Related papers: Helicity in Hamiltonian dynamical systems
The effect of the helicity on the dynamics of the turbulent flows is investigated. The aim is to disentangle the role of helicity in fixing the direction, the intensity and the fluctuations of the energy transfer across the inertial range…
From the sandpoint of neural network dynamics we consider dynamical system of special type pesesses gradient (symmetric) and Hamiltonian (antisymmetric) flows. The conditions when Hamiltonian flow properties are dominant in the system are…
By dispersive models of fluid mechanics we are referring to the Euler-Lagrange equations for the constrained Hamilton action functional where the internal energy depends on high order derivatives of unknowns. The mass conservation law is…
Starting from the continuum definition of helicity, we derive from first principles its different contributions for superfluid vortices. Our analysis shows that an internal twist contribution emerges naturally from the mathematical…
The effect of helicity (velocity-vorticity correlations) is studied in direct numerical simulations of rotating turbulence down to Rossby numbers of 0.02. The results suggest that the presence of net helicity plays an important role in the…
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
Topological constraints play a key role in the self-organizing processes that create structures in macro systems. In fact, if all possible degrees of freedom are actualized on equal footing without constraint, the state of "equipartition"…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
Describing open quantum systems in terms of effective non-Hermitian Hamiltonians gives rise to non-unitary time evolution. In this paper, we study the impact of non-unitary dynamics on the emergent hydrodynamics in quantum systems with a…
For a multicomponent wave field propagating into a multidimensional conversion region, the rays are shown to be helical, in general. For a ray-based quantity to have a fundamental physical meaning it must be invariant under two groups of…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
We provide a new sufficient condition for strong invariance for differential inclusions, under very general conditions on the dynamics, in terms of a Hamiltonian inequality. In lieu of the usual Lipschitzness assumption on the…
Complete Hamiltonian formalism is suggested for inertial waves in rotating incompressible fluid. Resonance three-wave interaction processes -- decay instability and confluence of two waves -- are shown to play a key role in the weakly…
It is shown that a vorticity, constructed from spin field of a quantum spinning plasma, combines with the classical generalized vorticity (representing the magnetic and the velocity fields) to yield a new grand generalized vorticity that…
Integrability in string/field theories is known to emerge when considering dynamics in the moduli space of physical theories. This implies that one has to look at the dynamics with respect to unusual time variables like coupling constants…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
We introduce an extension of hamiltonian dynamics, defined on hyperkahler manifolds, which we call ``hyperhamiltonian dynamics''. We show that this has many of the attractive features of standard hamiltonian dynamics. We also discuss the…
The Hamiltonian dynamics of a compressible inviscid fluid is formulated as a gauge theory. The idea of gauge equivalence is exploited to unify the study of apparantly distinct physical problems and solutions of new models can be generated…
For an isentropic (thus compressible) flow, fluid trajectories are considered as orbits of a family of one parameter, smooth, orientation preserving and nonsingular diffeomorphisms on a compact and smooth-boundary domain in the Euclidian…
The variational method is very important in mathematical and theoretical physics because it allows us to describe the natural systems by physical quantities independently from the frame of reference used. A global and statistical approach…