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1.
By a natural nonextensive generalization of the conservation of energy in the q-kinetic theory, we study the nonextensivity and the power-law distributions for the many-body systems with the self-gravitating long-range interactions. It is shown that the power-law distributions describe the long-range nature of the interactions and the non-local correlations within the self-gravitating system with the inhomogeneous velocity dispersion. A relation is established between the nonextensive parameter q≠1 and the measurable quantities of the self-gravitating system: the velocity dispersion and the mass density. Correspondingly, the nonextensive parameter q can be uniquely determined from the microscopic dynamical equation and thus the physical interpretation of q different from unity can be clearly presented. We derive a nonlinear differential equation for the radial density dependence of the self-gravitating system with the inhomogeneous velocity dispersion, which can correctly describe the density distribution for the dark matter in the above physical situation. We also apply this q-kinetic approach to analyze the nonextensivity of self-gravitating collisionless systems and self-gravitating gaseous dynamical systems, giving the power-law distributions the clear physical meaning.   相似文献   

2.
We consider the problem of finding the generalized potential function V = U i(q 1, q 2,..., q n)q i + U(q 1, q 2,...;q n) compatible with prescribed dynamical trajectories of a holonomic system. We obtain conditions necessary for the existence of solutions to the problem: these can be cast into a system of n – 1 first order nonlinear partial differential equations in the unknown functions U 1, U 2,...;, U n, U. In particular we study dynamical systems with two degrees of freedom. Using adapted coordinates on the configuration manifold M 2 we obtain, for potential function U(q 1, q 2), a classic first kind of Abel ordinary differential equation. Moreover, we show that, in special cases of dynamical interest, such an equation can be solved by quadrature. In particular we establish, for ordinary potential functions, a classical formula obtained in different way by Joukowsky for a particle moving on a surface.Work performed with the support of the Gruppo Nazionale di Fisica Matematica (G.N.F.M.) of the Italian National Research Council.  相似文献   

3.
According to the classical theory of equilibrium figures, surfaces of equal density, potential and pressure concur (let us call them isobars). Isobars can be represented by means of Liapunov power series in small parameter q, up to the first approximation coinciding with the centrifugal to gravitational force ratio at the equator. Liapunov has proved the existence of the universal convergence domain: the above mentioned series converge for all bodies (satisfying a natural condition that the density ρ decreases from the center to the surface) if |q| < q*. Using Liapunov’s algorithm and symbolic manipulation tools, we have found q*= 0.000370916. Evidently, the convergence radius q* may be much greater in common situations. To comfirm it it is reasonable to consider two limiting and one or two intermediate cases for the density behaviour: ρ is a constant, the Dirac’s δ-function, linear function of the distance from the center, etc. And indeed, in the previous paper we find a three orders of magnitude greater value for homogeneous figures. In the present paper we find that in the opposite case of Huygens-Roche figures (a point-mass surrounded by a weightless atmosphere) the convergence radius is unexpectedly large and coincides with the well-known biggest possible value q*= 0.541115598 for such a class of figures. To ascertain it we ought to use numerical calculations, so our main result is demonstrated by means of a computer assisted proof. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

4.
The problem of solitary electron acoustic (EA) wave propagation in a plasma with nonthermal hot electrons featuring the Tsallis distribution is addressed. A physically meaningful nonextensive nonthermal velocity distribution is outlined. It is shown that the effect of the nonthermal electron nonextensivity on EA waves can be quite important. Interestingly, we found that the phase speed of the linear EA mode increases as the entropic index q decreases. This enhancement is weak for q>1, and significant for q<1. For a given nonthermal state, the minimum value of the allowable Mach numbers is lowered as the nonextensive nature of the electrons becomes important. This critical limit is shifted towards higher values as the nonthermal character of the plasma is increased. Moreover, our plasma model supports rarefactive EA solitary waves the main quantities of which depend sensitively on q. This dependency (for q>1) becomes less noticeable as the nonthermal parameter decreases. Nevertheless, decreasing α yields for q<0 a different result, a trend which may be attributed to the functional form of the nonthermal nonextensive distribution. Our study (which is not aimed at putting the ad hoc Cairns distribution onto a more rigorous foundation) suggests that a background electron nonextensivity may influence the EA solitons.  相似文献   

