共查询到20条相似文献，搜索用时 609 毫秒
1.
We present a revised criterion for the double-mode pulsation in oscillator model equations with two-mode nonresonant coupling. By applying the criterion, we demonstrate that there are four cases, namely, mode 0-only, mode 1-only, either-or, and double-mode ones on limiting amplitude space. We also show that models with evolutionary masses are preferable for double-mode pulsations. Moreover, we study numerically modal selection properties of the oscillator model equations corresponding to various limiting amplitudes. The results show the suggested criterion to be useful for prediction of modal selection properties. Some examples of the phase-locking behaviour are also shown. 相似文献
2.
Frank Verheest 《Astrophysics and Space Science》1990,166(1):77-91
If one is only interested in the behaviour of a few longlived modes, the simplest model for the evolution to steady nonlinear stellar pulsation is nonresonant interaction. As the coupled-mode equations are generically not dependent upon a particular stellar model, qualitative ideas about the eventual evolution of mode energies give scenarios that depend mainly upon nonlinear coupling constants and linear growth rates. Two linearly unstable modes are considered in the presence of a representative stable or slave mode. One scenario models a double-mode pulsator, without it being necessary that all coupling constants be negative, if only the model is well behaved enough in excluding unbounded solutions and in avoiding finite amplitudes for the slave modes. The influence of driving on slave modes is then such that all slave modes ultimately decay away. Other scenarios show evolution to classic pulsators. A discussion is given of the modelling of a classic Cepheid in a mode which is not the linearly most unstable one. Findings of the present paper show the need for additional theoretical and numerical modelling and a cautious discussion thereof. 相似文献
3.
The periodic motion of a test particle (dust, grain, or a larger body) around a pulsating star with a luminosity oscillation of small amplitude (featured by a small parameterB) is being studied. The perturbations of all orbital elements are determined to first order inB, by using Delaunay-type canonical variables and a method whose bases were put forth by von Zeipel. According to the value of the ratio oscillation frequency/dynamic frequency, three possible situations are pointed out: nonresonant (NR), quasi-resonant (QR), and resonant (R). The solution of motion equations shows that only in the (QR) and (R) cases there are orbital parameters (argument of periastron and mean anomaly) affected by secular perturbations. These solutions (which indicate a secularly stable motion in a first approximation) are valid over prediction times of orderB
–1 in the (NR) case andB
–1/2 in the (QR) and (R) cases. The theory may be applied to various astronomical situations. 相似文献
4.
Energetic protons haying ring type distributions are shown to generate low-frequency electrostatic waves, propagating nearly transverse to the geomagnetic field lines, in the ring current region by exciting Mode 1 arid Mode 2 nonresonant instabilities and a resonant instability. Mode 1 nonresonant instability has frequencies around ~4 Hz with transverse wavelengths of ~(8–80) km, and it is likely to occur in the region L = (7–8). Mode 2 nonresonant instability can generate frequencies ~(850–1450) Hz with transverse wavelengths ~(2–20) km. The typical frequencies and transverse wavelengths associated with the resonant instability are (950–1250) Hz and (30–65) km. Both the Mode 2 nonresonant instability and the resonant instability can occur in the ring current region with L = (4–6). The low-frequency modes driven by energetic protons could attain maximum saturation electric field amplitude varying from 0.8 mV/m to 70 mV/m. It is suggested that the turbulence produced by the low-frequency modes may cause pitch angle scattering of ring current protons in the region outside the plasmapause resulting in the ring current decay. 相似文献
5.
Yoshio Kubo 《Celestial Mechanics and Dynamical Astronomy》1979,19(3):215-241
Effects of an interaction between the mantle and the core of the Earth on its rotational motion are investigated. Assuming that the Earth consists of a rigid mantle and a rigid core with a frictional coupling and a kind of inertial coupling between them, the equations of motion are derived, and they are solved in a close approximation. The solution gives the expressions for the precession, the nutation, the secular changes in the obliquity and the rotational speed, the polar motion and so on as functions of the magnitudes of these forces. A numerical estimation shows that the effect of the friction on the amplitude and phase of the nutation is small for a reasonable intensity of the friction while inertial coupling force has a decisive influence on the amplitude, and an appropriately chosen value of the latter force gives a nutation which closely agrees with observations. It is also indicated that this torque remarkably lessens the rates of the secular changes in the obliquity and the rotational speed. The possibility of a periodical change in the amplitude of the polar motion is suggested as a result of the interaction between the two consituents. 相似文献
6.
