Recrystallization Texture Development in CP-Titanium

Most of the structural components are subjected to annealing as a final forming operation for different applications. It is therefore very important to understand/know the texture development during annealing of a material. This will decide the mechanical property of the component. Annealing texture of cubic crystal system has been widely researched, but little work has been done for the hexagonal close-packing materials. In the present study recrystallization texture development in CP-titanium was investigated. CP-titanium plates were subjected to cold rolling of 90% reduction in thickness. The rolled samples were then subjected to isochronal annealing at 5000C, 6000C and 7000C for 30minutes to obtain the recrystallization temperature, determined by EBSD analysis. Final annealing was carried out at 600oC for different soaking time: 10sec, 20sec, 1min, 2min, 5min, 10min, 20min and 30min to establish the texture development during annealing. These annealed samples were subsequently characterized under XRD (X-ray Diffraction) for bulk texture measurement. The initial deformation texture i.e. (1 1 -2 4) got attenuated with time and development of new basal orientation i.e. (0 0 0 1) and non-basal orientations i.e. (2 1 -3 7), (3 1 -4 9) and (5 1 -6 15) were observed

ADVENTURES ON NETWORKS: DEGREES AND GAMES

A network consists of a set of nodes and edges with the edges representing pairwise connections between nodes. Examples of real-world networks include the Internet, the World Wide Web, social networks and transportation networks often modeled as random graphs. In the first half of this thesis, we explore the degree distributions of such random graphs. In homogeneous networks or graphs, the behavior of the (generic) degree of a single node is often thought to reflect the degree distribution of the graph defined as the usual fractions of nodes with given degree. To study this preconceived notion, we introduce a general framework to discuss the conditions under which these two degree distributions coincide asymptotically in large random networks. Although Erdos-Renyi graphs along with other well known random graph models satisfy the aforementioned conditions, we show that there might be homogeneous random graphs for which such a conclusion may fail to hold. A counterexample to this common notion is found in the class of random threshold graphs. An implication of this finding is that random threshold graphs cannot be used as a substitute to the Barabasi-Albert model for scale-free network modeling, as proposed in some works. Since the Barabasi-Albert model was proposed, other network growth models were introduced that were shown to generate scale-free networks. We study one such basic network growth model, called the fitness model, which captures the inherent attributes of individual nodes through fitness values (drawn from a fitness distribution) that influence network growth. We characterize the tail of the network-wide degree distribution through the fitness distribution and demonstrate that the fitness model is indeed richer than the Barabasi-Albert model, in that it is capable of producing power-law degree distributions with varying parameters along with other non-Poisson degree distributions. In the second half of the thesis, we look at the interactions between nodes in a game-theoretic setting. As an example, these nodes could represent interacting agents making decisions over time while the edges represent the dependence of their payoffs on the decisions taken by other nodes. We study learning rules that could be adopted by the agents so that the entire system of agents reaches a desired operating point in various scenarios motivated by practical concerns facing engineering systems. For our analysis, we abstract out the network and represent the problem in the strategic-form repeated game setting. We consider two classes of learning rules -- a class of better-reply rules and a new class of rules, which we call, the class of monitoring rules. Motivated by practical concerns, we first consider a scenario in which agents revise their actions asynchronously based on delayed payoff information. We prove that, under the better-reply rules (when certain mild assumptions hold), the action profiles played by the agents converge almost surely to a pure-strategy Nash equilibrium (PSNE) with finite expected convergence time in a large class of games called generalized weakly acyclic games (GWAGs). A similar result is shown to hold for the monitoring rules in GWAGs and also in games satisfying a payoff interdependency structure. Secondly, we investigate a scenario in which the payoff information is unreliable, causing agents to make erroneous decisions occasionally. When the agents follow the better-reply rules and the payoff information becomes more accurate over time, we demonstrate the agents will play a PSNE with probability tending to one in GWAGs. Under a similar setting, when the agents follow the monitoring rule, we show that the action profile weakly converges to certain characterizable PSNE(s). Finally, we study a scenario where an agent might erroneously execute an intended action from time to time. Under such a setting, we show that the monitoring rules ensure that the system reaches PSNE(s) which are resilient to deviations by potentially multiple agents

