the 3-D solute transport problems. The results obtained with SFEM are compared with the Monte Carlo simulation for 1-D problems.

Polymer drift in a solvent by force acting on one polymer end

We investigate the effect of hydrodynamic interactions on the non-equilibrium drift dynamics of an ideal flexible polymer pulled by a constant force applied at one polymer end using the perturbation theory and the renormalization group method. For moderate force, if the polymer elongation is small, the hydrodynamic interactions are not screened and the velocity and the longitudinal elongation of the polymer are computed using the renormalization group method. Both the velocity and elongation are nonlinear functions of the driving force in this regime. For large elongation we found two regimes. For large force but finite chain length L the hydrodynamic interactions are screened. For large chain lengths and a finite force the hydrodynamic interactions are only partially screened, which in three dimensions results in unusual logarithmic corrections to the velocity and the longitudinal elongation.

Asteroid identification using statistical orbital inversion methods

An efficient and statistically robust solution for the identification of asteroids among numerous sets of astrometry is presented. In particular, numerical methods have been developed for the short-term identification of asteroids at discovery, and for the long-term identification of scarcely observed asteroids over apparitions, a task which has been lacking a robust method until now. The methods are based on the solid foundation of statistical orbital inversion properly taking into account the observational uncertainties, which allows for the detection of practically all correct identifications. Through the use of dimensionality-reduction techniques and efficient data structures, the exact methods have a loglinear, that is, O(nlog(n)), computational complexity, where n is the number of included observation sets. The methods developed are thus suitable for future large-scale surveys which anticipate a substantial increase in the astrometric data rate. Due to the discontinuous nature of asteroid astrometry, separate sets of astrometry must be linked to a common asteroid from the very first discovery detections onwards. The reason for the discontinuity in the observed positions is the rotation of the observer with the Earth as well as the motion of the asteroid and the observer about the Sun. Therefore, the aim of identification is to find a set of orbital elements that reproduce the observed positions with residuals similar to the inevitable observational uncertainty. Unless the astrometric observation sets are linked, the corresponding asteroid is eventually lost as the uncertainty of the predicted positions grows too large to allow successful follow-up. Whereas the presented identification theory and the numerical comparison algorithm are generally applicable, that is, also in fields other than astronomy (e.g., in the identification of space debris), the numerical methods developed for asteroid identification can immediately be applied to all objects on heliocentric orbits with negligible effects due to non-gravitational forces in the time frame of the analysis. The methods developed have been successfully applied to various identification problems. Simulations have shown that the methods developed are able to find virtually all correct linkages despite challenges such as numerous scarce observation sets, astrometric uncertainty, numerous objects confined to a limited region on the celestial sphere, long linking intervals, and substantial parallaxes. Tens of previously unknown main-belt asteroids have been identified with the short-term method in a preliminary study to locate asteroids among numerous unidentified sets of single-night astrometry of moving objects, and scarce astrometry obtained nearly simultaneously with Earth-based and space-based telescopes has been successfully linked despite a substantial parallax. Using the long-term method, thousands of realistic 3-linkages typically spanning several apparitions have so far been found among designated observation sets each spanning less than 48 hours.

Non-Gaussian Cosmological Perturbations from Hybrid Inflation and Preheating

This thesis consists of four research papers and an introduction providing some background. The structure in the universe is generally considered to originate from quantum fluctuations in the very early universe. The standard lore of cosmology states that the primordial perturbations are almost scale-invariant, adiabatic, and Gaussian. A snapshot of the structure from the time when the universe became transparent can be seen in the cosmic microwave background (CMB). For a long time mainly the power spectrum of the CMB temperature fluctuations has been used to obtain observational constraints, especially on deviations from scale-invariance and pure adiabacity. Non-Gaussian perturbations provide a novel and very promising way to test theoretical predictions. They probe beyond the power spectrum, or two point correlator, since non-Gaussianity involves higher order statistics. The thesis concentrates on the non-Gaussian perturbations arising in several situations involving two scalar fields, namely, hybrid inflation and various forms of preheating. First we go through some basic concepts -- such as the cosmological inflation, reheating and preheating, and the role of scalar fields during inflation -- which are necessary for the understanding of the research papers. We also review the standard linear cosmological perturbation theory. The second order perturbation theory formalism for two scalar fields is developed. We explain what is meant by non-Gaussian perturbations, and discuss some difficulties in parametrisation and observation. In particular, we concentrate on the nonlinearity parameter. The prospects of observing non-Gaussianity are briefly discussed. We apply the formalism and calculate the evolution of the second order curvature perturbation during hybrid inflation. We estimate the amount of non-Gaussianity in the model and find that there is a possibility for an observational effect. The non-Gaussianity arising in preheating is also studied. We find that the level produced by the simplest model of instant preheating is insignificant, whereas standard preheating with parametric resonance as well as tachyonic preheating are prone to easily saturate and even exceed the observational limits. We also mention other approaches to the study of primordial non-Gaussianities, which differ from the perturbation theory method chosen in the thesis work.

