Related papers: Differential forms for plasma physics
In this article, we study the invariant differential forms which a correspondence of curves admits. We also try to classify the correspondences of $\mathbb{P}^1$ that admits such invariant differential forms.
A great number of works is devoted to qualitative investigation of Hamiltonian systems. One of tools of such investigation is the method of skew-symmetric differential forms. In present work, under investigation Hamiltonian systems in…
Two new forms of strongly coupled plasmas will be discussed. They have become possible to create and observe in the laboratory only recently and exhibit a wealth of intriguing complex behavior which can be studied, in many cases for the…
Wave-particle duality relations are fundamental for quantum physics. Previous experimental studies of duality relations mainly focus on the quadratic relation $D^2+V^2\leq1$, based on symmetric beam interference, while a linear form of the…
This work is devoted to the study of dissipative fluid systems, through the lens of a geometric variational formulation. Building upon previous works extending Hamilton's principle to non-equilibrium thermodynamics, the present method…
A representation of the static MHD equilibrium system in coordinates connected with magnetic surfaces is suggested. It is used for producing families of non-trivial 3D exact solutions of isotropic and anisotropic plasma equilibria in…
We introduce the historical development and physical idea behind topological Yang-Mills theory and explain how a physical framework describing subatomic physics can be used as a tool to study differential geometry. Further, we emphasize…
In this article we present pictorially the foundation of differential geometry which is a crucial tool for multiple areas of physics, notably general and special relativity, but also mechanics, thermodynamics and solving differential…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
In an inhomogeneous magnetised plasma the transport of energy and particles perpendicular to the magnetic field is in general mainly caused by quasi two-dimensional turbulent fluid mixing. The physics of turbulence and structure formation…
This work introduces a systematic method for identifying analytical and semi-analytical solutions of force-free magnetic fields with plane-parallel and axial symmetry. The method of separation of variables is used, allowing the…
Intended for mathematical physicists interested in applications of the division algebras to physics, this article highlights some of their more elegant properties with connections to the theories of Galois fields and quadratic residues.
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the…
The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on…
I construct combined electric and magnetic field variables which independently represent energy flows in the forward and backward directions respectively, and use these to re-formulate Maxwell's equations. The emphasis is on detailed…
This paper contains a set of lecture notes on manifolds with boundary and corners, with particular attention to the space of quantum states. A geometrically inspired way of dealing with these kind of manifolds is presented,and explicit…
Continuum equations are ubiquitous in physical modelling of elastic, viscous, and viscoelastic systems. The equations of continuum mechanics take nontrivial forms on curved surfaces. Although the curved surface formulation of the continuum…
Vector calculus in three-dimensional space is ubiquitous in applications of mathematics in physics and engineering. Its two-dimensional version is, however, quite rare. Here we try to provide a pedagogical account of the subject. It is…
Complex plasmas are low-temperature plasmas that contain micrometer-size particles in addition to the neutral gas particles and the ions and electrons that make up the plasma. The microparticles interact strongly and display a wealth of…
The homogeneous transform has many practical applications outside the realm of mathematics, for instance to represent the proportions of several chemical substances. We aim here to present results about the transformation of measures, which…