《Planetary and Space Science》2007,55(14):2192-2202
Nonlinear propagating dust-acoustic solitary waves (DASWs) in a warm magnetized dusty plasma containing different size and mass negatively charged dust particles, isothermal electrons, high- and low-temperature ions are investigated. For this purpose, a reasonable normalization of the hydrodynamic and Poisson equations is used to derive the Zakharov–Kuznetsov (ZK) equation for the first-order perturbed potential. As the wave amplitude increases, the width and the velocity of the solitons deviate from the prediction of the ZK equation, i.e., the breakdown of the ZK approximation. To describe the soliton of larger amplitude, a linear inhomogeneous Zakharov-Kuznetsov-type (ZK-type) equation for the second-order perturbed potential is derived. Stationary solutions of both equations are obtained using the renormalization method. Numerically, the effect of power law distribution on the higher-order corrections is examined. It is found that the soliton amplitude in case of power law distribution is smaller than that of monosized dust grains. The higher-order corrections play a role to reduce the strength of the nonlinearity for power law distribution case. The relevance of the present investigation to Saturn's F-ring and laboratory experiment is discussed. 相似文献
7.
Jean-Pierre Poyet 《Solar physics》1983,82(1-2):267-296
The coupling of non-radial pulsations and convection is studied on a simple example: an unstable semi-infinite polytrope. An expansion is proposed and the equations that should describe correctly the pulsations are isolated. The additional complications of the real solar case are discussed at the end. 相似文献
8.
We simulated two models of classical Cepheids with the same effective temperature and luminosity but different masses. Neither model has significant resonance among linear nonadiabatic periods of the fundamental, the first overtone, and the second overtone radial modes. The higher mass model found to approach to the second overtone-only state. The lower mass model shows a complicated three-mode interaction and none of the amplitudes of three modes is negligible. The relation of the higher mass model to the shortest period Cepheid HR 7308, and that of the lower mass model to the double-mode Cepheids are discussed. It appears that three-mode nonresonant coupling should be considered to explain the behaviours of both models. 相似文献
9.
Nuclear reactions govern major aspects of the chemical evolution of galaxies and stars. Analytic study of the reaction rates
and reaction probability integrals is attempted here. Exact expressions for the reaction rates and reaction probability integrals
for nuclear reactions in the cases of nonresonant, modified nonresonant, screened nonresonant and resonant cases are given.
These are expressed in terms of H-functions, G-functions and in computable series forms. Computational aspects are also discussed.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
10.
Astronomy Letters - We consider the spatial restricted circular three-body problem in the nonresonant case. The massless body (satellite) is assumed to have a large sail area and, therefore, the... 相似文献
11.
Jason W. Mitchell David L. Richardson 《Celestial Mechanics and Dynamical Astronomy》2001,81(1-2):13-25
Euler's equations, describing the rotation of an arbitrarily torqued mass asymmetric rigid body, are scaled using linear transformations that lead to a simplified set of first order ordinary differential equations without the explicit appearance of the principal moments of inertia. These scaled differential equations provide trivial access to an analytical solution and two constants of integration for the case of torque-free motion. Two additional representations for the third constant of integration are chosen to complete two new kinetic element sets that describe an osculating solution using the variation of parameters. The elements' physical representations are amplitudes and either angular displacement or initial time constant in the torque-free solution. These new kinetic elements lead to a considerably simplified variation of parameters solution to Euler's equations. The resulting variational equations are quite compact. To investigate error propagation behaviour of these new variational formulations in computer simulations, they are compared to the unmodified equations without kinematic coupling but under the influence of simulated gravity-gradient torques. 相似文献
12.
S. A. Petrova 《Monthly notices of the Royal Astronomical Society》2006,366(4):1539-1550
Propagation of radio waves in the ultrarelativistic magnetized electron–positron plasma of a pulsar magnetosphere is considered. The polarization state of the original natural waves is found to vary markedly on account of the wave mode coupling and cyclotron absorption. The change is most pronounced when the regions of mode coupling and cyclotron resonance approximately coincide. In cases when the wave mode coupling occurs above and below the resonance region, the resultant polarization appears essentially distinct. The main result of the paper is that in the former case the polarization modes become non-orthogonal. The analytical treatment of the equations of polarization transfer is accompanied by numerical calculations. The observational consequences of polarization evolution in pulsar plasma are discussed as well. 相似文献
13.
14.
The scalar field theory on the background of cosmological models with n(n ≥ 1) spaces of constant curvature is considered. We take the integrable case of Ricci flat internal spaces. The coupling between the scalar and the gravitational fields includes the minimal coupling as well as the conformal case. In the ground state of the scalar field we find the conditions for vacuum instability realized for most of the possible solutions to Einstein's equations if the coupling parameter takes appropriate values. For the excited states of the scalar field we show the induction of massive modes and discuss their properties. 相似文献
15.
