Related papers: Differential forms for plasma physics
Properties of a fundamental double-form of bi-degree $(p,p)$ for $p\ge 0$ are reviewed in order to establish a distributional framework for analysing equations of the form $$\Delta \Phi + \lambda^2 \Phi = {\cal S} $$ where $\Delta$ is the…
The present article deals with general mechanics in an unconventional manner. At first, Newtonian mechanics for a point particle has been described in vectorial picture, considering Cartesian, polar and tangent-normal formulations in a…
A new approach to simulating warm and hot dense matter that combines density functional theory based calculations of the electronic structure to classical molecular dynamics simulations with pair interaction potentials is presented. The new…
Starting from the concept of the universal exterior algebra in non-commutative differential geometry we construct differential forms on the quantum phase-space of an arbitrary system. They bear the same natural relationship to quantum…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
We present a variational formulation of electrodynamics using de Rham even and odd differential forms. Our formulation relies on a variational principle more complete than the Hamilton principle and thus leads to field equations with…
The quantum-mechanical expression for the polarization of a crystalline solid does not bear any resemblance to the (trivial) expression for the dipole of a bounded crystallite; and in fact it has been proved via a conceptually different…
Duality transformations are very important in both classical and quantum physics. They allow one to relate two seemingly different formulations of the same physical realm through clever mathematical manipulations, and offer numerous…
We predict the existence of new nonlinear electromagnetic wave modes in pair plasmas. The plasma may be either non-magnetized or immersed in an external magnetic field. The existence of these modes depends on the interaction of an intense…
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
In strong electromagnetic fields, unique plasma phenomena and applications emerge, whose description requires recently developed theories and simulations [Y. Shi, Ph.D. thesis, Princeton University (2018)]. In the classical regime, to…
Relativistic quantum plasma dispersion functions are defined and the longitudinal and transverse response functions for an electron (plus positron) gas are written in terms of them. The dispersion is separated into Landau-damping,…
We study derivations and differential forms on the arithmetic jet spaces of smooth schemes, relative to several primes. As applications we give a new interpretation of arithmetic Laplacians and we discuss the de Rham cohomology of some…
This paper provides a summary of the fractal calculus framework. It presents higher-order homogeneous and nonhomogeneous linear fractal differential equations with $\alpha$-order. Solutions for these equations with constant coefficients are…
Quantum plasmas is a rapidly expanding field of research, with applications ranging from nanoelectronics, nanoscale devices and ultracold plasmas, to inertial confinement fusion and astrophysics. Here we give a short systematic overview of…
We consider a two-dimensional complex plasma layer containing charged dust particles in a perpendicular magnetic field. Computer simulations of both one-component and binary systems are used to explore the equilibrium particle dynamics in…
Use of curvilinear coordinates is sometimes indicated by the inherent geometry of a fluid dynamics problem, but this introduces fictitious forces into the momentum equations that spoil strict conservative form. If one is willing to work in…
Under certain circumstances, the equations for the magnetic field lines can be recast in a canonical form, after defining a suitable field line Hamiltonian. This analogy is extremely useful for dealing with a variety of problems involving…
Differential Linear Logic (DiLL) is a sequent calculus that expresses differentiation via symmetries between linear and non-linear formulas. In this paper, we express categorical models of DiLL as a pair of Grothendieck fibrations equipped…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…