Micromechanics Of Fatigue Crack-Growth At Low Stress Intensities In A High-Strength Steel

An attempt to systematically investigate the effects of microstructural parameters in influencing the resistance to fatigue crack growth (FCG) in the near-threshold region under three different temper levels has been made for a high strength low alloy steel to observe in general, widely different trends in the dependence of both the total threshold stress intensity range, DELTA-K(th) and the intrinsic or effective threshold stress intensity range, DELTA-K(eff-th) on the prior austenitic grain size (PAGS). While a low strain hardening microstructure obtained by tempering at high temperatures exhibited strong dependence of DELTA-K(th) on the PAGS by virtue of strong interactions of crack tip slip with the grain boundary, a high strength, high strain hardening microstructure as a result of tempering at low temperature exhibited a weak dependence. The lack of a systematic variation of the near-threshold parameters with respect to grain size in temper embrittled structures appears to be related to the wide variations in the amount of intergranular fracture near threshold. Crack closure, to some extent provides a basis on which the increases in DELTA-K(th) at larger grain sizes can be rationalised. This study, in addition, provides a wide perspective on the relative roles of slip behaviour embrittlement and environment that result in the different trends observed in the grain size dependence of near-threshold fatigue parameters, based on which the inconsistency in the results reported in the literature can be clearly understood. Assessment of fracture modes through extensive fractography revealed that prior austenitic grain boundaries are effective barriers to cyclic crack growth compared to martensitic packet boundaries, especially at low stress intensities. Fracture morphologies comprising of low energy flat transgranular fracture can occur close to threshold depending on the combinations of strain hardening behaviour, yield strength and embrittlement effects. A detailed consideration is given to the discussion of cyclic stress strain behaviour, embrittlement and environmental effects and the implications of these phenomena on the crack growth behaviour near threshold.

Reduction In Metal-Mold Reactivity In Titanium Castings Through The Use Of Sodium Aluminate As Binder In Zircon Sand Molds

The present work is aimed at evaluating an alternative moulding system, namely, sodium aluminate bonded zircon sand mould and assess its suitability in relation to the much studied sodium silicate bonded zircon sand moulding system. It is described in the study presented here that with regard to metal - mould reaction, sodium aluminate bonded zircon sand mould system is a superior viable system as compared to sodium silicate bonded zircon moulding system at mould firing temperatures of 873 - 1473 K.

Playing Games on Sets and Models

The most prominent objective of the thesis is the development of the generalized descriptive set theory, as we call it. There, we study the space of all functions from a fixed uncountable cardinal to itself, or to a finite set of size two. These correspond to generalized notions of the universal Baire space (functions from natural numbers to themselves with the product topology) and the Cantor space (functions from natural numbers to the {0,1}-set) respectively. We generalize the notion of Borel sets in three different ways and study the corresponding Borel structures with the aims of generalizing classical theorems of descriptive set theory or providing counter examples. In particular we are interested in equivalence relations on these spaces and their Borel reducibility to each other. The last chapter shows, using game-theoretic techniques, that the order of Borel equivalence relations under Borel reduciblity has very high complexity. The techniques in the above described set theoretical side of the thesis include forcing, general topological notions such as meager sets and combinatorial games of infinite length. By coding uncountable models to functions, we are able to apply the understanding of the generalized descriptive set theory to the model theory of uncountable models. The links between the theorems of model theory (including Shelah's classification theory) and the theorems in pure set theory are provided using game theoretic techniques from Ehrenfeucht-Fraïssé games in model theory to cub-games in set theory. The bottom line of the research declairs that the descriptive (set theoretic) complexity of an isomorphism relation of a first-order definable model class goes in synch with the stability theoretical complexity of the corresponding first-order theory. The first chapter of the thesis has slightly different focus and is purely concerned with a certain modification of the well known Ehrenfeucht-Fraïssé games. There we (me and my supervisor Tapani Hyttinen) answer some natural questions about that game mainly concerning determinacy and its relation to the standard EF-game

Ability of human chorionic gonadotropin beta-subunit to inhibit the steroidogenic response to lutropin.

Ability of the beta-subunit of human chorionic gonadotropin to inhibit the response to lutropin (luteinizing hormone, LH) was tested in the immature rat ovarian system and pregnant-mare-serum-gonadotropin-primed rat ovarian system with progesterone production being used as the response. Human chorionic gonadotropin beta-subunit was found to inhibit human and ovine lutropin-stimulated progesterone production. At a constant dose of lutropin, inhibition was dependent on the concentration of beta-subunit. When concentration of the beta-subunit was kept constant at 5.0 microgram/ml and the concentration of lutropin was varied, the inhibition was maximum at the saturating concentration of the native hormone. The alpha-subunit of the human chorionic gonadotropin did not inhibit the response to lutropin. The lutropin/beta-subunit ratio required to produce an inhibition of response was much lower than that required to bring about an observable inhibition of binding.

On duality in linear fractional programming

In this paper, a dual of a given linear fractional program is defined and the weak, direct and converse duality theorems are proved. Both the primal and the dual are linear fractional programs. This duality theory leads to necessary and sufficient conditions for the optimality of a given feasible solution. A unmerical example is presented to illustrate the theory in this connection. The equivalence of Charnes and Cooper dual and Dinkelbach’s parametric dual of a linear fractional program is also established.