R. Pringle Jr. 《Celestial Mechanics and Dynamical Astronomy》1973,7(4):495-518
Coupled vibration-rotation motion of a satellite is considered using a perturbation theory based on the Lie transformation method. Short-period oscillating terms are removed from the Hamiltonian function. The transformed damping forces directly affect rotational variables which were not directly influenced in the original variables. Motions and stability are more easily studied in the new variables. A dual-spin spacecraft model is used as an example; results for the usual nonresonant case are identical with the energy-sink method. Resonance cases produce a wealth of new dynamical phenomena. This canonical method extends and unifies various approximation methods in attitude dynamics. 相似文献
16.
Joseph J. F. Liu Philip M. Fitzpatrick 《Celestial Mechanics and Dynamical Astronomy》1975,12(4):463-487
Differential equations are derived for studying the effects of either conservative or nonconservative torques on the attitude motion of a tumbling triaxial rigid satellite. These equations, which are analogous to the Lagrange planetary equations for osculating elements, are then used to study the attitude motions of a rapidly spinning, triaxial, rigid satellite about its center of mass, which, in turn, is constrained to move in an elliptic orbit about an attracting point mass. The only torques considered are the gravity-gradient torques associated with an inverse-square field. The effects of oblateness of the central body on the orbit are included, in that, the apsidal line of the orbit is permitted to rotate at a constant rate while the orbital plane is permitted to precess (either posigrade or retrograde) at a constant rate with constant inclination.A method of averaging is used to obtain an intermediate set of averaged differential equations for the nonresonant, secular behavior of the osculating elements which describe the complete rotational motions of the body about its center of mass. The averaged differential equations are then integrated to obtain long-term secular solutions for the osculating elements. These solutions may be used to predict both the orientation of the body with respect to a nonrotating coordinate system and the motion of the rotational angular momentum about the center of mass. The complete development is valid to first order in (n/w
0)2, wheren is the satellite's orbital mean motion andw
0 its initial rotational angular speed. 相似文献
17.
One zone modeling of the irregular variability of red super-giants is intended with regard to the nonlinear coupling of finite amplitude pulsation with convection. The nonlocal mixing length is employed for the evaluation of the convective flux, the turbulent pressure and the turbulent power of temperature fluctuations. The radial pulsation and the Boussinesq convection are assumed for simplicity. The one zone is defined as the layer having the entropy maximum and the minimum at the bottom and at the top, respectively. The quasi-adiabatic approximation is consistent with this definition in fixing the zone to the same mass range. The spatial derivatives are evaluated under the assumption of homologous changes with the equilibrium homologous parameters. Then, a set of 6 simultaneous first order nonlinear ordinary differential equations are obtained as the one zone representation of the irregular variability of the convective envelope. 相似文献
18.
I. N. Toptygin 《Astronomy Letters》2007,33(4):259-269
We analyze the nonresonant generation of large-scale magnetic inhomogeneities near a shock front by accelerated particles. The MHD disturbances are generated by the electric current excited by relativistic particles in the preshock medium in the presence of weak large-scale density inhomogeneities. The MHD modes considered can be amplified by other resonant and nonresonant mechanisms related to the presence of relativistic particles. We estimate the magnetic fields and the energies to which charged particles can be accelerated in different phases of the interstellar medium by taking into account the random magnetic fields generated by the mechanism considered. 相似文献
19.
We resume and consistently extend our previous researches concerning the Gyldén‐type problem (a two‐body problem with time‐dependent equivalent gravitational parameter). To approach most of the concrete astronomical situations to be modelled in this way, we consider a periodic small perturbation. For the nonresonant case, we present a second‐order analytical solution. For the resonant case, we adopt the most realistic astronomical situation: only one dominant term of the Hamiltonian. In this case we point out a fundamental model of resonance, common to every resonant situation, and, moreover, identical to the first fundamental model of resonance . Considering the simplest model of periodic change of the equivalent gravitational parameter, we .nd that all possible resonances are con.ned to the first fundamental model. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
20.
Mohsen Nejad-Asghar 《Astrophysics and Space Science》2011,334(1):27-33
The magnetic fields affect collapse of molecular cloud cores. Here, we consider a collapsing core with an axial magnetic field
and investigate its effect on infall of matter and formation of accretion disk. For this purpose, the equations of motion
of ions and neutral infalling particles are numerically solved to obtain the streamlines of trajectories. The results show
that in a non-steady state of ionization and ion–neutral coupling, which is not unexpected in the case of infall, the radius
of accretion disk will be larger as a consequence of axial magnetic field. 相似文献