Related papers: On Two Complementary Types of Directional Derivati…
The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the non-linear evolution of…
We review the canonical theory for perfect fluids, in Eulerian and Lagrangian formulations. The theory is related to a description of extended structures in higher dimensions. Internal symmetry and supersymmetry degrees of freedom are…
A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the…
We classify all the six derivative Lagrangians of gravity, whose traced field equations are of second or third order, in arbitrary dimensions. In the former case, the Lagrangian in dimensions greater than six, reduces to an arbitrary linear…
The present work investigates the evolution of linear perturbations of time-dependent ideal fluid flows with advected quantities, expressed in terms of the second order variations of the action corresponding to a Lagrangian defined on a…
Finite Euler hierarchies of field theory Lagrangians leading to universal equations of motion for new types of string and membrane theories and for {\it classical} topological field theories are constructed. The analysis uses two main…
The ordinary formalism for classical field theory is applied to dynamical group field theories. Focusing first on a local group field theory over one copy of SU(2) and, then, on more involved nonlocal theories (colored and non colored)…
We introduce a differential structure for the space of weakly geometric p rough paths over a Banach space V for 2<p<3. We begin by considering a certain natural family of smooth rough paths and differentiating in the truncated tensor…
The Lagrangian formalism is used to derive covariant equations that are suitable for use in continuously distributed matter in curved spacetime. Special attention is given to theoretical representation, in which the Lagrangian and its…
The aim of this note is to provide regularity results for Regular Lagrangian flows of Sobolev vector fields over compact metric measure spaces verifying the Riemannian curvature dimension condition. We first prove, borrowing some ideas…
Fractional mechanics describes both conservative and non-conservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics the…
In this paper I shall consider field theories in a space of four-dimensions which have field variables consisting of the components of a metric tensor and scalar field. The field equations of these scalar-tensor field theories will be…
Using the wave equation as an example, it is shown how to extend the hydrodynamic Lagrangian-picture method of constructing field evolution using a continuum of trajectories to second-order theories. The wave equation is represented through…
We consider the low-energy effective field theory describing the infrared dynamics of non-dissipative fluids. We extend previous work to accommodate conserved charges, and we clarify the matching between field theory variables and…
Most researches on fluid dynamics are mostly dedicated to obtain the solutions of Navier-Stokes equation which governs fluid flow with particular boundary conditions and approximations. We propose an alternative approach to deal with fluid…
The variational principle for the special and general relativistic hydrodynamics are discussed in view of its application to obtain approximate solutions to these problems. We show that effective Lagrangians can be obtained for suitable…
In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov…
The well-known Lagrangian of current superfluid systems is not relativistic covariant, this paper gives a general relativistic covariant Lagrangian of superfluid systems, and naturally finds the non-relativistic Lagrangian and its all…
Fluid deformation and strain history are central to wide range of fluid mechanical phenomena ranging from fluid mixing and particle transport to stress development in complex fluids and the formation of Lagrangian coherent structures…
This work deals with a number of questions relative to the discrete and continuous adjoint fields associated with the compressible Euler equations and classical aerodynamic functions. The consistency of the discrete adjoint equations with…