Semiclassical triton

The symmetric components of the spatial part of $S$- and $D$- states' wavefunctions for triton $(^{3}H)$ are investigated utilizing semiclassical expansion (in the powers of $\hbar$). Analysis of the diagonalized Hamiltonian reveals the existence of two different mass states within the ground state of triton. We have solved the coupled differential equations for the two admixed states $^{2}S_{1/2}$ and $^{4}D_{1/2}$ owing to tensor interactions exploiting classical WKB-theory using phenomenological Feshbach-Pease potentials. The relative probability of the $D$-state is found to be in good agreement with the experimentally inferred value (4 - 5 \%)

Transition to turbulence in particle laden flows

Suspended particles can alter the properties of fluids and in particular also affect the transition from laminar to turbulent flow. In the present experimental study, we investigate the impact of neutrally buoyant, spherical inertial particles on transition to turbulence in a pipe flow. At low particle concentrations, like in single phase Newtonian fluids, turbulence only sets in when triggered by sufficiently large perturbations and, as characteristic for this transition localized turbulent regions (puffs) co-exist with laminar flow. In agreement with earlier studies this transition point initially moves to lower Reynolds number (Re) as the particle concentration increases. At higher concentrations however the nature of the transition qualitatively changes: Laminar flow gives way to a globally fluctuating state following a continuous, non-hysteretic transition. A further increase in Re results in a secondary instability where localized puff-like structures arise on top of the uniformly fluctuating background flow. At even higher concentration only the uniformly fluctuating flow is found and signatures of Newtonian type turbulence are no longer observed

IMPACT OF INRUSH CURRENTS AND GEOMAGNETICALLY INDUCED CURRENTS ON TRANSFORMER BEHAVIOR

Transformers are the tie-points of electrical power systems. Their protection from power system faults and other innate issues is of prime importance. A few of the issues that are studied in this report are magnetic inrush currents, geomagnetically induced currents in power transformers and Over-excitation. This project develops a novel way of initializing and visualizing the flux linkage in the transformer core for studies on energization inrush currents. In addition, a quasi-DC source for GIC has been developed in order to study the GIC effects on power transformers and a sensitivity analysis has been carried out to understand effects of GIC amplitudes and frequencies on the transformer core. Lastly, a study has been carried out in order to understand Over-excitation effects on transformers. The cases have been simulated in ATP (Alternative Transients Program) using the hybrid transformer model available in the program. The simulation results suggest the models developed are capable of providing an in depth analysis of GIC, inrush currents and over-excitation. Future recommendations include studies on relationship of var absorption and GIC amplitude as well as developing a model for studying controlled switching with residual flux linkage monitoring for minimizing inrush currents

Orbit Classification of asteroids using implementation of radial Basis Function on Support Vector Machines

This research paper focuses on the implementation of radial Basis Function (RBF) Support Vector Machines (SVM) for classifying asteroid orbits. Asteroids are important astronomical objects, and their orbits play a crucial role in understanding the dynamics of the solar system. The International Astronomical Union maintains data archives that provide a playground to experiment with various machine-learning techniques. In this study, we explore the application of RBF SVM algorithm to classify asteroids. The results show that the RBF SVM algorithm provides a good efficiency and accuracy to the dataset. We also analyze the impact of various parameters on the performance of the RBF SVM algorithm and present the optimal parameter settings. Our study highlights the importance of using machine learning techniques for classifying asteroid orbits and the effectiveness of the RBF SVM algorithm in this regard.Comment: 15 pages, 8 figures, 3 table

What is the Title of this Paper? Solving logic puzzles using algorithms

This work delves into the realm of logic puzzles by focusing on the Knight and Knave problems popularized by Raymond Smullyan in his book series "What is the Name of This Book?". The puzzles revolve around characters known as Knights (truth-tellers) and Knaves (liars), challenging solvers to determine the true identity of each person based on their statements. This paper explores the utilization of Python algorithms to automate the process of solving these puzzles, offering a computational approach that enhances efficiency and accessibility. In this work, we aim to develop a Python algorithm capable of parsing and analyzing the statements provided in the Knight and Knave puzzles. A logical reasoning framework is integrated within the algorithm to deduce the identities of the characters based on their statements. The algorithm processes the input statements, create a knowledge base, and make deductions following the rules of Knight and Knave logic. The developed algorithm is thoroughly tested on various instances of Knight and Knave puzzles, comparing its results to known solutions and manual approaches. We further expand the scope of the problem by introducing a Normal (who can sometimes lie and sometimes say the truth).Comment: 8 page

