Related papers: Helicity Conservation via the Noether Theorem
In nonholonomic mechanics, the presence of constraints in the velocities breaks the well-under\-stood link between symmetries and first integrals of holonomic systems, expressed in Noether's Theorem. However there is a known special class…
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…
Electromagnetism contains an infinite dimensional symmetry group of large gauge transformations. This gives rise to an infinite number of conserved quantities called "soft charges" via Noether's theorem. When charged particles scatter, the…
In steady-state non-isentropic flows of perfect fluids there is always thermodynamic generation of vorticity when the difference between the product of the temperature with the gradient of the entropy and the gradient of total enthalpy is…
In analogy with the non-Abelian gauge helicities conserved in time for ``null fields", that we have defined previously, in this paper we first define non-Abelian fluid helicities and then total non-Abelian helicities for combined…
In the present paper geometric aspects of relationship between non-Noether symmetries and conservation laws in Hamiltonian systems is discussed. It is shown that integrals of motion associated with continuous non-Noether symmetry are in…
The geometric nature of Euler fluids has been clearly identified and extensively studied over the years, culminating with Lagrangian and Hamiltonian descriptions of fluid dynamics where the configuration space is defined as the…
A new symmetry for Newtonian Dynamics is analyzed, this corresponds to going to an accelerated frame, which introduces a constant gravitational field into the system and subsequently. We consider the addition of a linear contribution to the…
Liquid structure carries deep imprints of an inherent thermal invariance against a spatial transformation of the underlying classical many-body Hamiltonian. At first order in the transformation field the Noether theorem yields the local…
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…
Spherical symmetry for f(R)-gravity is discussed by searching for Noether symmetries. The method consists in selecting conserved quantities in form of currents that reduce dynamics of f(R)-models compatible with symmetries. In this way we…
The principles of energy, symmetry, entropy, and causality conservation are discussed in a "Tetrahedron Model" of a conceptually complete "T.O.E.:" "The charges of matter are the symmetry debts of light" (Noether's Theorem). Symmetry debts…
Local symmetry transformations play an important role for establishing the existence and form of a conserved (Noether) current in systems with a global continuous symmetry. We explain how this fact leads to the existence of linear relations…
We establish a new version of the first Noether Theorem, according to which the (equivalence classes of) first integrals of given Euler-Lagrange equations in one independent variable are in exact one-to-one correspondence with the…
A noetherian form is an abstract self-dual framework suitable for establishing homomorphism theorems (such as the isomorphism theorems and homological diagram lemmas) for group-like structures. In this paper we identify and carry out an…
To what extent does Noether's principle apply to quantum channels? Here, we quantify the degree to which imposing a symmetry constraint on quantum channels implies a conservation law, and show that this relates to physically impossible…
This paper deals with the systematic development of structure-preserving approximations for a class of nonlinear partial differential equations on networks. The class includes, for example, gas pipe network systems described by barotropic…
The paper is devoted to the Lie group properties of the one-dimensional Green-Naghdi equations describing the behavior of fluid flow over uneven bottom topography. The bottom topography is incorporated into the Green-Naghdi equations in two…
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…
Using the recent formulation of Noether's theorem for the problems of the calculus of variations with fractional derivatives, the Lagrange multiplier technique, and the fractional Euler-Lagrange equations, we prove a Noether-like theorem to…