5.
All the families of planar symmetric simple-periodic orbits of the photogravitational restricted plane circular three-body problem, are determined numerically in the case when the primaries are of equal mass and radiate with equal radiation factors (q 1=q2=q). We obtain a global view of the possible patterns of periodic three-body motion while the full range of values of the common radiation factor is explored, from the gravitational case (q=1) down to near the critical value at which the triangular equilibria disappear by coalescing with the inner equilibrium pointL 1 on the rotating axis of the primaries. It is found that for large deviations of its value from the gravitational case the radiation factorq can have a strong effect on the structure of the families.  相似文献   

6.
A new class of linear ordinary differential equations with periodic coefficients is found which can be transformed to the Gauss hypergeometric equation, and therefore the monodromy matrices are computable explicitly. These equations appear as the variational equations around a straight-line solution in Hamiltonian systems of the form H = T(p) + V(q), where T(p) and V(q) are homogeneous functions of p and q, respectively.  相似文献   

7.
We have worked out a ’statistical algorithm’ for obtaining the posterior probability density of the deceleration parameter q0 from quasars where there is a luminosity indicator available. We point out that the role of the luminosity indicator is to provide asecond estimate of individual luminosities after a first estimate has been obtained from measured brightness and redshift together with an assumed q0. Discrimination of q0 is to be sought in the statistical properties of the set of differences between the two estimates (the residuals). We show that the variance of the residuals and their correlation with redshifts (further refined to luminosity distances) are two independent test-statistics for q0, whose known distributions then lead to the probability density sought. We have applied the above algorithm to a sample of flat-spectrum radio quasars with measured CIV, MgII and Ly α lines. A combined Baldwin’s relation was used for all 3 lines. Our result is that log q0 is normally distributed with a mean value of + 0.270± 0.135 (s.d.), or, q0 = + 1.86 ± 0.135 dex. This result, we believe, is the sharpest result so far published on q0.  相似文献   

8.
We consider the changes of cometary perihelion distances as a process of diffusion in the value of q, due to perturbations by stars. We find more comets at large q values than is observed. This suggests that a large number of long-period comets is not observed.  相似文献   

9.
I present updated compilations of both observational data and theoretical predictions concerning excess line width and sizes in astrophysical bodies. After removing two well-known broadening mechanisms (thermal width and width due to large scale motions such as expansion), I analyse statistically the excess line widthW excess. The excess line width shows a changing behavior with object sizeR, of the formW excess ~R q. Taking all objects together, I find thatq = 0.55 with s.d. = 0.05. This resultextends previous studies to cover 5 decades in sizes, from 0.01 pc up to 1000 pc. Taking only objects withR < 1 pc, I find thatq = 0.7 with s.d.=0.1, while taking only objects withR > 1 pc givesq = 0.5 with s.d.=0.1; thus a steeper (not flatter) value ofq at smallR may be possible. Previous claims to derive a law for objects of sizesR > 1 kpc are discussed, in relation to the problem of removing obvious large scale motions from the observed line width. Thus several models with predictedq values between 0 and 1 can be eliminated, and the remaining ones could allow weak magnetic effects on the line widths.  相似文献   

10.
Weak ion-acoustic double-layers (IA-DLs) in a two-component plasma are investigated in the context of the nonextensive statistics proposed by Tsallis. Due to the entropic index q, our plasma model can admit compressive as well as rarefactive IA-DLs. It is shown that the values \frac53 < q < 3\frac{5}{3}q-parameters for the existence of small-DLs. As long as the Mach number M is less than ∼1.42, the only admissible q-values which may lead to IA-DLs are all positive. For −1<q<1 (1<q<5/3), the effect of increasing q is to lower (to shift towards higher values) the critical Mach number M cr above which only compressive IA-DL are admitted. Beyond q=3, only compressive small-amplitude ion-acoustic double layers are observed. Furthermore, due to the flexibility of the q-parameter, the obtained results bring a possibility to deal with small-DLs with relatively high Mach numbers. Our investigation may be of wide relevance to astronomers and space scientists working on interstellar plasmas.  相似文献   

11.
The properties of dust acoustic double-layers (DA-DLs) in an unmagnetized electron depleted dusty plasma consisting of inertial dust fluid and ions featuring Tsallis statistics are investigated. It is found that our plasma model can admit compressive as well as rarefactive DA-DLs depending on the value of nonextensive parameter q. As the value of q increases, the negative DA-DL shrinks and, beyond a certain critical value, develops into a positive structure allowing therefore the existence of compressive DA-DLs.  相似文献   

