68 research outputs found
Conservation Laws and Hamilton's Equations for Systems with Long-Range Interaction and Memory
Using the fact that extremum of variation of generalized action can lead to
the fractional dynamics in the case of systems with long-range interaction and
long-term memory function, we consider two different applications of the action
principle: generalized Noether's theorem and Hamiltonian type equations. In the
first case, we derive conservation laws in the form of continuity equations
that consist of fractional time-space derivatives. Among applications of these
results, we consider a chain of coupled oscillators with a power-wise memory
function and power-wise interaction between oscillators. In the second case, we
consider an example of fractional differential action 1-form and find the
corresponding Hamiltonian type equations from the closed condition of the form.Comment: 30 pages, LaTe
Fokker-Planck Equation with Fractional Coordinate Derivatives
Using the generalized Kolmogorov-Feller equation with long-range interaction,
we obtain kinetic equations with fractional derivatives with respect to
coordinates. The method of successive approximations with the averaging with
respect to fast variable is used. The main assumption is that the correlator of
probability densities of particles to make a step has a power-law dependence.
As a result, we obtain Fokker-Planck equation with fractional coordinate
derivative of order .Comment: LaTeX, 16 page
Anomalous transport in Charney-Hasegawa-Mima flows
Transport properties of particles evolving in a system governed by the
Charney-Hasegawa-Mima equation are investigated. Transport is found to be
anomalous with a non linear evolution of the second moments with time. The
origin of this anomaly is traced back to the presence of chaotic jets within
the flow. All characteristic transport exponents have a similar value around
, which is also the one found for simple point vortex flows in the
literature, indicating some kind of universality. Moreover the law
linking the trapping time exponent within jets to the transport
exponent is confirmed and an accumulation towards zero of the spectrum of
finite time Lyapunov exponent is observed. The localization of a jet is
performed, and its structure is analyzed. It is clearly shown that despite a
regular coarse grained picture of the jet, motion within the jet appears as
chaotic but chaos is bounded on successive small scales.Comment: revised versio
Recommended from our members
Investigation of Anomalous Transport and Study of Particle Dynamics in the Ergodic Layer
Chaotic Jets
The problem of characterizing the origin of the non-Gaussian properties of
transport resulting from Hamiltonian dynamics is addressed. For this purpose
the notion of chaotic jet is revisited and leads to the definition of a
diagnostic able to capture some singular properties of the dynamics. This
diagnostic is applied successfully to the problem of advection of passive
tracers in a flow generated by point vortices. We present and discuss this
diagnostic as a result of which clues on the origin of anomalous transport in
these systems emerge.Comment: Proceedings of the workshop Chaotic transport and complexity in
classical and quantum dynamics, Carry le rouet France (2002
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