Topological stability through tame retractions

A smooth map is said to be stable if small perturbations of the map only differ from the original one by a smooth change of coordinates. Smoothly stable maps are generic among the proper maps between given source and target manifolds when the source and target dimensions belong to the so-called nice dimensions, but outside this range of dimensions, smooth maps cannot generally be approximated by stable maps. This leads to the definition of topologically stable maps, where the smooth coordinate changes are replaced with homeomorphisms. The topologically stable maps are generic among proper maps for any dimensions of source and target. The purpose of this thesis is to investigate methods for proving topological stability by constructing extremely tame (E-tame) retractions onto the map in question from one of its smoothly stable unfoldings. In particular, we investigate how to use E-tame retractions from stable unfoldings to find topologically ministable unfoldings for certain weighted homogeneous maps or germs. Our first results are concerned with the construction of E-tame retractions and their relation to topological stability. We study how to construct the E-tame retractions from partial or local information, and these results form our toolbox for the main constructions. In the next chapter we study the group of right-left equivalences leaving a given multigerm f invariant, and show that when the multigerm is finitely determined, the group has a maximal compact subgroup and that the corresponding quotient is contractible. This means, essentially, that the group can be replaced with a compact Lie group of symmetries without much loss of information. We also show how to split the group into a product whose components only depend on the monogerm components of f. In the final chapter we investigate representatives of the E- and Z-series of singularities, discuss their instability and use our tools to construct E-tame retractions for some of them. The construction is based on describing the geometry of the set of points where the map is not smoothly stable, discovering that by using induction and our constructional tools, we already know how to construct local E-tame retractions along the set. The local solutions can then be glued together using our knowledge about the symmetry group of the local germs. We also discuss how to generalize our method to the whole E- and Z- series.

Preparation and thermal stability of trioxalatocobaltates of bivalent metals KM2+ [Co(C2O4)3]·xH2O

Trioxalatocobaltates of bivalent metals KM2+[Co(C2O4)3]·x H2O, with M2+ = Ba, Sr, Ca and Pb, have been prepared, characterized and their thermal behaviour studied. The compounds decompose to yield potassium carbonate, bivalent metal carbonate or oxide and cobalt oxide as final products. The formation of the final products of decomposition is influenced by the surrounding atmosphere. Bivalent metal cobaltites of the types KM2+CoO3 and M2+CoO3—x are not identified among the final products of decomposition. The study brings out the importance of the decomposition mode of the precursor in producing the desired end products.

Plasma polymer and biomolecule modification of 3-D scaffolds for tissue engineering

Plasma polymerization was used to coat a melt electrospun polycaprolactone scaffold to improve cell attachment and organization. Plasma polymerization was performed using an amine containing monomer, allylamine, which then allowed for the subsequent immobilization of biomolecules i.e. heparin and fibroblast growth factor-2. The stability of the plasma polymerized amine-coating was demonstrated by X-ray photoelectron spectroscopy analysis and imaging time-of-flight secondary ion mass spectrometry revealed that a uniform plasma amine-coating was deposited throughout the scaffold. Based upon comparison with controls it was evident that the combination scaffold aided cell ingress and the formation of distinct fibroblast and keratinocyte layers.

Stability of large flexible damped spacecraft modeled as elastic continua

Vibrational stability of a large flexible, structurally damped spacecraft subject to large rigid body rotations is analysed modelling the system as an elastic continuum. Using solution of rigid body attitude motion under torque free conditions and modal analysis, the vibrational equations are reduced to ordinary differential equations with time-varying coefficients. Stability analysis is carried out using Floquet theory and Sonin-Polya theorem. The cases of spinning and non-spinning spacecraft idealized as a flexible beam plate undergoing simple structural vibration are analysed in detail. The critical damping required for stabilization is shown to be a function of the spacecraft's inertia ratio and the level of disturbance.

Storage stability of solid rocket fuels. 2. Effect of oxidizer loadings

Ageing behaviour, leading to ballistic changes, has been studied as a function of oxidizer loading in polystyrene/ammonium perchlorate solid-propellants. The ageing studies were carried out at 100 °C in air. Change in burning rate decreased as the oxidizer loading increased from 75 to 80%. The change in thermal decomposition rates both at 230 and 260 °C also decreased as the oxidizer loading in the propellants increased. The shapes of the plots of the changes in burning rate and thermal decomposition rate (230 and 260 °C) at different storage times for different oxidizer-loaded propellants seem to be exactly similar. These results lead to the conclusion that the thermal decomposition of the propellant may be responsible for bringing about the ballistic changes during the ageing process. Infrared studies of the binder portion of the aged propellant indicate that peroxide formation takes place during the course of ageing and that peroxide formation for a particular storage time and temperature increases as the loading decreases.

