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81.
Qin-long Wang Yi-rong Liu 《应用数学学报(英文版)》2007,23(3):451-466
In this paper, we study the appearance of limit cycles from the equator and isochronicity of infinity in polynomial vector fields with no singular points at infinity. We give a recursive formula to compute the singular point quantities of a class of cubic polynomial systems, which is used to calculate the first seven singular point quantities. Further, we prove that such a cubic vector field can have maximal seven limit cycles in the neighborhood of infinity. We actually and construct a system that has seven limit cycles. The positions of these limit cycles can be given exactly without constructing the Poincare cycle fields. The technique employed in this work is essentially different from the previously widely used ones. Finally, the isochronous center conditions at infinity are given. 相似文献
82.
The projector formalism of Zwanzig-Mori type is extended to obtain generalized Fokker-Planck and generalized nonlinear Langevin equations for coarse-grained variables when the underlying microscopic dynamics is dissipative and noisy (stochastic). 相似文献
83.
84.
A classical Fermi accelerator model (FAM) is known to show chaotic behavior. The FAM is defined by a free particle bouncing elastically from two rigid walls, one fixed and the other oscillating periodically in time. The central aim of this paper is to connect the quantum and the classical solutions to the FAM in the semiclassical limit. This goal is accomplished using a finite inverted parametric oscillator (FIPO), confined to a box withfixed walls, as an alternative representation of the FAM. In the FIPO representation, an explicit correspondence between classical and quantum limits is accomplished using a Husimi representation of the quasienergy eigenfunctions. 相似文献
85.
Shaping command input or preshaping is used for reducing system oscillation in motion control. Desired systems inputs are altered so that the system finishes the requested move without residual oscillation. This technique, developed by N.C. Singer and W.P. Seering, is used for example in the aerospace field, in particular in flexible structure control. This paper presents the study of ZV shaper for explicit fractional derivative systems (generalized derivative systems). A robustness study of ZV shaper is then presented and applied to improve second generation CRONE control response time. Results from simulation and from a DC motor bench are also given. 相似文献
86.
Madalina Deaconu Nicolas Fournier Etienne Tanré 《Methodology and Computing in Applied Probability》2003,5(2):131-158
By continuing the probabilistic approach of Deaconu et al. (2001), we derive a stochastic particle approximation for the Smoluchowski coagulation equations. A convergence result for this model is obtained. Under quite stringent hypothesis we obtain a central limit theorem associated with our convergence. In spite of these restrictive technical assumptions, the rate of convergence result is interesting because it is the first obtained in this direction and seems to hold numerically under weaker hypothesis. This result answers a question closely connected to the Open Problem 16 formulated by Aldous (1999). 相似文献
87.
M.A. Grado-Caffaro 《Optik》2003,114(5):237-238
Sensitivity of the velocity of a single electron, in the relativistic case, to a perpendicular magnetic field is evaluated by defining a parameter which becomes useful in a number of cases related to dynamical systems. In particular, the ultrarelativistic case is examined. 相似文献
88.
A set of invariants describing the limit regimes of braking disk-type wound composite flywheels is suggested. The limit regime is determined by using a linear failure criterion. It is shown that, for generating short-time impulses of very high power, a set of small identical flywheels is more effective than one large flywheel with an equivalent mass. Particular examples illustrating the theory considered are discussed. 相似文献
89.
Constants of Motion for Several One-Dimensional Systems and Problems Associated with Getting Their Hamiltonians 总被引:1,自引:1,他引:0
G. López L. A. Barrera Y. Garibo H. Hernández J. C. Salazar C. A. Vargas 《International Journal of Theoretical Physics》2004,43(10):2009-2021
The constants of motion of the following systems are deduced: a relativistic particle with linear dissipation; a no-relativistic particle with a time explicitly depending force; a no-relativistic particle with a constant force and time depending mass; and a relativistic particle under a conservative force with position depending mass. The Hamiltonian for these systems, which is determined by getting the velocity as a function of position and generalized linear momentum, can be found explicitly at first approximation for the first system. The Hamiltonians for the other systems are kept implicitly in their expressions for their constants of motion. 相似文献
90.
High quality factor of dynamic structures at micro and nano scale is exploited in various applications of micro electro-mechanical
systems (MEMS) and nano electro-mechanical system. The quality factor of such devices can be very high in vacuum. However,
when vacuum is not desirable or not possible, the tiny structures must vibrate in air or some other gas at pressure levels
that may vary from atmospheric to low vacuum. The interaction of the surrounding fluid with the vibrating structure leads
to dissipation, thus bringing down the quality factor. Depending on the ambient fluid pressure or the gap between the vibrating
and the fixed structure, the fluid motion can range from continuum flow to molecular flow giving a wide range of dissipation.
The relevant fluid flow characteristics are determined by the Knudsen number which is the ratio of the mean free path of the
gas molecule to the characteristic flow length of the device. This number is very small for continuum flow and reasonably
big for molecular flow. In this paper, we study the effect of fluid pressure on the quality factor by carrying out experiments
on a MEMS device that consists of a double gimbaled torsional resonator. Such devices are commonly used in optical cross-connects
and switches. We only vary fluid pressure to make the Knudsen number go through the entire range of continuum flow, slip flow,
transition flow, and molecular flow. We experimentally determine the quality factor of the torsional resonator at different
air pressures ranging from 760 Torr to 0.001 Torr. The variation of this pressure over six orders of magnitude ensures required
rarefaction to range over all flow conditions. Finally, we get the variation of quality factor with pressure. The result indicates
that the quality factor, Q, follows a power law, Q ∝P
–r
, with different values of the exponent r in different flow regimes. In the second part of the paper, we propose the use of effective viscosity for considering velocity
slip conditions in solving Navier–Stokes equation numerically. This concept is validated with analytical results for a simple
case and then compared with the experimental results presented in this paper. The study shows that the effective viscosity
concept can be used effectively even for the molecular regime if the air-gap to length ratio is sufficiently small (h
0/L<0.01). As this ratio increases, the range of validity decreases. 相似文献