12.
The spectra of geopotential, Earth and ocean tidal perturbations on a satellite can be obtained using Kaula's linear theory, or an extension thereof, as summations of terms depending on four indices l, m, p, q. In this work algorithms are presented that generate the equivalence classes induced by the composition rule of frequency on the set of all (l, m, p, q) combinations up to a maximum degree L and maximum value Q of the last index. These algorithms eliminate the need to search the set of frequencies when the linear theory is programmed on a computer.  相似文献   

13.
The only existing photoelectric light curve of AI Cru has been re-analysed using the Wilson and Devinney (1971) direct method of solution. The system is found to be a semi-detached system of spectral type (B5 v+B8 v), with a mass ratioq=m c /m h =0.6. This solution differs somewhat from that obtained by Giuricinet al. (1980), using Wood's (1972) method, but seems more realistic because of the smaller value ofq and the reduced temperature difference between the components, which amounts to about 3300 K.  相似文献   

14.
According to the classical theory of equilibrium figures surfaces of equal density, potential and pressure concur (let call them isobars). Isobars may be represented by means of Liapunov power series in small parameter q, up to the first approximation coincident with centrifugal to gravitational force ratio on the equator. A. M. Liapunov has proved the existence of the universal convergence radius q : above mentioned series converge for all bodies if q < q . Using Liapunov's algorithm and symbolic calculus tools we have calculated q = 0.000370916. Evidently, convergence radius q 0 may be much greater in non-pathological situations. We plan to examine several simplest cases. In the present paper, we find q 0 for homogeneous liquid. The convergence radius turns out to be unexpectedly large coinciding with the upper boundary value q 0 = 0.337 for Maclaurin ellipsoids.  相似文献   

15.
On the largest scales there is evidence of discrete structure, examples of this are superclusters and voids and also by redshift taking discrete values. In this paper it is proposed that discrete redshift can be explained by using the spherical harmonic integer l; this occurs both in the metric or density perturbations and also in the solution of wave equations in Robertson-Walker spacetime. It is argued that the near conservation of energy implies that l varies regularly for wave equations in Robertson-Walker spacetime, whereas for density perturbations l cannot vary regularly. Once this is assumed then perhaps the observed value of discrete redshift provides the only observational or experimental data that directly requires an explanation using both gravitational and quantum theory. In principle a model using this data could predict the scale factor R (or equivalently the deceleration parameter q). Solutions of the Klein-Gordon equation in Robertson-Walker spacetimes are used to devise models which have redshift taking discrete values, but they predict a microscopic value for R. A model in which the stress of the Klein-Gordon equation induces a metrical perturbation of Robertson-Walker spacetime is devised. Calculations based upon this model predict that the Universe is closed with 2 q0 - 1=10-4. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

16.
The investigation of the angular momentum vs mass relation for binary stars is completed with a study of the 847 systems contained in theFourth Catalog of Orbits of Visual Binary Stars. Because bothJ andM of a visual binary depend steeply on the distance to the system (5th and 3rd powers, respectively), and many of the distances are not well known, the study makes use of an auxiliary parameterR which is independent of distance and proportional toJM –5/3.R appears to be uncorrelated withM for the 789 systems for which both can be determined. The non-correlation implies thatJ M 5/3, expected from Kepler's third law, provides a better fit to the visual binaries than doesJ M 2, predicted by some more complex considerations.The distribution functionf(q=M 2/M1) of mass ratios for the visual binaries results as a byproduct of the investigation. It peaks extremely sharply towardq=1.0 (much more so than for spectroscopic binaries). Because most visual binaries are wide enough to consist of stars that condensed independently (and so that can be thought of as chosen at random from an initial mass function), one expects the realf(q) to rise toward low ratios. Observational selection against the discovery and study of systems with large magnitude differences between the components must be very large indeed to account for the discrepancy between expectation and observation. The alternative is a mechanism for formation of wide binaries that favours equal components. The distribution of mass ratios for eclipsing binaries is given in an appendix. It peaks strongly atq=0.6–0.75 and largely reflects processes of angular momentum, mass, and energy exchange between the stars in contact systems.  相似文献   

