Related papers: Variational Integrators in Plasma Physics
The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…
The perturbative variational formulation of the Vlasov-Maxwell equations is presented up to third order in the perturbation analysis. From the second and third-order Lagrangian densities, respectively, the first-order and second-order…
This paper presents a geometric-variational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fundamental geometric structures as well as their preservation…
Discretizing variational principles, as opposed to discretizing differential equations, leads to discrete-time analogues of mechanics, and, systematically, to geometric numerical integrators. The phase space of such variational…
For integrable systems in the sense of multidimensional consistency (MDC) we can consider the Lagrangian as a form, which is closed on solutions of the equations of motion. For 2-dimensional systems, described by partial difference…
We derive axisymmetric equilibrium equations in the context of the hybrid Vlasov model with kinetic ions and massless fluid electrons, assuming isothermal electrons and deformed Maxwellian distribution functions for the kinetic ions. The…
The equations of Lagrangian, ideal, one-dimensional (1D), compressible gas dynamics are written in a multi-symplectic form using the Lagrangian mass coordinate $m$ and time $t$ as independent variables, and in which the Eulerian position of…
We consider a recently developed variational approach to the hydrodynamics of strongly coupled plasmas [D. Krimans and S. Putterman, Phys. Fluids 36, 037131 (2024)] and extend it to the Yukawa one-component plasma. This approach generalizes…
We develop the technique of the variational approximation for solitons in two directions. First, one may have a physical model which does not admit the usual Lagrangian representation, as some terms can be discarded for various reasons. For…
Numerical models of weather and climate critically depend on long-term stability of integrators for systems of hyperbolic conservation laws. While such stability is often obtained from (physical or numerical) dissipation terms, physical…
For more than half a century, most of the plasma scientists have encountered a violation of the conservation laws of charge, momentum, and energy whenever they have numerically solve the first-principle equations of kinetic plasmas, such as…
Variational integrators applied to degenerate Lagrangians that are linear in the velocities are two-step methods. The system of modified equations for a two-step method consists of the principal modified equation and one additional equation…
This paper develops moving frame theory for partial difference equations and for differential-difference equations with one continuous independent variable. In each case, the theory is applied to the invariant calculus of variations and the…
A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…
Extended irreversible thermodynamics is a theory that expands the classical framework of nonequilibrium thermodynamics by going beyond the local-equilibrium assumption. A notable example of this is the Maxwell-Cattaneo heat flux model,…
In this article we apply a discrete action principle for the Vlasov--Maxwell equations in a structure-preserving particle-field discretization framework. In this framework the finite-dimensional electromagnetic potentials and fields are…
Shielding effects in non-degenerate and degenerate plasmas are compared. A detailed derivation of the Wigner-Poisson system is provided for electrostatic quantum plasmas where relativistic, spin and collisional effects are not essential.…
Most physical systems are modelled by an ordinary or a partial differential equation, like the n-body problem in celestial mechanics. In some cases, for example when studying the long term behaviour of the solar system or for complex…
For the linearized setting of the dynamics of complex bodies we construct variational integrators and prove their convergence by making use of BV estimates on the rate fields. We allow for peculiar substructural inertia and internal…
Noether theorem establishes an interesting connection between symmetries of the action integral and conservation laws of a dynamical system. The aim of the present work is to classify the damped harmonic oscillator problem with respect to…