Turbulence excited frequency domain damping measurement and truncation effects

Existing frequency domain modal frequency and damping analysis methods are discussed. The effects of truncation in the Laplace and Fourier transform data analysis methods are described. Methods for eliminating truncation errors from measured damping are presented. Implications of truncation effects in fast Fourier transform analysis are discussed. Limited comparison with test data is presented

Formalization of Transform Methods using HOL Light

Transform methods, like Laplace and Fourier, are frequently used for analyzing the dynamical behaviour of engineering and physical systems, based on their transfer function, and frequency response or the solutions of their corresponding differential equations. In this paper, we present an ongoing project, which focuses on the higher-order logic formalization of transform methods using HOL Light theorem prover. In particular, we present the motivation of the formalization, which is followed by the related work. Next, we present the task completed so far while highlighting some of the challenges faced during the formalization. Finally, we present a roadmap to achieve our objectives, the current status and the future goals for this project.Comment: 15 Pages, CICM 201

Problems which are well-posed in a generalized sense with applications to the Einstein equations

In the harmonic description of general relativity, the principle part of Einstein equations reduces to a constrained system of 10 curved space wave equations for the components of the space-time metric. We use the pseudo-differential theory of systems which are well-posed in the generalized sense to establish the well-posedness of constraint preserving boundary conditions for this system when treated in second order differential form. The boundary conditions are of a generalized Sommerfeld type that is benevolent for numerical calculation.Comment: Final version to appear in Classical and Qunatum Gravit

A mathematical model for the spread of oil spills in high seas

This study aims to model the distribution pattern of oil spills in high seas with the influence of wind movements. The mathematical model is derived from the random walk process of the oil spill particles by using a probability measure on a unit circle with the help of Laplace and Fourier transform . The solution to the model is also obtained by using Laplace and the Fourier transform. Based on the analysis of the solution of the model, the oil spill tends to spread in the direction of wind movement.. The speed and direction of the wind movement affect the speed and direction of the spread of the oil spill particles. The larger the speed of wind movement, the faster the oil particles movement

INTEGRAL TRANSFORM AND FRACTIONAL KINETIC EQUATION

With the help of the Laplace and Fourier transforms, we arrive at the fractional kinetic equation's solution in this paper. Their respective solutions are given in terms of the Fox's H-function and the Mittag-Leffler function, which are also known as the generalisations and the Saigo-Maeda operator-based solution of the generalised fractional kinetic equation. The paper's findings have applications in a variety of engineering, astronomy, and physical scientific fields

NNLL Resummation for Jet Broadening

The resummation for the event-shape variable jet broadening is extended to next-to-next-to-leading logarithmic accuracy by computing the relevant jet and soft functions at one-loop order and the collinear anomaly to two-loop accuracy. The anomaly coefficient is extracted from the soft function and expressed in terms of polylogarithmic as well as elliptic functions. With our results, the uncertainty on jet-broadening distributions is reduced significantly, which should allow for a precise determination of the strong coupling constant from the existing experimental data and provide a consistency check on the extraction of alpha_s from higher-log resummations of thrust.Comment: 44 pages, 9 figure