Related papers: Variational Openness
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
Inspired by problems arising in the geometrical treatment of Yang-Mills theories and Palatini's gravity, the covariant formulation of Hamiltonian dynamical systems as a Hamiltonian field theory of dimension $1+0$ on a manifold with boundary…
A new variational approach for general relativity and modified theories of gravity is presented. In addition to the metric tensor, two independent affine connections enter the action as dynamical variables. In the matter action the…
Invariance principles determine many key properties in quantum field theory, including, in particular, the appropriate form of the boundary conditions. A crucial consistency check is the proof that the resulting boundary-value problem is…
We consider the initial boundary value problem for free-evolution formulations of general relativity coupled to a parametrized family of coordinate conditions that includes both the moving puncture and harmonic gauges. We concentrate…
We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of…
We present a generalization of the variational principle that is compatible with any Hamiltonian eigenstate that can be specified uniquely by a list of properties. This variational principle appears to be compatible with a wide range of…
We present variational and Hamiltonian formulations of incompressible fluid dynamics with free surface and nonvanishing odd viscosity. We show that within the variational principle the odd viscosity contribution corresponds to geometric…
Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and in the…
A series of stationary principles are developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of mixed variables, using temporal convolutions and fractional derivatives. Dynamical…
A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…
The Variant-rule derives from the Precursor-rule by interchanging two classes of its 28 isotropic mappings. Although this small mutation conserves most glider types and stable blocks, glider-gun engines are changed, as are most large scale…
In this work, it has been indicated that the key features requisite for preserving causality and stability of the popularly existing relativistic hydrodynamic theories, can be translated into each other. It has been shown here, that a…
A comparison between the two possible variational principles for the study of a free falling spinless particle in a space-time with torsion is noted. It is well known that the autoparallel trajectories can be obtained from a variational…
Stationary, axisymmetric, vacuum, solutions of Einstein's equations are obtained as critical points of the total mass among all axisymmetric and $(t,\phi)$ symmetric initial data with fixed angular momentum. In this variational principle…
A variation principle for mass transport in solids is derived that recasts transport coefficients as minima of local thermodynamic average quantities. The result is independent of diffusion mechanism, and applies to amorphous and…
After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to…
In many relevant cases -- e.g., in hamiltonian dynamics -- a given vector field can be characterized by means of a variational principle based on a one-form. We discuss how a vector field on a manifold can also be characterized in a similar…
This survey on stationary and evolutionary problems with gradient constraints is based on developments of monotonicity and compactness methods applied to large classes of scalar and vectorial solutions to variational and quasi-variational…
There is a qualitative difference between one-dimensional and multi-dimensional solutions to the Euler equations: new features that arise are vorticity and a nontrivial incompressible (low Mach number) limit. They present challenges to…