1,738 research outputs found
Newton method in the context of quaternion analysis
In this paper we propose a version of Newton method for finding zeros of a quaternion function of a quaternion variable, based on the concept of quaternion radial derivative. Several numerical examples involving elementary functions are presented
Methods for suspensions of passive and active filaments
Flexible filaments and fibres are essential components of important complex
fluids that appear in many biological and industrial settings. Direct
simulations of these systems that capture the motion and deformation of many
immersed filaments in suspension remain a formidable computational challenge
due to the complex, coupled fluid--structure interactions of all filaments, the
numerical stiffness associated with filament bending, and the various
constraints that must be maintained as the filaments deform. In this paper, we
address these challenges by describing filament kinematics using quaternions to
resolve both bending and twisting, applying implicit time-integration to
alleviate numerical stiffness, and using quasi-Newton methods to obtain
solutions to the resulting system of nonlinear equations. In particular, we
employ geometric time integration to ensure that the quaternions remain unit as
the filaments move. We also show that our framework can be used with a variety
of models and methods, including matrix-free fast methods, that resolve low
Reynolds number hydrodynamic interactions. We provide a series of tests and
example simulations to demonstrate the performance and possible applications of
our method. Finally, we provide a link to a MATLAB/Octave implementation of our
framework that can be used to learn more about our approach and as a tool for
filament simulation
NEUTROSOPHIC LOGIC, WAVE MECHANICS, AND OTHER STORIES
There is beginning for anything; we used to hear that phrase. The same wisdom word applies to the authors too. What began in 2005 as a short email on some ideas related to interpretation of the Wave Mechanics results in a number of papers and books up to now. Some of these papers can be found in Progress in Physics or elsewhere.
It is often recognized that when a mathematician meets a physics-inclined mind then the result is either a series of endless debates or publication. In this story, authors preferred to publish rather than perish.
Therefore, the purpose with this book is to present a selection of published papers in a compilation which enable the readers to find some coherent ideas which appear in those articles. For this reason, the ordering of the papers here is based on categories of ideas
Modified quaternion Newton methods
We revisit the quaternion Newton method for computing roots of a class of quaternion valued functions and propose modified algorithms for finding multiple roots of simple polynomials. We illustrate the performance of these new methods by presenting several numerical experiments.The research was partially supported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the " Fundcao para a Ciencia e a Tecnologia", through the Project PEstOE/ MAT/ UI0013/ 2014
Towards local-global compatibility for Hilbert modular forms of low weight
We prove some new cases of local--global compatibility for the Galois
representations associated to Hilbert modular forms of low weight (that is,
partial weight one).Comment: 14 page
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