Related papers: Helicity in Hamiltonian dynamical systems
Magnetic helicity is robustly conserved in systems with very large magnetic Reynolds numbers, including most systems of astrophysical interest, and unlike kinetic and magnetic energy is not dissipated at small scales. This plays a major…
Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
A generalization of the Hamilton-Jacobi theory to arbitrary dynamical systems, including non-Hamiltonian ones, is considered. The generalized Hamilton-Jacobi theory is constructed as a theory of ensemble of identical systems moving in the…
Exact, degenerate two-forms on time-extended space R X M which are invariant under the unsteady, incompressible fluid motion on 3D region M are introduced. The equivalence class up to exact one-forms of each potential one-form is splitted…
The decay of kinetic helicity is studied in numerical models of forced turbulence using either an externally imposed forcing function as an inhomogeneous term in the equations or, alternatively, a term linear in the velocity giving rise to…
Tangencies correspond to singularities of impact systems, separating between impacting and non-impacting trajectory segments. The closure of their orbits constitute the singularity set, which, even in the simpler billiard limit, is known to…
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject…
Quantum coherence, rooted in the superposition principle of quantum mechanics, is a crucial quantum resource. Various measures, operational interpretations, and generalizations of quantum coherence have been proposed. In recent years, its…
Described is n-level quantum system realized in the n-dimensional ''Hilbert'' space H with the scalar product G taken as a dynamical variable. The most general Lagrangian for the wave function and G is considered. Equations of motion and…
A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for…
The literature on dynamical systems has, for the most part, considered self-oscillators (i.e., systems capable of generating and maintaining a periodic motion at the expense of an external energy source with no corresponding periodicity)…
We study the statistical properties of helicity in direct numerical simulations of fully developed homogeneous and isotropic turbulence and in a class of turbulence shell models. We consider correlation functions based on combinations of…
Hamiltonian flows on compact surfaces are characterized, and the topological invariants of such flows with finitely many singular points are constructed from the viewpoints of integrable systems, fluid mechanics, and dynamical systems.…
Integrals of motion of a Hamiltonian system need not be commutative. The classical Mishchenko-Fomenko theorem enables one to quantize a noncommutative completely integrable Hamiltonian system around its invariant submanifold as an abelian…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
A reduced dynamical model is derived which describes the interaction of weak inertia-gravity waves with nonlinear vortical motion in the context of rotating shallow-water flow. The formal scaling assumptions are (i) that there is a…
We present a Hamiltonian approach for the wellknown Eigen model of the Darwin selection dynamics. Hamiltonization is carried out by means of the embedding of the population variable space, describing behavior of the system, into the space…
The statistical mechanical description of small systems staying in thermal equilibrium with an environment can be achieved by means of the Hamiltonian of mean force. In contrast to the reduced density matrix of an open quantum system, or…
Dynamical universality is the observation that the dynamical properties of different systems might exhibit universal behavior that are independent of the system details. In this paper, we study the long-time dynamics of an one-dimensional…