Dynamics of circular arrangements of vorticity in two dimensions

The merger of two like-signed vortices is a well-studied problem, but in a turbulent flow, we may often have more than two like-signed vortices interacting. We study the merger of three or more identical co-rotating vortices initially arranged on the vertices of a regular polygon. At low to moderate Reynolds numbers, we find an additional stage in the merger process, absent in the merger of two vortices, where an annular vortical structure is formed and is long-lived. Vortex merger is slowed down significantly due to this. Such annular vortices are known at far higher Reynolds numbers in studies of tropical cyclones, which have been noticed to a break down into individual vortices. In the pre-annular stage, vortical structures in a viscous flow are found here to tilt and realign in a manner similar to the inviscid case, but the pronounced filaments visible in the latter are practically absent in the former. Interestingly at higher Reynolds numbers, the merger of an odd number of vortices is found to proceed very differently from that of an even number. The former process is rapid and chaotic whereas the latter proceeds more slowly via pairing events. The annular vortex takes the form of a generalised Lamb-Oseen vortex (GLO), and diffuses inwards until it forms a standard Lamb-Oseen vortex. For lower Reynolds number, the numerical (fully nonlinear) evolution of the GLO vortex follows exactly the analytical evolution until merger. At higher Reynolds numbers, the annulus goes through instabilities whose nonlinear stages show a pronounced difference between even and odd mode disturbances. It is hoped that the present findings, that multiple vortex merger is qualitatively different from the merger of two vortices, will motivate studies on how multiple vortex interactions affect the inverse cascade in two-dimensional turbulence.Comment: Abstract truncated. Paper to appear in Physical Review

Near-Optimal Complexity Bounds for Fragments of the Skolem Problem

Given a linear recurrence sequence (LRS), specified using the initial conditions and the recurrence relation, the Skolem problem asks if zero ever occurs in the infinite sequence generated by the LRS. Despite active research over last few decades, its decidability is known only for a few restricted subclasses, by either restricting the order of the LRS (upto 4) or by restricting the structure of the LRS (e.g., roots of its characteristic polynomial). In this paper, we identify a subclass of LRS of arbitrary order for which the Skolem problem is easy, namely LRS all of whose characteristic roots are (possibly complex) roots of real algebraic numbers, i.e., roots satisfying x^d = r for r real algebraic. We show that for this subclass, the Skolem problem can be solved in NP^RP. As a byproduct, we implicitly obtain effective bounds on the zero set of the LRS for this subclass. While prior works in this area often exploit deep results from algebraic and transcendental number theory to get such effective results, our techniques are primarily algorithmic and use linear algebra and Galois theory. We also complement our upper bounds with a NP lower bound for the Skolem problem via a new direct reduction from 3-CNF-SAT, matching the best known lower bounds

Travel to extraterrestrial bodies over time: some exploratory analyses of mission data

This paper discusses data pertaining to space missions to astronomical bodies beyond earth. The analyses provide summarizing facts and graphs obtained by mining data about (1) missions launched by all countries that go to the moon and planets, and (2) Earth satellites obtained from a Union of Concerned Scientists (UCS) dataset and lists of publically available satellite data

Enhancing Binary Code Comment Quality Classification: Integrating Generative AI for Improved Accuracy

This report focuses on enhancing a binary code comment quality classification model by integrating generated code and comment pairs, to improve model accuracy. The dataset comprises 9048 pairs of code and comments written in the C programming language, each annotated as "Useful" or "Not Useful." Additionally, code and comment pairs are generated using a Large Language Model Architecture, and these generated pairs are labeled to indicate their utility. The outcome of this effort consists of two classification models: one utilizing the original dataset and another incorporating the augmented dataset with the newly generated code comment pairs and labels.Comment: 11 pages, 2 figures, 2 tables, Has been accepted for the Information Retrieval in Software Engineering track at Forum for Information Retrieval Evaluation 202

Effect of shape on mechanical properties and deformation behavior of Cu nanowires: An atomistic simulations study

We study the effect of nanowire shape on mechanical properties and deformation behaviour of Cu nanowires using atomistic simulations. Simulations were carried out on $[100]$ nanowires with different shapes such as triangular, square, pentagon, hexagon and circular.Results indicate yield strength is different for different shapes. In both cases, triangular nanowire exhibit the lowest yield strength, while circular nanowire is the strongest. Deformation in all the nanowires is dominated by partials slip and twinning. Due to twinning, different shapes expose different surfaces at the twinned region. All nanowires show ductile failure and square nanowire exhibits the highest failure strain, while it is lowest for triangular nanowire.Comment: 14 pages, 10 Figure

A Sub-Picosecond Digital Clock Monitoring System

We describe a low-cost system designed to monitor wander in digital clocks with a precision of $\le$ 1 ps. With this system we have shown that it is possible to track phase variations at the sub-picosecond level by adding noise to a reference clock. As in many cases where a clock is part of a complex distribution network small changes in temperature and other effects can lead to small changes in the a clock's phase. As a further demonstration of the system, we have used it to measure the phase changes induced in optical signals in fibers.Comment: 19 pages 26 figure

SURVEY, ISOLATION, BIOCHEMICAL CHARACTERIZATION, AND IDENTIFICATION OF HELICOBACTER PYLORI FROM GASTRIC PATIENT BIOPSY

Objective: This study was to isolate and identify the Helicobacter pylori from the biopsy samples of the gastric patient.Methods: Gastric biopsies were collected from the antral region of the gastric patient. Out of 96 patients, 59 males and 37 females in the age group between 11 and 70 years old were selected. A serial dilution of the sample was made. The bacterial colonies were examined on the basis of Gram staining, colony morphology, and biochemical reactions such as catalase, urease, oxidase, nitrate reduction, glycine utilization, growth (different media, different temperature, and salt tolerance), and antibiotic sensitivityResult: From the findings, it was found that 75% (65% of male and 35% of female) have H. pylori infection remaining 25% were not infected. The rate of infection was found to be more in age group 55-65 and less in age group below 25. Among 75% of H. pylori infected patients, 72% are affected with ulcer, 19% with gastric cancer, and 8.3% found to be non-gastric inflammated. Gram staining result declared that the isolated bacteria from the biopsy sample observed to be Gram-negative, spiral shaped rod. Biochemical reports produced positive indication to all the tests.Conclusion: Based on the morphological, staining and biochemical test result, it was confirmed that the isolated bacteria was found to be H. pylori.Gastric cancer is the fourth most common cancer and the second leading cause of cancer-related to death worldwide. In 1994, the international agencyfor research on cancer classified H. pylori as a Class I (definite) carcinogen, as H. pylori infection is considered as an important trigger in the processof carcinogenesis of both types of distal gastric cancer.Â