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1.
The notion of the family boundary curves (FBC), introduced recently for two-dimensional conservative systems, is extended to account for, generally, nonconservative autonomous systems of two degrees of freedom. Formulae are found for the force componentsX (x, y),Y (x, y) which produce a preassigned family of orbitsf(x, y)=c lying inside a preassigned, open or closed, regionB(x, y)0 of the xy plane.  相似文献   

2.
In radiative transfer, the intensities of radiation from the bounding faces of a scattering atmosphere of finite optical thickness can be expressed in terms of Chandrasekhar’s X- and Y-functions. The nonlinear nonhomogeneous coupled integral equations which the X- and Y-functions satisfy in the real plane are meromorphically extended to the complex plane to frame linear nonhomogeneous coupled singular integral equations. These singular integral equations are then transformed into nonhomogeneous Riemann–Hilbert problems using Plemelj’s formulae. Solutions of those Riemann–Hilbert problems are obtained using the theory of linear singular integral equations. New forms of linear nonhomogeneous decoupled expressions are derived for X- and Y-functions in the complex plane and real plane. Solutions of these two expressions are obtained in terms of one known N-function and two new unknown functions N 1- and N 2- in the complex plane for both nonconservative and conservative cases. The N 1- and N 2-functions are expressed in terms of the known N-function using the theory of contour integration. The unknown constants are derived from the solutions of Fredholm integral equations of the second kind uniquely using the new linear decoupled constraints. The expressions for the H-function for a semi-infinite atmosphere are obtained as a limiting case.  相似文献   

3.
Models for the motions of flare loops and ribbons   总被引：1，自引：0，他引：1  
We have found a conformal mapping which is valid for any magnetic boundary condition at the photosphere and which can be used to determine the evolution of an open, two-dimensional magnetic field configuration as it relaxes to a closed one. Solutions obtained with this mapping are in quasi-static equilibrium, and they contain a vertical current sheet and have line-tied boundary conditions. As a specific example, we determine the solution for a boundary condition corresponding to a submerged, two-dimensional dipole below the photosphere. We assume that the outer edges of the hottest X-ray loops correspond to field lines mapping from the outer edges of the H ribbon to the lower tip of the current sheet where field lines reconnect at aY-type neutral line which rises with time. The cooler H loops are assumed to lie along the field lines mapping to the inner edges of the flare ribbons. With this correspondence between the plasma structures and the magnetic field we determine the shrinkage that field lines are observed to undergo as they are disconnected from the neutral line. During the early phase of the flare, we predict that shrinkage inferred from the height of the H and X-ray loops is close to 100% of the loop height. However, the shrinkage should rapidly decrease with time to values on the order of 20% by the late phase. We also predict that the shrinkage in very large loops obeys a universal scaling law which is independent of the boundary condition, provided that the field becomes self-similar (i.e., all field lines have the same shape) at large distances. Specifically, for any self-similar field containing aY-type neutral line, the observed shrinkage at large distances should decrease as (X/X R)–2/3, where X is the ribbon width andX Ris the ribbon separation. Finally, we discuss the relation between the electric field at the neutral line and the motions of the flare loops and ribbons.  相似文献   

4.
The aim of the present paper is to investigate the influence both of gravity field and initial stress on the propagation of Rayleigh waves in an orthotropic thermoelastic medium subject to certain boundary conditions. We suppose that the body is under initial stress alonqx 1-direction and incremental thermal stresses. The wave velocity equation has been obtained. Many special cases and comparison with the previous results have been studied.  相似文献   

5.
Unsteady two-dimensional hydromagnetic flow of an electrically conducting viscous incompressible fluid past a semi-infinite porous flat plate with step function change in suction velocity is studied allowing a first order velocity slip at the boundary condition. The solution of the problem is obtained in closed form and the results are discussed with the aid of graphs for various parameters entering in the problem.Notations B intensity of magnetic field - H magnetic field parameter,H=(M+1/4)1/2–1/2 - h rarefaction parameter - L 1 slip coefficient; ;I, mean free path of gas molecules;f, Maxwell's reflection coefficient - M magnetic field parameter - r suction parameter - t time - t dimensionless time - u velocity of the fluid - u dimensionless velocity of the fluid - U velocity of the fluid at infinity - v suction velocity - v 1 suction velocity att<=0 - v 2 suction velocity att>0 - x distance parallel to the plate - y distance normal to the plate - y nondimensional distance normal to the plate - v kinematic viscosity - electric conductivity of the fluid - density of the fluid - shear stress at the wall - nondimensional shear stress at the wall - erf error function - erfc complementary error function  相似文献   

