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21.
We present a new verified optimization method to find regions for Hénon systems where the conditions of chaotic behaviour
hold. The present paper provides a methodology to verify chaos for certain mappings and regions. We discuss first how to check
the set theoretical conditions of a respective theorem in a reliable way by computer programs. Then we introduce optimization
problems that provide a model to locate chaotic regions. We prove the correctness of the underlying checking algorithms and
the optimization model. We have verified an earlier published chaotic region, and we also give new chaotic places located
by the new technique. 相似文献
22.
23.
J.O. Andersen 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,28(4):389-396
We consider an interacting homogeneous Bose gas at zero temperature in two spatial dimensions. The properties of the system
can be calculated as an expansion in powers of g, where g is the coupling constant. We calculate the ground state pressure and the ground state energy density to second order in the
quantum loop expansion. The renormalization group is used to sum up leading and subleading logarithms from all orders in perturbation
theory. In the dilute limit, the renormalization group improved pressure and energy density are expansions in powers of the
T
2B and T
2Bln(T
2B), respectively, where T
2B is the two-body T-matrix.
Received 19 April 2002 Published online 13 August 2002 相似文献
24.
T.M. Mishonov N. Chéenne D. Robbes J.O. Indekeu 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,26(3):291-296
The generation of harmonics of the voltage response is considered when an AC current is applied through a superconducting
film above Tc. It is shown that almost at all temperatures the mechanism of the temperature oscillations created by the AC current and
the temperature dependence of the resistance dominates over the isothermal nonlinear electric conductivity. Only in a narrow
critical region close to Tc the latter is essential for the generation of the harmonics. A detailed investigation of harmonics generation provides an
accurate method for measuring the thermal boundary conductance between the film and the insulating substrate. The critical
behaviour of the third harmonic will give a new method for the determination of the lifetime of metastable Cooper pairs above
Tc. The comparison of the calculated fifth harmonics of the voltage with the experiment is proposed as an important test for
the applicability of the employed theoretical models.
Received 8 September 2001 相似文献
25.
Transition from chaotic to ordered state has been observed during the initial stage of a discharge in a cylindrical DC glow
discharge plasma. Initially it shows a chaotic behavior but increasing the discharge voltage changes the characteristics of
the discharge glow and shows a period subtraction of order 7 period → 5 period → 3 period → 1 period, i.e. the system goes
to single mode through odd cycle subtraction. On further increasing the discharge voltage, the system goes through period
doubling, like 1 period → 2 period → 4 period. On further increasing the voltage, the system goes to stable state through
two period subtraction, like 4 period → 2 period → stable. 相似文献
26.
We show that there is a threshold in energy for the onset of chaos in cosmology for the Universe described as a dynamical system derived from the Einstein equations of General Relativity (GR). In the case of the mixmaster model (homogeneous and anisotropic cosmology with a Bianchi IX metric), the chaos occurs precisely at the prescribed necessary value H
vac=0 of the GR for the energy of the Universe while the system is found to be regular for H<0 and chaotic for H>0 with respect to its pure vacuum part. In the case of generalized scalar tensor theories within the Bianchi IX model, we show using the ADM formalism and a conformal transformation that the energy of the dynamical system as compared to vacuum lies below the zero energy threshold. The system is thus not exhibiting chaos and the conclusion still holds in the presence of ordinary matter as well. The suppression of chaos occurs in a similar way for stiff matter alone. 相似文献
27.
研究捕食者具有非单调功能反应和周期脉冲扰动的捕食者一食饵系统,利用脉冲微分方程的Floquet理论和比较定理,得到了系统灭绝和持续生存的充分条件.最后,通过数值模拟阐明系统在周期脉冲扰动下的复杂性. 相似文献
28.
29.
P. Schlagheck A. Buchleitner 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2003,22(3):401-415
We provide a detailed quantum treatment of the spectral characteristics and of the dynamics of nondispersive two-electron
wave packets along the periodically driven, collinear frozen planet configuration of helium. These highly correlated, long-lived
wave packets arise as a quantum manifestation of regular islands in a mixed classical phase space, which are induced by nonlinear
resonances between the external driving and the unperturbed dynamics of the frozen-planet configuration. Particular emphasis
is given to the dependence of the ionization rates of the wave packet states on the driving field parameters and on the quantum
mechanical phase space resolution, preceded by a comparison of 1D and 3D life times of the unperturbed frozen planet. Furthermore,
we study the effect of a superimposed static electric field component, which, on the grounds of classical considerations,
is expected to stabilize the real 3D dynamics against large (and possibly ionizing) deviations from collinearity.
Received 7 November 2002 / Received in final form 2 December 2002 Published online 28 January 2003 相似文献
30.
Nonlinear and chaotic oscillations of a constrained cantilevered pipe conveying fluid: A full nonlinear analysis 总被引:2,自引:0,他引:2
In this paper, the planar dynamics of a nonlinearly constrained pipe conveying fluid is examined numerically, by considering the full nonlinear equation of motions and a refined trilinear-spring model for the impact constraints—completing the circle of several studies on the subject. The effect of varying system parameters is investigated for the two-degree-of-freedom (N=2) model of the system, followed by less extensive similar investigations forN=3 and 4. Phase portraits, bifurcation diagrams, power spectra and Lyapunov exponents are presented for a selected set of system parameters, showing some rather interesting, and sometimes unexpected, results. The numerical results are compared with experimental ones obtained previously. It is found that in the parameter space that includesN, there exists a subspace wherein excellent qualitative, and reasonably good (N=2) to excellent (N=4) quantitative agreement with experiment. In the latter case, excellent agreement is not only obtained in the threshold flow velocities (u) for the key bifurcations, but the inclusion of the nonlinear terms improves agreement with experiment in terms of amplitudes of motion and by capturing features of behaviour not hitherto predicted by theory. 相似文献