Related papers: Quaternion Mathematics in Electromagnetic Modeling…
This article investigates Kak neural networks, which can be instantaneously trained, for complex and quaternion inputs. The performance of the basic algorithm has been analyzed and shown how it provides a plausible model of human perception…
In the last one and a half centuries, the analysis of quaternions has not only led to further developments in mathematics but has also been and remains an important catalyst for the further development of theories in physics. At the same…
We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is…
The possibility of an incompletness of the equations of electromagnetism is analyzed using a thought experiment that shows a non-physical behavior according to classical electromagnetism. Basically, from Maxwell equations it is shown that a…
Three thought experiments demonstrate that under certain circumstances electromagnetic fields have to be attenuated or amplified multiplicatively in order not to violate the conservation of energy. Modulation of radiation by means other…
Electric and magnetic fields of fractal distribution of charged particles are considered. The fractional integrals are used to describe fractal distribution. The fractional integrals are considered as approximations of integrals on…
We begin with the time-dependent electric and magnetic dipole solution of Maxwell's equations in Minkowski space. This Maxwell field is then used to determine the behavior of the gravitational field (the Weyl tensor) as a second-order…
We present a systematic geometric framework for the dimensional reduction of classical electromagnetism based on the concept of descent along vector fields of invariance. By exploring the interplay between the Lie derivative and the Hodge…
The interpretations of octonion wave equations in eight dimensional space-time have been discussed. We have made an attempt to discuss the octonion field equation as the equation of motion for particles carrying simultaneously electric and…
After introduction we focus on: the transport of charged particles, the acceleration of ions at shocks, and the acceleration of electrons at shocks. Chapter 2 studies the propagation of solar energetic particles(SEPs) in turbulent magnetic…
Despite being studied for over a century, the use of quadrupoles have been limited to Cartesian coordinates in flat spacetime due to the incorrect transformation rules used to define them. Here the correct transformation rules are derived,…
Binary collisions between ions and electrons in an external magnetic field are considered in second-order perturbation theory, starting from the unperturbed helical motion of the electrons. The calculations are done with the help of an…
The recently re-discovered multipole vector approach to understanding the harmonic decomposition of the cosmic microwave background traces its roots to Maxwell's Treatise on Electricity and Magnetism. Taking Maxwell's directional derivative…
Quaternion valued neural networks experienced rising popularity and interest from researchers in the last years, whereby the derivatives with respect to quaternions needed for optimization are calculated as the sum of the partial…
A new generalized St\"ormer problem is proposed. The charged particles motion around a rotating axisymmetric magnetic planet is studied using various conditions mainly in planetary magnetospheres. It is shown that the existence of specific…
In this paper, we present some applications of quaternions and octonions. We present the real matrix representations for complex octonions and some of their properties which can be used in computations where these elements are involved.…
The work aims effective and low-dimensional systems. Some different contexts involving gravitational and electromagnetic interactions are investigated. The electromagnetic one approaches bosonic and fermionic Effective Quantum Field…
The electromagnetic theory is considered in the framework of the generally covariant approach, that is applied to the analysis of electromagnetism in noninertial coordinate and frame systems. The special-relat\-ivistic formulation of…
Angular momentum is traditionally taught as a (pseudo)vector quantity, tied closely to the cross product. This approach is familiar to experts but challenging for students, and full of subtleties. Here, we present an alternative pedagogical…
Most of theoretical physics is based on the mathematics of functions of a real or a complex variable; yet we frequently are drawn to try extending our reach to include quaternions. The non-commutativity of the quaternion algebra poses…