Transformation Strain and Crystallographic Texture in Steels

The transformation strain associated with displacive phase transformations can be utilised to improve mechanical properties of structural components in steels. The advantages of the transformation plasticity can be fully utilised by allowing the transformation to occur under the influence of external stress or strain. In this thesis, mathematical models have been formulated to calculate the transformation strain and texture during martensitic and bainitic transformations. The models are able to deal with a variety of complexities including various starting austenite textures and different states of externally applied stress. A variant selection model has been proposed based on Patel and Cohen’s theory and the effect of variant selection on the transformation strain and texture has been discussed in detail. A new theory has been proposed to calculate the extent of variant selection. An attempt has been made to separate the effects of stress and strain on transformation plasticity and variant selection. It has been shown that Patel and Cohen’s plastic strain theory is more suitable than the elastic infinitesimal strain deformation model to calculate the interaction energies between crystallographic variants and external load. Using theoretical knowledge and with the help of a neural network model, new alloys have been prepared to be used as the welding filler metals to reduce the residual stress and to achieve higher toughness. Neutron diffraction studies have revealed that newly developed filler metals do indeed reduce the residual stress. Synchrotron X-ray data have been utilised to determine the texture of austenite and martensite as transformation occurs under load. A mathematical model has been developed to predict the Debye diffraction patterns observed experimentally

Mill Scales Blended Polymer Composites For Electrical Insulation Application

Standalone composite films were prepared using modified polyester as a binder and waste iron oxides (mill scales) collected from a steel plant as inorganic filler. The morphology, structure, composition, strength and electrical insulation properties of polymer-iron composites were studied using various analytical techniques such as X-ray diffraction (XRD), Scanning electron microscope (SEM), Atomic force microscopy (AFM), optical microscopy, Fourier transform infrared (FTIR) spectroscopy, X-ray fluorescence (XRF), Brunauer–Emmett–Teller (BET) test, particle size analysis and electrical insulation test. The mill scales collected from the hot strip rolling mill (HSM) have found to comprise three different phases such as wustite, magnetite and hematite. Composites prepared using mill scales were showing three times higher strength compared to the mother polymer film. Electrical insulation of these composites were found to increase in the range of 55-230 MV/mm with increasing iron oxide content from 0.0125 g to 0.25 g in 2.5 g polymer. These results show a potential research field on the mill scales based composites for various advanced applications in improving insulation behaviour of materials which can withstand at higher temperatures and electrical stresses

Fixed-Parameter Algorithms for Fair Hitting Set Problems

Selection of a group of representatives satisfying certain fairness constraints, is a commonly occurring scenario. Motivated by this, we initiate a systematic algorithmic study of a \emph{fair} version of \textsc{Hitting Set}. In the classical \textsc{Hitting Set} problem, the input is a universe $\mathcal{U}$, a family $\mathcal{F}$ of subsets of $\mathcal{U}$, and a non-negative integer $k$. The goal is to determine whether there exists a subset $S \subseteq \mathcal{U}$ of size $k$ that \emph{hits} (i.e., intersects) every set in $\mathcal{F}$. Inspired by several recent works, we formulate a fair version of this problem, as follows. The input additionally contains a family $\mathcal{B}$ of subsets of $\mathcal{U}$, where each subset in $\mathcal{B}$ can be thought of as the group of elements of the same \emph{type}. We want to find a set $S \subseteq \mathcal{U}$ of size $k$ that (i) hits all sets of $\mathcal{F}$, and (ii) does not contain \emph{too many} elements of each type. We call this problem \textsc{Fair Hitting Set}, and chart out its tractability boundary from both classical as well as multivariate perspective. Our results use a multitude of techniques from parameterized complexity including classical to advanced tools, such as, methods of representative sets for matroids, FO model checking, and a generalization of best known kernels for \textsc{Hitting Set}

Fixed-Parameter Algorithms for Fair Hitting Set Problems

Selection of a group of representatives satisfying certain fairness constraints, is a commonly occurring scenario. Motivated by this, we initiate a systematic algorithmic study of a fair version of Hitting Set. In the classical Hitting Set problem, the input is a universe ?, a family ? of subsets of ?, and a non-negative integer k. The goal is to determine whether there exists a subset S ? ? of size k that hits (i.e., intersects) every set in ?. Inspired by several recent works, we formulate a fair version of this problem, as follows. The input additionally contains a family ? of subsets of ?, where each subset in ? can be thought of as the group of elements of the same type. We want to find a set S ? ? of size k that (i) hits all sets of ?, and (ii) does not contain too many elements of each type. We call this problem Fair Hitting Set, and chart out its tractability boundary from both classical as well as multivariate perspective. Our results use a multitude of techniques from parameterized complexity including classical to advanced tools, such as, methods of representative sets for matroids, FO model checking, and a generalization of best known kernels for Hitting Set