On the positivity and stability of non-stationary systems

The positivity of operators in Hilbert spaces is an important concept finding wide application in various branches of Mathematical System Theory. A frequency- domain condition that ensures the positivity of time-varying operators in L2 with a state-space description, is derived in this paper by using certain newly developed inequalities concerning the input-state relation of such operators. As an interesting application of these results, an L2 stability criterion for time-varying feedback systems consisting of a finite-sector non-linearity is also developed.

On the computation of two-dimensional compressible flow fields by the modified local stability scheme

The modified local stability scheme is applied to several two-dimensional problems—blunt body flow, regular reflection of a shock and lambda shock. The resolution of the flow features obtained by the modified local stability scheme is found to be better than that achieved by the other first order schemes and almost identical to that achieved by the second order schemes incorporating artificial viscosity. The scheme is easy for coding, consumes moderate amount of computer storage and time. The scheme can be advantageously used in place of second order schemes.

Storage stability of solid rocket fuel. 1. Effect of temperature

Ageing behaviour of polystyrene (PS)/ammonium perchlorate (AP) propellent leading to ballistic changes has been studied. It follows a zero-order kinetic law. Ageing behaviour leading to change in burning rate ( ) in the temperature range of 60–200 ° C was found to remain the same. The dependence of the change of the average thermal decomposition (TD) rate at 230 and 260°C on the change in burning rate for the propellant aged at 100 ° C in air suggests that the slow TD of the propellant is the cause of ageing. The safe-life (for a pre-assigned burning-rate change limit) at 25 ° C in air has been calculated as a function of the rate of change.

Unusual structural stability and ligand induced alterations in oligomerization of a galectin

Abstract L-14, a 14-kDa S-type lectin shows the jelly roll tertiary structural fold akin to legume lectins yet, unlike them, it does not dissociate on thermal unfolding. In the absence of ligand L-14 displays denaturation transitions corresponding to tetrameric and octameric entities. The presence of complementary ligand reduces the association of L-14, which is in stark contrast with legume lectins where no alterations in quaternary structures are brought about by saccharides. From the magnitude of the increase in denaturation temperature induced by disaccharides the binding constants calculated from differential scanning calorimetry are comparable with those extrapolated from titration calorimetry indicating that L-14 interacts with ligands essentially in the folded state.

Effect of soil variability on the bearing capacity of clay and in slope stability problems

Site-specific geotechnical data are always random and variable in space. In the present study, a procedure for quantifying the variability in geotechnical characterization and design parameters is discussed using the site-specific cone tip resistance data (qc) obtained from static cone penetration test (SCPT). The parameters for the spatial variability modeling of geotechnical parameters i.e. (i) existing trend function in the in situ qc data; (ii) second moment statistics i.e. analysis of mean, variance, and auto-correlation structure of the soil strength and stiffness parameters; and (iii) inputs from the spatial correlation analysis, are utilized in the numerical modeling procedures using the finite difference numerical code FLAC 5.0. The influence of consideration of spatially variable soil parameters on the reliability-based geotechnical deign is studied for the two cases i.e. (a) bearing capacity analysis of a shallow foundation resting on a clayey soil, and (b) analysis of stability and deformation pattern of a cohesive-frictional soil slope. The study highlights the procedure for conducting a site-specific study using field test data such as SCPT in geotechnical analysis and demonstrates that a few additional computations involving soil variability provide a better insight into the role of variability in designs.

Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis

In recent years, spatial variability modeling of soil parameters using random field theory has gained distinct importance in geotechnical analysis. In the present Study, commercially available finite difference numerical code FLAC 5.0 is used for modeling the permeability parameter as spatially correlated log-normally distributed random variable and its influence on the steady state seepage flow and on the slope stability analysis are studied. Considering the case of a 5.0 m high cohesive-frictional soil slope of 30 degrees, a range of coefficients of variation (CoV%) from 60 to 90% in the permeability Values, and taking different values of correlation distance in the range of 0.5-15 m, parametric studies, using Monte Carlo simulations, are performed to study the following three aspects, i.e., (i) effect ostochastic soil permeability on the statistics of seepage flow in comparison to the analytic (Dupuit's) solution available for the uniformly constant permeability property; (ii) strain and deformation pattern, and (iii) stability of the given slope assessed in terms of factor of safety (FS). The results obtained in this study are useful to understand the role of permeability variations in slope stability analysis under different slope conditions and material properties. (C) 2009 Elsevier B.V. All rights reserved.