6.
This study follows the numerical results presented in Marsenić & Ševčík (2010) that explored the influence of the critical level position on stability of a system. The model was a horizontal fluid layer between z = ±0.5d rotating with an angular velocity Ω = Ω0 ž about the vertical axis z . The fluid was considered to be inviscid, finitely electrically conducting and incompressible and was permeated by a horizontal magnetic field B 0 = ℬ︁0B0(z) y̌ , where ℬ︁0 was the magnitude of the field and the function B0(z) = tanh [γ (z –z0)]. When γ is large, the field gradient is concentrated near z = z0, the critical level, the field being almost homogeneous elsewhere. In this way it controls the width of the magnetic shear layer associated with the current sheet. It was found that at conditions when the magnetic field gradient was large enough (γ = O (10)) and the critical level was placed close enough to the (bottom) perfectly conducting boundary (z0 < –0.388d for γ = 80), magnetically driven convection appeared localized to a close neighbourhood of the critical level – the so called critical layer. Based on the circumstances of its rise and its properties it was identified with the resistive tearing‐mode instability. This paper presents an analytical treatment of the problem assuming γ ≥ 1. The approach consists in separation of the computational domain into an outer region where the diffusionless limit (Elsasser number Λ → ∞) applies and an inner region (the critical layer) of finite conductivity. According to the tearing‐mode theory in classical systems, the solution in the inner region is sought as long‐wavelength with respect to the width of the critical layer. The obtained solution shows features similar to the one obtained numerically and confirmed relevance of the simplifying physical assumptions made in each region. The convection in the critical layer is strictly conditioned by a sharp magnetic shear. If the shear region is removed by further positioning of the critical level towards the perfectly conducting boundary, the localized convection disappears. It is in compliance with the fact that the system is stabilised by a perfectly conducting boundary with respect to the tearing mode. Stability is then checked numerically in the layer bounded by perfectly conducting boundaries where the critical point of the magnetic field lies on one of them. The existence of a magnetically driven instability is confirmed. Depending on the value γ, it may rise as a stationary convection (for γ < 1.5) or as a wave which for γ > 16 exhibits similarity properties (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

7.
We describe a method for determining the primordial helium abundance (Y p) from radio recombination lines and present results of the first stage of our measurements. We analyze the observational data for hydrogen and helium radio recombination lines from six Galactic H II regions obtained at different times. We have found Y p = 25.2−25.5% with an error of ±0.9% from four sources.  相似文献   

8.
The occurrence at a heliocentric distance of 1 AU of alpha particle streaming velocities larger than proton streaming velocities,v /v p >1 (Ogilvie, 1975) is investigated on the basis of the theory suggesting the existence in the solar wind of an accelerating force acting preferentially on the alpha particles.Accurate solution of the three-fluid model equations for the quiet solar wind indicates that anecessary andsufficient condition for (v /v p )1 AU>1 is the presence of a relativelyweak accelerating forceacting in a limited region in the vicinity of 1 AU. If the force is effectiveonly at small heliocentric distances, the alpha particle streaming velocity excess vanishes at distances less than 1 AU, because of the (equalization) action of the dynamical friction force.  相似文献   

9.
Regular high-precision determinations of the Earth’s orientation parameters (EOPs) on the Quasar VLBI Network were begun in August 2006. The observations are performed within the framework of two national programs: daily sessions at three observatories of the Network to determine all five EOPs (the RU-E program) and 8-h sessions on the Zelenchukskaya-Badary and Svetloe-Badary baselines to determine the Universal Time (the RU-U program). The observations from August 2006 through May 2007 are analyzed. The rms deviations of the EOP values obtained in the RU-E program from the IERS C04 series are 1.1 mas for X p and Y p, 37 μs for UT1-UTC, and 0.7 and 0.6 mas for X c and Y c, respectively. These results closely match the prospective requirements of GLONASS. The rms deviations of the Universal Times obtained in the RU-U program from the IERS C04 series are 146 μs. We consider the immediate prospects for improving the accuracy of EOP determinations in daily sessions and for implementing the e-VLBI mode for an online determination of the Universal Time. Original Russian Text ? A.M. Finkelstein, E.A. Skurikhina, I.F. Surkis, A.V. Ipatov, I.A. Rakhimov, S.G. Smolentsev, 2008, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2008, Vol. 34, No. 1, pp. 66–76.  相似文献   