Puzzles of excited charm meson masses

We attempt a comprehensive analysis of the low lying charm meson states which present several puzzles, including the poor determination of masses of several non-strange excited mesons. We use the well-determined masses of the ground states and the strange first excited states to 'predict' the mass of the non-strange first excited state in the framework of heavy hadron chiral perturbation theory, an approach that is complementary to the well-known analysis of Mehen and Springer. This approach points to values for the masses of these states that are smaller than the experimental determinations. We provide a critical assessment of these mass measurements and point out the need for new experimental information. (c) 2007 Elsevier B.V. All rights reserved.

Spectral states and accretion geometries in Galactic black hole binaries

Black hole X-ray binaries, binary systems where matter from a companion star is accreted by a stellar mass black hole, thereby releasing enormous amounts of gravitational energy converted into radiation, are seen as strong X-ray sources in the sky. As a black hole can only be detected via its interaction with its surroundings, these binary systems provide important evidence for the existence of black holes. There are now at least twenty cases where the measured mass of the X-ray emitting compact object in a binary exceeds the upper limit for a neutron star, thus inferring the presence of a black hole. These binary systems serve as excellent laboratories not only to study the physics of accretion but also to test predictions of general relativity in strongly curved space time. An understanding of the accretion flow onto these, the most compact objects in our Universe, is therefore of great importance to physics. We are only now slowly beginning to understand the spectra and variability observed in these X-ray sources. During the last decade, a framework has developed that provides an interpretation of the spectral evolution as a function of changes in the physics and geometry of the accretion flow driven by a variable accretion rate. This doctoral thesis presents studies of two black hole binary systems, Cygnus~X-1 and GRS~1915+105, plus the possible black hole candidate Cygnus~X-3, and the results from an attempt to interpret their observed properties within this emerging framework. The main result presented in this thesis is an interpretation of the spectral variability in the enigmatic source Cygnus~X-3, including the nature and accretion geometry of its so-called hard spectral state. The results suggest that the compact object in this source, which has not been uniquely identified as a black hole on the basis of standard mass measurements, is most probably a massive, ~30 Msun, black hole, and thus the most massive black hole observed in a binary in our Galaxy so far. In addition, results concerning a possible observation of limit-cycle variability in the microquasar GRS~1915+105 are presented as well as evidence of `mini-hysteresis' in the extreme hard state of Cygnus X-1.

Measuring the Cosmic Microwave Background : Topics along the analysis pipeline

The first quarter of the 20th century witnessed a rebirth of cosmology, study of our Universe, as a field of scientific research with testable theoretical predictions. The amount of available cosmological data grew slowly from a few galaxy redshift measurements, rotation curves and local light element abundances into the first detection of the cos- mic microwave background (CMB) in 1965. By the turn of the century the amount of data exploded incorporating fields of new, exciting cosmological observables such as lensing, Lyman alpha forests, type Ia supernovae, baryon acoustic oscillations and Sunyaev-Zeldovich regions to name a few. -- CMB, the ubiquitous afterglow of the Big Bang, carries with it a wealth of cosmological information. Unfortunately, that information, delicate intensity variations, turned out hard to extract from the overall temperature. Since the first detection, it took nearly 30 years before first evidence of fluctuations on the microwave background were presented. At present, high precision cosmology is solidly based on precise measurements of the CMB anisotropy making it possible to pinpoint cosmological parameters to one-in-a-hundred level precision. The progress has made it possible to build and test models of the Universe that differ in the way the cosmos evolved some fraction of the first second since the Big Bang. -- This thesis is concerned with the high precision CMB observations. It presents three selected topics along a CMB experiment analysis pipeline. Map-making and residual noise estimation are studied using an approach called destriping. The studied approximate methods are invaluable for the large datasets of any modern CMB experiment and will undoubtedly become even more so when the next generation of experiments reach the operational stage. -- We begin with a brief overview of cosmological observations and describe the general relativistic perturbation theory. Next we discuss the map-making problem of a CMB experiment and the characterization of residual noise present in the maps. In the end, the use of modern cosmological data is presented in the study of an extended cosmological model, the correlated isocurvature fluctuations. Current available data is shown to indicate that future experiments are certainly needed to provide more information on these extra degrees of freedom. Any solid evidence of the isocurvature modes would have a considerable impact due to their power in model selection.