Analysis of stability of earthen dams in kachchh region, Gujarat, India

The Kachchh region of Gujarat, India bore the brunt of a disastrous earthquake of magnitude M-w=7.6 that occurred on January 26, 2001. The major cause of failure of various structures including earthen dams was noted to be the presence of liquefiable alluvium in the foundation soil. Results of back-analysis of failures of Chang, Tappar, Kaswati and Rudramata earth dams using pseudo-static limit equilibrium approach presented in this paper confirm that the presence of liquefiable layer contributed to lesser factors of safety leading to a base type of failure that was also observed in the field. Following the earthquake, earth dams have been rehabilitated by the concerned authority and it is imperative that the reconstructed sections of earth dams be reanalyzed. It is also increasingly realized that risk assessment of dams in view of the large-scale investment made and probabilistic analysis is necessary. In this study, it is demonstrated that the probabilistic approach when used in conjunction with deterministic approach helps in providing a rational solution for quantification of safety of the dam and in the estimation of risk associated with the dam construction. (C) 2007 Elsevier B.V. All rights reserved.

Effect of residual stresses and metallographic stability on the over all performance of integral diaphragm material

The integral diaphragm pressure transducer consists of a diaphragm machined from precipitation hardened martensitic (APX4) steel. Its performance is quite significant as it depends upon various factors such as mechanical properties including induced residual stress levels, metallurgical and physical parameters due to different stages of processing involved. Hence, the measurement and analysis of residual stress becomes very important from the point of in-service assessment of a component. In the present work, the stress measurements have been done using the X-ray diffraction (XRD) technique, which is a non-destructive test (NDT). This method is more reliable and widely used compared to the other NDT techniques. The metallurgical aspects have been studied by adopting the conventional metallographic practices including examination of microstructure using light microscope. The dimensional measurements have been carried out using dimensional gauge. The results of the present investigation reveals that the diaphragm material after undergoing series of realization processes has yielded good amount of retained austenite in it. Also, the presence of higher compressive stresses induced in the transducer results in non-linearity, zero shift and dimensional instability. The problem of higher retained austenite content and higher compressive stress have been overcome by adopting a new realization process involving machining and cold and hot stabilization soak which has brought down the retained austenite content to about 5–6% and acceptable level of compressive stress in the range −100 to −150 MPa with fine tempered martensitic phase structure and good dimensional stability. The new realization process seems to be quite effective in terms of controlling retained austenite content, residual stress, metallurgical phase as well as dimensional stability and this may result in minimum zero shift of the diaphragm system.

Determination of the thermodynamic stability of TiB2

The standard free energy of formation of titanium boride (TiB2) Was measured by the Electro Motive Force (EMF) method (by using yttria doped thoria (YDT) as the solid electrolyte). Two galvanic cells viz. Cell (I): Pt, TiB2 (s), TiO2 (s), B (s) vertical bar YDT vertical bar NiO (s), Ni (s), Pt and cell (II): Pt, TiB2 (s), TiO2 (s), B (s) vertical bar YDT vertical bar FeO (s). Fe (s), Pt were constructed in order to determine the Delta(f)G degrees, of TiB2. Enthalpy increments on TiB2 were measured by using inverse drop calorimetry over the temperature range 583-1769 K. The heat capacity, entropy and the free energy function have been derived from these experimental data in the temperature range 298-1800 K. The mean value of the standard enthalpy of formation of TiB2 (Delta H-f(298)degrees (TiB2)) was obtained by combining these Delta(f)G degrees, values and the free energy functions of TiB2 derived from the drop calorimetry data. The mean values of Delta H-f(298)degrees (TiB2) derived from the Delta(f)G degrees, data obtained from cell I and II were -322 +/- 1.2 kJ mol(-1) and -323.3 +/- 2.1 kJ mol(-1), respectively. These values were found to be in very good agreement with the assessed data. (C) 2009 Elsevier B.V. All rights reserved.