10.
Earlier work on the oscillations of an ellipsoid is extended to investigate the behaviour of a nonequilibrium compressible homogeneous rotating gaseous ellipsoid, with the components of the velocity field as linear functions of the coordinates, and with parallel angular velocity and uniform vorticity. The dynamical behaviour of the ellipsoid is obtained by numerically integrating the relevant differential equations for different values of the initial angular velocity and vorticity. This behaviour is displayed by the (a 1,a 2) and (a 1,a 3) phase plots, where thea i's (i = 1, 2, 3) are the semi-diameters, and by the graphs ofa 1,a 2,a 3, the volume, and the angular velocity as functions of time.The dynamical behaviour of the nonequilibrium ellipsoid depends on the deviation of the angular momentum from its equilibrium value; for larger deviations, the oscillations are more nonperiodic with larger amplitudes.An initially ellipsoidal configuration always remains ellipsoidal, but it cannot become spheroidal about its rotation axis, though it may become spheroidal instantaneously about either one of the other two principal axes.For an ellipsoid approaching axisymmetry about its axis of rotation, the angular velocity can suddenly increase by a large amount. Thus if an astrophysical object can be modelled by a nonequilibrium ellipsoid, it may occasionally undergo sudden large increases of angular velocity.  相似文献   

11.
The Gibbs thermodynamic potential of a proton vortex interacting with the normal core of a neutron vortex of radius r << λ (λ is the penetration depth) that is parallel to it and has an outer boundary of radius b is calculated. It is shown that, under this assumption, the capture of only one vortex by the core is energetically favorable. The force acting on the proton vortex owing to the entrained current is found and it is always directed toward the core. The corresponding force for a proton antivortex is directed toward the outer boundary of the neutron vortex. The Ginzburg-Landau equation is solved for a vortex-antivortex system and its Gibbs function is calculated. It is shown that at large distances from the core, vortex-antivortex pairs can form because of fluctuations. Acted on by the entrainment current, the antivortex moves outward, while the vortex stays inside the neutron vortex. It is shown that the best conditions for fluctuational pair production, followed by separation, exist near the outer boundary. It is shown that new proton vortices can develop only in a region where the entrainment magnetic field strength H (ρ) > HC1 (HC1 is the lower critical field). __________ Translated from Astrofizika, Vol. 51, No. 1, pp. 139–149 (February 2008).  相似文献   

12.
The diffusion of scalar fields (temperature, density number of some admixture) in a compressible medium showing an isotropic, homogeneous and stationary turbulence is considered. The derived formulae for turbulent diffusivity χT(ξ) hold up to ξ ≈ 1, where ξ = u0 τ0/R0 (u0, τ0, and R0 are characteristic velocity, life-time, and correlation length of turbulent pulsations, respectively. The velocity field of turbulent motions u(r, t) is assumed to be known and the influence of the scalar field onto u(r, t) is neglected. It is shown that the velocity correlators, which change their signs in dependence on the space corrdinates, may give negative values for ξT(ξ) when ξ ≠ 0.  相似文献   

13.
G. M. Webb  G. P. Zank 《Solar physics》1990,127(2):229-252
Solutions of the sine-Poisson equation are used to construct a class of isothermal magnetostatic atmospheres, with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model j is directed along the x-axis, where x is the horizontal ignorable coordinate. The current j varies as the sine of the magnetostatic potential and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. We investigate in detail solutions for the magnetostatic potential A corresponding to the one-soliton, two soliton, and breather solutions of the sine-Gordon equation. Depending on the values of the free parameters in the soliton solutions, horizontally, periodic magnetostatic structures are obtained possessing either (a) a single X-type neutral point, (b) multiple neutral X-points, or (c) solutions without X-points. The solution cases (b) and (c) contain two families of intersecting current sheets, in which the line of intersection forms flux concentration points (or singularities) for the magnetic field. The solutions illustrate the contribution of the anisotropic J × B force (B, magnetic field induction), the gravitational force, and the gas pressure gradient to the force balance.  相似文献   

14.
For studying the first compression phase of a Plasma Focus machine, we developed a 2-fluid, time-dependent, 2-D code. The code includes two species (ions and electrons), two temperatures, radiation, thermal conductivity, electrical conductivity, magnetic diffusion, and viscosity and is coupled to an external circuit. In order to get reasonable initial conditions for the pinch phase, a simple 1-D model is used for the run-down phase. Under this somewhat ideal Plasma Focus discharge condition, relatively simple scaling laws are obtained. In particular, for a given machine, the pressure (po) of maximum thermonuclear production scales with the charging voltage (Vo) as po Vo 2; the thermonuclear production (Yn) at these pressures increases with the current (Io) as Yn Io 4 and the mean energy per particle is almost independent of all parameters (note that this means that the converging speed should be almost the same regardless of the machine at the optimum conditions). These laws show a reasonable agreement with experimental data and can be explained with a dimensional analysis.  相似文献   

15.
The molecular gas mass in nearby galaxies is generally estimated using 12CO(1-0) line intensities and assuming the X conversion factor between I(CO) and N(H2) measured in the solar neighborhood. It is however known that this X conversion factor is not universal since it changes with metallicity, cosmic ray density and UV radiation field. Far-IR data in the spectral range 100-1000 μm can be used to estimate the molecular gas content of late-type galaxies in an independent way of CO line measurements once a metallicity-dependent dust to gas ratio is assumed, allowing a direct estimate of X. This exercise is presented here for a large sample of galaxies with available multifrequency data. X spans from ∼ 1020 mol cm-2 (K km s-1)-1 in giant spirals to ∼ 1021 mol cm-2 (K km s-1)-1 in dwarf irregulars. This revised version was published online in September 2006 with corrections to the Cover Date.  相似文献   