A comparative data study on dinosaur, bird and human bone attributes -- A supporting study for convergent evolution

For over 165 million years, dinosaurs reigned on this planet. Their entire existence saw variations in their body size and mass . Understanding the relationship between various attributes such as femur length, breadth; humerus length, breadth; tibia length, breadth and body mass of dinosaurs contributes to our understanding of the Jurassic era and further provides reasoning for bone and body size evolution of modern day descendants of those from the Dinosauria clade. The following work consists of statistical evidence derived from an encyclopedic data set consisting of a wide variety of measurements pertaining to discovered fossils of a particular taxa of dinosaur. Our study establishes linearly regressive correspondence between femur and humerus length and radii. Furthermore, there is also a comparison with terrestrial bird bone lengths, to verify the claim of birds being closest alive species to dinosaurs. An analysis into bone ratios of early humans shows that terrestrial birds are closer to humans than that of dinosaurs. Not only on one hand it challenges the closeness of birds with dinosaurs, but on the other hand it makes a case of convergent evolution between birds and humans, due to their closeness in regressive fits. A correlation between bone ratios of dinosaurs and early humans also advances understanding in the structural and physical distinctions between the two species. Overall, the work contains evaluation of dinosaur skeletons and promotes further exploration and research in the paleontological field to strengthen the conclusions drawn thus far.Comment: 13 pages, 14 figures, 7 table

Machine Learning Algorithms to Predict Chess960 Result and Develop Opening Themes

This work focuses on the analysis of Chess 960, also known as Fischer Random Chess, a variant of traditional chess where the starting positions of the pieces are randomized. The study aims to predict the game outcome using machine learning techniques and develop an opening theme for each starting position. The first part of the analysis utilizes machine learning models to predict the game result based on certain moves in each position. The methodology involves segregating raw data from .pgn files into usable formats and creating datasets comprising approximately 500 games for each starting position. Three machine learning algorithms -- KNN Clustering, Random Forest, and Gradient Boosted Trees -- have been used to predict the game outcome. To establish an opening theme, the board is divided into five regions: center, white kingside, white queenside, black kingside, and black queenside. The data from games played by top engines in all 960 positions is used to track the movement of pieces in the opening. By analysing the change in the number of pieces in each region at specific moves, the report predicts the region towards which the game is developing. These models provide valuable insights into predicting game outcomes and understanding the opening theme in Chess 960.Comment: 16 pages, 6 figures and 3 table

Adaptive Control of Unknown Pure Feedback Systems with Pure State Constraints

This paper deals with the tracking control problem for a class of unknown pure feedback system with pure state constraints on the state variables and unknown time-varying bounded disturbances. An adaptive controller is presented for such systems for the very first time. The controller is designed using the backstepping method. While designing it, Barrier Lyapunov Functions is used so that the state variables do not contravene its constraints. In order to cope with the unknown dynamics of the system, an online approximator is designed using a neural network with a novel adaptive law for its weight update. In the stability analysis of the system, the time derivative of Lyapunov function involves known virtual control coefficient with unknown direction and to deal with such problem Nussbaum gain is used to design the control law. Furthermore, to make the controller robust and computationally inexpensive, a novel disturbance observer is designed to estimate the disturbance along with neural network approximation error and the time derivative of virtual control input. The effectiveness of the proposed approach is demonstrated through a simulation study on the third-order nonlinear system

Dyanmics of falling raindrops

Studying water droplets is a rich lesson in fields of fluid dynamics, nonlinear systems, and differential equations. Understanding various physical aspects of raindrops can help us in understanding drop dynamics, rainfall density estimation, size distributions which can be grant insights in the fields of meteorology, hydrology, and climate science. This work identifies the real world significance in developing more accurate atmospheric attenuation correction algorithms that could potentially overcome the scattering effect of rain on radio and micro wave communication. This works presents and aims to compile some historical work which focuses on the influence of surface tension in the droplet nucleation and formation, raindrop oscillation, burst cycles, and transformation into parachute-like shapes before fragmentation. The interplay between surface tension and air resistance in raindrop dynamics is also explored.Comment: 15 pages, 2 figure