A comparison between conceptual clustering and conventional clustering

Clustering is a process of partitioning a given set of patterns into meaningful groups. The clustering process can be viewed as consisting of the following three phases: (i) feature selection phase, (ii) classification phase, and (iii) description generation phase. Conventional clustering algorithms implicitly use knowledge about the clustering environment to a large extent in the feature selection phase. This reduces the need for the environmental knowledge in the remaining two phases, permitting the usage of simple numerical measure of similarity in the classification phase. Conceptual clustering algorithms proposed by Michalski and Stepp [IEEE Trans. PAMI, PAMI-5, 396–410 (1983)] and Stepp and Michalski [Artif. Intell., pp. 43–69 (1986)] make use of the knowledge about the clustering environment in the form of a set of predefined concepts to compute the conceptual cohesiveness during the classification phase. Michalski and Stepp [IEEE Trans. PAMI, PAMI-5, 396–410 (1983)] have argued that the results obtained with the conceptual clustering algorithms are superior to conventional methods of numerical classification. However, this claim was not supported by the experimental results obtained by Dale [IEEE Trans. PAMI, PAMI-7, 241–244 (1985)]. In this paper a theoretical framework, based on an intuitively appealing set of axioms, is developed to characterize the equivalence between the conceptual clustering and conventional clustering. In other words, it is shown that any classification obtained using conceptual clustering can also be obtained using conventional clustering and vice versa.

On extremal solutions to stochastic control problems, II

The set of attainable laws of the joint state-control process of a controlled diffusion is analyzed from a convex analytic viewpoint. Various equivalence relations depending on one-dimensional marginals thereof are defined on this set and the corresponding equivalence classes are studied.

Target space of an asymmetric chiral gauged wzw model

It is shown that the asymmetric chiral gauging of the WZW models give rise to consistent string backgrounds. The target space structure of the chiral gauged SL(2,R) WZW model, with the gauging of subgroups SO(1, 1) in the left and U(1) in the right moving sector, is obtained. We then analyze the symmetries of the background and show the presence of a non-trivial isometry in the canonical parametrization of the WZW model. Using these results, the equivalence of the asymmetric models with the symmetric ones is demonstrated.

Two-mode quantum systems: Invariant classification of squeezing transformations and squeezed states

A general analysis of squeezing transformations for two-mode systems is given based on the four-dimensional real symplectic group Sp(4, R). Within the framework of the unitary (metaplectic) representation of this group, a distinction between compact photon-number-conserving and noncompact photon-number-nonconserving squeezing transformations is made. We exploit the U(2) invariant squeezing criterion to divide the set of all squeezing transformations into a two-parameter family of distinct equivalence classes with representative elements chosen for each class. Familiar two-mode squeezing transformations in the literature are recognized in our framework and seen to form a set of measure zero. Examples of squeezed coherent and thermal states are worked out. The need to extend the heterodyne detection scheme to encompass all of U(2) is emphasized, and known experimental situations where all U(2) elements can be reproduced are briefly described.

Coherent-mode decomposition of general anisotropic Gaussian Schell-model beams

We present a complete solution to the problem of coherent-mode decomposition of the most general anisotropic Gaussian Schell-model (AGSM) beams, which constitute a ten-parameter family. Our approach is based on symmetry considerations. Concepts and techniques familiar from the context of quantum mechanics in the two-dimensional plane are used to exploit the Sp(4, R) dynamical symmetry underlying the AGSM problem. We take advantage of the fact that the symplectic group of first-order optical system acts unitarily through the metaplectic operators on the Hilbert space of wave amplitudes over the transverse plane, and, using the Iwasawa decomposition for the metaplectic operator and the classic theorem of Williamson on the normal forms of positive definite symmetric matrices under linear canonical transformations, we demonstrate the unitary equivalence of the AGSM problem to a separable problem earlier studied by Li and Wolf [Opt. Lett. 7, 256 (1982)] and Gori and Guattari [Opt. Commun. 48, 7 (1983)]. This conn ction enables one to write down, almost by inspection, the coherent-mode decomposition of the general AGSM beam. A universal feature of the eigenvalue spectrum of the AGSM family is noted.

BSSB: BLAST Server for Structural Biologists

The Basic Local Alignment Search Tool (BLAST) is one of the most widely used sequence alignment programs with which similarity searches, for both protein and nucleic acid sequences, can be performed against large databases at high speed. A large number of tools exist for processing BLAST output, but none of them provide three-dimensional structure visualization. This shortcoming has been addressed in the proposed tool BLAST Server for Structural Biologists (BSSB), which maps a BLAST output onto the three-dimensional structure of the subject protein. The three-dimensional structure of the subject protein is represented using a three-color coding scheme (identical: red; similar: yellow; and mismatch: white) based on the pairwise alignment obtained. Thus, the user will be able to visualize a possible three-dimensional structure for the query protein sequence. This information can be used to gain a deeper insight into the sequence-structure correlation. Furthermore, the additional structure-level information enables the user to make coherent and logical decisions regarding the type of input model structure or fragment that can be used for molecular replacement calculations. This tool is freely available to all users at http://bioserver1.physics.iisc.ernet.in/bssb/.

Topological phases, Majorana modes and quench dynamics in a spin ladder system

We explore the salient features of the `Kitaev ladder', a two-legged ladder version of the spin-1/2 Kitaev model on a honeycomb lattice, by mapping it to a one-dimensional fermionic p-wave superconducting system. We examine the connections between spin phases and topologically non-trivial phases of non-interacting fermionic systems, demonstrating the equivalence between the spontaneous breaking of global Z(2) symmetry in spin systems and the existence of isolated Majorana modes. In the Kitaev ladder, we investigate topological properties of the system in different sectors characterized by the presence or absence of a vortex in each plaquette of the ladder. We show that vortex patterns can yield a rich parameter space for tuning into topologically non-trivial phases. We introduce and employ a new topological invariant for explicitly determining the presence of zero energy Majorana modes at the boundaries of such phases. Finally, we discuss dynamic quenching between topologically non-trivial phases in the Kitaev ladder and, in particular, the post-quench dynamics governed by tuning through a quantum critical point.