17.
Combining the kinematical definitions of the two dimensionless parameters, the deceleration q(x) and the Hubble t 0 H(x), we get a differential equation (where x=t/t 0 is the age of the universe relative to its present value t 0). First integration gives the function H(x). The present values of the Hubble parameter H(1) [approximately t 0 H(1)≈1], and the deceleration parameter [approximately q(1)≈−0.5], determine the function H(x). A second integration gives the cosmological scale factor a(x). Differentiation of a(x) gives the speed of expansion of the universe. The evolution of the universe that results from our approach is: an initial extremely fast exponential expansion (inflation), followed by an almost linear expansion (first decelerated, and later accelerated). For the future, at approximately t≈3t 0 there is a final exponential expansion, a second inflation that produces a disaggregation of the universe to infinity. We find the necessary and sufficient conditions for this disaggregation to occur. The precise value of the final age is given only with one parameter: the present value of the deceleration parameter [q(1)≈−0.5]. This emerging picture of the history of the universe represents an important challenge, an opportunity for the immediate research on the Universe. These conclusions have been elaborated without the use of any particular cosmological model of the universe.  相似文献   

18.
In order to determine the mass-ratio distribution of spectroscopic binary stars, the selection effects that govern the observations of this class of binary systems are investigated. The selection effects are modelled numerically and analytically. The results of the models are compared to the data inThe Eighth Catalogue of the Orbital Elements of Spectroscopic Binary Stars (DAO8) compiled by Battenet al. (1989). The investigations involve binary systems with Main-Sequence primary components only, in order to avoid confusion of evolutionary and selection effects.For single-lined spectroscopic binaries (SBI) it is found that the mass ratios (q=M sec/M prim) in general adhere to a distribution q q -2 forq>q 0, withq 0=0.3. The observations are consistent with a distribution that is flat forq<q 0. The turn-over value varies fromq 0=0.3 for systems with B-type primaries, toq 0=0.55 for systems with K-type primaries. The semi-major axesa 1 are distributed according to a (a 1)a 1 -a with an average value of a =1.3. The power varies from a =1.7 for systems with B-type primaries to a =0 for systems with K-type primaries. The eccentricitiese of the orbits of SBI systems are distributed according to e (e)e -1.For double-lined spectroscopic binary stars (SBII) it is found that the shape of theq-distribution, as derived from observations, is almost entirely determined by selection effects. It is shown that the distribution is compatible with theq-distribution found for SBI systems. A sub-sample, consisting of the SBII systems from DAO8 with magnitudesm V 5 m , is less hampered by selection effects, and shows the same shape of theq-distribution as the SBI systems, at theq-interval (0.67, 1).It is estimated that 19–45% of the stars in the solar neighbourhood are spectroscopic binary systems.  相似文献   

19.
The selection effects that govern the observations of Visual Binary Stars are investigated, in order to obtain a realistic statistical distribution of the mass-ratioq=M sec/M prim. To this end a numerical simulation programme has been developed, which generates binary stars and looks at them to determine whether an observer on Earth would be able to detect them. The simulations show that for mass-ratiosq>0.35, observations are expected to reveal the realq-distributions, while for mass-ratiosq<0.35 selection effects begin to play a major part. It is found that the observed mass-ratio distribution for Main-Sequence systems, derived from theIndex Catalogue of Visual Binary Stars (IDS), can be explained by a distribution of secondary masses according to the Initial Mass Function (IMF), i.e., (M)M –2.7.From theFourth Catalogue of Orbits of Visual Binary Stars (OVB) authors find aq-distribution that peaks strongly forq-values close toq=1. It is shown that this mass-ratio distribution may be the result of a sampling selection effect. Due to this sampling selection effect, the OVB is a considerably morebiased sample of the binary population in our Galaxy than the IDS. Numerical simulations of biased sampling show that theq-distribution, found from the OVB, is not incompatible with the distribution of secondary masses according to the IMF (forq>0.35), found from the IDS.Because of the selection effects, it is difficult to establish the realq-distribution forq<0.35. If the realq-distribution departs from (q)q –2.7 forq0.35, about 36% of all stars are in visual binaries (i.e., if theq-distribution is assumed to be flat for 0<q<0.35); if the distribution flattens forq0.25, about 60% of the stars must be primaries of visual binaries.  相似文献   

20.
The purpose of this paper is the presentation of an integrator for the average motion of an asteroid in mean motion commensurability with Jupiter. The program is valid for any (p+q)/p mean motion commensurability (except whenq=0) and uses a double precision version of DE (Shampine and Gordon 1975) as propagator. The averaged equations of motion of the asteroid are evaluated in a non-singular way for any value of the eccentricities and the inclinations and the orbit of Jupiter is described by the most important terms in Longstop 1B (Nobiliet al. 1989). This integrator can be considered as an extension of the well known Schubart Averaging (Schubart 1978) in which Jupiter is moving on a fixed ellipse.  相似文献   

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