16.
The electron surfing acceleration in the current sheet with perpendicular propagating electrostatic waves is studied using analytical theories and test particle simulations. The trapped electron moving with the phase velocity v p of wave may be accelerated effectively in the outflow direction by force until the electron is de-trapped from the wave potential. A criterion K>0 for the electron surfing acceleration is obtained. The electron will escape from the boundary of current sheet quickly, if this criterion does not hold. The maximum velocity of surfing acceleration is about the same as the electric drift velocity. Superposed longitudinal magnetic field along the wave propagation is favorable for the electron surfing acceleration in the current sheet.   相似文献   

17.
The partial frequency redistribution function for zero natural line width with dipole scattering (RI) has been considered in obtaining the simultaneous solution of the statistical equilibrium and line transfer equations in the comoving frame of the expanding gas. We have considered a non-LTE two level atom in an expanding spherical medium whose outer radii are 3, 10 and 20 times the stellar radius with a total optical depthT ≃ 2 × 103. In all the cases, we have calculated the population ratio of the two levels N2/N1 and compared these results with those obtained by using different expansion velocities and geometrical extensions. Initially, the upper level population (N2) is set equal to zero. The converged simultaneous solution shows that the upper level population is enhanced considerably from the initial value. Variation in velocity gradients seem to have little effect on the ratio N2/N1 when the geometrical thickness of the medium is 3 or 10 times the stellar radius. However, when the thickness is increased to 20 times the central radius, the velocity gradients change the ratio N2/N1 considerably in the region where log T ≤ 2. The effect of variation of geometrical thickness is to reduce the N2/N1 ratio atτ = 0.  相似文献   

18.
Three-dimensional periodic motions of three bodies are shown to exist in the infinitesimal neighbourhood of their collinear equilibrium configurations. These configurations and some characteristic quantities of the emanating three-dimensional periodic orbits are given for many values of the two mass parameters, =m 2/(m 1+m 2) andm 3, of the general three-body problem, under the assumption that the straight line containing the bodies at equilibrium rotates with unit angular velocity. The analysis of the small periodic orbits near the equilibrium configurations is carried out to second-order terms in the small quantities describing the deviation from plane motion but the analytical solution obtained for the horizontal components of the state vector is valid to third-order terms in those quantities. The families of three-dimensional periodic orbits emanating from two of the collinear equilibrium configurations are continued numerically to large orbits. These families are found to terminate at large vertical-critical orbits of the familym of retrograde periodic orbits ofm 3 around the primariesm 1 andm 2. The series of these termination orbits, formed when the value ofm 3 varies, are also given. The three-dimensional orbits are computed form 3=0.1.  相似文献   

19.
The bulk flow of the solar wind plasma in the flank-side of the magnetospheric boundary layer, where the magnetic field lines are closed, has a component transverse to the ambient field. There is quite a strong velocity shear. The theoretical model ignores inhomogeneities in the ambient field and the mass density which occur at the magnetopause on about the same length scale as that of the velocity shear.Consideration is restricted to hydromagnetic waves which have a k-vector nearly normal to the Bo-Vo plane, i.e., approximately the magnetopause surface (kx >kz ～ ky′kxLB > 1 and LB = 0.1 ～ 1.0 RE where LB is a characteristic length of the boundary layer). It is found that a long-period (T ? 40 sec) hydromagnetic wave [the Alfvén-like wave (ΩA)] driven by velocity shear instability can be excited in the shear plasma. It is also found that the group velocity of the HM-wave is directed almost along the magnetic field line and that the magnetic variance in the shear plasma tends to be parallel to the Bo-Vo plane. The velocity shear instability in the magnetospheric boundary layer is judged to be a likely source of long-period magnetic pulsations.  相似文献   

20.
With 1353 vector magnetograms observed at Huairou Solar Observing Station (HSOS), a statistical analysis is made on the relationship among solar flares, magnetic gradient, and magnetic shear. The results suggest that flare productivity has positive correlations with the gradient and the shear, which can be well fitted by the Boltzmann sigmoidal function. In the vicinity of neutral lines, high gradient and strong shear are roughly coincident in time but barely in position. In addition, flare productivity is more sensitive to the length of neutral lines with strong gradient and shear (L gs) than independently with strong gradient (L g) or strong shear (L s), which means that L gs can be a better parameter for solar flare forecasting models. Finally, an algorithm to evaluate projection effects on the statistical results is proposed.  相似文献   

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