Fick-Jacobs description and first passage dynamics for diffusion in a channel under stochastic resetting

Transport of particles through channels is of paramount importance in physics, chemistry and surface science due to its broad real world applications. Much insights can be gained by observing the transition paths of a particle through a channel and collecting statistics on the lifetimes in the channel or the escape probabilities from the channel. In this paper, we consider the diffusive transport through a narrow conical channel of a Brownian particle subject to intermittent dynamics, namely, stochastic resetting. As such, resetting brings the particle back to a desired location from where it resumes its diffusive phase. To this end, we extend the Fick-Jacobs theory of channel-facilitated diffusive transport to resetting-induced transport. Exact expressions for the conditional mean first passage times, escape probabilities and the total average lifetime in the channel are obtained, and their behaviour as a function of the resetting rate are highlighted. It is shown that resetting can expedite the transport through the channel -- rigorous constraints for such conditions are then illustrated. Furthermore, we observe that a carefully chosen resetting rate can render the average lifetime of the particle inside the channel minimal. Interestingly, the optimal rate undergoes continuous and discontinuous transitions as some relevant system parameters are varied. The validity of our one-dimensional analysis and the corresponding theoretical predictions are supported by three-dimensional Brownian dynamics simulations. We thus believe that resetting can be useful to facilitate particle transport across biological membranes -- a phenomena that can spearhead further theoretical and experimental studies

Controlled coalescence-induced droplet jumping on flexible superhydrophobic substrates

Sessile droplets coalescing on superhydrophobic substrates spontaneously jump from the surface. In this process, the excess surface energy available at the initiation of coalescence overcomes the minimal surface adhesion and manifests as sufficient kinetic energy to propel the droplets away from the substrate. Here, we show that the coalescence induced droplet jumping velocity is significantly curtailed if the superhydrophobic substrate is flexible in nature. Through detailed experimental measurements and numerical simulations, we demonstrate that the droplet jumping velocity and jumping height can be reduced by as much as 40 % and 64%, respectively, by synergistically tuning the substrate stiffness and substrate frequency. We show that this hitherto unexplored aspect of droplet coalescence jumping can be gainfully exploited in water harvesting from dew and fog harvesting. Additionally, through an exemplar butterfly wing substrate, we demonstrate that this effect is likely to manifest on many natural superhydrophobic substrates due to their inherent flexibility

Bandwidth Optimal Pipeline Schedule for Collective Communication

We present a strongly polynomial-time algorithm to generate bandwidth optimal allgather/reduce-scatter on any network topology, with or without switches. Our algorithm constructs pipeline schedules achieving provably the best possible bandwidth performance on a given topology. To provide a universal solution, we model the network topology as a directed graph with heterogeneous link capacities and switches directly as vertices in the graph representation. The algorithm is strongly polynomial-time with respect to the topology size. This work heavily relies on previous graph theory work on edge-disjoint spanning trees and edge splitting. While we focus on allgather, the methods in this paper can be easily extended to generate schedules for reduce, broadcast, reduce-scatter, and allreduce

Primary transitional cell carcinoma of bulbar urethra

Primary urethral carcinoma (UC) is a rare entity, and bulbar UCs of transitional cell origin are even rarer. Primary presentation as a scrotal abscess and urethrocutaneous fistula is rarely documented in UC patients. We present a case of a 66-year-old male presenting to emergency department with a scrotal abscess. Following blind incision and drainage, the urethral injury was suspected, and biopsy of suspicious lesion was taken from scrotum which came out to be invasive transitional cell carcinoma. A wide local excision of the tumor was done after workup. Hence, all patients with scrotal abscess and urethrocutaneous fistula should be investigated before performing any blind procedure