Unfolding of Plasmodium falciparum Triosephosphate Isomerase in Urea and Guanidinium Chloride: Evidence for a Novel Disulfide Exchange Reaction in a Covalently Cross-Linked Mutant†

The conformational stability of Plasmodium falciparum triosephosphate isomerase (TIMWT) enzyme has been investigated in urea and guanidinium chloride (GdmCl) solutions using circular dichroism, fluorescence, and size-exclusion chromatography. The dimeric enzyme is remarkably stable in urea solutions. It retains considerable secondary, tertiary, and quaternary structure even in 8 M urea. In contrast, the unfolding transition is complete by 2.4 M GdmCl. Although the secondary as well as the tertiary interactions melt before the perturbation of the quaternary structure, these studies imply that the dissociation of the dimer into monomers ultimately leads to the collapse of the structure, suggesting that the interfacial interactions play a major role in determining multimeric protein stability. The C-m(urea)/C-m(GdmCl) ratio (where C-m is the concentration of the denaturant required at the transition midpoint) is unusually high for triosephosphate isomerase as compared to other monomeric and dimeric proteins. A disulfide crosslinked mutant protein (Y74C) engineered to form two disulfide cross-links across the interface (13-74') and (13'-74) is dramatically destablized in urea. The unfolding transition is complete by 6 M urea and involves a novel mechanism of dimer dissociation through intramolecular thiol-disulfide exchange.

Structural Insights into the Acyl Intermediates of the Plasmodium falciparum Fatty Acid Synthesis Pathway THE MECHANISM OF EXPANSION OF THE ACYL CARRIER PROTEIN CORE

Acyl carrier protein (ACP) plays a central role in fatty acid biosynthesis. However, the molecular machinery that mediates its function is not yet fully understood. Therefore, structural studies were carried out on the acyl-ACP intermediates of Plasmodium falciparum using NMR as a spectroscopic probe. Chemical shift perturbation studies put forth a new picture of the interaction of ACP molecule with the acyl chain, namely, the hydrophobic core can protect up to 12 carbon units, and additional carbons protrude out from the top of the hydrophobic cavity. The latter hypothesis stems from chemical shift changes observed in C-alpha and C-beta of Ser-37 in tetradecanoyl-ACP. C-13, N-15-Double-filtered nuclear Overhauser effect (NOE) spectroscopy experiments further substantiate the concept; in octanoyl (C-8)- and dodecanoyl (C-12)-ACP, a long range NOE is observed within the phosphopantetheine arm, suggesting an arch-like conformation. This NOE is nearly invisible in tetradecanoyl (C-14)-ACP, indicating a change in conformation of the prosthetic group. Furthermore, the present study provides insights into the molecular mechanism of ACP expansion, as revealed from a unique side chain-to-backbone hydrogen bond between two fairly conserved residues, Ile-55 HN and Glu-48 O. The backbone amide of Ile-55 HN reports a pK(a) value for the carboxylate, similar to 1.9 pH units higher than model compound value, suggesting strong electrostatic repulsion between helix II and helix III. Charge-charge repulsion between the helices in combination with thrust from inside due to acyl chain would energetically favor the separation of the two helices. Helix III has fewer structural restraints and, hence, undergoes major conformational change without altering the overall-fold of P. falciparum ACP.