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In Ref.~\cite{Sag} we proposed a geometric formulation of generalized Nambu mechanics. In the present paper we extend the class of Nambu systems by replacing the stringent condition of constancy of 3-form by closedness. We also explore the…
This paper develops a comprehensive mathematical framework for energy-based modeling of physical systems, with particular emphasis on preserving fundamental structural properties throughout the modeling and discretization process. The…
In this article, we will review Noether's Theorems and their application in General Relativity. We will present Noether's Theorems in their original form and restate them as they are usually applied to physics. Some basic equations of…
We give a comprehensive review of various methods to define currents and the energy-momentum tensor in classical field theory, with emphasis on a geometric point of view. The necessity of ``improving'' the expressions provided by the…
Two applications of the Noether method for fluids and plasmas are presented based on the Euler-Lagrange and Euler-Poincare variational principles, which depend on whether the dynamical fields are to be varied independently or not,…
This paper brings a methodological character where we present a comprehensive formalism for constructing conserved quantities in the Teleparallel Equivalent of General Relativity (TEGR) and Symmetric Teleparallel Equivalent of General…
We summarize a recent work on the title subject, skipping the detailed calculations but introducing the basic points with enough detail. The theory considered is formulated in a preferred reference frame in a four-dimensional spacetime…
The dynamics of a physical system is linked to its phase-space geometry by Noether's theorem, which holds under standard hypotheses including continuity. Does an analogous theorem hold for discrete systems? As a testbed, we take the Ising…
We sketch the main features of the Noether Symmetry Approach, a method to reduce and solve dynamics of physical systems by selecting Noether symmetries, which correspond to conserved quantities. Specifically, we take into account the…
We establish an extended version of the kinetic theory of the relativistic axionically active multi-component plasma, which is based on the inclusion of a unit time-like vector field, associated with the velocity of dynamic aether, into the…
The momentum conservation law for general dissipationless reduced-fluid (e.g., gyrofluid) models is derived by Noether method from a variational principle. The reduced-fluid momentum density and the reduced-fluid canonical momentum-stress…
This paper presents a formulation of Noether's theorem for fractional classical fields. We extend the variational formulations for fractional discrete systems to fractional field systems. By applying the variational principle to a…
Noether's calculus of invariant variations yields exact identities from functional symmetries. The standard application to an action integral allows to identify conservation laws. Here we rather consider generating functionals, such as the…
The last decades have seen growing interest in connecting principles of thermodynamics with methods from analytical mechanics. The thermodynamic formalism has become an inspiring framework in the study of smooth dynamical systems, and…
In the present work, we formulate a generalization of the Noether Theorem for action-dependent Lagrangian functions. The Noether's theorem is one of the most important theorems for physics. It is well known that all conservation laws,…
Balance equations are derived from Enskog's kinetic equation for a two-dimensional system of hard disks using Grad's moment expansion method. This set of equations constitute an extended hydrodynamics for moderately dense bi-dimensional…
In continuum mechanics, stress concept plays an essential role. For complicated materials, different stress concepts are used with ambiguity or different understanding. Geometrically, a material element is expressed by a closed region with…
Noether's theorem provides a powerful link between continuous symmetries and conserved quantities for systems governed by some variational principle. Perhaps unfortunately, most dynamical systems of interest in neuroscience and artificial…
We consider the problem of a conditional extremum of an action in a class of fields constrained by differential equations. For this setup, we propose an extension of Noether's first theorem to connect the symmetries of the action and the…
We study various definitions of the gravitational field energy based on the usage of isometric embeddings in the Regge-Teitelboim approach. For the embedding theory we consider the coordinate translations on the surface as well as the…