1,721,022 research outputs found
Stability properties of the N/4 (pi/2-mode) one-mode nonlinear solution of the Fermi-Pasta-Ulam- beta system
No full textWe present a detailed numerical and analytical study of the stability properties of the pi/2-mode nonlinear solution of the Fermi-Pasta-Ulam- system. The numerical analysis is made as a function of the number N of the particles of the system and of the product epsilon*beta, where epsilon is the energy density and beta is the parameter characterizing the nonlinearity. It is shown that, both for beta>0 and beta>0, the instability threshold value converges, with increasing N, to the same value , that for beta>0 it is a decreasing function of N as in the pi -mode, whereas, for beta< 0, it is an increasing one. The asymptotic behavior of the threshold value for large values of N is analytically obtained in both cases with a Floquet analysis of the stability
Application of the Bogoliubov-Krylov method of averaging to the Fermi-Pasta-Ulam system.
No full textWe apply the Bogoliubov-Krilov method of averaging to the study of the stability of the pi-mode solution of the Fermi-Pasta-Ulam beta-system, with negative values of the nonlinearity parameter beta in the Hamiltonian of the system. The analysis is made as a function of the number N of the particles and of the product epsilon*|beta|, where epsilon is the energy density. The results of this application are in excellent agreement with those obtained by the direct integration of motion equation
Thermostatistics in the neighbourhoodof the pi-mode solution for theFermi–Pasta–Ulam beta system: fromweak to strong chaos
Full text linkWe consider a π-mode solution of the Fermi–Pasta–Ulam β system.
By perturbing it, we study the system as a function of the energy density from a
regime where the solution is stable to a regime where it is unstable, first weakly
and then strongly chaotic. We introduce, as an indicator of stochasticity, the
ratio ρ (when it is defined) between the second and the first moment of a given
probability distribution. We will show numerically that the transition between
weak and strong chaos can be interpreted as the symmetry breaking of a set
of suitable dynamical variables. Moreover, we show that in the region of weak
chaos there is numerical evidence that the thermostatistic is governed by the
Tsallis distribution
Properties of a special function related to self-similar solutions of certain nonlinear wave equations
No full textNon-linear superposition formula for the three-wave resonant interaction via the Hilbert - Riemann problem
No full textA non-Boltzmannian behaviour of the energy distribution for quasi-stationary regimes of the Fermi-Pasta-Ulam β system
No full textIn a recent paper [M. Leo, R.A. Leo, P. Tempesta, C. Tsallis, Physical Review E 85 (2012) 031149], the existence of quasi-stationary states for the Fermi-Pasta-Ulam β system has been shown numerically, by analyzing the stability properties of the N/4-mode exact nonlinear solution. Here we study the energy distribution of the modes N/4, N/3 and N/2, when they are unstable, as a function of N and of the initial excitation energy. We observe that the classical Boltzmann weight is repaced by a different weight, expressed by a q-exponential function
The eigenvalue problem for the three-wave resonant interaction via the prolongation structure
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