Exponential-time approximation schemes via compression

In this paper, we give a framework to design exponential-time approximation schemes for basic graph partitioning problems such as k-way cut, Multiway Cut, Steiner k-cut and Multicut, where the goal is to minimize the number of edges going across the parts. Our motivation to focus on approximation schemes for these problems comes from the fact that while it is possible to solve them exactly in 2^nn^{

FPT approximations for packing and covering problems parameterized by elimination distance and even less

For numerous graph problems in the realm of parameterized algorithms, using the size of a smallest deletion set (called a modulator) into well-understood graph families as parameterization has led to a long and successful line of research. Recently, however, there has been an extensive study of structural parameters that are potentially much smaller than the modulator size. In particular, recent papers [Jansen et al. STOC 2021; Agrawal et al. SODA 2022] have studied parameterization by the size of the modulator to a graph family ℋ(mod_ℋ(⋅)), elimination distance to ℋ(ed_ℋ(⋅)), and ℋ-treewidth (tw_ℋ(⋅)). These parameters are related by the fact that tw_ℋ lower bounds ed_ℋ, which in turn lower bounds mod_ℋ. While these new parameters have been successfully exploited to design fast exact algorithms their utility (especially that of ed_ℋ and tw_ℋ) in the context of approximation algorithms is mostly unexplored. The conceptual contribution of this paper is to present novel algorithmic meta-theorems that expand the impact of these structural parameters to the area of FPT Approximation, mirroring their utility in the design of exact FPT algorithms. Precisely, we show that if a covering or packing problem is definable in Monadic Second Order Logic and has a property called Finite Integer Index (FII), then the existence of an FPT Approximation Scheme (FPT-AS, i.e., (1±ε)-approximation) parameterized by mod_ℋ(⋅), ed_ℋ(⋅), and tw_ℋ(⋅) is in fact equivalent. As a consequence, we obtain FPT-ASes for a wide range of covering, packing, and domination problems on graphs with respect to these parameters. In the process, we show that several graph problems, that are W[1]-hard parameterized by mod_ℋ, admit FPT-ASes not only when parameterized by mod_ℋ, but even when parameterized by the potentially much smaller parameter tw_ℋ(⋅). In the spirit of [Agrawal et al. SODA 2022], our algorithmic results highlight a broader connection between these parameters in the world of approximation. As concrete exemplifications of our meta-theorems, we obtain FPT-ASes for well-studied graph problems such as Vertex Cover, Feedback Vertex Set, Cycle Packing and Dominating Set, parameterized by tw_ℋ(⋅) (and hence, also by mod_ℋ(⋅) or ed_ℋ(⋅)), where ℋ is any family of minor free graphs

No association of TNFRSF1B variants with type 2 diabetes in Indians of Indo-European origin

<p>Abstract</p> <p>Background</p> <p>There has been no systematic evaluation of the association between genetic variants of type 2 receptor for TNFα (TNFR2) and type 2 diabetes, despite strong biological evidence for the role of this receptor in the pathogenesis of this complex disorder. In view of this, we performed a comprehensive association analysis of <it>TNFRSF1B </it>variants with type 2 diabetes in 4,200 Indo-European subjects from North India.</p> <p>Methods</p> <p>The initial phase evaluated association of seven SNPs viz. rs652625, rs496888, rs6697733, rs945439, rs235249, rs17883432 and rs17884213 with type 2 diabetes in 2,115 participants (1,073 type 2 diabetes patients and 1,042 control subjects). Further, we conducted replication analysis of three associated SNPs in 2,085 subjects (1,047 type 2 diabetes patients and 1,038 control subjects).</p> <p>Results</p> <p>We observed nominal association of rs945439, rs235249 and rs17884213 with type 2 diabetes (<it>P </it>< 0.05) in the initial phase. Haplotype CC of rs945439 and rs235249 conferred increased susceptibility for type 2 diabetes [OR = 1.19 (95%CI 1.03-1.37), <it>P </it>= 0.019/<it>P</it>_perm= 0.076] whereas, TG haplotype of rs235249 and rs17884213 provided protection against type 2 diabetes [OR = 0.83 (95%CI 0.72-0.95, <it>P </it>= 7.2 × 10^-3/<it>P</it>_perm= 0.019]. We also observed suggestive association of rs496888 with plasma hsCRP levels [<it>P </it>= 0.042]. However, the association of rs945439, rs235249 and rs17884213 with type 2 diabetes was not replicated in the second study population. Meta-analysis of the two studies also failed to detect any association with type 2 diabetes.</p> <p>Conclusions</p> <p>Our two-stage association analysis suggests that <it>TNFRSF1B </it>variants are not the determinants of genetic risk of type 2 diabetes in North Indians.</p