Related papers: Gyrokinetics from variational averaging: existence…
We explore the recently-proposed Virtual Element Method (VEM) for numerical solution of boundary value problems on arbitrary polyhedral meshes. More specifically, we focus on the elasticity equations in three-dimensions and elaborate upon…
Irrotational and monochromatic surface gravity waves possess a mean Lagrangian drift which transports mass and enhances mixing in the upper ocean. In the ocean, where many surface waves are present, it is commonly assumed that the mean…
We establish a Lagrangian variational framework for general relativistic continuum theories that permits the development of the process of Lagrangian reduction by symmetry in the relativistic context. Starting with a continuum version of…
We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the…
We present a high-order spatial discretization of a continuum gyrokinetic Vlasov model in axisymmetric tokamak edge plasma geometries. Such models describe the phase space advection of plasma species distribution functions in the absence of…
We formulate the quantum version of non-projectable Ho\v{r}ava gravity as a Lagrangian theory with a path integral in the configuration space with an ultra-local in time, but non-local in space, field-dependent measure. Using auxiliary…
We derive the equations of motion for the dynamics of a porous media filled with an incompressible fluid. We use a variational approach with a Lagrangian written as the sum of terms representing the kinetic and potential energy of the…
Using well known Lagrangean techniques for uncovering the gauge symmetries of a Lagrangean, we derive the transformation laws for the phase space variables corresponding to local symmetries of the Hamilton equations of motion. These…
Taking advantage of the flexibility of the variational method with coordinate transformations, we derive a self-consistent set of equations of motion from a discretized Lagrangian to study kinetic plasmas using a Fourier decomposed…
Varying the gravitational Lagrangian produces a boundary contribution that has various physical applications. It determines the right boundary terms to be added to the action once boundary conditions are specified, and defines the…
Inaccurate description of the equilibrium can yield to spurious effects in gyrokinetic turbulence simulations. Also, the Vlasov solver and time integration schemes impact the conservation of physical quantities, especially in long-term…
The super simple Vlasov (ssV) code was developed to study instabilities, turbulence, and reconnection in weakly magnetized plasmas, such as the solar wind in the dissipation range and the edge of fusion plasmas. The ssV code overcomes the…
Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…
A recently proposed pregeometric auxiliary vector mediated gauge theory is studied in its canonical domain, by performing the Legendre transform on a curved background and by considering its covariant phase space, with further application…
Hierarchies of Lagrangians of degree two, each only partly determined by the choice of leading terms and with some coefficients remaining free, are considered. The free coefficients they contain satisfy the most general differential…
Our main aim in this paper is to promote the coframe variational method as a unified approach to derive field equations for any given gravitational action containing the algebraic functions of the scalars constructed from the Riemann…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
In this paper, we explore dynamics of the nonholonomic system called vakonomic mechanics in the context of Lagrange-Dirac dynamical systems using a Dirac structure and its associated Hamilton-Pontryagin variational principle. We first show…
A geometrical method is used for the analysis of stochastic processes in plasma turbulence. Distances between thermodynamic states can be computed according the thermodynamic length methodology which allows the use of a Riemannian metric on…
This review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy functional. Contrary to…